Multiaxial fatigue of extruded ZK60 magnesium alloy

Multiaxial monotonic and cyclic behaviors of ZK60‐T5 magnesium extrusion are investigated. Strain‐controlled tests were performed at standard laboratory condition with fully reversed straining. Twinning‐detwinning deformation plays an important role in the cyclic axial behavior for tests that were performed under strain amplitudes higher than 0.4%. However, the hysteresis loop for the 0.4% was found symmetric and no sign of twinning‐detwinning deformation was observed. On the contrary, the cyclic shear behavior was found to be similar to conventional alloys and no significant asymmetric or twinning‐detwinning deformations were observed. The multiaxial fatigue tests suggest that multiaxiality and nonproportionality are not detrimental to fatigue life. Three multiaxial fatigue damage models were used: Smith‐Watson‐Topper, Fatemi‐Socie, and Jahed‐Varvani. While Fatemi‐Socie and Jahed‐Varvani models show comparable estimation, Smith‐Watson‐Topper overestimates shear and nonproportional lives.     

Low‐cycle fatigue of 316L stainless steel under proportional and nonproportional loadings

This paper discusses low‐cycle fatigue characteristics of 316L stainless steel under proportional and nonproportional loadings. Tension–torsion multiaxial low‐cycle fatigue tests were performed using five strain paths. Additional hardening was observed under nonproportional loadings and was more significant in tests with larger nonproportionality. Mises equivalent strain, Smith–Watson–Topper, Fatemi–Socie, Kandil–Brown–Miller and nonproportional strain parameters were applied to the experimental data to evaluate the multiaxial low‐cycle fatigue damage. The applicability of the damage laws to practical design was discussed.     

Damage-based modification for fatigue life prediction under non-proportional loadings

This paper proposes a new fatigue model based on virtual strain energy to predict fatigue life under both proportional and non-proportional loadings for different materials including, 1045 Steel, 30CrNiMo8HH, Titanium TC4, and AZ31B magnesium. The results were strongly correlated with experimental results available in the literature. In addition, two damage-based modifications for fatigue life prediction under non-proportional loadings are studied. These modifications are then applied to the fatigue parameters including Smith–Watson–Topper, Fatemi–Socie, maximum shear strain, and the proposed parameter for fatigue life predictions of the studied materials. The results show considering these modifications significantly improves the accuracy of the models.     

A method for assessing critical plane‐based multiaxial fatigue damage models

Fatigue failure is a complex phenomenon. Therefore, development of a fatigue damage model that considers all associated complexities resulting from the application of different cyclic loading types, geometries, materials, and environmental conditions is a challenging task. Nevertheless, fatigue damage models such as critical plane‐based models are popular because of their capability to estimate life mostly within ±2 and ±3 factors of life for smooth specimens. In this study, a method is proposed for assessing the fatigue life estimation capability of different critical plane‐based models. In this method, a subroutine was developed and used to search for best estimated life regardless of critical plane assumption. Therefore, different fatigue damage models were evaluated at all possible planes to search for the best life. Smith‐Watson‐Topper (normal strain‐based), Fatemi‐Socie (shear strain‐based), and Jahed‐Varvani (total strain energy density‐based) models are compared by using the proposed assessment method. The assessment is done on smooth specimen level by using the experimental multiaxial fatigue data of 3 alloys, namely, AZ31B and AZ61A extruded magnesium alloys and S460N structural steel alloy. Using the proposed assessment method, it was found that the examined models may not be able to reproduce the experimental lives even if they were evaluated at all physical planes.     

A fatigue model for sensitive materials to non-proportional loadings

The present study proposes a novel fatigue model based on virtual strain energy. This model separates loading paths based on their non-proportionality where directly takes into account the loading in fatigue life prediction. The proposed fatigue model is expressed in two tension-based and shear-based equations for two tensile and shear cracking failure modes. The model was validated against several experimental datasets available in the literature. In addition, obtained results were compared to predicted lives through some well-known fatigue models comprising maximum shear strain, Smith–Watson–Topper, and Fatemi–Socie. The results were strongly correlated with the experimental data indicating accuracy of the model.     

Experimental and numerical investigation on crack initiation of fretting fatigue of dovetail

The present study investigated the fretting fatigue crack initiation of dovetail structure based on experimental observation and multiple axial criteria. Two typical critical plane approaches of the Smith‐Watson‐Topper (SWT) and the Fatemi and Socie (FS) model were used to predict the crack initiation location, orientation angle, and fatigue life. The results indicate that both SWT and FS models predict consistent results with the experiment in crack initiation location. Regarding the crack initiation angle, FS model shows good agreement with the experimental observation, but SWT model exhibits a large difference. The two models give conservative results in fretting fatigue life. In view of this, the theory of critical distance (TCD) was incorporated into the SWT and the FS models. It shows that both the TCD‐SWT and the TCD‐FS predict fatigue lives within a scatter band of 2. It suggests that introducing the TCD into the critical plane model can greatly reduce the conservatism of the prediction. Furthermore, the prediction has less dependence on specific models.     

Low-cycle fatigue of 1Cr–18Ni–9Ti stainless steel and related weld metal under axial, torsional and 90° out-of-phase loading

The fatigue behaviour of base metal and weld joints of 1Cr–18Ni–9Ti stainless steel has been studied under uniaxial, torsional and 90° out‐of‐phase loading. A significant degree of additional hardening is found for both base metal and weld metal under 90° out‐of‐phase loading. Both base metal and weld metal have the same cyclic stable stress–strain relationship under torsional cyclic loading and 90° out‐of‐phase cyclic loading. Base metal exhibits higher cyclic stress than weld metal under uniaxial loading, and Young's modulus and yield stress of weld metal are smaller than those of base metal. Weld metal exhibited lower fatigue resistance than base metal under uniaxial and torsional loading, but no significant difference was found between the two materials under 90° out‐of‐phase loading. A large scatter of fatigue life is observed for weld metal, perhaps because of heterogeneity of the microstructure. The Wang–Brown (WB) damage parameter and the Fatemi–Socie (FS) damage parameter, both based on the shear critical plane approach, were evaluated relative to the fatigue data obtained.     

Finite element analysis of fretting fatigue behavior of steel wires and crack initiation characteristics

The effects of fretting parameters on stress distributions of contacting wires during the initial stage of fretting–fatigue of steel wires were investigated using the finite element method. The roles of fretting parameters on crack initiation characteristics were discussed employing the multiaxial fatigue criteria of Fatemi–Socie and Smith–Watson–Topper, and three-dimensional coordinate transformation. Non-uniform stress distributions on contact surfaces and ring-shaped stress distributions near the contact zone on the symmetric plane are observed. Different fretting parameters induce distinct fretting regimes, stress distributions and abrupt changes of stress near the trailing edge. Crack initiation becomes more difficult with increasing contact load as compared to the increased possibility of crack initiation with increasing relative displacement.     

Fatigue life estimation of coach peel riveted joints using multi-axial fatigue criteria

This study investigates fatigue behaviour of riveted joints in a coach peel configuration under various load ranges and load ratios. Three well-known multi-axial fatigue criteria of Smith–Watson–Topper, Glinka and Fatemi–Socie are used to predict the fatigue life of the joint based on the stress and strain components obtained from a finite element analysis. A three-dimensional finite element model was developed with considering elastic–plastic behaviour of aluminium alloy 2024-T3 for the joint plates as well as frictional contact between all the contacting parts. Fatigue life estimation results agreed well with existing experimental data for the same joint. This verifies the finite element results and shows how well the multi-axial fatigue equations can predict fatigue life of the riveted joints. The finite element modelling approach may be then used with confidence for fatigue life estimations of different configurations of riveted joints.     

Analytical and experimental studies on fatigue crack path under complex multi-axial loading

In real engineering components and structures, many accidental failures are due to unexpected or additional loadings, such as additional bending or torsion, etc. Fractographical analyses of the failure surface and the crack orientation are helpful for identifying the effects of the non‐proportional multi‐axial loading. There are many factors that influence fatigue crack paths. This paper studies the effects of multi‐axial loading path on the crack path. Two kinds of materials were studied and compared in this paper: AISI 303 stainless steel and 42CrMo4 steel. Experiments were conducted in a biaxial testing machine INSTRON 8800. Six different biaxial loading paths were selected and applied in the tests to observe the effects of multi‐axial loading paths on the additional hardening, fatigue life and the crack propagation orientation. Fractographic analyses of the plane orientations of crack initiation and propagation were carried out by optical microscope and SEM approaches. It was shown that the two materials studied had different crack orientations under the same loading path, due to their different cyclic plasticity behaviour and different sensitivity to non‐proportional loading. Theoretical predictions of the damage plane were made using the critical plane approaches such as the Brown–Miller, the Findley, the Wang–Brown, the Fatemi–Socie, the Smith–Watson–Topper and the Liu's criteria. Comparisons of the predicted orientation of the damage plane with the experimental observations show that the critical plane models give satisfactory predictions for the orientations of early crack growth of the 42CrMo4 steel, but less accurate predictions were obtained for the AISI 303 stainless steel. This observation appears to show that the applicability of the fatigue models is dependent on the material type and multi‐axial microstructure characteristics.     

Numerical modeling and simulation of wheel radial fatigue tests

A computational methodology is proposed for fatigue damage assessment of metallic automotive components and its application is presented with numerical simulations of wheel radial fatigue tests. The technique is based on the local strain approach in conjunction with linear elastic FE stress analyses. The stress–strain response at a material point is computed with a cyclic plasticity model coupled with a notch stress–strain approximation scheme. Critical plane damage parameters are used in the characterization of fatigue damage under multiaxial loading conditions. All computational modules are implemented into a software tool and used in the simulation of radial fatigue tests of a disk-type truck wheel. In numerical models, the wheel rotation is included with a nonproportional cyclic loading history, and dynamic effects due to wheel–tire interaction are neglected. The fatigue lives and potential crack locations are predicted using effective strain, Smith–Watson–Topper and Fatemi–Socie parameters using computed stress–strain histories. Three-different test conditions are simulated, and both number of test cycles and crack initiation sites are estimated. Comparisons with the actual tests proved the applicability of the proposed approach.     

Low cycle fatigue life prediction in shot‐peened components of different geometries – part II: life prediction

This study investigates the effects of shot peening on the low‐cycle fatigue performance of a low‐pressure steam turbine blade material. The finite element model incorporating shot‐peening effects, which has been introduced in part I, has been used to predict the stabilised stress/strain state in shot‐peened samples during fatigue loading. The application of this model has been extended to different notched geometries in this study. Based on the modelling results, both the Smith–Watson–Topper and Fatemi–Socie critical plane fatigue criteria have been used to predict the fatigue life of shot‐peened samples (treated with two different peening intensities) with varying notched geometries. A good agreement between experiments and predictions was obtained. The application of a critical distance method considering the stress and strain hardening gradients near the shot‐peened surface has been found to improve the life prediction results. The effects of surface defects on the accuracy of life predictions using the proposed method were also discussed.     

Finite element and experimental study on multiaxial fatigue analysis of rail clip failures

The rail clip fastening system is an important structural component of railway track systems providing flexibility and turnover resistance for running rails. High replacement frequency of fasteners was observed compared with other components because of fatigue failures of rail clips. In this study, implicit and explicit finite element (FE) models were developed for E‐clip and Fast‐clip with material and fatigue properties obtained from experimental testing. The fatigue loading experiments were conducted to determine the strain‐life relationship. The assessments of the fatigue damage and fatigue life were analysed using the FE results for the rail clip strain/stress components with the Fatemi‐Socie multiaxial fatigue criterion. A time‐efficient smallest enclosing circle algorithm was developed to search the critical plane orientation and the maximum shear strain amplitude for fatigue analysis. This work provides a method for FE and experimental study of multiaxial fatigue analysis of rail clip failures subjected to dynamic loading.     

An investigation of the fatigue of CK45 steel in the as‐received state and after pre‐fatigue deformation

Fatigue failure, ratcheting behaviour and influence of pre‐fatigue on fatigue behaviour were investigated under uniaxial cyclic loading for CK45 steel at room temperature. The fatigue life was recorded for various stress ratios, and then, three mean stress models were considered. The Walker model showed an acceptable accuracy in comparison with Smith–Watson–Topper and Park et al. models. The ratcheting strains were measured for various loading conditions in order to evaluate the impact of mean stress, stress amplitude and stress ratio on ratcheting behaviour. The experimental results showed that the ratcheting strain increased with increasing mean stress, stress amplitude and stress ratio. In addition, the results of the post‐ratcheting‐fatigue tests showed that although the fatigue life decreased with increasing pre‐ratcheting strain (the ratcheting strain that is accumulated in pre‐fatigue), the loading condition that pre‐fatigue experiments were conducted has a significant effect on subsequent fatigue behaviour.     

Notched fatigue behavior including load sequence effects under axial and torsional loadings

Notch effects on axial and torsion fatigue behaviors of low carbon steel were investigated. Fully-reversed tests were conducted on thin-walled tubular specimens with or without a transverse circular hole. A shear failure mechanism was observed for both smooth and notched specimens and under both axial and torsion loadings. The notch effect was more pronounced under axial loading, in spite of higher stress concentration factor in torsion. The commonly used nominal S–N approach with fatigue notch factor in conjunction with von Mises effective stress resulted in overly conservative life predictions of both smooth and notched torsion fatigue lives. Neuber’s rule yielded notch root stress and strain amplitudes close to the FEA results for both axial and torsion loadings. The local strain approach based on effective strain obtained from Neuber’s rule or FEA resulted in poor correlation of the fatigue life data of smooth and notched specimens. The Fatemi–Socie critical plane parameter represented the observed failure mechanism and resulted in very good correlations of smooth and notched specimens fatigue data under both axial and torsion loadings. In block loading tests with equal number of alternating axial and torsion cycles at the same stress level, beneficial effect of axial loading was observed. Possible potential reasons for this unexpected behavior are discussed.     

A modification of Smith–Watson–Topper damage parameter for fatigue life prediction under non‐proportional loading

In this paper, the shortcomings of the Smith–Watson–Topper (SWT) damage parameter are analysed on the basis of the critical plane concept. It is found that the SWT model usually overestimates the fatigue lives of materials since it only takes into account the fatigue damage caused by the tensile components. To solve this problem, Chen et al. (CXH) modified the SWT model through considering the shear components. However, there are at least two problems present in CXH model: (1) the mean stress is not considered and (2) the different influence of the normal and shear components on fatigue life is not included. Besides, experimental validations show that the modification by Chen et al. usually leads to conservative fatigue life predictions during non‐proportional loading. In order to overcome the shortcomings of SWT and CXH models, a damage parameter as the effective strain energy density (ESED) is proposed. Experimental validations by using eight kinds of materials show that the ESED model can give satisfactory fatigue life predictions under the non‐proportional loading.     

Multiaxial low‐cycle fatigue life evaluation under different non‐proportional loading paths

This paper presents analytical and experimental investigations for fatigue lives of structures under uniaxial, torsional, multiaxial proportional, and non‐proportional loading conditions. It is known that the rotation of principal stress/strain axes and material additional hardening due to non‐proportionality of cycle loading are the 2 main causes resulting in shorter fatigue lives compared with those under proportional loading. This paper treats these 2 causes as independent factors influencing multiaxial fatigue damage and proposes a new non‐proportional influencing parameter to consider their combined effects on the fatigue lives of structures. A critical plane model for multiaxial fatigue lives prediction is also proposed by using the proposed non‐proportional influencing factor to modify the Fatemi‐Socie model. The comparison between experiment results and theoretical evaluation shows that the proposed model can effectively predict the fatigue life due to multiaxial non‐proportional loading.     

Evaluation of the Fatemi‐Socie damage parameter for the fatigue life calculation with application of the Chaboche plasticity model

This paper presents an approach to the evaluation of the Fatemi‐Socie parameter applied to the lifetime calculation of specimens made of CuZn37 brass. In particular, two factors affecting the calculated fatigue lives are analysed: (i) the influence of stresses calculated by applying the Chaboche plasticity model on the computed lifetime and (ii) the influence of a variability of parameter k of material sensitivity to normal stress on the calculated lifetime. The novelty of the presented research is associated with the fatigue life calculation according to the Fatemi‐Socie model with the introduced k dependence accounting for the lifetime. Underestimation of the calculated stresses results in the higher calculated fatigue lives but with acceptable scatter band. The parameter of material sensitivity to normal stress for the CuZn37 brass varies insignificantly having little impact on the calculated fatigue lives.