1. Introduction
Research on crack behavior subjected to fracture or fatigue processes has traditionally relied on analyzing their behavior in specimens under controlled conditions, through either experimental or numerical models. CT specimens have been widely used to simulate states of flat crack subjected to solicitations favoring mode I crack growth.
The following describes several studies and works conducted on flat specimens, with an emphasis on materials, universal testing machines, as well as numerical models, among other aspects.
For example, Jong Henk [
1] analyzed fatigue crack geometry in 25-mm thick flat specimens of 7075 T651 aluminum alloy, using servo-hydraulic equipment to apply cyclic loads up to 200 kN at frequencies up to 10 Hz. Correia et al. [
2] investigated the fatigue crack growth of 6082-T6 aluminum alloy per ASTM E647 standards [
3], using standard CT, sharp-notched, and circular samples. They found that notch configuration significantly affects the stress intensity factor (K), with round notches yielding higher stress thresholds. CT specimens were 10 mm thick, with chevron-type notches used as stress concentrators. Loads from 2.8 to 6.2 kN extended cracks to 2 mm, requiring 14,400 to 16,600 cycles for failure. Chun-Jun [
4] studied compact tension samples under 8–10 kN loads and load ratios of R = 0.1, 0.3, and 0.5, using an MTS 858 system at frequencies up to 20 Hz. Bretschneider [
5] examined non-standard geometries in aluminum alloy, applying R = 0.1 load ratios until cracks reached 2.5 mm, noting similar displacement on the external faces. L. Cai [
6] used optical microscopy and SEM to assess crack geometry under overloads, finding that the Paris law-based crack closure effect did not align with post-overload growth. Vasco-Olmo [
7] applied digital image correlation to evaluate fatigue crack growth, proposing alternative parameters for stress intensity factors. Additionally, extensive 2D and 3D numerical modeling has been developed. Computational cost remains a critical factor in these studies. Various models have analyzed crack edge behavior, focusing on plastic deformation and stress [
8,
9,
10,
11,
12,
13,
14,
15]. Camas et al. [
16] demonstrated that plastic deformation is more pronounced near the external faces of flat specimens, with similar deformation observed on both faces.
Having thoroughly reviewed the extensive research on flat specimens, attention is now directed towards investigating studies conducted on tubular specimens.
Tanaka [
17] performed fatigue crack growth tests using thin-walled tubular specimens with a circular hole made of low-carbon steel. Cyclic uniaxial compression, tensile loads, and cyclic torsion were applied. Crack growth rates for torsion and torsion, combined with axial loading, were higher than uniaxial loading. The crack growth acceleration was attributed to increased plasticity at the crack tip. Shamsaei [
18] conducted research involving strain-controlled tests on tubular specimens made from pure titanium and titanium alloy BT9. The study included both constant and variable amplitude axial and torsional loads, as well as in-phase and out-of-phase axial-torsional loading conditions. Gladskyi [
19] investigated the effects of notches on the fatigue behavior under axial and torsional loading in thin-walled tubular specimens of low-carbon steel. He evaluated specimens with and without a transverse circular hole. It was determined that the notch effect was more pronounced under axial loading. Fatemi [
20] conducted fatigue tests of thin-walled 7075-T6 and 2024-T3 aluminum tubular specimens with a circular notch. The loading conditions applied were torsional and axial ones. Macroscopic crack growth in notched specimens occurred along planes experiencing the maximum range of nominal principal stress, i.e., mode I crack growth; crack growth was performed by evaluating the growth on the external face associated with the external radius. Gladskyi [
21] evaluated the fatigue crack growth of tubular specimens with a circular through-hole in carbon steel specimens subjected to axial and torsional loads, observed mode I crack growth, and the crack growth rates were correlated with the stress intensity factor, and graphs of da/dn versus
were generated to investigate the crack growth behavior of tubular specimens. Mokhtarishirazabad [
22] carried out research related to tubular specimens, where he focused his research on the analysis of crack displacement by DIC; this research was based on the growth of the visible crack, the outer one, and the crack growth variables correlated with the stress concentration factor. Macek [
23,
24] investigated the fracture surface topographies of tubular specimens using an optical measurement system. It was established that these topographies are a critical factor affecting the service life of the specimens.
Regarding the numerical models of tubular specimens, numerous investigations have been conducted on this subject [
25,
26,
27]. However, the conclusions of these studies consistently reveal three-dimensional crack behavior in the region near the crack, where the curvature of the crack is influenced by the distribution of the stress intensity factor (
) through the thickness and the phenomenon of crack closure [
27]. The conclusions validated the methodology, and interesting study parameters regarding crack growth rates between the outer and inner faces of the specimen under mode I fatigue were established. Building upon the previous results, an experimental campaign is proposed on tubular specimens under mode I solicitations, the results of which are presented in this paper.
As mentioned before, previous work focusing on fracture numerical models of tubular specimens under mode I has been conducted [
27]. The analysis of the results obtained from the plastic zones was influenced by the thickness, the level of applied load, and by the radius of curvature. The work presented in this article is proposed as a continuation of the previous one and presents a fatigue-testing campaign of different specimens of aluminum tubular specimens subjected to tensile loads. The internal radius has been kept constant and the crack is evaluated in three cases with different thicknesses, focusing on the evolution of the crack on the outside. The relationship with the analytical values of the stress intensity factor (both internally and externally) is analyzed.
This article is structured as follows: A brief description and justification of the methodology used. Next, the results obtained are presented, followed by an extensive analysis of the results, and finally the research conclusions are described.
4. Conclusions
An experimental analysis of the fracture zone and crack growth of tubular specimens subjected to cyclic loads in mode I was carried out, with a sinusoidal shape function and a frequency of 3 Hz. The analysis of results focuses on the variation of the stress intensity factor and in the crack geometries produced by fatigue until overloading and final fracture. A quantitative graphic analysis of the presented phenomenon was carried out. These results led to the observation of characteristic behaviors in tubular specimens. Regarding the results, the following conclusions can be defined:
The parameter F0 and the stress intensity factor increase their values proportionally to the growth of the crack. A marked difference was found in the values of the stress intensity factor on the external faces of the internal and external radii.
The maximum value of the stress intensity factor at which the specimens fail is associated with the internal radius for the specimen with a wall thickness of 2 mm and a value of 26.98 MPa m1/2, while for the specimens with 3 and 4 mm of wall thickness, this occurs in the outer radius with values of 26.39 MPa m1/2 and 24.76 MPa m1/2, respectively. The three analyzed specimens exhaust their capacity to support loads when the stress intensity factor takes an average value of 26.04 MPa m1/2, a different value from the static stress intensity factor due to crack growth.
In the tubular specimen with 3 mm thickness, four stages of crack growth were identified using artificial vision techniques. The crack was marked in the fatigue fracture zone in the tubular specimens with a wall thickness of 2 and 4 mm. For this, an overload was applied over 1500 cycles after starting the mechanical test by applying cyclic loads.
The geometry of the overburden crack was identified to be similar to that of the final fracture, when compared using a linear data trend, and its slopes were identified to change as the crack moved due to the application of cyclic loads. The difference in slopes was found with a value less than 0.44.
When evaluating the crack displacement of the tubular specimens, it was found that the crack propagation distance on the external faces of the specimen was different and was associated with the internal radii Ri and Re, a particularity that does not occur in the flat specimens, with similar crack displacement on their external faces. The area associated with the internal radius Ri and the external radius Re was calculated. A mean curved plane was defined for the calculation of the areas. A variation was identified in the calculated areas that are associated with Re and Ri. The variations related to the length of crack displacement and the calculated areas again highlight the differences with flat specimens.
The 2 mm thickness specimen followed its pattern with a more significant internal growth until breaking; we can consider it thin-walled.
The 4 mm thickness specimen presented in most of its development a tridimensional lenticular crack development, which would be the end of the very thick wall.
The sample with a wall thickness of 3 mm achieved behavior analogous to samples with two-dimensional cracks, but a transitory adaptation process occurred that is important to consider in order to correctly interpret the results obtained from the studies carried out with these tubular-type specimens.
The difficulty of evaluating the growth results of the crack on the outside alone is also shown. A numerical model approach is needed to improve the situation of the different stages detected.
The need to carefully analyze the mode I behavior of these specimens before addressing biaxial problems is highlighted.
Author Contributions
Methodology, L.A.-J., L.C., A.G.-H. and J.M.G.-M.; validation, A.G.-H. and J.M.G.-M.; formal analysis, L.A.-J.; investigation, L.A.-J., L.C., A.G.-H. and J.M.G.-M.; writing—original draft, L.A.-J.; writing—review and editing, L.A.-J., L.C., A.G.-H. and J.M.G.-M.; supervision, A.G.-H. and J.M.G.-M. All authors have read and agreed to the published version of the manuscript.
Funding
This research received no external funding.
Data Availability Statement
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.
Acknowledgments
The authors would like to thank the Universidad de Malaga/CBUA and the University of the Armed Forces ESPE (Ecuador) for their contribution to this research.
Conflicts of Interest
The authors declare no conflicts of interest.
Nomenclature
a | Crack length |
| Crack displacement angle |
b | Specimen thickness |
| Stress intensity factor |
R | Crack radius |
Ri | Internal radius of the tubular specimen |
Re | External radius of the tubular specimen |
References
- De Jong, H.F. Effects of crack length and crack front geometry on KQ-values of aluminum 7075-t651 CT-specimens. Eng. Fract. Mech. 1981, 14, 539–547. [Google Scholar] [CrossRef]
- Correia, J.A.F.O.; De Jesus, A.M.P.; Alves, A.S.F.; Lesiuk, G.; Tavares, P.J.S.; Moreira, P.M.G.P. Fatigue crack growth behaviour of the 6082-T6 aluminium using CT specimens with distinct notches. In Procedia Structural Integrity; Elsevier B.V.: Amsterdam, The Netherlands, 2016; pp. 3272–3279. [Google Scholar] [CrossRef]
- ASTM E647; Method for Measurement of Fatigue Crack Growth Rates. ASTM—American Society for Testing and Materials: West Conshohocken, PA, USA, 1999; pp. 591–630.
- Chen, C.J.; Su, M.N.; Wang, Y.H.; Deng, X.W. Experimental research on the fatigue crack growth behaviour of Q420C. J. Constr. Steel Res. 2022, 192, 107241. [Google Scholar] [CrossRef]
- Bretschneider, E.; Lehmann, T.; Ihlemann, J. Experimental investigation of crack initiation and crack propagation in aluminum demonstrator specimens. Mater. Today Proc. 2022, 62, 2594–2598. [Google Scholar] [CrossRef]
- Cai, L.; Li, W.; Hu, T.; Ji, B.; Zhang, Y.; Sakai, T.; Wang, P. In-situ experimental investigation and prediction of fatigue crack growth for aluminum alloys under single spike-overloads. Eng. Fract. Mech. 2022, 260, 108195. [Google Scholar] [CrossRef]
- Vasco-Olmo, J.M.; Díaz, F.A.; Antunes, F.V.; James, M.N. Characterisation of fatigue crack growth using digital image correlation measurements of plastic CTOD. Theor. Appl. Fract. Mech. 2019, 101, 332–341. [Google Scholar] [CrossRef]
- She, C.; Guo, W. Three-dimensional stress concentrations at elliptic holes in elastic isotropic plates subjected to tensile stress. Int. J. Fatigue 2007, 29, 330–335. [Google Scholar] [CrossRef]
- Simandjuntak, S.; Alizadeh, H.; Smith, D.J.; Pavier, M.J. Three dimensional finite element prediction of crack closure and fatigue crack growth rate for a corner crack. Int. J. Fatigue 2006, 28, 335–345. [Google Scholar] [CrossRef]
- Roychowdhury, S.; Dodds, R.H. A numerical investigation of 3-D small-scale yielding fatigue crack growth. Eng. Fract. Mech. 2003, 70, 2363–2383. [Google Scholar] [CrossRef]
- Ellyin, F.; Wu, J. A numerical investigation on the effect of an overload on fatigue crack opening and closure behavior. Fract. Eng. Mater. Struct. 1999, 22, 835–847. [Google Scholar] [CrossRef]
- Sehitoglu, H.; Gall, K.; Garcia, A.M. Recent advances in fatigue crack growth modeling. Int. J. Fract. 1996, 80, 165–192. [Google Scholar] [CrossRef]
- Ferreira, S.E.; de Castro, J.T.P.; Meggiolaro, M.A.; de Oliveira Miranda, A.C. Crack closure effects on fatigue damage ahead of crack tips. Int. J. Fatigue 2019, 125, 187–198. [Google Scholar] [CrossRef]
- Urrego, L.F.; García-Beltrán, O.; Arzola, N.; Araque, O. Mechanical Fracture of Aluminium Alloy (AA 2024-T4), Used in the Manufacture of a Bioproducts Plant. Metals 2023, 13, 1134. [Google Scholar] [CrossRef]
- Vasco-Olmo, J.M.; Camacho-Reyes, A.; Gonzales, G.L.G.; Díaz, F. Investigation of Plasticity Effects on Growing Fatigue Cracks Using the CJP Model of Crack Tip Fields. Materials 2023, 16, 5744. [Google Scholar] [CrossRef] [PubMed]
- Camas, D.; Garcia-Manrique, J.; Gonzalez-Herrera, A. Numerical study of the thickness transition in bi-dimensional specimen cracks. Int. J. Fatigue 2011, 33, 921–928. [Google Scholar] [CrossRef]
- Tanaka, K.; Takahash, H.; Akiniwa, Y. Fatigue crack propagation from a hole in tubular specimens under axial and torsional loading. Int. J. Fatigue 2006, 28, 324–334. [Google Scholar] [CrossRef]
- Shamsaei, N.; Gladskyi, M.; Panasovskyi, K.; Shukaev, S.; Fatemi, A. Multiaxial fatigue of titanium including step loading and load path alteration and sequence effects. Int. J. Fatigue 2010, 32, 1862–1874. [Google Scholar] [CrossRef]
- Gladskyi, M.; Fatemi, A. Notched fatigue behavior including load sequence effects under axial and torsional loadings. Int. J. Fatigue 2013, 55, 43–53. [Google Scholar] [CrossRef]
- Fatemi, A.; Gates, N.; Socie, D.F.; Phan, N. Fatigue crack growth behaviour of tubular aluminium specimens with a circular hole under axial and torsion loadings. Eng. Fract. Mech. 2014, 123, 137–147. [Google Scholar] [CrossRef]
- Gladskyi, M.; Fatemi, A. Load sequence effects on fatigue crack growth in notched tubular specimens subjected to axial and torsion loadings. Theor. Appl. Fract. Mech. 2014, 69, 63–70. [Google Scholar] [CrossRef]
- Mokhtarishirazabad, M.; Lopez-Crespo, P.; Moreno, B.; Lopez-Moreno, A.; Zanganeh, M. Optical and analytical investigation of overloads in biaxial fatigue cracks. Int. J. Fatigue 2017, 100, 583–590. [Google Scholar] [CrossRef]
- Macek, W.; Pejkowski, Ł.; Branco, R.; Nejad, R.M.; Żak, K. Fatigue fracture surface metrology of thin-walled tubular austenitic steel specimens after asynchronous loadings. Eng. Fail Anal. 2022, 138, 106354. [Google Scholar] [CrossRef]
- Macek, W.; Branco, R.; Szala, M.; Marciniak, Z.; Ulewicz, R.; Sczygiol, N.; Kardasz, P. Profile and areal surface parameters for fatigue fracture characterisation. Materials 2020, 13, 3691. [Google Scholar] [CrossRef] [PubMed]
- Lv, W.; Ding, B.; Zhang, K.; Qin, T. High-Cycle Fatigue Crack Growth in T-Shaped Tubular Joints Based on Extended Finite Element Method. Buildings 2023, 13, 2722. [Google Scholar] [CrossRef]
- Hu, C.; Xia, Q.; Zeng, E.; Zhu, J.; Yu, S.; Zhang, L.; Xu, F. Experimental and Numerical Investigation on Stress Concentration Factors of Offshore Steel Tubular Column-to-Steel Beam (STCSB) Connections. Buildings 2024, 14, 2004. [Google Scholar] [CrossRef]
- Abatta-Jacome, L.; Lima-Rodriguez, A.; Gonzalez-Herrera, A.; Garcia-Manrique, J.M. Numerical Study of the Plastic Zone at the Crack Front in Cylindrical Aluminum Specimens Subjected to Tensile Loads. Materials 2023, 16, 6759. [Google Scholar] [CrossRef]
- Sefene, E.M.; Tsai, Y.H.; Jamil, M.; Jatti, V.S.; Mishra, A.; AsmareTsegaw, A.; Costa, E.C. A multi-criterion optimization of mechanical properties and sustainability performance in friction stir welding of 6061-T6 AA. Mater. Today Commun. 2023, 36, 106838. [Google Scholar] [CrossRef]
- Sanders, J.L. Circumferential through-Cracks in Cylindrical Shells under Tension. 1982. Available online: https://asmedigitalcollection.asme.org/appliedmechanics/article-abstract/49/1/103/388580/Circumferential-Through-Cracks-in-Cylindrical?redirectedFrom=fulltext (accessed on 15 January 2024).
- Forman, R.G.; Hickman, J.C.; Shivakumar, V. Stress intensity factors for circumferential through cracks in hollow cylinders subjected to combined tension and bending loads. Eng. Fract. Mech. 1985, 21, 563–571. [Google Scholar] [CrossRef]
- Maiti, S.K.; Savla, P.D. Experimental and finite element study on mode I stable crack growth in symmetrically stiffened compact tension specimen. Eng. Fract. Mech. 1993, 44, 721–733. [Google Scholar] [CrossRef]
- Garcia-Manrique, J.; Camas, D.; Gonzalez-Herrera, A. Study of the stress intensity factor analysis through thickness: Methodological aspects. Fatigue Fract. Eng. Mater. Struct. 2017, 40, 1295–1308. [Google Scholar] [CrossRef]
- Jin, H.J.; Wu, S.J. A new driving force parameter for fatigue growth of multiple cracks. Int. J. Fatigue 2017, 96, 10–16. [Google Scholar] [CrossRef]
- Assias, S.L.G.; Kotik, H.G.; Ipiña, J.E.P. Fracture surface analysis of fracture mechanics specimens with splits: Determination of the physical crack extension. Theor. Appl. Fract. Mech. 2024, 133, 104509. [Google Scholar] [CrossRef]
Figure 1.
The geometry of 6061-T6 aluminum tubular specimens. Units in mm.
Figure 2.
Geometric considerations for calculating the stress intensity factor, units in millimeters.
Figure 3.
Tensile test, monotonic loading, and failure verification through the stress concentrator.
Figure 4.
Static mechanical test of a tubular specimen with a wall thickness of 2 mm.
Figure 5.
The fracture zone in the stress concentrator is a specimen with 2 mm of wall thickness.
Figure 6.
Variation of the factor concerning crack growth.
Figure 7.
Variation of the stress intensity factor concerning crack advancement.
Figure 8.
Fracture zone specimen with 2 mm wall thickness; blue overload crack, red final fracture.
Figure 9.
The fracture zone of a specimen with 3 mm wall thickness.
Figure 10.
Fracture zone of the tubular specimen with a wall thickness of 4 mm; the blue line indicates the marking of an overload-induced crack, while the red line indicates the final fracture.
Figure 11.
Specimen 2 mm thickness. (a) Arc length at the crack end associated with Re and Ri. (b) Angles generated in the notch and the crack.
Figure 12.
Specimen of 2 mm thickness, left until overload, right until final fracture, fracture areas associated with Re and Ri.
Figure 13.
Crack growth associated with the external face of the specimen with a 3 mm thickness.
Figure 14.
Relationship between crack growth rate and stress intensity factor range. Specimen with a 3 mm thickness.
Figure 15.
Normalized final fracture of thicknesses of 2, 3, and 4 mm.
Figure 16.
Crack shape with overload and final fracture. (a) 2 mm thickness; (b) 4 mm thickness.
Table 1.
Loading conditions applied to tubular specimens.
Wall Thickness [mm] | Loading Frequency [Hz] | Load Function | Re MPa m1/2 | Re MPa m1/2 | Maximum Load [N] | Minimum Load [N] |
---|
2 | 3 | Sinusoidal | 7.9456 | 0.79456 | 11,770.0 | 1177.2 |
3 | 3 | Sinusoidal | 8.5064 | 0.85064 | 20,600.0 | 2060.1 |
4 | 3 | Sinusoidal | 15.9591 | 1.59591 | 55,720.0 | 5572.08 |
Table 2.
Global summary of results of the final fracture zone, specimens of 2, 3, and 4 mm of wall thickness.
Wall Thickness [mm] | Number of Cycles | Arc Length Re [mm] | Arc Length Ri [mm] | Fracture Zone Area Re [mm2] | Fracture Zone Area Ri [mm2] | The Angle between the Start and End of the Crack |
---|
2 | 3664.0 | 2.03 | 2.83 | 2.439 | 2.721 | 18.23 |
3 | 7025.0 | 3.33 | 2.00 | 4.954 | 3.999 | 2.34 |
4 | 3968.0 | 0.89 | 0.47 | 2.062 | 1.120 | 3.62 |
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