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.     

Strain-based multiaxial fatigue damage modelling

A new multiaxial fatigue damage model named characteristic plane approach is proposed in this paper, in which the strain components are used to correlate with the fatigue damage. The characteristic plane is defined as a material plane on which the complex three‐dimensional (3D) fatigue problem can be approximated using the plane strain components. Compared with most available critical plane‐based models for multiaxial fatigue problem, the physical basis of the characteristic plane does not rely on the observations of the fatigue crack in the proposed model. The cracking information is not required for multiaxial fatigue analysis, and the proposed model can automatically adapt for different failure modes, such as shear or tensile‐dominated failure. Mean stress effect is also included in the proposed model by a correction factor. The life predictions of the proposed fatigue damage model under constant amplitude loading are compared with a wide range of metal fatigue results in the literature.     

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 new path‐dependent multiaxial fatigue model for metals under different paths

Based on the critical plane approach, a new path‐dependent multiaxial fatigue model in low‐cycle fatigue is proposed. The proposed model includes damage contribution from four sources: the normal strain amplitude, the shear strain amplitude on the critical plane, the hydrostatic mean strain and a new path‐dependent factor. The effect of mean strain is considered by the hydrostatic mean strain. The experimental data of 11 kinds of materials are used to demonstrate the effectiveness of this new model under both zero and non‐zero mean strain multiaxial loading path.     

A fatigue criterion for general multiaxial loading

An incremental fatigue damage model is proposed. The model incorporates the critical plane concept in multiaxial fatigue, plastic strain energy and material memory in cyclic plasticity. With an incremental form the model does not require a cycle counting method for variable amplitude loading. The model is designed to consider mean stress and loading sequence effects. Features of the new model are discussed and the determination of material constants is detailed. Verification of the model is achieved by comparing the predictions obtained by using the new model and experimental data of four materials under different loading conditions.     

The use of multiaxial fatigue models to predict fretting fatigue life of components subjected to different contact stress fields

This work describes the application of multiaxial fatigue criteria based on critical plane and mesoscopic (Dang Van, 1973, Sciences et Techniques de lÁrmement, 47 , 647—722) approaches to predict the fatigue initiation life of fretted components. To validate the analysis, several tests under closely controlled laboratory conditions are carried out in a Ti‐6Al‐4V alloy. These classical Hertzian tests reveal a size effect where fretting fatigue lives vary with contact size. Experimentally available data for fretting fatigue of an Al‐4Cu alloy are also used to assess the models. Neither the critical plane models nor the mesoscopic criterion considered can account for the effects of different contact stress fields on the initiation life, if the calculation is based only on highly stressed points on the surface. It is shown, however, that satisfactory results can be achieved if high values of the fatigue parameters are sustained over a critical volume.     

A multiaxial fatigue criterion for random loading

ABSTRACT A multiaxial fatigue criterion for random loading is proposed. Firstly, the orientation of the critical plane, where fatigue life estimation is carried out, is determined from the weighted mean position of the principal stress directions. Then, the scalar value of the normal stress vector N (t) perpendicular to the critical plane is taken as the cycle counting variable since the direction of such a vector is fixed with respect to time (conversely to the time‐varying direction of the shear stress vector C (t)), and a nonlinear combination of normal and shear stress components acting on the critical plane is used to define an equivalent stress amplitude. Finally, a damage accumulation model is employed to process such an equivalent stress amplitude and to determine fatigue endurance. This criterion is herein applied to some relevant random fatigue tests (proportional bending and torsion).     

An improved critical plane and cycle counting method to assess damage under variable amplitude multiaxial fatigue loading

The plane with the maximum variance of the resolved shear stress is taken as the critical plane. Two algorithms are used along with the maximum variance method (MVM) to determine the orientation of the critical plane. The maximum variance of the normal stress on the potential critical planes is calculated to determine the one experiencing the maximum extent of fatigue damage. A new multiaxial cycle counting method is proposed to count cycles on the critical plane. The modified Wöhler curve method is used to assess fatigue damage. About 200 experimental results were collected from the technical literature to validate the approaches being proposed. The results show that the improved design technique being proposed is successful in assessing fatigue damage under variable amplitude multiaxial cyclic loading.     

An improved multiaxial high‐cycle fatigue criterion based on critical plane approach

Several groups of fatigue damage parameters are discussed and then an improved multiaxial high‐cycle fatigue criterion based on critical plane defined by the plane of maximum shear stress range is presented in this paper. A compromising solution to consider the mean normal stress acting on the critical plane is also proposed. The new fatigue criterion extends the range of metallic materials which is valid for the ratio 1.25 < f_?1/t_?1 < 2. The predictions based on the presented model show a good agreement with test data.     

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.     

A fracture plane approach in multiaxial high-cycle fatigue of metals

The high-cycle fatigue behaviour of metals under multiaxial loading is examined. By employing the weight function method, the authors propose to correlate the fatigue fracture plane orientation with the averaged principal stress directions. The results derived by applying such an approach are compared with the experimental data collected from the relevant literature, concerning different types of metals under in-phase or out-of-phase sinusoidal biaxial normal and shear stress states. Theoretical results determined by McDiarmid are also reported.     

Criteria of multiaxial random fatigue based on stress,strain and energy parameters of damage in the critical plane

In this paper generalized criteria of multiaxial random fatigue based on stress, strain and strain energy density parameters in the critical plane have been discussed. The proposed criteria reduce multiaxial state of stress to the equivalent uniaxial tension–compression or alternating bending. Relations between the coefficients occurring in the considered criteria have been derived. Thus, it is possible to take into account fatigue properties of materials under simple loading states during determination of the multiaxial fatigue life. Presented models have successfully correlated fatigue lives of cast iron GGG40 and steel 18G2A specimens under constant amplitude in‐phase and out‐of‐phase loadings including different frequencies.     

Small crack growth in combined bending–torsion fatigue of A533B steel

Crack growth rate data from bending, torsional and in-plane and 90° out-of-phase combined bending–torsional fatigue tests of A533B steel are presented. Crack growth was monitored from initial sizes generally in the range of 50–300  μm to final sizes of several millimetres. Crack growth rate was found to vary linearly with crack size. Two approaches for correlating the A533B crack growth rate were evaluated, an effective strain-based intensity factor range and a method based on total cyclic strain energy density. The approaches were also evaluated using small crack growth data from the literature for SAE 1045 steel and Inconel 718 specimens tested under axial–torsional loadings. Predicted crack growth lives using both approaches were found to agree within a factor of two of observed lives for nearly all of the data examined.     

Evaluation of fatigue life for titanium alloy TC4 under variable amplitude multiaxial loading

Fatigue tests under variable amplitude multiaxial loading were conducted on titanium alloy TC4 tubular specimens. A method to estimate the fatigue life under variable amplitude multiaxial loading has been proposed. Multiaxial fatigue parameter based on Wu–Hu–Song approach and rainflow cycle counting and Miner–Palmgren rule were applied in this method. The capability of fatigue life prediction for the proposed method was checked against the test data of TC4 alloy under variable amplitude multiaxial loading. The prediction results are all within a factor of two scatter band of the test results.     

A notch critical plane approach of multiaxial fatigue life prediction for metallic notched specimens

An approach based on the local stress response is proposed to locate the fatigue critical point for metallic blunt notched specimens under multiaxial fatigue loading. According to the stress analysis, both stress gradient and gradient of loading nonproportionality exist at notch root. The plane in the vicinity of the notch that passes through the fatigue critical point and experiences the maximum shear stress amplitude is defined as the critical plane for notch specimens (CPN). Furthermore, the Susmel's fatigue damage parameter is modified to assess fatigue life of notched components by combining CPN and the theory of critical distance (TCD). The multiaxial fatigue test of the thin‐walled round tube specimens made of Ni‐base alloy GH4169 is carried out to verify the above approaches. In addition, test data of two kinds of materials are collected. The results show that the maximum absolute error of the fatigue critical point is 9.6° and the majority of the predicted life falls within the three‐time scatter band.     

Proportional/nonproportional constant/variable amplitude multiaxial notch fatigue: cyclic plasticity,non‐zero mean stresses,and critical distance/plane

This paper deals with the formulation and experimental validation of a novel fatigue lifetime estimation technique suitable for assessing the extent of damage in notched metallic materials subjected to in‐service proportional/nonproportional constant/variable amplitude multiaxial load histories. The methodology being formulated makes use of the Modified Manson‐Coffin Curve Method, the Shear Strain–Maximum Variance Method, and the elasto‐plastic Theory of Critical Distances, with the latter theory being applied in the form of the Point Method. The accuracy and reliability of our novel fatigue lifetime estimation technique were checked against a large number of experimental results we generated by testing, under proportional/nonproportional constant/variable amplitude axial‐torsional loading, V‐notched cylindrical specimens made of unalloyed medium‐carbon steel En8 (080M40). Specific experimental trials were run to investigate also the effect of non‐zero mean stresses as well as of different frequencies between the axial and torsional stress/strain components. This systematic validation exercise allowed us to demonstrate that our novel multiaxial fatigue assessment methodology is remarkably accurate, with the estimates falling within an error factor of 2. By modelling the cyclic elasto‐plastic behaviour of metals explicitly, the design methodology being formulated and validated in the present paper offers a complete solution to the problem of estimating multiaxial fatigue lifetime of notched metallic materials, with this holding true independently of sharpness of the stress/strain raiser and complexity of the load history.     

Multiaxial fatigue life modelling using hybrid approach of critical plane and genetic algorithm

This paper presents a new hybrid approach for multiaxial fatigue life estimation, based on continuum damage mechanics theory and a genetic algorithm with critical plane model formulation. The hybrid model employs a genetic algorithm based setup for calibration with standard proportional and non‐proportional profiles to predict fatigue life for complex loading profiles. The model is evaluated using experimental fatigue life data for SS304 steel. Calibration using simplified profiles is in agreement with the requirement for cost‐effective experimental fatigue life testing. In‐phase and out‐of‐phase loads are used for calibration, and fatigue life is predicted for more complicated profiles. The results show good agreement between the estimated and experimental fatigue life, and calibration through simple loading histories to predict fatigue life for complex histories appears to be an effective solution using the proposed model. A brief comparison is presented with fatigue life estimation performance of the proposed model with models available in commercial codes. Proposed model found to be more consistent in fatigue life prediction against various loading conditions.     

Prediction of multiaxial fatigue life for complex three‐dimensional stress state considering effect of additional hardening

In engineering practice, it is generally accepted that most of components are subjected to multiaxial stress‐strain state. To analyse this complicated loading state, different types of specimens of 2A12 (2124 in the United States) aluminium alloy were tested under multiaxial loading conditions and a new multiaxial fatigue analysis method for the state of three‐dimensional stress and strain is proposed. Elastic‐plastic finite element method (FEM) and a proposed vector computing method are used to describe the loading state at the critical point of specimen, by which the parameter Γ_T is calculated at the new defined subcritical plane to consider the effect of additional cyclic hardening. Meanwhile, the principal equivalent strain is still calculated at the traditional critical plane. The new damage parameter is composed of different process parameters, by which the dynamic path of strain state, including loading environments and material properties, are fully considered in one loading cycle. According to experimental verifications with 2A12 aluminium alloy, the results show that the proposed method shows satisfactory, accurate, and reliable results for multiaxial fatigue life prediction in the state of three‐dimensional stress and strain.     

Multiaxial fatigue limits and material sensitivity to non-zero mean stresses normal to the critical planes

This paper is concerned with an attempt to reformulate the so-called Modified Wöhler Curve Method (MWCM) in order to more efficiently account for the detrimental effect of non-zero mean stresses perpendicular to the critical planes. In more detail, by taking as a starting point the well-established experimental evidence that engineering materials exhibit different sensitivities to superimposed tensile static stresses, an effective value of the normal mean stress relative to the critical plane was attempted to be calculated by introducing a suitable correction factor. Such a mean stress sensitivity index was assumed to be a material constant, i.e. a material parameter to be determined by running appropriate experiments. The accuracy of the novel reformulation of the MWCM proposed here was systematically checked by using several experimental data taken from the literature. In particular, in order to better explore the main features of the improved MWCM, its accuracy in estimating multiaxial high-cycle fatigue damage was evaluated by considering fatigue results generated not only under non-zero mean stresses but also under non-proportional loading. Such a validation exercise allowed us to prove that the systematic use of the mean stress sensitivity index resulted in estimates falling within an error interval equal to about ±10%, and this held true independently of considered material and complexity of the investigated loading path. Finally, such a novel reformulation of the MWCM was also applied along with the Theory of Critical Distances (TCD) to predict the high-cycle fatigue strength of notched samples tested under in-phase bending and torsion with superimposed tensile and torsional static stresses: again our method was seen to be highly accurate, correctly predicting high-cycle multiaxial fatigue damage also in the presence of stress concentration phenomena.     

The Modified Wöhler Curve Method applied along with the Theory of Critical Distances to estimate finite life of notched components subjected to complex multiaxial loading paths

This paper is concerned with the use of the Modified Wöhler Curve Method (MWCM) applied in conjunction with the Theory of Critical Distances (TCD) to estimate fatigue lifetime of mechanical components subjected to multiaxial cyclic loading and experiencing stress concentration phenomena. In more detail, our engineering approach takes as its starting point the idea that accurate estimates can be obtained by simply assuming that the value of the critical length, L_M, to be used to evaluate fatigue damage in the medium–cycle multiaxial fatigue regime is a function of the number of cycles to failure, N_f. In other words, the MWCM, which is a bi‐parametrical critical plane approach, is suggested here to be applied by directly post‐processing the linear‐elastic stress state damaging a material point whose distance from the notch tip increases as N_f decreases. According to the main feature of the TCD, the above L_M versus N_f relationship is assumed to be a material property to be determined experimentally: such an hypothesis results in a great simplification of the fatigue assessment problem because, for a given material, the same critical length can be used to estimate fatigue damage independent of the considered geometrical feature. The accuracy of the devised approach was checked by analysing about 150 experimental results we generated by testing V‐notched cylindrical samples made of a commercial cold‐rolled low‐carbon steel. The above specimens were tested under in‐phase and out‐of‐phase combined tension and torsion, considering the damaging effect of superimposed static stresses as well. Moreover, in order to better check its accuracy in assessing notched components subjected to complex loading paths, our method was also applied to several data sets taken from the literature. This extensive validation exercise allowed us to prove that the MWCM applied along with the TCD is successful in estimating medium‐cycle multiaxial fatigue damage (N_f values in the range 10⁴–10⁶), resulting in predictions falling within the widest scatter band between the two used to calibrate the method itself. Such a high accuracy level is very promising, especially in light of the fact that the proposed approach predicts multiaxial fatigue lifetime by post‐processing the linear elastic stress fields in the fatigue process zone: this makes our method suitable for being used to assess real components by performing the stress analysis through simple linear‐elastic FE models.