Fatigue and Fracture of Materials

The distribution of stresses near holes is of great importance in fracture mechanics and material modeling. The present paper provides a general stress solution near a traction-free surface for an arbitrary piecewise linear yield criterion, assuming plane-strain conditions. The generalized method of moving coordinates is proven efficient in this case. In particular, the solution reduces to evaluating one ordinary integral. The boundary value problem solved is a Cauchy problem for a hyperbolic system of equations. Therefore, the stress solution in the plastic region is independent of other boundary conditions, though the occurrence of plastic yielding at a specific point is path-dependent. The general solution applies to calculating the stress field near an elliptic hole. It is shown that the parameter that controls the pressure-dependency of the yield criterion affects the stress field significantly. The aspect ratio is less significant as compared to that parameter. However, for a given material, the aspect ratio should also be considered to predict the stress field accurately, especially in the near vicinity of the hole. The solution reduces to an available solution for the pressure-independent yield criterion, which is a particular yield criterion of the considered class of yield criteria. Full article

Spruce wood (Picea Mariana) is a highly orthotropic material whose fracture behavior in the presence of U-shaped notches and under combined tensile-tearing loading (so-called mixed-mode I/III loading) is analyzed in this work. Thus, several tests are carried out on U-notched samples with different notch tip radii (1 mm, 2 mm, and 4 mm) under various combinations of loading modes I and III (pure mode I, pure mode III, and three mixed-mode I/III loadings), from which both the experimental fracture loads and the fracture angles of the specimens are obtained. Because of the linear elastic behavior of the spruce wood, the point stress (PS) and mean stress (MS) methods, both being stress-based criteria, are used in combination with the Virtual Isotropic Material Concept (VIMC) for predicting the fracture loads and the fracture angles. By employing the VIMC, the spruce wood as an orthotropic material is modeled as a homogeneous and isotropic material with linear elastic behavior. The stress components required for calculating the experimental values of notch stress intensity factors are obtained by finite element (FE) analyses of the test configuration using commercial FE software from the fracture loads obtained experimentally. The discrepancies between the experimental and theoretical results of the critical notch stress intensity factors are obtained between −12.1% and −15% for the PS criterion and between −5.9% and −14.6% for the MS criterion, respectively. The discrepancies related to fracture initiation angle range from −1.0% to +12.1% for the PS criterion and from +1.5% to +12.2% for the MS criterion, respectively. Thus, both the PS and MS models have good accuracy when compared with the experimental data. It is also found that both failure criteria underestimate the fracture resistance of spruce wood under mixed-mode I/III loading. Full article

This paper presents different CPT methodologies for the prediction of the pile shaft resistance in tension on the example of three reference screw piles of the Jazowa test site in Poland. The shaft capacity was estimated based on the cone resistance, sleeve friction and CPT excess pore water pressure. Three piles with a diameter of 0.4 m and the length varied from 8 m to 14.6 m were subjected to static load tests in tension. Their results were used to determine the ultimate bearing capacity of the reference piles. The pile shaft resistance was estimated according to the AFNOR standard, Doan and Lehane 2018 centrifuge tests based method (Delft University of Technology approach), the Modified Unicone method, KTRI (Kajima Technical Research Institute) and LCPC (Laboratoire Central des Ponts et Chaussées) method. Then, the ultimate bearing capacity determined in static load tests was compared to the estimated values according to five different methods. The best estimation, fitting almost perfectly to static load test values, was obtained with the AFNOR method, whereas the other predictions significantly underestimated the ultimate bearing capacity. Full article

This paper presents the idea and provides an analysis of the rock breakout mechanism utilizing an undercut/breakout anchor. The new design is a modification of a standard undercut anchor, which is commonly found in applications involving steel-to-concrete anchorage. Of particular concern was the effect of the rock breakout strength on the anchor-pullout-induced failure of the rock mass. A numerical analysis was employed to model the effect of the changes to the shape and size of the breakout cones under varying rock strength conditions as a result of modifying the anchor design and loading pattern. The problem in question is pivotal for the potential evaluation of the effectiveness of the said anchor design under the non-standard conditions of its utilization. Full article

This paper discusses how the strain gradient influences the fatigue life of carbon steel in the low-cycle and high-cycle fatigue regimes. To obtain fatigue data under different strain distributions, cyclic alternating bending tests using specimens with different thicknesses and cyclic tension–compression tests were conducted on carbon steel for pressure vessels (SPV235). The crack initiation life and total failure life were evaluated via the strain-based approach. The experimental results showed that the crack initiation life became short with decreasing strain gradient from 10² to 10⁶ cycles in fatigue life. On the other hand, the influence of the strain gradient on the total failure life was different from that on the crack initiation life: although the total failure life of the specimen subjected to cyclic tension–compression was also the shortest, the strain gradient did not affect the total failure life of the specimen subjected to cyclic bending from 10² to 10⁶ cycles in fatigue life. This was because the crack propagation life became longer in a thicker specimen. Hence, these experimental results implied that the fatigue crack initiation life could be characterized by not only strain but also the strain gradient in the low-cycle and high-cycle fatigue regimes. Full article

Problems concerning the influence of the geometric parameters of an undercutting anchor on the range of the failure zone of rock medium during the pulling out of the anchor constitute one of the aspects that arouse the interest of authors due to attempts to use undercutting anchors in the process of rock lump separation. This method is considered an alternative to the existing methods of separation, especially in special cases of mining technologies. This article presents the results of numerical investigations into the effect of changes in the head geometry that occur as a result of wear on the conical part of the undercutting anchor and the extent of failure of the rock medium during its pulling out. This is an extension of considerations presented in previous work, where special attention was paid to the influence of potential errors in anchor installation, leading to changes in head geometry and, consequently, to changes in the extent of the failure zone of the rock medium. As a result, significant changes in the volume of the detached rock masses are observed. This study shows that the increasing surface friction of the stripping anchor head leads to a decrease in the angle of the undercutting head. As a result, the extent of the failure zone measured on the free rock surface increases, the value of the angle of the failure cone at the initial stage of the stripping decreases, and the deformation of rock in the plane perpendicular to the anchor axis increases. Full article

The literature in the area of material fatigue indicates that the fatigue properties may change with the number of cycles. Researchers recommend taking this into account in fatigue life calculation algorithms. The results of simulation research presented in this paper relate to an algorithm for estimating the fatigue life of specimens subjected to block loading with a nonzero mean value. The problem of block loads using a novel calculation model is presented in this paper. The model takes into account the change in stress–strain curve parameters caused by mean strain. Simulation tests were performed for generated triangular waveforms of strains, where load blocks with changed mean strain values were applied. During the analysis, the degree of fatigue damage was compared. The results of calculations obtained for standard values of stress–strain parameters (for symmetric loads) and those determined, taking into account changes in the curve parameters, are compared and presented in this paper. It is shown that by neglecting the effect of the mean strain value on the K′ and n′ parameters and by considering only the parameters of the cyclic deformation curve for ε_m = 0 (symmetric loads), the ratio of the total degree of fatigue damage varies from 10% for ε_a = 0.2% to 3.5% for ε_a = 0.6%. The largest differences in the calculation for ratios of the partial degrees of fatigue damage were observed in relation to the reference case for the sequence of block n₃, where ε_m = 0.4%. The simulation results show that higher mean strains change the properties of the material, and in such cases, it is necessary to take into account the influence of the mean value on the material response under block loads. Full article

The paper presents the results of a numerical analysis (FEM) describing the effect of the undercutting head angle on the formation of the rock mass failure zone during the initial stages of failure propagation. The research was carried out in the context of developing a technology for rock extraction by controlled pull-out of undercut anchors installed in the rock mass. The focus was on the initial stage of crack propagation and its trajectory for anchors embedded at an assumed constant depth and a value of the friction coefficient of the rock against the anchor head. It is shown that smaller angles favor smaller stripping angles and an increased radial impact of the head on the rock material (in the plane perpendicular to the head axis), while the impact of heads with larger angles is found to favor larger fracture penetration angles and faster penetration towards the free rock surface. Full article

The paper deals with the problem of stress concentration at the weld toe of a plate T-joint subjected to axial, bending, and shearing loading modes. Theoretical stress concentration factors were obtained from numerical simulations using the finite element method for several thousand geometrical cases, where five of the most important geometrical parameters of the joint were considered to be independent variables. For each loading mode—axial, bending, and shearing—highly accurate closed form parametric expression has been derived with a maximum percentage error lower than 2% with respect to the numerical values. Validity of each approximating formula covers the range of dimensional proportions of welded plate T-joints used in engineering applications. Two limiting cases are also included in the solutions—when the weld toe radius tends to zero and the main plate thickness becomes infinite. Full article

The current study investigates the load controlled fatigue properties of the microplasma arc welded thin titanium Grade 5 (6Al-4V) sheets. In order to explore the effect of weld geometry on the fatigue, two different welded joints were used in the experimental studies. Load controlled fatigue test results were evaluated to present an outlook on the behaviour of microplasma welded titanium alloy Grade 5 sheets under cyclic loading. Even though the previously published monotonic tests showed successful use of microplasma arc welding to join thin titanium Grade 5 sheets with mechanical properties comparable to the base metal, fatigue life of the welded joints was lower than the lives of samples without welds. In particular, the fatigue performance of overlap joints was very poor. This was presumed to be due to the changed material properties of the heat affected zone which was formed by the excess heat of the welding process as fractures often occurred at such locations. Based on experimental findings and fractographic observations, a clear adverse effect of welding process in material behaviour was discovered. Despite the concentrated heat of microplasma arc welding, post-weld heat treatment of the weld area is recommended to improve the mechanical behaviour of the welded joints. Full article

The paper presents a method for estimating the value of equibiaxial stress in a surface layer of a material by using a modified hardness measurement procedure with a Vickers indenter. A certain characteristic parameter was defined and related to the surface stress. A hybrid approach, based on experimental tests and accompanied by the complementary results obtained by the finite element modelling of X20Cr13 steel in elastic–plastic range, confirmed a linear relationship between the value of the characteristic parameter and the magnitude of equibiaxial stress at the surface. This linear relationship was valid in both elastic and elastic–plastic strain range beyond the yield stress of the material. Full article

In this paper a fracture assessment in additive manufactured acrylonitrile butadiene styrene (ABS) fracture specimens containing U-notches is performed. We performed 33 fracture tests and 9 tensile tests, combining five different notch radii (0 mm, 0.25 mm, 0.50 mm, 1 mm and 2 mm) and three different raster orientations: 0/90, 30/−60 and 45/−45. The theory of critical distances (TCD) was then used in the analysis of fracture test results, obtaining additional validation of this theoretical framework. Different versions of TCD provided suitable results contrasting with the experimental tests performed. Moreover, the fracture mechanisms were evaluated using scanning electron microscopy in order to establish relationships with the behaviour observed. It was demonstrated that 3D-printed ABS material presents a clear notch effect, and also that the TCD, through both the point method and the line method, captured the physics of the notch effect in 3D-printed ABS. Finally, it was observed that the change in the fracture mechanisms when introducing a finite notch radius was limited to a narrow band behind the original defect, which appeared in cracked specimens but not in notched specimens. Full article

This study employs the numerical analysis and experimental testing to analyze the fracturing mechanics and the size of rock cones formed in the pull-out of a system of three undercut anchors. The research sets out to broaden the knowledge regarding: (a) the potential of the undercut anchor pull-out process in mining of the rock mass, and (b) estimating the load-carrying capacity of anchors embedded in the rock mass (which is distinctly different from the anchorage to concrete). Undercut anchors are most commonly applied as fasteners of steel components in concrete structures. The new application for undercut anchors postulated in this paper is their use in rock mining in exceptional conditions, such as during mining rescue operations, which for safety considerations may exclude mechanical mining techniques, mining machines, or explosives. The remaining solution is manual rock fracture, whose effectiveness is hard to assess. The key issue in the analyzed aspect is the rock fracture mechanics, which requires in-depth consideration that could provide the assistance in predicting the breakout prism dimensions and the load-displacement behavior of specific anchorage systems, embedment depth, and rock strength parameters. The volume of rock breakout prisms is an interesting factor to study as it is critical to energy consumption and, ultimately, the efficiency of the process. Our investigations are supported by the FEM (Finite Element Method) analysis, and the developed models have been validated by the results from experimental testing performed in a sandstone mine. The findings presented here illuminate the discrepancies between the current technology, test results, and standards that favor anchorage to concrete, particularly in the light of a distinct lack of scientific and industry documentation describing the anchorage systems’ interaction with rock materials, which exhibit high heterogeneity of the internal structure or bedding. The Concrete Capacity Design (CCD) method approximates that the maximum projected radius of the breakout cone on the free surface of concrete corresponds to the length of at the most three embedment depths (h_ef). In rock, the dimensions of the breakout prism are found to exceed the CCD recommendations by 20–33%. The numerical computations have demonstrated that, for the nominal breakout prism angle of approx. 35% (CCD), the critical spacing for which the anchor group effect occurs is ~4.5 (a cross-section through two anchor axes). On average, the observed spacing values were in the range of 3.6–4.0. Full article

Fatigue damage affects both durability and safety, and it has been the most important distress in asphalt concrete. Fatigue damage occurs as a result of repeated traffic loading. An asphalt mixture is a typical viscoelastic material, and its fatigue damage is related to its viscoelastic properties. Under repeated traffic loading, the combined effects of creep damage and fatigue damage will shorten its fatigue life. Currently, the evaluation of the fatigue damage of asphalt mixtures rarely considers the combined effects of creep damage and fatigue damage. To solve this problem, a viscoelastic fatigue damage prediction model of an asphalt mixture considering the combined effects of creep damage and fatigue damage is put forward by introducing parameter β and a displacement factor based on theoretical derivations and testing. The results show that the model can embody the viscoelastic fatigue damage essence of asphalt mixtures, and it can also consider the effects of aging degree, temperature, load frequency and stress on fatigue damage of asphalt mixtures. The maximum relative error of the testing and prediction results of fatigue life is 0.15, and it is a reasonable prediction model. Full article

The paper contains the results of fatigue tests of smooth and notched specimens made of 10HNAP (S355J2G1W) subjected to proportional cyclic loading with use of mean values stress. The results obtained for specimens under bending, torsion and one combination of bending with torsion for four mean values have been compared. The experimental data have been collected in the tables and shown in the figures with use of various σ_a(τ_a)-N fatigue characteristics for which parameters of the regression equations have been determined. The influence of average values on the allowable stress amplitudes and amplitude of moments at the level close to the fatigue limit depending on the angle α determining loading combination and the average stress is also shown. The greatest effect of the notch on fatigue life compared to smooth specimens is observed at symmetrical loads. At unsymmetrical loads with non-zero mean stress, this effect clearly weakens or disappears. Full article

This paper deals with the analysis of stress concentration at the weld toe of a Double-V and a Single-V butt-welded joints subjected to tensile, bending and shearing loads. For each geometrical and loading case accurate close form stress concentration factor formula based on more than 3.3 thousand finite element method solutions were obtained. The percentage error of the formulas is lower than 2.5% for a wide range of values of geometrical parameters including weld toe radius, weld width, plate thickness and weld toe angle. The limiting case, in which the weld toe radius tends to zero is also considered. In the cases of shearing loads, a plane model based on thermal analogy was developed. The whole analysis was performed assuming that a circular arc represents the shape of the excess weld metal. Presented solutions may be used in computer aided fatigue assessment of structural elements. Full article

In this paper, a novel algorithm for the determination of Walker damage in loaded disc springs is presented. The algorithm takes a 3D-scan of a disc spring, measured residual stresses, material parameters, and spring loads as inputs. It outputs a distribution of Walker damage over the surface area of the input disc spring. As the algorithm allows a fully automated determination of the Walker damage, it can be used by disc spring manufacturers to reduce the working time spent on this task by specialized engineers significantly. Compared to spreadsheet applications using analytical formulas and finite element models using idealized geometry, this approach offers a superior description of the stress states in disc springs. Full article

This study presents the results of tests involving determining quantities used to describe fracture toughness of a heat-treated AA2519 aluminum alloy applied in, among other things, constructing American military amphibians. These quantities were determined using the J–R curve method for two temperature values, 293 K and 77 K. The low temperature was provided by putting the tested specimen into a liquid nitrogen bath and keeping it there throughout the experiment. Based on the tests results, cryogenic conditions cause an increase in the maximum experimental value of the J–J_Q integral, from 66.3 to 87.3 kJ/m² Moreover, an analysis of the fatigue fracture microstructure revealed differences between specimens tested in ambient temperature and those tested in cryogenic temperature. Full article

An objective of this study was to investigate the group effect in rock cone failure occurring in pull-out with the use of 3D finite element analysis. At present, undercut anchors are typically applied as structural fasteners of steel elements in concrete buildings; however, new areas for their use are being explored. The reported study set out to evaluate the use of undercut anchors in special-purpose rock mining, e.g., in mining rescue operations. In such emergencies, mechanical mining may prove impossible, whereas the use of explosives is even prohibited. Although manual methods could be considered, their effectiveness is hard to assess. Prior to considering the use of undercut anchors in mining, several aspects must essentially be determined: The mechanics of cone failure, including the extent of surface failure and the values of the pull-out force of the anchor for a given rock mass relative to the anchor system, the embedment depth, or the rock strength parameters. These factors may be investigated successfully using finite element analysis, the results of which are presented in the study. Full article

The Smith-Watson-Topper parameter (SWT) in its original form was designed to estimate the fatigue life of metal materials in a uniaxial load state (tension–compression) in the range up to fatigue crack initiation, with non-zero mean values. This parameter is based on the analysis of both stress and strain. Therefore, the stress–strain criterion is the focus, rather than the energy criterion. This paper presents the original SWT model and its numerous modifications. The first part presents different versions of this parameter defined by the normal parameters. Then, it presents versions defined through the tangent parameter and the most promising parameter defined through the tangent and normal parameters. It was noted that the final form of the equivalent value is defined either by stress or by an energy parameter. Therefore, the possible characteristics from which the fatigue life can be determined are also presented. Full article