**Fatigue Property and Improvement of a Rounded Welding Region between the Diaphragm Plate and Closed Rib of an Orthotropic Steel Bridge Deck**

#### **Datao Li \*, Chunguo Zhang and Pengmin Lu \***

Key Laboratory of Road Construction Technology and Equipment, MOE, Chang'an University, Xi'an 710064, China; zcguo2008@163.com

**\*** Correspondence: ldt1688@chd.edu.cn (D.L.); lpmin@chd.edu.cn (P.L.)

Received: 31 December 2019; Accepted: 20 January 2020; Published: 21 January 2020

**Abstract:** By means of finite element modeling (FEM) and fatigue experiments, we study the fatigue performance of the rounded welding region between the diaphragm plate and closed rib of orthotropic steel bridge deck in this work. A local sub-model of the rounded welding region from the orthotropic steel bridge deck was developed to analyze the stress distributions. Based on the analysis results we designed the fatigue specimen for the fatigue test of this detailed structure. The fatigue experimental results revealed that the crack initiates from the weld toe of the rounded welding region and the stress concentration at the rounded welding region is the main mechanism of fatigue crack initiation. In addition, we propose three improvements to reduce the stress concentration of the rounded welding region, and the local structure optimization scheme of the diaphragm–rib weld can effectively improve the fatigue resistance of the detailed weld structure.

**Keywords:** fatigue performance; rounded welding region; finite element modeling (FEM); structure optimization; reinforcing plate

#### **1. Introduction**

The orthotropic steel bridge decks are used in most of the world's major long span bridges with an important character of low dead weight. The orthotropic steel deck consists of a deck plate supported in mutually perpendicular directions; all these elements are connected by welded connections. Owing to the cyclic load stress caused by a high number of vehicles, fatigue cracks in orthotropic steel bridges significantly occur at partial-penetration fillet-welded connections [1–7]. Usually, enhancing the fatigue strength of welded joints, such as the rib-to-rib welded details, rib-to-crossbeam welded joints, and field splice joints of longitudinal ribs [3,8–10] is an effective method to improve the fatigue resistance of the orthotropic steel decks.

Till now, numerous works have focused on the fatigue behaviors of structure details in orthotropic bridges decks. Taking orthotropic decks of the Williamsburg Bridge for instance, Tsakopoulos and Fisher [11] studied fatigue resistance of local welding structure between rib and diaphragm, and the observations are recommended in the 1994 AASHTO LRFD Bridge Design Specifications. Several modifications are proposed for orthotropic deck design and some modifications are adopted in the 2000 Interim AASHTO LRFD Specifications. In addition, Connor and Fisher [12] explored an identical method to examine how fatigue stress range is defined and determined during the testing, then the fatigue resistance of welded rib-to-web connections in steel orthotropic bridge decks is obtained. Furthermore, Xiao et al. [13] evaluated the stress distributions and fatigue life of the rib-deck welded joints in orthotropic steel decks using finite element modeling (FEM). Ya et al. [14] further measured the fatigue behavior of rib-deck welded joints on the orthotropic steel bridge deck. Moreover, the effects of fabrication procedures on fatigue resistance of welded joints in orthotropic steel decks have

also been discussed [15]. Miki [16] used the FE sub-models of rib-to-deck joint derived from the global model of a real bridge to investigate the notch stresses at the weld root, the observations show the increase of the weld penetration results in the higher fatigue resistance. In addition, the effects of concrete cracking on the stress range response of welded joint in rib-to-floor beam can be evaluated through the FE analysis [17].

Although numerous efforts have been invested into the weld fatigue of the orthotropic steel bridge deck, the investigations on fatigue behaviors of the rounded welding region between diaphragm plate and closed rib are still under-researched. Facing to the fatigue behavior of this structure detail, we may think about a question, i.e., how does the fatigue behavior of this detail perform under cyclic loading? In this study, we attempt to answer this question using experimental method and FEM. In addition, this study is organized as follows: Firstly, we design fatigue specimens based on the simulated stress distributions of the detailed structures. Then, we perform the fatigue tests of specimens (nine specimens) and obtain the fatigue strength. Finally, we propose three schemes to improve the fatigue strength of this detail, and find that scheme 2 can effectively reduce the stress concentration of the rounded welding region.

#### **2. Experiment**

#### *2.1. Design of Fatigue Specimen*

According to the general code for design of highway bridges and culverts [18], we could analyze the stress distribution of the detailed structure in the orthotropic steel bridge deck. Firstly, the standard load of a vehicle for the stress analysis is chosen as 550 kN, the axle-loads for the middle and rear are 2 × 120 kN and 2 × 140 kN, respectively. In addition, the wheel contact area of two tires is assumed as a rectangle of 600 mm × 200 mm. The thickness of the asphalt pavement layer is about 55 mm and the load distribution angle is 45◦. Thus, the actual load area on the deck is 710 mm × 310 mm, as shown in Figure 1. Moreover, we choose a bridge deck (3750 mm × 4800 mm) as the stress analysis object (Figure 2). Based on the aforementioned standard, an assumed truck wheel load along the transverse direction of the bridge deck is used to determine the maximum stress of our interest point (Figure 2). Furthermore, an FE model consisting of a diaphragm and eight closed ribs is created in ANSYS software. In this model, Shell63 element is applied in the FE model, and it contains about 83800 elements and 83500 nodes. For the FE model, the bottom of the diaphragm is fully fixed. At one side of the closed rib, the freedoms in the Y and Z directions are restrained. For the other end, the freedom in the Y direction is fixed. The location of the rear axle (2 × 140 kN) is just on the top of the diaphragm (Figure 1). In addition, for the FE model, we can find a similar mesh generation in Ref. [13]. Moreover, in Figure 1, we can see the rounded welding region of the orthotropic steel bridge deck as shown in the red-squared part in the A direction. Usually, the fatigue crack initiates in the weld toe of the rounded welding region.

**Figure 1.** Fatigue crack of the rounded welding region between a closed rib and a diaphragm (in mm).

**Figure 2.** finite element (FE) model and the interest point of the rounded welding region.

Moreover, Figure 3a exhibits a simulated maximum principal stress–time curve of the interest point when the wheel loads are running along the transverse direction (Z direction in Figure 2) of the bridge deck. And the wheels load just locates on the diaphragm and closed rib when the maximum principal stress reaches the maximum value as shown in the curve (Figure 3b). Furthermore, a sub-model is developed to simulate the stress distribution around the interest point. Then, the boundary conditions applied to the sub-model are obtained from the FE model as shown in Figure 3b as the maximum principal stress reaches the maximum value (Figure 3a). In the sub-model, the element (Solid185, it is a 3-dimensional solid element with eight nodes in ANSYS software) sizes of the weld are about 2~3 mm (Figure 4). In addition, a schematic diagram of the diaphragm–rib structure of an orthotropic steel bridge deck and the weld details of interest regions are shown in Figure 5.

**Figure 3.** (**a**) Maximum principal stress–time curve of the interest point, and (**b**) the position of wheel load as the maximum principal stress of the interest point reaches its peak.

**Figure 4.** Sub-model of the rounded welding region.

**Figure 5.** (**a**) Structure schematic diagram (in mm) and (**b**) the fillet weld between closed rib and diaphragm (in mm).

As shown in Figure 5b, double-sided fillet welds are adopted for welding the diaphragm and the closed rib, and the weld width is about 6 mm. The contact elements are created on the contact area between the diaphragm and the closed rib. In addition, the cross section of the fillet weld is a triangular shape (partial view A-A in Figure 5b), the weld toes (in the diaphragm plate and the closed rib plate, respectively) and the weld root are the potential fatigue-crack-initiating points affected by the weld size, plate thickness and weld penetration [19]. Moreover, the maximum principal stress distributions in the welding direction (welding direction is the red arrow route of the local B-B structure in Figure 5b) are shown in Figure 6, and the simulated stresses are from the FE model of the sub-model (Figure 4). The simulated results also indicate that the stress at the weld toe in the closed rib plate is significantly higher than those at weld toe in the diaphragm plate and the weld root. Therefore, the weld toe in the closed rib plate is considered as the interest point, and it is a potential fatigue-crack-initiating point during service condition of the bridge. In addition, the symmetrical principal stress curves in the weld toe in the rib plate may be caused by the boundary conditions applied to the sub-model. Moreover, the node position of weld toe in the rib plate is longer than the weld root and the weld toe in the diaphragm as shown in Figure 5b. Thus, the peak stress region of the weld toe in the rib plate does not line up with the peak stress regions for the weld root and the weld toe in the diaphragm plate.

**Figure 6.** Stress–ode position curves of the rounded welding region in the sub-model (Node position is along the welding direction).

#### *2.2. Fatigue Specimen*

Based on the simulated stress distribution around the rounded welding region, we design a fatigue specimen of the structure detail with a rounded welding region (Figure 7). The material of fatigue specimen is Q345qD; it is a common steel material served as the bridge deck in China. In addition, the mechanical properties of the specimen material are shown in Table 1. Manual welding is employed to perform the welding, and the welding process parameters are listed in Table 2. Moreover, weld toes in the rib plate, the diaphragm plate, and the weld root are similar with weld details of the sub-model in Figure 5. In our simulation, the applied load is set as 50 kN. As shown in Figure 8, the maximum stress at the weld toe in the closed rib plate is higher than that at the weld root and the weld toe in the diaphragm plate. Because the weld length of our designed fatigue specimen is about half the length in sub-model (see node positions in Figures 6 and 8), the stress curves of the specimen welds are similar to the stress curves obtained from the sub-model (Figure 6). The similarity of the two stress distribution curves indicates the specimen can be used for the fatigue strength test of this weld detail.

**Figure 7.** Specimen and fixture (in mm).

**Figure 8.** Stress–node position curves of the rounded welding region in the specimen.

**Table 1.** Mechanical properties of Q345qD.




#### *2.3. Fatigue Tests and Results*

In the rounded welding region of the fatigue specimen, strain rosettes are placed at a distance of approximately 1.5 t (t is the thickness of the closed rib) far away from the weld toe (Figure 9). In Figure 9a, the strain gauges 7 and 8 are used to determine the offset load caused by fabrication process. In Figure 9b, the strain rosettes 1–3 and 4–6 are distributed symmetrically, they can test the stress distribution of the weld toe in the rib plate. In addition, Figure 9c shows the photo of the fatigue specimen and the testing field. The fatigue tests are conducted by a hydraulic servo fatigue testing machine (SD-500, Changchun Research Institute for Mechanical Science CO. LTD, Changchun, China). During the testing, the load mode is the constant amplitude with a sine waveform at a frequency of 2 Hz, and the averaging stress ratio is about 0.06. Moreover, cameras with 40 magnifications are used to monitor and measure the crack initiation and propagation. In the fatigue test, fatigue cracks of the specimens firstly initiate from the rounded welding region between the diaphragm and closed rib, and the fatigue test results are summarized in Table 3. In addition, the stress range is measured by the strain rosettes 2 and 5 [20].

**Figure 9.** *Cont.*

**Figure 9.** Schematic of the strain rosette location: (**a**) Strain gauges on the diaphragm, (**b**) Strain rosettes on the closed rib in A and B directions, respectively (in mm), (**c**) Photo of and the testing field and fatigue specimen.

Based on the fatigue results in Table 3, Δσ-N equation is fitted by the least square method and the fatigue life curve with 50% confidence bound is given as following:

$$\text{lgN} = 12.33 - 3.4 \text{ (lg}\Lambda \sigma\text{)}\tag{1}$$

where fatigue cycles N are 2 million, the stress range Δσ is about 59.32 MPa.

The fatigue life equation with 97.7% confidence bound is obtained by subtracting 2*s* (*s* is the standard deviation of lgN, its value is 0.38) from the mean line of Equation (1):

$$\text{lgN} = 11.57 - 3.4 \text{ (lg}\Delta\sigma\text{)}\tag{2}$$

where fatigue cycles N are 2 million, the stress range Δσ is about 35.46 MPa. The Δσ-N curves under two confidence bounds are plotted in Figure 10. Moreover, almost all cracks initiate from the rounded welding region between the diaphragm and the closed rib. We do not find a similar structure detail in the design codes for steel structures [21–24]. Therefore, Equation (2) could provide a reference for the fatigue design of this detailed structure.


**Table 3.** Fatigue test results.

**Figure 10.** Δσ-N curves of fatigue specimens.

#### **3. Discussion**

#### *3.1. Fatigue Crack*

The fatigue crack of the tested specimens initiates from the rounded welding region (Figure 11a), then the crack propagates along the weld toe (see red arrows in Figure 11b–d). Based on these fatigue tests observations, the weld toe in the closed rib plate is most susceptible to failure, therefore, the initiated position of the crack and the crack propagation path can indirectly demonstrate the validity of these fatigue specimens.

**Figure 11.** Cracks in the fatigue specimen: (**a**) Crack position in the specimen and Cracks of specimens (**b**) SY-3-1-2, (**c**) SY-3-1-5, (**d**) SY-3-1-6, respectively.

#### *3.2. Hardness Measurements around the Crack*

In order to analyze the mechanism of crack initiation, the hardness distribution of the welding region around the fatigue crack is measured by using a Vickers hardness tester [25–27] (Figure 12). The route of indentations successively crosses the parent metal (closed rib plate), heat-affected zone, weld toe (around the fatigue-crack-initiating point) and weld of specimen (from left to right in Figure 12b), and the distance between indentations is about 0.5 mm. Before the test, the surface of the specimen is well polished. In addition, the hardness distribution along the route reveals that the hardness fluctuates at the weld region (Figure 12b). However, the hardness value near the fatigue-crack-initiating point is about 200 HV, the value is slightly higher than the parent material's hardness (~180 HV). This phenomenon indicates the welding process has no significant effects on material hardness at the weld toe in the closed rib plate. But the maximum stress of the rounded

welding region still locates at the weld toe, then we get the conclusion that the stress concentration in the rounded welding region is the main mechanism of the fatigue crack initiation.

**Figure 12.** Vickers hardness test: (**a**) Sliced specimen (in mm) and (**b**) hardness distribution along the route.

#### *3.3. Improvement of the Local Structure: Scheme 1*

The previous analysis clearly states that the stress concentration is the major mechanism of fatigue crack initiation. Furthermore, we infer the stress concentration results from the size mutations between the diaphragm and the closed rib (see the arc in the diaphragm in Figure 1). Aiming to reduce the stress concentration, a reinforcing plate is incorporated onto the closed rib by welding. The details of the plate and the welding position are marked out in Figure 13a. With the purpose of reducing the peak value of the maximum principal stress in the rounded welding region, a parametric model in ANSYS software is developed to optimize the design parameters (*h1*, *h2* and *t*, where *t* is the thickness of the reinforcing plate). Finally, the optimized results of the *h1*, *h2* and *t* are 5 mm, 84 mm and 4 mm, respectively, and the maximum stress at the weld toe in the closed rib plate is 45.135 MPa in scheme 1 (Figure 13b). This value represents a decrease of 35.54% compared with the original peak stress. However, the stress at the weld toe in the diaphragm plate of the optimized reinforcing plate increases from 32.397 to 56.49 MPa (Figure 13b). The peak stress of the weld root is 39.65 MPa, and this value is very close to its original value. In summary, the stress concentration in the rounded welding region is reduced by welding the reinforcing plate. However, the stress at the weld toe in the diaphragm plate becomes larger than the stress at the weld toe in the rib plate. This means the expected failure location will change.

**Figure 13.** (**a**) Reinforcing plates in improvement scheme 1 and (**b**) stress–node position curves of the rounded welding region.

#### *3.4. Improvement of the Local Structure: Scheme 2*

In scheme 2, two reinforcing plates are installed on both sides of the closed rib by welding. The details of the reinforcing plates and the welding positions are identified in Figure 14a. Make sure the complete contact between the reinforcing plate and the closed rib, fusion-through welding is required. In this scheme, the plate thickness *t1* is larger than (*a1* + *a2*)/2. Variables *a1*, *a2*, *t1*, and *b* are considered as design variables, while the state variable is the peak value of the maximum principal stress in the rounded welding region.

**Figure 14.** *Cont.*

**Figure 14.** (**a**) Reinforcing plates in improvement scheme 2 and (**b**) stress—node position curves of the rounded welding region.

Furthermore, the optimized results of the *a1*, *a2*, *t1*, and *b* are 13 mm, 14 mm, 14 mm, and 135 mm, respectively, and the maximum stress at the weld toe in the closed rib plate is 46.711 MPa in scheme 2 (Figure 14b). This value represents a decrease of 33.29% compared with the original maximum stress. The maximum stress at weld toe in the diaphragm plate is 37.99 MPa and increases by 5.593 MPa (an increase of 17.26%) as compared with the original value. The peak stress at weld root is 40.51 MPa and increases by 1.151 MPa (an increase of 2.9%). In this scheme, the stress concentration in welded region is reduced, while the peak stresses at the weld toe in the diaphragm plate and weld root also increase.

#### *3.5. Improvement of the Local Structure: Scheme 3*

In scheme 3, two reinforcing plates are welded on both sides of the closed rib, respectively. We can see the details of reinforcing plates and the welding positions in Figure 15a. An original point is chosen (marked as "0") for optimizing the dimensions of the reinforcing plate. Fusion-through welding is also required, thus the plate thickness *t2* should be larger than *b1*. The variables *a3*, *a4*, *t2*, and *b1* are considered as design variables, and the state variable still is the peak value of the maximum principal stress in the rounded welding region.

**Figure 15.** *Cont.*

**Figure 15.** (**a**) Reinforcing plates in improvement scheme 3 and (**b**) stress—node position curves of the rounded welding region.

Finally, the optimized results of the *a3*, *a4*, *t2*, and *b1* are 12 mm, 15 mm, 11.5 mm, and 21 mm, respectively, and the peak stress at the weld toe in the rib plate is 52.8 MPa in scheme 3 (Figure 15b). This value means a decrease of 24.6% compared with the original peak stress. The peak stress at weld toe in the diaphragm plate is 32.673 MPa and increases 0.276 MPa (an increase of 0.85%) as compared with the original value. The peak stress at weld root increases from 39.359 to 40.532 MPa. In this scheme, the reinforcing plate reduces the stress concentration in welded region, but the peak stress at the weld toes in the diaphragm and the weld root does not significantly increase.

#### *3.6. Comparisons of Three Improvement Schemes*

Following the above descriptions, distribution curves of the maximum principal stress for the weld toe in the closed rib plate, the weld toe for the diaphragm plate and the weld root of three improvement schemes are plotted in Figure 16a–c, respectively. Moreover, the maximum principal stresses of the rounded welding regions with and without reinforcing plate are listed in Table 4. For the rounded welding region, three improvement schemes can effectively reduce the stress concentration at the weld toe in the closed rib plate. However, the scheme 2 is better than the schemes 1 and 3. Because both schemes 1 and 2 reduce the peak stress more than scheme 3, but scheme 1 increases the stress at the weld toe in the diaphragm plate to be more than the stress at the weld toe in the closed rib plate. Thus, we consider scheme 2 is the best and effectively improve the fatigue resistance of the rounded welding region of the diaphragm–rib structure.

**Figure 16.** *Cont.*

**Figure 16.** Stress–node position curves in the rounded welding region before and after improvement: Stress curves of (**a**) weld toe in the closed rib plate, (**b**) weld toe in the diaphragm plate and (**c**) weld root.

**Table 4.** Peak value of the maximum principal stress in the rounded welding region before and after improvement.


#### **4. Conclusions**

In this study, the fatigue performance of the rounded welding region between diaphragm plate and closed rib of an orthotropic steel bridge deck is investigated using experimental methods and FEM. The main conclusions are summarized as follows


concentration of the rounded welding region, and the fatigue strength of this welded structure can be enhanced.

**Author Contributions:** Writing—original draft preparation, D.L.; writing—review and editing, C.Z.; supervision, P.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Project of Jiangxi Provincial Communication Department, grant number 2010C00003. This research was also funded by the National Natural Science Foundation of China, grant number 11902046 and the Fundamental Research Funds for the Central Universities, CHD, grant number 300102259302.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

#### *Article*

## **Modelling of Fracture Toughness of X80 Pipeline Steels in DTB Transition Region Involving the E**ff**ect of Temperature and Crack Growth**

#### **Jie Xu 1, Wei Song 2,\*, Wenfeng Cheng 3, Lingyu Chu 1, Hanlin Gao 1, Pengpeng Li <sup>1</sup> and Filippo Berto <sup>4</sup>**


Received: 21 November 2019; Accepted: 16 December 2019; Published: 23 December 2019

**Abstract:** This work presents an investigation of the effects of temperature and crack growth on cleavage fracture toughness for weld thermal simulated X80 pipeline steels in the ductile-to-brittle transition (DBT) regime. A great bulk of fracture toughness (crack tip opening displacement—CTOD) tests and numerical simulations are carried out by deep-cracked single-edge-notched bending (SENB) and shallow-cracked single-edge-notched tension (SENT) specimens at various temperatures (−90 ◦C, −60 ◦C, −30 ◦C, and 0 ◦C). Three-dimensional (3D) finite element (FE) models of tested specimens have been employed to obtain computational data. The results show that temperature exerts only a slight effect on the material hardening behavior, which indicates the crack tip constraint (as denoted by Q-parameter) is less dependent on the temperature. The measured CTOD-values give considerable scatter but confirm well-established trends of increasing toughness with increasing temperature and reducing constraint. Crack growth and 3D effect exhibited significant influences on CTOD-CMOD relations at higher temperatures, −30 ◦C and 0 ◦C for the SENT specimen.

**Keywords:** fracture toughness; coarse-grained heat affected zone (CGHAZ); X80 pipeline steels; weld thermal simulation; finite element analysis (FEA)

#### **1. Introduction**

Significant effects of crack size and loading mode (bending vs. tension) on fracture toughness values have been revealed from fracture mechanics testing of ferritic structural steels [1]. Previous numerical investigations [2,3] illustrate the strong dependence of crack-tip fields on specimen geometry and remote loading. According to experimental studies by, e.g., Sorem et al., [4] Joyce and Link [5], and others, significant elevations in fracture toughness (characterized as *JC* or *KIC*) for shallow-cracked specimens and/or subjected to tensile loading have been shown. With increasing loads in specific objects, such as a cracked specimen or a structural component, the crack-tip plastic zone is increasingly affected by the nearby traction free boundary according to small-scale yielding (SSY) theory. Due to the crack tip stress relaxation, the constraint level of specimens decreases and further contributes to the apparently increased toughness of shallow-cracked and tension-loaded geometries from fracture mechanics testing [6–8]. The stress field surrounding the crack is influenced by the crack tip constraint, which cannot be characterized by single fracture mechanics indicator. The second parameter, such as

*T*-stress [9] or *Q*-parameter [10,11], has been proposed and developed to further describe the crack-tip stress fields and quantify constraint levels for various geometries and loading modes.

High-strength low-alloyed (HSLA) steels increasingly used for high-pressure pipeline operation and offshore structural installation. The installation of pipelines used for transporting oil and gas sometimes takes place in severe environments, such as in the low-temperature region, where the pipelines must have low-temperature toughness [12]. Thus, the major motivation for the improvement of HSLA steels has been provided by the demands for higher strength as well as improved toughness, ductility, and weldability at low temperatures [13,14]. Though the HSLA steels own the excellent properties of tensile strength and ductile to brittle transition (DBT), according to the Charpy-impact test investigation, the ductile brittle transition (DBT) on the basis of microscopic mechanism occurs with decreases of temperature. On the other hand, X80 steel pipelines are exposed in extreme low-temperature environments, and it is meaningful to characterize the fracture toughness with temperature variations during the processing of DBT. The balance of high strength and toughness can be deteriorated by welding thermal cycles, producing local poor toughness in the welded joints [15]. The heat-affected zone (HAZ) of a weldment is in many cases considered to be the weakest part and is crucial in the failure of steel structures because of its heterogeneous microstructure produced during the welding process [16,17]. Therefore, treatment of brittle fracture in weldment and HAZ is challenging. In the 1990s, there was a significant focus on characterizing the local stress fields in weldment and HAZ. SINTEF/NTNU developed the so-called *J-Q-M* theory (see, e.g., Zhang et al. [18–20]) where both constraint effects due to geometry and material mismatch were included in characterization of the local stress field ahead of the crack tip. In addition, some researchers have investigated the related HAZ properties of high-strength steels on the basis of physical simulation, welding heat input effect on HAZ in S960QL steel, and the matching effect on fatigue crack growth behavior of high-strength steels GMA welded joints [21–24].

This paper mainly focuses on the single-edge-notched tension (SENT) and single-edge-notched bending (SENB) specimens, which are usually used to characterize pipeline steels with thin-walled thickness, as specified recently by a so-called SENT methodology to identify a SENT specimen(s) to match the crack tip constraint of cracked pipe sections. The effect of constraint on the fracture toughness of weld thermal simulated X80 pipeline steels in the ductile-to-brittle transition relationship is clarified by combination of experimental assessment and numerical simulation. The fracture toughness comparison of X80 steel SENB specimens (*a*/*W* = 0.5) under different temperature have been presented in [25]. The material is determined by the increasing demand due to a great account of applications for manufacturing high-strength pipes for the oil and gas industry. Fracture toughness (as denoted by crack tip opening displacement (CTOD)) tests are performed at different temperatures, −90 ◦C, −60 ◦C, −30 ◦C, and 0 ◦C. Both the traditionally used deeply cracked SENB specimens with *a*/W = 0.5 and SENT specimens with *a*/*W* = 0.3 are used to characterize the crack tip constraint effect on the fracture toughness in the ductile-to-brittle transition region. 3D nonlinear finite element models are employed to analyze the crack-tip stress fields of tested specimens by considering the effects of the constraint and without/with crack growth on fracture toughness. The numerical analysis is compared with the experimental results.

#### **2. Experimental Details**

#### *2.1. Material Description*

The material used in our study is the HSLA X80-grade steel, which has a minimum yield strength of 555 MPa (tensile strength 625 MPa). The nominal outer diameter of the pipe is 510 mm, and the nominal wall thickness is 14.6 mm. The typical chemical composition of this material is listed in Table 1.


**Table 1.** Chemical composition of the X80 steel (wt. %).

#### *2.2. Weld Thermal Simulation Technique*

The weld thermal simulation technique is used to obtain the tested specimens. The single welding cycle simulation is intended to represent the coarse-grained HAZ (CGHAZ) of the welds [26], which has been used in the preparation of weld thermally simulated specimens. In this study, the specimens were heated to the maximum temperature of 1350 ◦C by resistance-heating in a computer-controlled Gleeble weld thermal simulator (Figure 1a). The whole temperature vs. time history applied during the weld thermal simulation can be seen in Figure 1b. The thermal history is described as a sequence of heating and cooling intervals. The simulation was performed by heating the sample to 1350 ◦C for 2 s followed by controlled cooling; the cooling intervals were 2 s in the 1350 ◦C–1200 ◦C range, and 15 s between 800 ◦C–500 ◦C. Thus, the T8/5 is 15 s. The synthetic CGHAZ microstructure was thereafter produced in a certain region in the specimen where the fatigue pre-crack is introduced after being machined. The prior austenite grain size of CGHAZ was measured to be about 50 μm.

**Figure 1.** (**a**) Gleeble weld thermal simulator; (**b**) temperature vs. time history during the weld thermal simulation.

#### *2.3. The True Stress-Strain Curves*

To characterize the material flow properties in 3D finite element model, the true stress-strain curves of material (CGHAZ in X80) were measured by smooth round bar tensile tests at four temperatures as shown in Figure 2. The results show that yield strength here slightly increases with decreasing temperatures. There is also a weak trend of increasing work hardening with decreasing temperatures.

**Figure 2.** True stress-strain curves in coarse-grained heat affected zone (CGHAZ) of X80 at various temperatures [25].

#### *2.4. Specimen Configurations and Test Program*

The geometrical configurations are schematically drawn in Figure 3 for SENB and SENT specimens, which are directly extracted from the X80 pipeline with specimen length along the pipeline longitudinal direction and crack propagation following the pipe thickness orientation, as shown in Figure 3a. For all specimens, a thickness of *B* = 10 mm and width of *W* = 10 mm with crack length (denoted by *a*), to width ratio of *a*/*W* = 0.5 for SENB and *a*/*W* = 0.3 for SENT specimens have been considered. The span of the specimen, *S*, is chosen to be four times of width, *W*, for SENB (*S*/*W* = 4) and *L*/*W* = 3 for SENT.

**Figure 3.** Specimen configurations. (**a**) Schematic plot of the relationship between single-edge-notched tension (SENT) and pipe; (**b**) single-edge-notched bending (SENB) with *a*/*W* = 0.5; (**c**) SENT with *a*/*W* = 0.3.

The SENB specimens are prepared and tested according to the standard of BS 7448 [27], while the SENT fracture specimens are machined in accordance with the "Recommended Practice DNV-RP-F108" [28]. Double clip gauge was used to digitally record the load-CMOD (crack mouth

opening displacement) curves during the tests. The CTOD values are determined at the maximum load through measured load-CMOD records. The tensile and bending tests were performed at four different temperatures, −90 ◦C, −60 ◦C, −30 ◦C, and 0 ◦C. The testing rate is 0.5 mm/min of crosshead displacement for each specimen. For each specimen geometry, 10 parallel tests have been carried out at each temperature. After each test, the fatigue pre-cracking length and ductile crack extension that occurred during the test were measured using an optical microscope. The notches were located in the center of the weld, as can be seen in Figure 3.

#### **3. Numerical Procedures**

#### *3.1. 3D Finite Element Models*

3D finite element models were built using ABAQUS [29] for SENB and SENT specimens as shown in Figure 4. Due to symmetry, one-quarter of the specimen is modeled for finite element analysis considering the geometrical symmetry. A typical mesh configuration of elements surrounding the crack front is used with a small notch (with a notch root radius of *r* = 2 μm) in front of the crack tip. A 3D continuum element with eight-node, full integration (ABAQUS: C3D8), is used for FE calculations. The X80 steel true stress-strain curves obtained from the smooth round bar tensile tests at corresponding temperatures are applied for 3D model calculations. Meanwhile, the nonlinear geometric effect (NLG) is considered in all the finite element analyses. The CTOD-value is extracted from the displacement of a node in front of the initial crack tip [30].

**Figure 4.** 3D FE models (1/4 model). (**a**) SENB with *a*/*W* = 0.5; (**b**) SENT with *a*/*W* = 0.3.

#### *3.2. The MBL (Modified Boundary Layer) Model*

In calculating the *Q*-parameter (quantitative characterization of crack tip constraint), the MBL model solution with *T* = 0 (here, *T* is the elastic *T*-stress, which is defined as constant stress acting parallel to the crack and its magnitude is proportional to the nominal stress in the vicinity of the crack) is adopted herein to represent the reference stress field for each case. Due to symmetry, only one-half of the model has been used in the MBL model, as shown in Figure 5. The global finite element mesh for the MBL model is drawn in Figure 5a. Similar models have been used in other studies [31–33]. Details of the mesh in the local region of the crack tip can be seen in Figure 5b. The MBL is a plane strain model with the same mesh arrangement in front of the crack tip (with a notch root radius of *r* = 2 μm) as in 3D models.

**Figure 5.** Finite element mesh of the modified boundary layer (MBL) model. (**a**) Global mesh; (**b**) local mesh around crack tip region.

#### **4. Results and Discussion**

#### *4.1. Measured and Calculated Load-CMOD Curves*

The measured and calculated load-CMOD curves for all specimens at various temperatures are plotted in Figure 6. Only mid-thickness values of CMODs are extracted through the specimen thickness for all cases in this subsection. It can be seen that numerical simulations of load-CMOD curves are in good accord with experimental results for all temperatures. The material becomes quite brittle, which can be clearly seen from the flat fracture surface, and no significant crack growth has been observed from optical microscope observations for both the SENB and SENT specimens at lower temperatures, for example −90 ◦C and −60 ◦C. For the SENB specimens at −30 ◦C and 0 ◦C, small subcritical (mostly less than 0.2 mm) crack growth has been observed; whereas evident crack growth (Δ*a* > 0.2 mm) have been observed for the SENT specimens at −30 ◦C and 0 ◦C. For the sake of simplicity, no crack growth has been considered in the 3D models in this subsection.

**Figure 6.** *Cont*.

**Figure 6.** Comparisons of measured and calculated load-CMOD curves for SENB [25] and SENT specimens at various temperatures. (**a**) 0 ◦C for SENB specimens, (**b**) −30 ◦C for SENB specimens, (**c**) −60 ◦C for SENB specimens, and (**d**) −90 ◦C for SENB specimens, (**e**) 0 ◦C for SENT specimens, (**f**) −30 ◦C for SENT specimens, (**g**) −60 ◦C for SENT specimens, and (**h**) −90 ◦C for SENT specimens.

According to test demands of SENT and SENB specimen, 10 parallel tests have been carried out at each temperature. In addition, it can be argued that the transferability of the true σ − ε curve from round thermal simulated tensile bar to the fracture mechanics specimens is quiet well. One thing that should be noted is that the average crack depth for both the SENB and SENT specimens at each temperature is used in these 3D models.

#### *4.2. Measured CTOD-Values and Calculated Q-CTOD Relations at Di*ff*erent Temperatures*

The results of fracture toughness (CTOD-value) as a function of temperature and their related average curves for SENT and SENB specimens are presented in Figure 7. It shows that the average CTOD values of SENT specimens at each temperature are obviously higher than that of SENB specimens. To illustrate the scatter degree of fracture toughness test data in Figure 7, the statistical characteristics are conducted quantitatively. The related analysis results for SENB and SENT specimens are summarized in Table 2. According to the average CTOD variations in statistical characteristics, these data increase with the temperature elevation from −90 ◦C to 0 ◦C for these two specimen types. In addition, from the perspective of standards variation coefficient, it stands for the ratio of the standard deviation to the mean. The higher the coefficient of variation, the greater the level of dispersion around the mean. It can be seen from Table 2 that the dispersion of −30 ◦C test data is the largest for SENB specimens, and −60 ◦C test data dispersion is the largest for SENT specimens. Thus, a definite temperature-dependence on dispersion characteristic cannot be drawn from these test data.

**Figure 7.** Crack tip opening displacement (CTOD) vs. temperature for HAZ in X80 pipeline steels.


**Table 2.** Statistical characteristics of test data for SENB and SENT specimens.

It shows that the fracture toughness tends to be scattered at each temperature. Also, the scatter of fracture toughness increases rapidly with increasing temperatures (upper transition region), for instance −30 ◦C and 0 ◦C, where a ductile mechanism is involved and cleavage instability may intervene after a certain amount of ductile crack growth as have been observed from the tests, especially for SENT specimens.

Additionally, the average fracture toughness values are higher for SENT specimens with a shorter crack of *a*/*W* = 0.3 compared to the SENB specimens with *a*/*W* = 0.5 at each test temperature. Moreover, this difference becomes larger with increasing temperatures.

The detailed effects of temperature and specimen geometry (as quantitatively characterized by crack tip constraint—*Q*-parameter) on fracture toughness will be studied in the following. As has been known, the *J*-*Q* methodology gives a direct measurement of the crack-tip stress field of interest that is related to a reference field [10,11], and can therefore describe the evolution of constraint ahead of the crack tip throughout the loading to large-scale yielding (LSY), where *J* sets the deformation level and *Q* is a stress triaxiality parameter. In this paper, the *Q*-parameter has been used to quantify the crack tip constraint for each specimen at each temperature.

The *Q*-parameter was originally defined as follows [10],

$$Q = \frac{\sigma\_{\ell\ell\theta} - (\sigma\_{\ell\theta}^{\text{Ref}})\_{T=0}}{\sigma\_0}, \text{ x/(J/\sigma\_0)} = 2, \ \theta = 0. \tag{1}$$

where σθθ is the opening stress component of interest, (σθθ*Re f*)*T*=<sup>0</sup> is the reference stress component characterized by MBL model solution with *T* = 0, σ<sup>0</sup> is the yield stress, and *x* denotes the distance from the crack tip along the crack plane (θ = 0).

CTOD is selected as the crack driving force in our stud; the following constrain effect definition of *Q* has been used [27,28]:

$$Q = \frac{\sigma\_{\ell 0} \rho^{\text{spcinen}} - (\sigma\_{\ell 0} \overset{\text{Ref}}{\text{.}})\_{T=0}}{\sigma\_0}, \text{ at } \text{x/CTOD} = 4, \theta = 0. \tag{2}$$

where σθθ*specimen* is the opening stress component of the specimen at a certain temperature, (σθθ*Re f*)*T*=<sup>0</sup> is the reference stress component at the same temperature, and other parameters are the same as defined in Equation (1). Only the distribution of the crack tip opening stress (σ<sup>22</sup> at θ = 0) has been studied. In the following, the results of crack tip opening stress distribution at different CTODs are presented in Figure 8 for specimens at 0 ◦C.

**Figure 8.** Opening stress distributions ahead of the crack tip, *T* = 0 ◦C. (**a**) SENB; (**b**) SENT.

For SENT specimen as shown in Figure 8b, it demonstrates that the opening stress distribution in front of the crack tip is nearly parallel to the reference stress field. However, global bending causes the slope of the opening stress distribution to gradually deviate from the reference field for SENB specimen, but still remainsquite similar, as can be seen in Figure 8a. Similar observations have also been found for specimens at other temperatures while the results are not included herein for the sake of simplicity.

The calculated *Q*-CTODs relations are displayed in Figure 9 for SENB and SENT specimens at various temperatures. Only the mid-thickness layer was used to compute *Q*-parameter herein. The *Q*-parameter stands for constraint effect decreases with the increases of CTODs. Meanwhile, the *Q*-parameter for SENB specimen for each temperature level is considerably larger than that of SENT at same CTODs, which means the crack tip constraint of SENB specimen is higher than that of SENT as has been observed. Nearly constant *Q*-parameters have been computed for all temperatures considered at the same CTOD values. The results present a weak dependence of temperature on the constraint ahead of the crack tip that can be expected for SENT specimen compared with that of SENB specimen.

**Figure 9.** *Q* vs. CTODs for both SENB and SENT specimens, *T* = 0 ◦C, −30 ◦C, −60 ◦C, and −90 ◦C.

#### *4.3. Measured and Calculated CTOD-CMOD Relations*

As has been shown in Section 4.1, the experimental results are in good accordance with numerical simulations for the load-CMOD curves for all specimens at each temperature; how the 3D finite element models work for predicting the local fracture parameter as denoted by CTOD will be discussed in this subsection.

Figures 10 and 11 draws the CTODs vs. CMODs relationship obtained from both experiments and numerical calculations for all specimens at various temperatures without considering crack growth. Still, only mid-thickness values of CTODs versus CMODs are extracted herein. It can be seen that the tested results of CTOD-CMOD relations for the SENB specimens (Figure 10) can be quite well predicted by 3D FEA results at all temperatures.

**Figure 10.** CTOD vs. CMOD relations from experiments and 3D FE analyses for SENB specimens without crack growth at different temperatures, (**a**) 0 ◦C, (**b**) −30 ◦C, (**c**) −60 ◦C, and (**d**) −90 ◦C [25].

**Figure 11.** CTOD vs. CMOD relations from experiments and 3D FE analyses for SENT specimens without crack growth at different temperatures, (**a**) 0 ◦C, (**b**) −30 ◦C, (**c**) −60 ◦C, and (**d**) −90 ◦C.

As for the SENT specimens (Figure 11), a certain difference between experiments and 3D FE simulations can be observed at all temperatures. For small CTODs (less than 0.2 mm), quite good accordance can be obtained between experiments and simulations for all temperatures. However, the predicted CTOD values from the 3D models start to deviate from experimental results with the increases of CTODs, especially for the cases at higher temperatures, 0 ◦C and −30 ◦C. This is a remaining issue and more efforts are needed in further work, for example, the influences of local inhomogeneity of microstructure in HAZ and ductile crack propagation can be considered to further modify the models so as to improve the validity and accuracy of simulations with respect to the experiments. In this respect, it is noted that no standard for CTOD measurements in SENT specimens currently exists. The results in this paper warrant the need for further work in order to arrive at a method for experimental measurements of CTOD in SENT specimens, which could eventually form the basis for a standard document.

#### *4.4. The E*ff*ect of Crack Growth on the CTOD-CMOD Relations*

In this subsection, the effect of crack growth on CTOD-CMOD relations for the SENT specimen at 0 ◦C and −30 ◦C are considered in 3D models. Only mid-thickness values for both the CTODs and the CMODs are plotted in Figure 12. The complete Gurson model (see Reference [34]) is involved in calculating crack growth in 3D models. It can be seen that a significant elevation in fracture toughness for SENT specimens by considering crack growth. Also, a wonderful agreement between experiments and 3D FE simulations can be achieved by considering the influence of crack growth on fracture toughness for SENT specimens at both 0 ◦C and −30 ◦C. It can be concluded that the ductile crack extension is dependent on the temperature. In the low temperature range, it almost occurs at the cleavage fracture. The ductile crack extension mechanism involved in the upper transition zone of DBT, which cannot be ignored to predict CTOD-value for pipeline steel integrity assessment.

**Figure 12.** Effect of crack growth on the CTOD vs. CMOD relations for the SENT specimens under 0 ◦C and 30 ◦C.

#### *4.5. The Influence of 3D E*ff*ect on the Fracture Toughness*

In order to find the influence of 3D effect on fracture toughness, the calculated CTOD-CMOD relations at different layers through the specimen thickness compared with experiments are displayed in Figure 13. Two cases of SENT specimens considering crack growth at 0 ◦C and −30 ◦C are selected for this question. It can be seen that CTOD-CMOD values change considerably through the specimen thickness. The greater the distance from the specimen mid-thickness, the greater the deviation from experiments. In addition, the predicted CTOD-CMOD relations near the mid-thickness layer are coincident well with the experiments.

**Figure 13.** CTOD vs. CMOD relations at different layers through the specimen thickness for the SENT specimens considering crack growth at (**a**) 0 ◦C; (**b**) −30 ◦C.

#### **5. Conclusions**

In this paper, the HAZ of X80 high-strength steel is studied by experimental and simulation methods. The following conclusion can be drawn as follows:


between experiments and numerical simulations can also be obtained by considering the effect of crack growth in the 3D models.


**Author Contributions:** Conceptualization, J.X.; Methodology, H.G.; Software, L.C.; Validation, W.S.; Investigation, W.C.; Writing-Review & Editing, F.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China (Project No. 51301197) and the Natural Science Foundation of Jiangsu Province (Project No. BK20130182) and the Fundamental Research Funds for the Central University (Project No. 2011QNA07) as well as the National Key R&D Program of China (2018YFB2001200).

**Acknowledgments:** The first author sincerely appreciates Zhiliang Zhang from Norwegian University of Science and Technology for his valuable comments. Erling Østby and Bård Nyhus from SINTEF are also gratefully acknowledged for their kind help.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## **On the Behaviour of 316 and 304 Stainless Steel under Multiaxial Fatigue Loading: Application of the Critical Plane Approach**

#### **Alejandro S. Cruces 1, Pablo Lopez-Crespo 1,\*, Stefano Bressan 2, Takamoto Itoh <sup>3</sup> and Belen Moreno <sup>1</sup>**


Received: 23 July 2019; Accepted: 2 September 2019; Published: 3 September 2019

**Abstract:** In this work, the multiaxial fatigue behaviour of 316 and 304 stainless steel was studied. The study was based on the critical plane approach which is based on observations that cracks tend to nucleate and grow in specific planes. Three different critical plane models were employed to this end, namely Fatemi–Socie (FS), Smith–Watson–Topper (SWT) and the newly proposed Sandip–Kallmeyer– Smith (SKS) model. The study allowed equi-biaxial stress state, mean strain and non–proportional hardening effects to be taken into consideration. Experimental tests including different combinations of tension, torsion and inner pressure were performed and were useful to identify the predominant failure mode for the two materials. The results also showed that the SKS damage parameter returned more conservative results than FS with lower scatter level in both materials, with prediction values between FS and SWT.

**Keywords:** critical plane model; multiaxial fatigue; non–proportional loading; 316 stainless steel; 304 stainless steel

#### **1. Introduction**

Fatigue failure is a common problem for a wide range of industries. Since the first reported study, new materials and advanced methods to predict the number of cycles until failure has appeared. Uniaxial or bending rotation cyclic tests are often conducted to characterise the fatigue behaviour of different metals [1]. However, most mechanical applications imply more complex scenarios, real service loads are usually variable and designs include complex profile shapes instead of just flat or cylindrical surfaces. As a consequence, different stresses/strain distributions appear on the real structures subjected to cyclic loads [2–4]. For characterising such complex scenarios there exists more sophisticated methods such as the critical plane approaches as an alternative to the classical models [5]. Critical plane models have been successfully applied for different materials and service loads. For example Chu observed improvements using these methods for AISI 1045 steel under complex loading conditions [6]. Sharifimehr employed critical plane methods to predict the fatigue life of a brittle and a ductile material under variable amplitude loads [7]. Llavori also used the critical plane methods to study the fatigue performance of a welded joint of S275JR, and was able to achieve better predictions as compared to classical methods [8]. One of the main strengths of critical plane methods is that they take into consideration the physical mechanisms involved in the nucleation and growth of the fatigue crack [9,10]. Nevertheless, there exists other alternative approaches that allow more accurate predictions to be

achieved. One such approach is the Strip Yield Model (implemented in Nasgro software [11]). Besides the total fatigue life, these cycle by cycle models can also describe with certain accuracy the propagation stage until final failure takes place [12]. Depending on the material and the loading conditions, certain mechanisms will show a dominant presence along the fatigue process. For example, brittle materials tend to show a dominant Mode I crack growth along the fatigue process while ductile materials tend to have a dominant Mode II crack growth [13]. Critical plane methods are based on defining the plane where the highest damage takes place. This also means that they allow the crack growth angle to be predicted. This has been shown by Reis et al. who assessed the crack path initiation and growth for several structural steels [14,15]. The procedure requires evaluating the damage along the cycle from some stress and strain components. In some cases, obtaining such stress and strain components can be difficult and might introduce an additional source of error. Depending on the type of material, different critical plane models have been proposed. Models that include only stress variables are more useful in the high cycle regime but often fail at computing the fatigue damage in the low-cycle regime based on S–N curves. Stress values used in such models are frequently unrealistic and different to the actual stress experienced by the specimen due to the material behaviour above yield stress. Models that include strain variables are more robust in that sense.

To date, there is not a universal critical plane model that is valid for all the types of materials and all loading conditions. A very comprehensive review of different critical plane models can be found in the literature [16].

Well established models such as the Fatemi–Socie [17] or Smith et al. [18] were thoroughly studied, showing good results for ductile and brittle behaviour materials, respectively. Usually these models are chosen as a benchmark to propose new damage parameters [19,20]. In some cases the new model will return better results for the studied material and load condition [21,22], considering it more appropriate for those scenarios.

In this work a newly proposed critical plane damage parameter, called Sandip–Kallmeyer–Smith (SKS) was assessed based on its excellent performance on a low carbon steel [22]. First, the collapse capacity of the newly proposed damage parameter was evaluated. This was done by fitting the model to a set of experimental data with different loading paths both under proportional and non-proportional loads. Then, the fitted curve was used to predict fatigue lives for different multiaxial cases. The study was conducted on two stainless steels, namely 316 stainless steel and 304 stainless steel. The efficacy of the SKS damage parameter was compared with Fatemi–Socie model and Smith–Watson–Topper model.

#### **2. Materials and Methods**

The different models were tested on 316 and 304 stainless steels that are widely used in the industry. Previous studies observed better results with Mode II/III dominant critical plane methods for 316 stainless steel and with Mode I for 304 stainless steel [19,23].

All the tests were carried out on hollow cylindrical samples with 8.5 mm gauge length, 14 mm outer diameter and 12 mm inner diameter. The specimens were carefully polished to a surface roughness of approximately 0.3 μm both in the external and the internal surface. An in-house built fatigue machine allowed axial loads as well as inner pressure to be applied, thus allowing a very wide range of loading paths to be applied (see Figures 1 and 2). All tests were conducted in air. More details about the biaxial loading rigs, as well as additional details about the experiments can be found elsewhere [24,25].

The experimental tests employed for fitting the models and to evaluate the collapse capacity of the models on the 316 and the 304 stainless steel are shown in Tables 1 and 2, respectively [26]. Both experimental sets include proportional and non-proportional (out-of-phase between axial and shear strain) fatigue tests, as described in Figure 1. There are no mean stress tests among the experimental tests used for the 316 stainless steel. This is because no significant effect of the means stress on the fatigue life was observed for this material [27]. A comparison of the equivalent tests between 316 and 304 stainless steel (Tables 1 and 2) indicates that 304 stainless steel presents a higher hardening level.

**Figure 1.** Proportional and non-proportional loading paths.

**Figure 2.** Proportional multiaxial loading paths applied on the 316 stainless steel specimens.



**Table 2.** Summary of the experimental data used to fit the model parameters for 304 stainless steel.


The tests were used to fit the SKS model that was subsequently used to predict fatigue lives for both materials under a range of multiaxial loading conditions. The predictions given by the SKS model are valid for the range of fatigue lives covered in Tables 1 and 2 for 316 and 304 stainless steel, respectively.

Fifteen different tests were conducted on 316 stainless steel to evaluate the different critical plane models, which are described in Table 3. The loading path used for the 316 stainless steel are shown in Figure 2. The load control mode was used to conduct the tests. It was possible to produce a triaxial stress state at the inner surface of the specimen and a biaxial stress state at the outer surface. On the outer surface, cases 1, 2 and 3 produced a uniaxial stress state, cases 4 and 7 a biaxial stress state and cases 5 and 6 an alternating pulsating stress state in perpendicular directions. For all the cases, a high level of ratchetting was observed [27]. The total reverse stress was applied in the case 3 (Figure 1) which promoted a non-zero mean strain probably because of the real stress asymmetry caused by the high load levels. Accordingly, a biaxial stress condition was induced on the outer surface. Since the principal stress directions are constant in time, all loading paths can be considered as proportional, given that the main slip plane does not change along the load cycle. The load ratio for Path 3 in Figure 2 is *R* = −1. The rest of tests had a zero load ratio, *R* = 0. These tests will be used in Section 4 to evaluate the accuracy of the different models, as well as the response of the models under mean stress loads and biaxial conditions.


**Table 3.** Summary of the 316 stainless steel experimental data used to evaluate the fitted models.

The experimental tests used to evaluate the different models on the 304 stainless steel are shown in Table 4. The loading path used for studying the 304 stainless steel are shown in Figure 3. That is 29 experimental tests, three for path 0, and two for each of the other paths in Figure 3. These tests will allow the different models to be evaluated in terms of their capacity to take into account the fatigue damage produced by the hardening caused by non-proportional loads. For the same range of applied strains, increasing the non-proportionality in the loads requires increasing stresses to conduct the test. Previous results showed a high-hardening level for the 304 stainless steel [26]. Cases 1 and 6 can be considered proportional as the principal stress direction are constant along the cycle. The maximum non-proportionality factor appeared for cases 9, 10, 11, 13 and 14 [28]. Further experimental details are available elsewhere [25,26,28].

The coordinates adopted in this work are shown in Figure 4a. The radial and axial directions are defined as *R* and *Z*, respectively. The hoop direction θ is defined as being perpendicular to both other directions. The plane ϕ is defined by the normal vector <sup>→</sup> *n* Figure 4b. This vector forms an angle α between its projection over the plane [θ*R*] and the direction *R*. It also forms an angle β between <sup>→</sup> *n* and the *Z* direction. The vector <sup>→</sup> *p* , parallel to the intersection between ϕ and [θ*R*] is defined to consider the shear values. In addition, another vector <sup>→</sup> *s* contained on ϕ and perpendicular to <sup>→</sup> *p* is also defined for handling the shear component.

For the 316 stainless steel loading paths, the stresses and strains are computed at different planes ϕ. This is done by evaluating α and β angles in 15◦ increments in the range 0◦ to 90◦ [10]. For the 304 stainless steel loading paths, the hoop and radial strain should be the same on the surface (i.e., εθ = ε*R*). The maximum strain values are found on planes perpendicular to the surface (α = 90◦), with β ranging between 0◦ and 180◦.

Once the strain and stress values are defined on each plane, a cycle counting process was performed using the rainflow method [29]. For dominant Mode II models, the shear strain cycles were counted and for dominant Mode I models, the normal strain cycles were counted. Mean and amplitude values for shear strain and shear stress were obtained using the circumscribed theory proposed by Papadopoulus [30]. Finally the damage was computed following Miner's linear rule [31].


**Table 4.** Summary of the 304 stainless steel experimental data used to evaluate the models.

**Figure 3.** Proportional and non-proportional multiaxial loading paths applied on the 304 stainless steel specimens.

**Figure 4.** (**a**) Coordinates adopted in this work and (**b**) definition of the plane φ that was used to evaluate the critical plane.

#### **3. Critical Plane Models**

Critical plane models are based on observations of the nucleation and growth of fatigue cracks [10]. They are based on a damage parameter (DP) which incorporates stress and/or strain information that is subsequently used to predict the fatigue life. The plane where the DP is maximised is called the critical plane. The DP is defined for each cycle extracted along the entire loading block. For the sake of computational speed, the damage below 25% of the maximum damage along the loading block was not taken into account in the algorithm. This is because the effect of such low damage values on the fatigue life is negligible. Subsequently, a damage accumulation rule was used to obtain the number of cycles until the failure. In this work, three different critical plane models were used to characterise the multiaxial fatigue behaviour of the 316 and 304 stainless steels. The Fatemi—-Socie (FS) critical plane model is normally employed for materials prone to shear failure [17]. The Smith–Watson–Topper (SWT) critical plane model gives accurate predictions for materials with predominant tension failure [21]. In addition, a newly proposed critical plane model by Suman, Kallmeyer and Smith (SKS) was also used to investigate the two materials. By studying the two materials with the FS and SWT models, it will be possible to identify the predominant failure mechanism for each of the materials. In addition, the study will also be useful to assess the predictive capabilities of the newly proposed model via comparison with two widely used critical plane models.

#### *3.1. Fatemi–Socie model (FS)*

The Fatemi–Socie model defines a strain type DP (Equation (1)) [17]. The model is based on that proposed by Brown and Miller [1]. They suggested substituting the normal strain component by a normal stress component. The DP is defined on the plane ϕ\* that maximises the shear strain range, Δγ.

$$DP\_{FS} = \frac{\Delta \gamma\_{\text{max}}}{2} \left( 1 + k \frac{\sigma\_{n,\text{max}}}{\sigma\_y} \right) \tag{1}$$

where Δγ*max*/2 is the maximum shear strain amplitude, σ*n,max* is the maximum tensile stress at ϕ\*, σ*<sup>y</sup>* is the yield stress and k is a material parameter. The values for the yield stress were set to 260 MPa and 290 MPa for 316 and 304 stainless steel, respectively [26].

The strain hardening effect is considered with the Δγ*max* to be 2 times the σ*n,max* product. The mean normal stress effect is also considered via σ*n,max*.

The parameter k represents the sensitivity of the material to normal stresses. This parameter can be estimated from the fatigue life *Nf* [10], through Equation (2).

*Metals* **2019**, *9*, 978

$$k = \left[ \frac{\frac{\tau\_f'}{G} \left( 2N\_f \right)^{b\_f} + \nu\_f' \left( 2N\_f \right)^{c\_f}}{\left( 1 + \nu\_c \right) \frac{\sigma\_f'}{E} \left( 2N\_f \right)^b + \left( 1 + \nu\_p \right) \varepsilon\_f' \left( 2N\_f \right)^c} - 1 \right] \frac{\sigma\_y'}{\sigma\_f' \left( 2N\_f \right)^b} \tag{2}$$

where ν*<sup>e</sup>* and ν*<sup>p</sup>* are the Poisson's ration in the elastic and plastic regimes, respectively, *E* the Young modulus, σ*'f* the fatigue strength coefficient, *b* the fatigue strength exponent, ε*'f* the fatigue ductility coefficient, *c* the fatigue ductility exponent, σ*'y* the cyclic yield stress, *G* the shear modulus, τ*'f* the shear fatigue strength coefficient, *b*<sup>γ</sup> the shear fatigue strength exponent, γ*'f* the shear fatigue ductility coefficient and *c*γ the shear fatigue ductility exponent.

Figure 5 shows the k values for 316 and 304 stainless steel against fatigue life *Nf*. For the 316 stainless steel, there is little variation of the k parameter with respect to the fatigue life. In addition the *k* parameter is very small (around 0.1) throughout the entire life. Figure 5 indicates that *k* parameter is much more sensitive to the fatigue life for the 304 stainless steel, with values ranging between ~0.5 and ~1.25. It is noted that the sensitivity parameter increases with the fatigue life for both materials, although with a much greater gradient for the 304 steel. For the cases where little information is gathered at either low fatigue lives or high fatigue lives, it is possible to use a constant sensitivity factor [10,19]. Nevertheless, in general this might reduce the accuracy of the fatigue predictions.

**Figure 5.** Fatemi–Socie normal stress sensitive factor k for 304 and 316 stainless steel.

#### *3.2. Smith–Watson–Topper Model (SWT)*

The Smith, Watson and Topper model [18] defines a strain energy density type DP (Equation (3)). The DP considers the normal strain and stress acting on the critical plane ϕ\*. The DP is defined on the plane ϕ\* that maximises the normal strain range, Δε.

$$DP\_{SWT} = \frac{\Delta \varepsilon}{2} \sigma\_{n,\text{max}} \tag{3}$$

where Δε/2 is normal strain amplitude, σ*n,max* is the maximum tensile stress at ϕ\*.

The strain hardening effect is considered in the SWT model through the Δε/2 and σ*n,max* product. The mean normal stress effect is also taken into account via σ*n,max*.

#### *3.3. Sandip–Kallmeyer–Smith Model (SKS)*

The multiaxial fatigue behaviour of the two steels is also evaluated with the Suman, Kallmeyer and Smith newly proposed critical plane model [21]. The SKS model defines a stress type DP (Equation (4)). Stress based models, such as Findley [32] and McDiarmid [33] normally give worse predictions for low-cycle fatigue due to lack of real stress information under such conditions. This is overcome with SKS model because it includes a strain component, in a similar way to the FS [17] and SWT [18] models. By using shear strain and shear stress elements, the SKS damage is more suitable for ductile

failing materials. Following Sines compilation of ductile failing materials [34], such an effect is more predominant in the low-cycle regime. The DP is defined on the plane ϕ\* that maximises the shear strain range, Δγ.

$$DP\_{SKS} = (G\Delta\gamma')^w \tau\_{\max}^{(1-w)} \left( 1 + k \frac{(\sigma \cdot \tau)\_{\max}}{\sigma\_0^2} \right) \tag{4}$$

where *G* is the shear modulus, Δγ is the shear strain range, τ*ma*<sup>x</sup> is the maximum shear stress, (σ τ)max is the maximum shear and tensile stress product value, σ*<sup>o</sup>* is a factor used to maintain unit consistency, *w* and *k* are material fitting parameters. The values for the shear modulus were set to 75 GPa to 316 and 304 stainless steel [26]. A value of 500 MPa was set to σ*o*, following the suggestions given by the authors [21]. The σ*<sup>o</sup>* parameter in the SKS damage parameter (Equation (4)) currently does not have a physical meaning, other than consistency of the units. Its value is corrected with the value of k in the fitting.

The strain hardening effect that takes place in the LCF regime is considered by Δγ and τ*max* values. The mean shear stress effect in the high cycle fatigue (HCF) regime is also considered by the shear ratio τ*min*/τ*max*. The parameter w weights the hardening and mean shear stress effects. The product (σ τ)max introduces the detrimental effect over fatigue life observed when sub-cycle load peaks are applied simultaneously. The parameter k gauges the interaction effect between the shear and the normal stresses.

Unlike the FS model, there is not an equation to define the *w* and *k* parameters (Equation (4)). *w* parameter is tuned by fitting the experimental data with a mean shear stress effect. w incorporates the mean shear stress effect and the strain hardening effect. Unlike in the FS model, the *w* parameter has a constant value for all fatigue lives. By using tests for the fitting of the model with a wide range of lives, the *w* parameter cross the different fatigue regimes.

#### *3.4. Fitted Models*

Models damage parameter *DPexp* (Equations (1), (3) and (4)), are related to the fatigue life *Nf* using the same double exponential curve Equation (5). All the material parameters used in the fitting were obtained from previous experimental data, Tables 1 and 2 [26]. The parameters were obtained with an optimisation process based on a least square error minimisation between *DPexp* and *DPcalc* [9]. As the number of experimental data used to fit the parameter were relatively low, the expected difference between the minimisation of the *DP* instead of the fatigue life *Nf* should be negligible over the fitted values.

$$DP\_{\text{calc}} = AN\_f^b + CN\_f^d \tag{5}$$

where *A*, *b*, *C* and *d* are material dependent parameters and *Nf* is the fatigue life in cycles. When fitting the models, *Nf* is the experimental value of each test. Thus, utilisation of SWT requires evaluating those four parameters (*A*, *b*, *C* and *d*). FS requires those four parameters plus the sensitivity factor described in Section 3.1. SKS requires those four parameter plus the two material parameters described in Section 3.2. Fatigue live data are required in order to fit the material parameters for SKS model. Since the SKS model has six fitting parameters, in order to obtain a deterministic (or an over-deterministic) system of equations, six fatigue tests (or more than six tests) were required. These tests should be conducted in conditions as general as possible, to make it as versatile as possible. Accordingly, both proportional and non-proportional tests with a wide range of fatigue lives were employed. In our case we observed an improvement by using an over-deterministic system of equations (Nine and eight tests for 316 and 304 steels, respectively, as shown in Tables 1 and 2).

The collapse capacity of the different models was evaluated by studying the mean and the standard deviation of the error [35]. The error is defined as the difference between the predicted and the experimental life in logarithmic scale (Equation (6)).

$$\text{error} = \log\_{10}(N\_{mod}) - \log\_{10}(N\_{exp}) \tag{6}$$

where *Nmod* is the fatigue life predicted by the fitted model and *Nexp* is the experimental fatigue life.

Table 5 includes the mean and standard deviation of the error values observed in the fitting. Negative mean values are indicative of conservative results and vice versa. A better fitting is obtained with mean values as close as possible to zero. In a similar way, a better fitting is also obtained with the standard deviation value as close as possible to zero. It is observed that the lowest mean values for both materials were obtained with the SKS critical plane model, followed by FS. The mean values in Table 5 indicated that the SWT model appears to produce the least accurate predictions for the type of experiments under study. For both materials, SKS returns the best fit and SWT the worst fit, probably because of the different number of material parameters used in the different models. Materials that normally exhibit a ductile behaviour were more sensitive to damage mechanisms caused by shear stress rather than by normal stress. Materials that normally present a brittle behaviour were more sensitive to damage mechanisms caused by normal stress [16]. Accordingly, the Fatemi–Socie model will be more appropriate for ductile materials failing predominantly under shear mode (Mode II and III); and Smith–Watson–Topper for brittle materials failing predominantly under tension mode (Mode I).

**Table 5.** Statistical analysis for the comparison of the models collapse capacity.


#### **4. Results and Discussion**

The fatigue life predictions of each fitted model are shown in Figures 6 and 7 for 316 and 304 stainless steels, respectively. The experimental fatigue life *Nexp* is defined in the horizontal axis and the predicted fatigue life *Nmod* in the vertical axis. Logarithmic scale is used in both Figures 6 and 7. The points falling along the solid line present coincidence between *Nmod* and *Nexp*. The values along the dashed lines have a factor 2 deviation between *Nmod* and *Nexp*, that is the prediction given by the model that is twice or half of that measured experimentally [9,36]. The estimations of FS are shown by the blue crosses, SWT by green circles and SKS by purple diamonds on both Figures 6 and 7. It was observed that most of the predictions fall within the factor 2 band deviation.

Figures 6 and 7 show that the predictions returned by SKS are mostly between those of FS and those of SWT. The SKS predictions appear to be overall closer to the FS predictions. For the 316 stainless steel, better results were obtained with SKS and FS models (Figure 6). This is in agreement with previous research that indicated that dominant Mode II critical plane models appear to be more suitable for 316 stainless steel [37]. Figure 6 also shows that both SKS and FS models produced less conservative predictions for the square-shape and equi-biaxial tests (cases 4 and 7 in Figure 2). These cases correspond to the two FS points in Figure 6 where the predictions were beyond the twice fatigue life bound. In these tests, the simultaneous application of the loads in the different directions highly restrict the deformation of the material. As a consequence the range of strains were reduced considerably as compared to the equivalent uniaxial loading test. This in turn reduced the value of the damage parameter thus decreasing the accuracy of the predictions towards the non-conservative side [38,39]. The most conservative prediction by the SKS in Figure 6 has *Nexp* = 159,600 cycles. This is indeed the most conservative prediction given by the SKS model. Since the 316 study was conducted with nearly half the samples of the 304 study, the relative weight of this single prediction is larger on the 316 than on the 304 material. It is not surprising that that point produces the longest fatigue life, since it corresponds to the simplest loading case: Pure uniaxial cyclic tension, as shown in Table 3 and Figure 2. The SWT model appears to yield the most conservative predictions, in agreement

with previous research [40] where a different steel with tendency to ductile failure was subjected to proportional loadings.

**Figure 6.** Fatigue life predicted by each model, *Nmod* versus experimental fatigue life, *Nexp* for 316 stainless steel.

**Figure 7.** Fatigue life predicted by each model, *Nmod* versus experimental fatigue life, *Nexp* for 304 stainless steel.

Figure 7 shows that most of the predictions given by the different models on the 304 steel are inside the factor of 2 deviation. Comparison between Figures 6 and 7 indicate the best predictions were overall achieved on the 304 steel. In general the best results were obtained by SWT, as it was observed for this material by Socie [23]. Previous analysis showed that only torsion tests promoted predominant Mode II crack growth and only axial loading tests promoted predominant Mode I cracking on 304 stainless steel, for a range of fatigue lives below 10<sup>5</sup> cycles [10]. As mentioned previously, SWT should then produce more accurate predictions for only axial loading tests and FS present better accuracy for purely torsional tests. Loading cases 2 and 3 in Figure 3 pose a challenging problem in this sense because each loading block is formed of alternating cycles of pure Mode I load and pure Mode II load. That is pure axial load and pure torsional load applied but non-simultaneously. Accordingly, the

predictions given by FS and by SWT should be similar. This is indeed observed for the loading cases 2 and 3 in Figure 7.

As it can be seen in Figure 5, the sensitivity parameter k in FS model changes from ~0.5 to ~1.25 in the range from 10<sup>2</sup> to 105 cycles. If not enough experimental data in the entire range were available, it would be possible to take a constant value of 1 for the FS sensitivity parameter [10]. Nevertheless, the effect in the accuracy of the predictions would be detrimental, producing more conservative predictions in the lower range of the fatigue life (between 102 and 103 cycles in Figure 5) and non-conservative predictions in the higher range of the fatigue life (between 105 and 10<sup>6</sup> cycles in Figure 5).

FS and SWT models allow the additional hardening of the material caused by the non-proportionality of the loads to be taken into account because their damage parameter includes both stress and strain variables. SKS also includes the additional hardening cause by the non-proportionality because its damage parameter has both stress and strain information. This is clear for the loading cases with high non-proportionality (cases 9, 10, 11, 13 and 14 in Figure 3) where the three critical plane models yielded predictions within the factor 2 error bound. Tests with the loads applied proportionally (cases 6, 7 and 8 in Figure 3) were also handled satisfactorily by the three models.

In order to assess numerically the overall performance of the different models, the probability density function (PDF) of the error (Equation (6)) was computed [35]. The results of the PDF for the 316 material are shown in Figure 8a and the results for the 304 material are shown in Figure 8b. In addition, Table 6 summarises the mean value and standard deviation for both materials. The PDF curves closer to a zero mean error and with lower deviation indicated a better accuracy of the model.

For the 316 stainless steel, Table 6 shows a slightly higher mean value for SKS than for FS but a slightly smaller standard deviation for SKS than for FS, thus indicating a similar performance of SKS and FS for the loads analysed on the 316 stainless steel. It was also noted that the mean SKS values were negative while the mean FS values were positive. That is because the SKS predictions are overall more on the conservative side while the FS predictions are more on the non-conservative side for the 316 steel. The larger mean and standard deviation values observed for the SWT indicate overall worst predictions as compared to SKS and FS models. In addition, this is symptomatic of the SKS model being more appropriate for predominantly shear mode failing materials.

On the other hand, for the 304 steel SWT shows the lowest values of both the mean and the standard deviation. This suggests that 304 fails predominantly under tensile mode for the tests described. In addition, the FS the mean value is lower than the SKS, while for the SKS model the standard deviation is lower than that of FS model. The performance of both SKS and FS appears to be similar for the 304 steel but again, the SKS model tends to yield predictions on the conservative side and FS more on the non-conservative side.

**Figure 8.** Probability density function of prediction error for (**a**) 316 stainless steel and (**b**) 304 stainless steel.


**Table 6.** Statistical analysis for the comparison of the model prediction errors.

Table 6 also indicates that the three mean values are smaller for the 304 than for the 316 material, thus indicating that the predictions obtained for the 304 steel are slightly more accurate than for the 316 steel.

The different performance of the different types of models were useful for identify the predominant failure mode of the two materials. The 316 steel appears to fail predominantly under shear mode because FS produces better estimations. Conversely, the 304 steel appears to fail predominantly under tension mode since SWT generated the best predictions. This appears to hold for the wide range of multiaxial loads analysed. Moreover, the alignment of SKS with FS in terms of predictions suggests that SKS model is most suitable for predominantly shear mode failing materials.

#### **5. Conclusions and Future Works**

The multiaxial fatigue behaviour of two widely used materials, 316 and 304 stainless steels, was studied by means of the critical plane approach. The analysis has been performed on a wide range of experimental tests including different combinations of tension, torsion and inner pressure. Three different critical plane models were used, namely FS, SWT and the newly proposed SKS model. First, the collapse capacity of the different models were evaluated. The larger number of material parameters of SKS model appeared to offer a higher flexibility in this sense, thus producing the best fitting. Nevertheless SKS did not offer any expression to define the k and w parameters included in the damage parameter. In addition, the σ*<sup>o</sup>* parameter also included in the SKS damage parameter did not have any physical meaning. Producing analytical expressions relating the k and w parameters to different fatigue properties of the material remain as challenging prospective research activities. The SKS could also be improved by relating σ*<sup>o</sup>* to another characteristic material property, to promote a more uniform use of the model. Unlike the FS model, the parameter k and w parameters take the same value across the whole range of fatigue lives. This can be a weakness for design situations where a very wide range of conditions and very different fatigue regimes are studied. In addition, the SKS model should also be applied to other different materials, to evaluate its performance for other types of alloys.

The efficacy of the different models has also been analysed in terms of their accuracy for predicting the fatigue life. To this end, the damage parameter was correlated with the fatigue life using a double exponential curve. The fitted curves for 316 and 304 stainless steel were used to predict fatigue life under different loading path for the same materials. Most of the predictions given by the three models fall in the band defined by the factor of 2 deviation. For cases with a higher level of hardening, the critical plane models have shown to also generate satisfactory predictions. SKS and FS produced the best predictions for the 316 material while SWT generated the best predictions for the 304 material. Such a trend has been useful to identify the predominant failure mode of the two materials: 316 fails predominantly under the shear mode loading and 304 material fails predominantly under the tension mode loading. The results also indicated that the SKS model appears to be most suitable for shear mode failing materials. For the experimental tests described, SKS has proven to generate predictions on the conservative side and FS on the non-conservative side. This suggests that SKS could be more suitable from a design point of view.

*Metals* **2019**, *9*, 978

**Author Contributions:** Conceptualization, A.S.C. and P.L.-C.; methodology, A.S.C., P.L.-C., T.I., S.B. and B.M.; software, A.S.C. and B.M.; validation, P.L.-C., B.M. and T.I.; formal analysis, A.S.C., P.L.-C. and B.M.; investigation, A.S.C., P.L.-C., T.I., S.B. and B.M.; resources, A.S.C. and S.B.; data curation, A.S.C. and P.L.-C.; writing—original draft preparation, A.S.C.; writing—review and editing, P.L.-C.; visualization, A.S.C.; supervision, P.L.-C.; project administration, P.L.-C.; funding acquisition, P.L.-C.

**Funding:** This research was funded by Ministerio de Economia y Competitividad (Spain), grant number MAT2016-76951-C2-2-P. The APC was funded by Ministerio de Economia y Competitividad (Spain).

**Acknowledgments:** The financial support of Ministerio de Economia y Competitividad (Spain) through grant reference MAT2016-76951-C2-2-P is acknowledged. Fernando V Antunes from University of Coimbra (Portugal) is also greatly acknowledged for his help in conducting the experiments, analysis ideas and interesting discussions. Industrial support from Sandip Suman and UTC Aerospace Systems (CA, USA) is also greatly acknowledged.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Study on the Corrosion Fatigue Properties of 12Cr1MoV Steel at High Temperature in Di**ff**erent Salt Environments**

#### **Jianjun He, Jiangyong Bao, Kailiang Long, Cong Li \* and Gang Wang**

School of Energy and Power Engineering, Changsha University of Science and Technology, Changsha 410114, China

**\*** Correspondence: liconghntu@csust.edu.cn; Tel.: +86-0731-85258409

Received: 6 June 2019; Accepted: 7 July 2019; Published: 10 July 2019

**Abstract:** Biomass energy, as a reliable renewable energy source, has gained more and more attention. However, microstructure degradation and corrosion fatigue damage of heat pipes hinder its further application. In this paper, high temperature corrosion fatigue characteristics of 12Cr1MoV steel under a mixed alkali metal chloride salt environment and mixed sulfate salt environment were investigated. Fatigue tests with different total strain amplitudes were performed. Results show that the effect of total strain amplitude on the cyclic stress response of the alloy is approximately the same under three different deformation conditions. With the increase of the cyclic numbers, the alloyed steel mainly exhibited cyclic hardening during loading. The fatigue properties in air environment were the best, which is most obvious when the total strain amplitude is ±0.3%. The fatigue life of samples in mixed alkali metal salts is the shortest. Furthermore, the fatigue fracture morphology of the alloyed steel in different environments were also deeply analyzed. This experimental study attempts to provide a theoretical reference for solving the problem of rapid failure of heat pipes in biomass boilers, and to establish a scientific basis for the material selection and safety operation.

**Keywords:** high temperature; 12Cr1MoV steel; mixed salt environments; corrosion fatigue; heat pipe failure

#### **1. Introduction**

As a kind of renewable energy, biomass energy has attracted considerable attention in recent years due to its rich resources and lower pollution. However, most of the biomass fuels generally contain a large number of alkali metals, alkaline earth metals, sulfides, and chlorine elements with high concentration [1]. Alkali metal chlorides and sulfides are the main compounds produced during biomass combustion. They generally exist in the form of KCl, NaCl, K2SO4, and Na2SO4. Alkali metal compounds in fuels tend to flow with flue gas at high temperatures, then deposit on the wall of the superheater, and form alkali metal salt slagging with complex composition [2]. This phenomenon easily leads to local overheating, which makes the high temperature salt exist in a liquid pool state. On the other hand, when biomass burns, the sulfur content will be released. Part of the released sulfur is combined with oxygen to form SO2 gas, which is mixed with flue gas and discharged outside of the boiler The other part will deposit in the form of sulfate onto the inside of the boiler. These sulfates will react with the oxide film on the metal surface at high temperatures, which results in corrosion. At the same time, because the heat pipe of the boiler superheater works in high temperature environments [3], the components need to bear more complex loading, which will lead to a local stress concentration, thus resulting in a local plastic deformation and fatigue damage of the material [4]. With the accumulation of deformation, defect structures and cracks are formed [5]. Cracks propagate unstably under the

combined action of a hot corrosion environment [6] and high temperature fatigue [7], which leads to bursting and failure of the steel tube.

The molten salt corrosion is a complex process, involving chemical corrosion, electrochemical corrosion, as well as the interface reaction and the dissolution of oxides. The corrosion resistance at high temperatures is largely dependent on the formation of protective oxidation layer. Cl–Cl-containing environments are well known to cause accelerated corrosion, resulting in increased oxidation, metal wastage, void formation, and loose non-adherent scales, hence destroying the protective oxidation layers [8]. During the fatigue process, corrosion caused by alkali chloride and sulfate salt is one of the most important factors that determine the service life of the heat pipe. In terms of research on the corrosion fatigue of alloys in a salt environment, the following papers are listed. Liu et al. found that the NaCl–KCl mixture could accelerate the corrosion process of TP347H stainless steel and C22 alloy in molten chloride [9]. Zhang et al. have reported that Ni–20Cr–18W alloy suffered severe thermal corrosion in mixed molten salt, the main corrosion products are almost the same at different temperatures [10]. Tsaur et al. used a 310 stainless steel with pre-coated NaCl–Na2SO4 mixture for hot corrosion tests. The experiments have proved that NaCl is the main corrosion catalyst at high temperature. The presence of the NaCl in deposits inhibits the formation of protective oxidation layers at the initial stage, leading to an acceleration of hot corrosion of 310 stainless steel [11].

However, to our best knowledge, until now most experimental research on corrosion fatigue has been carried out mainly from the aspects of salt corrosion, solution corrosion, and so on. In fact, the actual operating environment of the biomass boiler superheater heat pipe is very complex. In many cases, thermal corrosion and fatigue damage caused by biomass combustion will act on the heat pipe material simultaneously, thus accelerating the degradation and failure of the material. Therefore, it is of great significance to study corrosion fatigue characteristics of the heat pipe materials for biomass boilers from the perspective of an interaction between corrosion and fatigue. As a kind of high strength alloyed steel, 12Cr1MoV steel possesses excellent corrosion resistance and mechanical properties. It is widely used in coal-fired boilers and biomass boiler heat pipes at temperatures below 600 ◦C. In this study, 12Cr1MoV steel was chosen as the research material, and corrosion fatigue characteristics of 12Cr1MoV steel at a high temperature under different loading conditions and chemical environments were deeply investigated.

#### **2. Materials and Methods**

The experimental material used in this study was 12Cr1MoV rolled round steel with a diameter of 20 mm. The chemical composition is shown in Table 1.


**Table 1.** Chemical composition of 12Cr1MoV steel (wt%).

In this paper, fatigue tests of alloyed steel were carried out under three different environments: an air environment (reference test), a mixed alkali metal salt environment, and a mixed sulfate environment. The alkali metal salts used in this experiment are KCl and NaCl, which are mixed according to the mass ratio of 70% NaCl + 30% KCl (mixed chloride salt). The composition of mixed sulfates is 70% Na2SO4 + 30% K2SO4. Most biomass boilers set their rated steam temperatures at 450 ◦C, 540 ◦C, and 580 ◦C. Considering that there is a heat storage process on the surface of the steam pipe when the boiler is in operation, the temperature of the heat pipe surface is actually higher than that of the rated steam temperature, therefore in our experiments, the temperature was set to be 600 ◦C. The total strain amplitudes of each group were selected to be +0.5%, +0.4%, +0.3%, and +0.2% for low-cycle fatigue tests, the frequency was 0.2 Hz, and the strain rate was 10−3/s. Specific experimental schemes are shown in Table 2.


**Table 2.** Fatigue experimental scheme of 12Cr1MoV alloy.

The fatigue specimens with a dimension of 40 mm standard distance, 8 mm diameter, and M14 threads at both sides were prepared, as shown in Figure 1a. Specimens were polished smoothly with different sandpapers. Before any further experiments, samples were cleaned with alcohol for 15 min and repeated twice in order to remove impurities and grease on the surface of the samples. The mechanical property tests were conducted on a RDL05 electronic creep-fatigue testing machine. Extensometers and thermocouples were used to measure the strain and temperature respectively. The installation is schematically shown in Figure 1b. The tensile tests were performed at room temperature and 600 ◦C in the air with a strain rate of 10−<sup>3</sup> s−1. In order to assure the repeatability of the results, each test was performed three times.

**Figure 1.** Experimental sample and device, (**a**) shape and dimensions of fatigue test specimens (dimensions in mm), and (**b**) installation of extensometers and thermocouples.

Saturated salt solutions were prepared according to the set mass ratio evenly coated on the sample surface using a small brush. In order to volatilize the water, samples were preheated in a furnace at 100 ◦C. After several minutes, a salt layer of a certain thickness was adhered to the surface of the samples. This process was repeated until a certain thickness of salt layer was uniformly attached. The fracture surfaces of the fatigue samples were observed by Quanta FEG 250 SEM using a voltage of 20 kV.

#### **3. Results and Discussion**

#### *3.1. E*ff*ect of Total Strain Amplitudes*

In order to identify the effect of total strain amplitudes on the fatigue property of 12Cr1MoV steel, low-cycle fatigue experiments with different total strain amplitudes under a mixed chloride salt environment, a mixed sulfate salt environment, and an air condition were carried out at 600 ◦C. Figure 2 shows the cyclic stress as a function of cyclic numbers. As seen in Figure 2, the effect of total strain amplitude on the cyclic stress response of the alloy is approximately the same under three different deformation conditions. For all samples, with the increase of total strain amplitude, the cyclic stress values increased and the fatigue life decreased significantly. This is a very normal and reasonable result. On the other hand, with the increase of the cyclic numbers, all of the samples presented an increment of the cyclic stress, especially at the strain amplitudes of ±0.3% and ±0.2%. Therefore, it can be concluded that the alloyed steel mainly exhibited cyclic hardening during the loading. This phenomenon is consistent with the data calculated from the uni-axial tensile test, as shown in Table 3. Generally,

cyclic hardening and softening of material can be determined by the data of the uni-axial tensile test. When σb/σ0.2 > 1.4, the material exhibits cyclic hardening; when σb/σ0.2 < 1.2, the material exhibits cyclic softening; and when 1.4 > σb/σ0.2 > 1.2, it is impossible to determine whether the material is cyclic hardening or cyclic softening [12]. Based on the data of the tensile test at 600 ◦C, it can be calculated that: σb/σ0.2 = 544/311 = 1.749 > 1.4. According to the calculation, cyclic hardening should occur during the fatigue test at 600 ◦C for the 12Cr1MoV steel, which is consistent with the curves drawn from the experiments.

**Figure 2.** Cyclic stress response of the steel at 600 ◦C (**a**) air environment, (**b**) mixed chloride salt environment, and (**c**) mixed sulfate salt environment.

**Table 3.** Tensile mechanical properties of 12Cr1MoV steel.


The Holomon expression is used to depict the relationship between the magnitude of the stress and the amplitude of the plastic strain [13], as shown in Equation (1):

$$\frac{\Delta\sigma}{2} = K'(\frac{\Delta\varepsilon\_{\rm p}}{2})^{n'} \tag{1}$$

where *K* is the cyclic strength coefficient, and *n* is the strain hardening exponent. After taking logarithms on both sides, the relationship between the total strain amplitude and stress of the samples under different deformation environments was plotted in Figure 3. In this figure, Type A represents mixed alkali metal salt samples, and Type B represents mixed sulfate samples. It can be seen that for all of the samples, the three fitting lines are almost parallel to each other. The *n* value is the slope of a straight line, and the *K* value is the intercept of a straight line on the longitudinal axis. It can be concluded the values of the cyclic strength coefficient *K* and the strain hardening exponent *n* in the three environments are almost the same. After extensive research on high-strength materials commonly used in industry, Landgra [14] proposed that the strain hardening exponent *n* can be used to evaluate the effect of cyclic strain on material properties. When *n* < 0.1, the material behaves as cyclic softening, when *n* > 0.1, the material exhibits cyclic hardening or cycle stability. After fitting, the strain hardening exponent is obtained, as shown in Table 4, with *n* air = 0.1083 > 0.1, *n* mcs = 0.1102 > 0.1, *n* mss = 0.1107 > 0.1. According to this standard, 12Cr1MoV steel mainly exhibits cyclic hardening or cycle stability, which is consistent with the results of the monotonic tensile determination and the cyclic stress response determination. In addition, all of the samples show a cyclic softening before the final fracture, with the cyclic stress decreasing rapidly during the last several cycles. The reason is that the fatigue crack becomes unstable and propagates rapidly and fractures eventually after the nucleation and coalescence.

**Figure 3.** Cyclic stress–strain relationships of samples under different deformation environments.



#### *3.2. E*ff*ect of Deformation Environments*

The cyclic stress response of alloyed steel under different loading environments is shown in Figure 4. It can be seen that different deformation environments have a great influence on the mechanical properties of the specimens. Generally speaking, the fatigue properties of samples in the air environment are the best, which is most obvious when the total strain amplitude is ±0.3%. The fatigue life of samples in mixed alkali metal salts is the shortest. The fatigue life (loading cycles) of all samples are listed in Table 5. It can be clearly seen that the differences in fatigue life caused by environments are different under various total strain amplitudes. When the total strain amplitude is ±0.2%, the fatigue life of the alloy under a mixed alkali metal salt environment is almost the same as that under a mixed sulfate environment, but it is lower than that of the sample under an air environment. When the total strain amplitude is ±0.3%, the fatigue life of the samples under the three environments has the greatest distinction. When the total strain amplitude is ±0.4% and ±0.5%, the effect of mixed sulfate on the fatigue properties of samples is very limited.

**Figure 4.** Cyclic stress response of alloyed steel in different environments (**a**) ±0.2%, (**b**) ±0.3%, (**c**) ±0.4%, and (**d**) ±0.5%.

**Table 5.** Fatigue life of specimens in the three environments (cycles).


In low-cycle fatigue tests, the plastic fatigue strain is relatively high, therefore the life–stress curve (N–S) cannot be used to describe the fatigue property of the material, and the strain fatigue curve is applied. Coffin and Manson proposed a fatigue life description method in which plastic strain amplitude was taken as a key parameter. The formula is given below:

$$
\Delta \varepsilon\_{\rm P}/2 = \varepsilon\_{\rm f}'(2N\_{\rm f})^{\varepsilon} \tag{2}
$$

where Δεp/2 is the plastic strain, ε <sup>f</sup> is the fatigue ductility coefficient, and *c* is the fatigue ductility exponent. According to Equation (2), the plastic strain fatigue life of three different steel samples is fitted by using the logarithmically processed Coffin–Manson relationship, as shown in Figure 5. It can be clearly seen that there is a linear relationship between the plastic deformation and the service life, in both air and mixed salt environments. The *c* value is the slope of the fitting line, and the value ε <sup>f</sup> is the intercept of the line on the longitudinal axis. After fitting, ε <sup>f</sup> and *c* values are obtained as

listed in Table 6. The fatigue ductility coefficient ε <sup>f</sup> represents the fatigue resistance of materials, with a higher value of ε <sup>f</sup> indicating a better fatigue resistance of materials. Additionally, according to the Coffin–Manson equation, the lower the absolute value of fatigue ductility index *c*, the longer the fatigue life. The values of fatigue ductility coefficient and fatigue ductility exponent obtained by the data fitting, show that the fatigue resistance of 12Cr1MoV steel in two mixed salt environments are lower than that of an air environment.

**Figure 5.** Relationship between plastic deformation and fatigue life of steel tested in different environments.


**Table 6.** Low-cycle fatigue characteristics parameters ε <sup>f</sup> and *c*.

#### *3.3. Fracture Surface Observation*

Figure 6 shows the fatigue fracture morphology of the alloyed steel in different environments with the total strain amplitude of +0.2% and +0.5% respectively. All fracture surfaces can be clearly divided into either a fatigue crack initiation zone, a fatigue crack propagation zone, or an instantaneous fracture zone, which are marked by A, B, and C in figures respectively. It can be seen that in region A, there are many crack sources located near the surface. Additionally, the number of crack sources is the least in the air environment (Figure 6a,b), and the number of crack sources is the most in the mixed alkali metal chloride environment (Figure 6c,d). This indicates that under a mixed salt environment, cracks are easier to form due to the combined action of corrosion and cyclic stress. In the same environment, the higher the total strain amplitude, the more the crack sources. In the fatigue crack propagation area (B zone), there are obvious cowrie patterns, especially under low load conditions (Figure 6b,d,f). These cowrie patterns look like a group of arcs centered on the fatigue source, with the concave side pointing to the fatigue source area, and the convex side pointing to the direction of crack propagation. In places near the fatigue source, the crack propagation is slow and the cowrie patterns are dense. In places far away from the fatigue source area, the cowrie patterns are sparse and the fatigue crack propagation is fast. Under the same conditions, the higher the total strain amplitude, the smaller the fatigue crack growth zone and the less cowrie patterns. With an increase of loading cycles, the cracks increase continuously. When the critical length is reached, the stress intensity factor is higher than the fracture toughness of the material, and the cracks expand rapidly, leading to an instantaneous fracture. Furthermore, it can be seen that shear lips exists in the instantaneous fracture zone, and the shear lip surface is at a certain angle with the loading direction, indicating that the instantaneous fracture is mainly caused by shear stress.

**Figure 6.** Overview of the fatigue fracture surface (**a**) ±0.5% (air), (**b**) ±0.2% (air), (**c**) ±0.5% (mixed chloride salt), (**d**) ±0.2% (mixed chloride salt), (**e**) ±0.5% (mixed sulfate salt), and (**f**) ±0.2% (mixed sulfate salt).

Figure 7 shows the detailed morphology of the fatigue crack propagation region. It can be seen that the spacing distance between fatigue striations increases with an increase of strain amplitude. This is because the higher the strain amplitude is, the faster the crack propagation is, subsequently resulting in a shortening of the macroscopic fatigue life. The crack growth region are not as flat as the crack nucleation area, instead the surface is rough and there are many parallel striations on it. During this stage, the stress peaks and valleys are relatively stable, and the cracks propagate at a certain rate. Usually the area of the crack propagation region is very large, which consumes most of the fatigue life of the specimens. When comparing the morphology of crack propagation area between an air environment and a mixed chloride salt environment under the same strain amplitude, it can be seen that the spacing distance of fatigue striation in a mixed chloride salt environment is larger than that in an air environment, and that the depth of cracks in the mixed chloride salt environment are deeper, as shown in Figure 7a–d. This result indicates that the crack growth rate in a mixed chloride salt environment is greater than that in an air environment. The observation of fracture surface shows that a mixed alkali metal chloride environment can be harmful to the fatigue crack resistance of this alloy. Figure 7e,f are images of the fatigue crack propagation region of alloyed steel in a mixed sulfate environment. Its characteristics lie between the air environment and the mixed alkali metal salt environment.

Figure 8 is the typical dimple morphology of the instantaneous fracture region. It can be seen that the surface of the instantaneous fracture zone is rough, and there are many holes and voids with some inclusions. When the interface of inclusions is plastically deformed, it is easy to cause stress concentration, and then cracks are generated and propagate continuously. Subsequently, the matrix between the inclusions forms an "internal plastic neck", which is torn or sheared when the internal plastic neck reaches a certain extent, thus connecting the voids. Finally, forming the observed dimple fracture morphology.

**Figure 7.** *Cont*.

**Figure 7.** The fatigue crack propagation region (**a**) ±0.5% (air), (**b**) ±0.2% (air), (**c**) ±0.5% (mixed chloride salt), (**d**) ±0.2% (mixed chloride salt), (**e**) ±0.5% (mixed sulfate salt), and (**f**) ±0.2% (mixed sulfate salt).

**Figure 8.** The fatigue fracture region of the alloy with strain amplitude of ±0.5% (**a**) air, (**b**) mixed chloride salt, and (**c**) mixed sulfate salt.

From the above analysis, it can be concluded that the surface and matrix of 12Cr1MoV steel will be corroded seriously under a high temperature mixed molten chloride environment. With the increase of KCl content in alkali metal molten salt, the structure of corrosion products on the surface of 12Cr1MoV steel will change from round granular to flocculent state. The corrosion rate and thickness of corrosion products increase obviously. The corrosion mechanism of test steel in molten salt is the activation and oxidation behavior of chlorine element. The corrosion products of a section are mostly in porous distribution, and the pore size is larger when Cl element content is higher. The thickness of the corrosion inner layer increases further with an increase of temperature. When corrosion reaction continues, it is easy to change the material quality from weight gain to weight loss by separating some corrosion products from matrix. Under the action of high temperature thermal stress, stress concentration easily occurs near the hole. This results in the initiation and instability propagation of corrosive cracks, further affecting the strength and properties of materials. In a sulfate environment, such corrosion rate is lower, therefore in a fatigue test we can observe that the fatigue property of the samples in chloride environment is the worst.

#### **4. Conclusions**

The corrosion fatigue properties of 12Cr1MoV steel under different amplitudes and different environments were studied. The following conclusions can be drawn:


**Author Contributions:** Data curation, J.B.; investigation, G.W.; methodology, K.L.; writing—original draft, J.H.; writing—review and editing, C.L.

**Funding:** This research was funded by National Natural Science Foundation of China, grant number 51275058. **Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## **Influence of Residual Stress on Fatigue Weak Areas and Simulation Analysis on Fatigue Properties Based on Continuous Performance of FSW Joints**

#### **Guoqin Sun 1,\*, Xinhai Wei 1, Jiangpei Niu 2, Deguang Shang <sup>1</sup> and Shujun Chen <sup>1</sup>**


Received: 1 February 2019; Accepted: 26 February 2019; Published: 2 March 2019

**Abstract:** The fatigue weak area of aluminum alloy for a friction stir-welded joint is investigated based on the hardness profile, the residual stress measurement and the simulation analysis of fatigue property. The maximum residual stresses appeared at the heat-affected zone of the joint in the fatigue damage process, which was consistent with the fracture location of the fatigue specimen. The fatigue joint model of continuous performance is established ignoring the original negative residual stress; considering that it will be relaxed soon when the joint is under tension-tension cyclic loading. The fatigue parameters of joint model is based on the static mechanical properties of the joint that obtained from the micro-tensile tests and four-point correlation method. The predicted results for the fatigue weak locations and fatigue lives based on the continuous performance joint model are closer to the fatigue experimental results by comparison with the simulation results of the partitioned performance joint model.

**Keywords:** friction stir welding; residual stress; weak area; finite element simulation; life prediction

#### **1. Introduction**

Friction stir welding (FSW) of aluminum alloy has been widely used in the automotive, aerospace and ship industries. The anti-fatigue design is worthy of attention for the load-carrying FSW components. The influencing factors on the failure location of the joints are needed to be focused on. The hardness distribution of the friction stir-welded joints is related to the materials and welding process. It is considered that it has a relation to the fatigue fracture position of alloy joints [1–6]. But some studies showed that fatigue cracks were independent from hardness distributions in the weld seams and the fatigue cracks initiated at the inhomogeneous microstructure [7]. Fatigue fracture of the large plate happened at the lowest hardness location in the heat affect zone (HAZ) [8]. But the tensile strength of the FSW joint has a linear relationship with the weld nugget hardness [9]. The fatigue properties of aluminum alloy FSW joints are also affected by the residual stress [2–4]. The residual stresses of aluminum alloy welded joints are dependent on the welding parameters and their distribution has a typical "M" profile [10–13]. The locations of the maximum residual tensile stress are different for different alloy joints. The compressive residual stress delays the crack growth and increases the fatigue life of the welded joint and the tensile residual stress accelerates the propagation of the crack [14–17]. Fratini et al. [4] found that the residual stress had an influence on the crack propagation of base metal area and had no obvious effect on the welding area. The effect of residual stress on the joint would weaken with the increase of fatigue cycle or the crack length [18,19].

Finite element numerical simulation has been applied on the evaluation of mechanical properties for FSW joints. In addition, the residual stress can be preloaded into the joint model as a prestress if it is non-negligible [20]. Rao and Simar [21,22] established the finite element model of the FSW joint through the partition method to obtain the tensile properties. The friction stir welding joints were divided into different regions to simulate the mechanical properties of the weak regions [23,24].

The simulation method with the partitioned performance joint model has the stress concentration at the regional boundary positions because of the discontinuity of material properties. The continuous performance joint model does not have the effect of the area partition and obtains more accurate stress–strain data. Therefore, the fatigue finite element model of continuous performance for the FSW joint is established to simulate the weak areas and the stress–strain response. The life prediction is proceeded based on the simulation results and a comparison between the continuous performance joint model and the partitioned performance joint model is carried out. Also, the relationship between the fatigue weak areas of 2219-T6 aluminum alloy friction stir-welded joints and mechanical properties is analyzed with experimental.

#### **2. Experimental**

#### *2.1. Materials and Specimens*

The test specimens is cut from 2219-T6 aluminum alloy FSW butt plate of 800 mm × 300 mm × 6 mm size. The chemical compositions and mechanical properties of base metal are given in Tables 1 and 2. The alloy plates were welded perpendicular to the rolling direction with a rotation speed of 800 rpm and an advancing speed of 180 mm/min. The FSW tool consists of a shoulder with a diameter of 18 mm and a tool pin of 5.7 mm in length and 6 mm in diameter. The tool axis is tilted by 2◦ with respect to the vertical axis of the plate surface. The welding was finished in the China Academy of Launch Vehicle Technology. The fatigue samples were wire cut from the plate, which its axial direction was perpendicular to the weld line. The surfaces and sides of the specimens were ground with silicon carbide sandpaper from 150 to 2000 grit and the surfaces were polished with diamond polishing pastes from 4000 to 10,000 grit. The thickness of the fatigue specimen is 6 mm and the dimensions is shown in Figure 1.


**Table 1.** Chemical composition of 2219 aluminum alloy.


**Table 2.** Mechanical properties of 2219-T6 aluminum alloy.

**Figure 1.** Shape and size of fatigue specimen.

#### *2.2. Metallographic Morphology*

The cross-sectional metallographic morphology of the specimen was observed with the optical microscope (Shanghai optical instrument factory, Shanghai, China) after the specimen was etched with keller's reagent consisting of 2.5 mL HNO3, 1.5 mL HCL, 1 mL HF and 95 mL H2O for about 15 s. According to the metallographic morphology of the welded joint in Figure 2 and the sizes of the grain, the welded joint is divided into different regions: the weld nugget zone (WNZ), the thermo-mechanically affected zone (TMAZ), the HAZ and the base material (BM). The HAZ is further divided into high-hardness heat affect zone (HHAZ) and low-hardness heat affect zone (LHAZ) based on the hardness distribution and the phase sizes. The phase in the HHAZ has the similar size as that in the BM, while the hardness in HHAZ is lower than that of BM. In addition, according to the rotation direction of the welding tool, the joint is divided into the advancing side (AS) and the retreating side (RS). The dimensions of the different zones that marked in the hardness profiles can be obtained by combining the metallographic morphology, phase size and the hardness profile.

**Figure 2.** Metallograph of the aluminum alloy FSW joints: (**A**) WNZ, (**B**) TMAZ, (**C**) HAZ, (**D**) BM.

#### *2.3. Hardness Measurements*

The microhardness distributions were measured on the upper and the lower surfaces of the welded joint with a load of 1.95 N for 15 s with a SCTMC DHV-1000Z Vickers hardness tester (Shangcai tester machine Co, Ltd, Shanghai, China). The measurement spacing between each two adjacent points was 0.5 mm.

#### *2.4. Fatigue Experiments*

All fatigue tests were carried out using MTS858 hydraulic servo system (MTS Systems Corporation, Minneapolis, MN, USA) under the axial stress range from 216 to 261 MPa with a stress ratio of 0.1 and a frequency of 10 Hz until the specimens fractured. The fatigue loading parameters and total fatigue lives are available from Ref. [25]. The curve of cyclic stress range versus fatigue lives for the FSW specimens is shown in Figure 3.

#### *2.5. Residual Stress Measurements*

The residual stresses of the original and the fatigue-damaged specimens were measured by D8 Discover X-ray diffraction meter (Bruker Corporation, Karlsruhe, Germany). The specimen was electrochemically polished to remove the effect of mechanical polishing before the residual stress measurement. The original residual stress distributions of the upper and the lower surfaces for the joint were measured before fatigue test. Then, the cyclic stress range of 216 MPa with a stress ratio of 0.1 was loaded on the joint and the fatigue test was stopped when the fatigue life was 30,000 cycles. Then, the surface residual stresses of the fatigue-damaged specimen were measured again to analyze the effect of the residual stress distribution in the fatigue process on fatigue damage.

**Figure 3.** S-N curve of FSW specimens.

#### **3. Experimental Results**

#### *3.1. Hardness Distribution*

The upper and the lower surfaces hardness profiles of the welded joint are shown in Figure 4. The hardness distributions of the joint upper and lower surfaces present the approximate "W" shape. The hardness in the welded region is obviously lower than the base material. The minimum hardness values of the upper and the lower surfaces are both in the LHAZ according to the hardness distribution of the joints, which is not in coincidence with the failure position of HHAZ for most fatigue specimens. Hardness has a relation with the material strength but the fatigue weak area of the joint is not necessarily corresponding to the location of minimum hardness [7]. It has a relation with the variation of the hardness gradient, which corresponds to the variation of the mechanical property and heterogeneous microstructure.

**Figure 4.** Hardness distributions of (**a**) upper and (**b**) lower surfaces in the joint.

#### *3.2. Fatigue Experimental Results*

The failure locations in the joints were observed with the optical microscope after the specimens fractured. First, the locations of the fatigue crack sources are needed to be found and observed. Then, the sides or the surfaces of the sample near the location of fatigue crack sources are etched with Keller's reagent. The failure locations can be affirmed through the metallographic morphologies of the samples. The statistics of failure locations for 11 specimens are listed as follow: 10 specimens fractured in HHAZ, 1 specimen broke in WNZ.

#### *3.3. Residual Stress Distribution*

The residual stress distributions are shown in Figures 5 and 6. The transverse residual stresses are the stresses perpendicular to the weld and the longitudinal residual stresses are the stresses parallel to the weld direction. The center of the WNZ was taken as the zero coordinate and the test points were selected on both sides along the axial direction of the specimen. The measured residual stresses before fatigue test are called as the original residual stresses of the specimen in this paper. The residual stresses of the fatigue-damaged specimens were measured after the fatigue cycle reached 30,000 cycles under the cyclic stress range of 216 MPa with a stress ratio of 0.1.

(**a**) (**b**)

**Figure 5.** (**a**) Transverse and (**b**) longitudinal residual stress distributions of upper surface in the joint.

**Figure 6.** (**a**) Transverse and (**b**) longitudinal residual stress distributions of lower surface in the joint.

Figure 5 shows the variation of the transverse and longitudinal residual stress distribution curves in the upper surface of the welded joint. It can be seen that the maximums of the transverse and longitudinal residual stresses in the original welded joint appear in the WNZ and the values are basically negative or near zero. The original negative residual stresses in the welded joint is beneficial to the fatigue life. However, the original compress residual stress will be relaxed and the positive stress will appear soon once the tension-tension stress is loaded. The positive transverse and longitudinal residual stresses arose in the fatigue process and the maximum residual stress appeared at the LHAZ during the cyclic loading.

Figure 6 shows the variation of the transverse and longitudinal residual stress distribution curves in the lower surface of the welded joint. The residual stresses is negative in the original joint. The maximum stresses appeared near the boundary of NZ and TMAZ in the fatigue process and the values were far lower than the residual stresses in the upper surface. The residual stress of the upper surface in the joint that produced in the fatigue process should have more effect on the fatigue damage.

#### **4. Fatigue Numerical Simulation**

#### *4.1. Fatigue Parameters of the Welded Joint*

The fatigue finite element numerical analysis is further proceeded in order to obtain the stress–strain responses and evaluate the weak area of the joint with the simulation method. Since the original residual stress was negative and would be relaxed once the tension-tension stress was loaded. It did not considered to be added on the joint as a prestress in the numerical analysis under the tension-tension cyclic loading.

The fatigue parameters are different in different zones since the materials of different zones in the joint have different microstructures and mechanical properties. They can be used in some fatigue life prediction models to calculate fatigue lives or as the intermediate variables to calculate other cyclic strength parameters. The fatigue parameters of different positions in the welded joint were obtained by four-point correlation method proposed by Manson [26].

The four-point correlation method is based on the elastic and plastic strain-life lines. The respective two points on elastic and plastic lines are definite. On the elastic line, a point is at 1/4 cycle with a strain range of 2.5 *σ*f/*E*, where *σ*<sup>f</sup> is the fracture strength, *E* is the elastic modulus. The other point is at 10<sup>5</sup> cycles with a strain range of 0.9 *σ*u/*E*, where *σ*<sup>u</sup> is the ultimate tensile strength. On the plastic line, a point locates at 10 cycles with a strain range of 1/4*D*3/4, where *D* is the logarithmic ductility of the material. Another point is at 104 cycles with a strain range of 0.0132−Δ*ε*<sup>∗</sup> e 1.91 , Δ*ε*<sup>∗</sup> <sup>e</sup> indicates the value of elastic strain range at 10<sup>4</sup> cycles on the elastic line, as shown in Figure 7.

**Figure 7.** Four-point correlation method by Manson.

The static mechanical properties of different positions in the joint were obtained from the micro-tensile tests. Microspecimens from different regions were cut parallel to the weld direction of welded joints. The static mechanical properties of each zone were measured by using Instron 5948 Microtester (Instron Corporation, Norwood, MA, USA). The calculated fatigue parameters of different positions in the welded joint are listed in Table 3.


**Table 3.** Fatigue parameters of the welded joint.

#### *4.2. Continuous Performance Joint Model*

The continuous performance joint model is established by inputting different elastic moduli and fatigue stress–strain data at different areas of the joint with ABAQUS software. The WNZ center of the joint is the zero coordinate of the X axis in the model. The different coordinates correspond to the different locations of the joint along the axial loading direction. The elastic moduli of different positions with the coordinate X that listed in Table 3 were obtained from the micro tension tests. The elastic moduli of the other positions in the joint can be obtained by interpolation according to the data in Table 3. The mechanical properties of the joint also vary with change of the coordinate. The materials in different zones of the joint have different stress–strain responses. The cyclic stress–strain at different locations of the joint were obtained using Ramberg–Osgood equation and applied to the finite element simulation. The Ramberg–Osgood equation is shown below.

$$
\varepsilon\_{\mathbf{a}} = \frac{\sigma\_{\mathbf{a}}}{E} + \left(\frac{\sigma\_{\mathbf{a}}}{K'}\right)^{\frac{1}{N'}} \tag{1}
$$

where *ε*<sup>a</sup> is the strain amplitude, *σ*<sup>a</sup> is the stress amplitude, *K* is cyclic strength coefficient, *n* is the cyclic strain hardening exponent. They can be obtained from the following equations.

$$K' = \frac{\sigma\_{\rm f}'}{\varepsilon\_{\rm f}'^{\rm n'}} \tag{2}$$

$$
\mathfrak{n}' = \mathfrak{b}/\mathfrak{c} \tag{3}
$$

The cyclic yield strength was measured by the stress value of 0.2% plastic strain in the cyclic stress–strain curve. The nonlinear kinematic hardening model of the material attribute was adopted for the joint material.

User subroutine USDFLD in the ABAQUS software can be used to describe material properties. The material properties is defined as a function of field variables and the variables can be solved with USDFLD subroutine. The variation of elastic modulus, yield stress and plastic strain with the coordinate X were computed with the interpolation method using the known data of the specific coordinate through the subroutine.

The joint model is constrained at one end and loaded the cyclic stress range of 216 MPa with a stress ratio of 0.1 at another end of the joint in the X-axial direction. The loaded cyclic stress is schematically drawn in Figure 8. The hexahedron mesh with eight nodes element type of C3D8R is selected to solve the structure. The size of each element is approximately 1.3 mm × 0.8 mm × 1.2 mm. 3600 elements and 4758 nodes are obtained to simulate the FSW joints, as shown in Figure 9. The model does not include the clamping part and the cyclic stress as a surface load is directly applied to the section of the right end.

**Figure 8.** Schematic of loaded cyclic stress on the joint.

**Figure 9.** Meshed joint.

#### *4.3. Partitioned Performance Joint Model*

To compare the effectiveness of the continuous performance joint model for the fatigue performance simulation of the FSW joints, the partitioned performance joint model was established according to the metallurgical morphologies, hardness profile of the joints and the material attributes in different regions of the joint [25]. The joint is composed of the WNZ, TMAZ, HHAZ, LHAZ and BM, as shown in Figure 10. The fatigue parameters of different positions of the FSW joints were calculated according to the four-point correlation methods. The stress–strain data in different zones of the joint were obtained with Ramberg–Osgood equation. The material property does not have a change within each region.

**Figure 10.** Partitioned performance joint model of the FSW joint.

#### **5. Simulation Results**

#### *5.1. Stress Distribution*

Von Mises stress distributions of continuous and partitioned performance joints are shown in Figure 11a,b. The stress distribution of the partitioned performance joint shows a significant mutation at the junction of different regions, especially at the junction of TMAZ and HAZ. The simulation results of continuous performance joints show the changes of stress and strain are smoother.

**Figure 11.** Von Mises stress contour plots of (**a**) continuous joint model and (**b**) partitioned joint model.

To observe the fatigue performance of the joint, the cyclic stress range of 216 MPa with the stress ratio of 0.1 was loaded on the joint. The maximum von Mises equivalent stress appeared in the upper surface of the joint in the partitioned performance joint model. The stress distribution trend of the upper and the lower surfaces in the continuous performance joint model is the same. The von Mises stress data of upper surface centerline were extracted from the simulation results of the continuous and the partitioned performance joint models. The maximum von Mises stresses both appeared in the HHAZ for the two models, as shown in Figure 12.

**Figure 12.** Von Mises stresses distributions of upper surface in the joint model.

The sudden change of stress in the partitioned performance joint model is obvious at the junction of adjacent regions in the joint. The distribution of von Mises equivalent stress obtained from the continuous performance joint model is relatively continuous for the joint, which is closer to the practical condition. The maximum stress appeared at the boundary of LHAZ and HHAZ for the partitioned performance joint model and it occurred at HHAZ near the LHAZ for the continuous performance joint model. The location of the maximum stress has a little difference for the two models.

The stress components of continuous and partitioned joint models were analyzed. There is no stress in the Z direction. The shear stresses are so small that their effects on the fatigue performance of the welded joint are ignored. It can be considered that the stresses in the X and the Y directions determine the total stress distribution of the FSW joints. The stresses in the X and the Y directions of upper surface in the models were extracted for analysis as an example, as shown in Figure 13. The stresses in the X direction are larger in the two models since the tension-tension stress is loaded in the X direction. The stress fluctuation appeared in the X and the Y directions of the partitioned performance joint model. The stress distribution of the continuous performance joint model has no obvious sudden change.

**Figure 13.** Stress distributions in the X and Y directions in upper surface of the joint model.

#### *5.2. Strain Distribution*

The weak area of joint fatigue performance can be determined by the stress and strain response of different zones in the joint from the simulation results of the fatigue property. The maximum principal strains at the centerline of upper surface, which extracted from the continuous and the partitioned performance joint models under the cyclic stress range of 216 MPa with a stress ratio of 0.1, are presented in Figure 14. Due to the abrupt change of material properties, the partitioned performance joint model caused a corresponding stress concentration at the junction of different regions and resulted in larger maximum principal strains than that of the continuous performance joint model. The larger the loaded cyclic stress in the model, the more obvious the abrupt change of strain distribution. The maximum principal strain is in the LHAZ near the TMAZ for the partitioned performance joint model and it appears in the HHAZ close to the LHAZ for the continuous performance joint model, which is approximately consistent with the fatigue failure position. The simulated fatigue weak area with the continuous performance joint model is more close to the fatigue experimental results.

**Figure 14.** Maximum principal strain distributions of upper surface in the joint model.

By comparison with the partitioned performance joint model, the continuous performance joint model has a higher accuracy on predicting the fatigue weak areas of the FSW joint according to the stress and strain distributions. It eliminates the large stress concentration caused by the abrupt change of material properties in the adjacent area and more accurately simulates the fatigue performance of the joint.

#### **6. Fatigue Life Prediction**

The joint models established in this paper not only evaluate the fatigue weak areas and obtain the stress and strain values of the joint, but they also predict the fatigue lives of the joints. In this section, the stress and strain values of the weak areas obtained from the continuous and the partitioned performance joint models are used to predict the fatigue lives of the FSW joints. The validity of the continuous performance joint model is further verified by comparison with the experimental results.

Crack initiation lives were estimated with Smith–Watson–Topper (SWT) method, which considered the effect of average stress [27]. The maximum principal stresses and corresponding maximum principal strain ranges of the weak area of the joint were extracted from the simulation results of the joint models. Fatigue parameters of weak areas are used to predict the fatigue crack initiation lives of joints. The SWT formula is shown below.

$$
\sigma\_{\text{max}} \frac{\Delta \varepsilon}{2} = \frac{\sigma\_{\text{f}}'^2}{E} (2N)^{2b} + \sigma\_{\text{f}}' \varepsilon\_{\text{f}}' (2N)^{b+c} \tag{4}
$$

where *σ*max is the maximum principal stress, Δ*ε* is the maximum principal strain range, *N* is the fatigue life.

The experimental results in Ref. [28] showed that the size of fatigue crack initiation was defined as 1 mm and the crack initiation lives for the HAZ and the WNZ of aluminum alloy welded joints were 40.21% and 60.67% of the total fatigue lives, respectively. The research in Ref. [29] showed that the crack initiation lives accounted for 40–50% of total fatigue lives. Therefore, the crack initiation life is selected as 50% of the total fatigue life in this paper.

The life prediction results of FSW joints are shown in Figure 15. The predicted errors of the fatigue lives based on the continuous and the partitioned performance joint models are basically within the factor of two by comparison with the experimental results. The fatigue life prediction results with the simulation data obtained from the continuous performance joint model are closer to the experimental lives because the continuous performance joint model has not the stress and strain concentrations caused by the area partition. It is shown that the continuous performance joint model is suitable for life prediction of the FSW joints.

**Figure 15.** Life prediction of joint based on continuous and partitioned performance joint models.

#### **7. Conclusions**

(1) The original transverse and longitudinal residual stresses in the welded joint before fatigue are negative and the maximum tensile residual stress occurs in the HAZ during the tension–tension cyclic loading process.

(2) The fatigue parameters of different areas are obtained with four-point correlation method and the static mechanical property parameters of micro-tensile specimen at different locations of the joint. The continuous performance joint model is established by inputting different elastic moduli and fatigue stress–strain data at different locations of the FSW joint with user subroutine USDFLD. The stress components in the X and the Y directions determine the stress distribution of the FSW joints. The continuous performance joint model eliminates the stress and strain concentration caused by the area partition and more accurately simulates the fatigue performance of the joint by comparison with the partitioned performance joint model. The simulated fatigue weak area with the continuous performance joint model is more close to the fatigue experimental results.

(3) The fatigue life prediction of the FSW joints is proceeded with SWT method based on the simulation results of the continuous and the partitioned performance joint models. The results show that the predicted lives with the continuous performance joint model are closer to the experimental results and the life prediction error is within the factor of two.

**Author Contributions:** G.S. designed and performed the experiments; G.S., J.N. and X.W. analyzed the experimental data and simulated the joint model; D.S. and S.C. gave some advices for the research; G.S. and X.W. wrote the paper.

**Funding:** This research was founded by the National Natural Science Foundation of China (Grant No. 11672010, 51535001 and 51575012).

**Conflicts of Interest:** The authors declare no conflicst of interest.

#### **Abbreviations**


#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
