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.     

Multiaxial fatigue life calculation model for components in rolling‐sliding line contact with application to gears

Important components such as gears, rollers, or bearings operate in rolling‐sliding contact loading conditions. Determination of their fatigue lives remains a challenging task due to complex states of stress and strain in the contact region, as well as complex contact conditions such as variable loading amplitude and complex geometry of contact. A mathematical model of rolling‐sliding line contact combined with a multiaxial fatigue life calculation model based on the Fatemi‐Socie critical plane crack initiation criterion is proposed. The developed model was applied to gears' teeth in mesh and compared with fatigue lives of gears reported in the literature. Good agreement was determined confirming the validity of the proposed model. A further advantage is obtaining locations of initiated cracks and the orientation of critical plane(s), which can subsequently be used for the estimation of crack shapes in initial phases of their growth and the damage type that they can be expected to develop into.     

Application of a semianalytical strain assessment and multiaxial fatigue analysis to compare rolling contact fatigue in twin-disk and full-scale wheel/rail contact conditions

A semianalytical model is introduced to assess rolling contact fatigue problems in railway applications. The constitutive law is based on the nonlinear kinematic and isotropic hardening model of Chaboche–Lemaitre, which allows the cyclic elastoplastic strain under the contact surface to be evaluated. The much higher computational effectiveness in comparison with finite element (FE) analyses is quantified. The Dang Van multiaxial fatigue criterion is implemented to evaluate the rolling contact fatigue in the subsurface elastic region where cracking is relatively rare but more dangerous than surface cracks. The influence of the presence of sulfides in the wheel matrix in decreasing fatigue strength is also assessed by means of Murakami's approach. The model is used to compare conditions under small-scale twin-disk experiments to full-scale wheel/rail contact conditions. It is found that, for the same Hertzian pressure, the small-scale contact is more conservative in that it causes a deeper plasticized layer as compared with the elliptical full-scale contact. In the investigated cases, crack initiation is also not expected according to Dang Van criterion in neither of the studied contact conditions.     

Multiaxial fatigue of a railway wheel steel under non-proportional loading

The results of an experimental investigation of the multiaxial fatigue behaviour of the R7T steel are presented. The R7T steel is currently employed in the production of solid high-speed railway wheels. Wheel failures due to rolling contact fatigue may occur and, on some occasions, fatigue cracks nucleate in the sub-surface region under the contact area between wheel and rail. Here, the stress field is multiaxial and the loading path is non-proportional. Specimens extracted from the rim of railway wheels were subjected to combined out-of-phase alternating torsion and pulsating compressive axial loads, a non-proportional stress state which is similar to that observed under the contact area in the wheel rim. The tests results are discussed in the light of some multiaxial fatigue theories, chosen among those based on the critical plane concept and those implementing an integral approach, with the aim of selecting a fatigue criterion suitable for the sub-surface fatigue assessment of railway wheels.     

Low‐cycle fatigue life prediction of various metallic materials under multiaxial loading

This paper proposed a simple life prediction model for assessing fatigue lives of metallic materials subjected to multiaxial low‐cycle fatigue (LCF) loading. This proposed model consists of the maximum shear strain range, the normal strain range and the maximum normal stress on the maximum shear strain range plane. Additional cyclic hardening developed during non‐proportional loading is included in the normal stress and strain terms. A computer‐based procedure for multiaxial fatigue life prediction incorporating critical plane damage parameters is presented as well. The accuracy and reliability of the proposed model are systematically checked by using about 300 test data through testing nine kinds of material under both zero and non‐zero mean stress multiaxial loading paths.     

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.     

A novel accumulative fatigue damage model for multiaxial step spectrum considering the variations of loading amplitude and loading path

In this paper, based on the process of the fatigue crack initiation and the critical plane theory, a continuous stress parameter was proposed to quantify the driving force of the fatigue crack initiation for the fully reversed multiaxial fatigue loading. In this stress parameter, the shear stress amplitude and normal stress amplitude on the critical plane were combined with the variable coefficients which were affected by the normalized fatigue life and the loading non‐proportionality. Owing to these coefficients, for the multiaxial loadings with different non‐proportionalities, the driving force of the fatigue crack initiation during the whole life could be described. After that, a novel accumulative fatigue damage model was established for the multiaxial two‐stage step spectrum. In this model, the accumulative damage was calculated according to the variation of the proposed stress parameter on the critical plane. Considering the directionality of the multiaxial fatigue damage, for the spectrum in which the loading path was variable, the damage accumulation was carried out on the critical planes of the both loadings, and the larger one was chosen as the final accumulative fatigue damage. In order to verify the new model, up to 41 different multiaxial two‐stage step spectrum loading tests on 2024‐T4 aluminium alloy were collected. The new model, as well as other five commonly used models, was applied to calculate the accumulative fatigue damage. The final results showed that, compared with other commonly used models, the new model had the most accurate results with the smallest scatters.     

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.     

Effects of non-proportional loading paths on the orientation of fatigue crack path

Fatigue crack path prediction and crack arrest are very important for structural safety. In real engineering structures, there are many factors influencing the fatigue crack paths, such as the material type (microstructure), structural geometry and loading path, etc. In this paper, both experimental and numerical methods are applied to study the effects of loading path on crack orientations. Experiments were conducted on a biaxial testing machine, using specimens made of two steels: 42CrMo4 and CK45 (equivalent to AISI 1045), with six different biaxial loading paths. Fractographical analyses of the plane of the stage I crack propagation were carried out and the crack orientations were measured using optical microscopy. The multiaxial fatigue models, such as the critical plane models and also the energy‐based critical plane models, were applied for predicting the orientation of the critical plane. Comparisons of the predicted orientation of the damage plane with the experimental observations show that the shear‐based multiaxial fatigue models provide good predictions for stage I crack growth for the ductile materials studied in this paper.     

Life prediction based on weight‐averaged maximum shear strain range plane under multiaxial variable amplitude loading

Based on Wang and Brown's reversal counting method, a new approach to the determination of the critical plane is proposed by the defined plane with a weight‐averaged maximum shear strain range under multiaxial variable amplitude loading. According to the determined critical plane, a detailed procedure of multiaxial fatigue life prediction is introduced to predict lives in the low‐cycle multiaxial fatigue regime. The proposed approach is verified by two multiaxial fatigue damage models and Miner's linear cumulative damage law. The results showed that the proposed approach can effectively predict the orientation of the failure plane under multiaxial variable amplitude loading and give a satisfactory life prediction.     

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.     

Investigation of rolling contact crack initiation in bainitic and pearlitic rail steels

The stress–strain history and the crack initiation lives of bainitic and head‐hardened pearlitic rail steels were determined under rolling contact loading by implementing the semi‐analytical Jiang–Sehitoglu rolling contact model that incorporates both ratchetting and multiaxial fatigue damage. The calculations revealed that the bainitic steel withstands higher loads than the pearlitic steel at low shear tractions, however; both materials behave in an increasingly similar manner as the shear tractions increase. Furthermore, maximum damage occurs in both steels when ratchetting and fatigue damage coincide on the surface. In addition to shedding light on the rolling contact fatigue (RCF) performance of bainitic and pearlitic rail steels, the current work also establishes a methodology for the realistic prediction of crack initiation under RCF.     

A single parameter to evaluate stress state in rail head for rolling contact fatigue analysis

Based on the Smith‐Watson‐Topper (SWT) method, a phenomenological approach for multiaxial fatigue analysis, the maximum SWT parameter is proposed as a single parameter to evaluate the stress state in the rail head for assessing the fatigue integrity of the structure. A numerical procedure to calculate the maximum SWT parameter from a finite element analysis is presented and applied in a case study, where the stress and strain fields due to wheel/rail rolling contact are obtained from a three‐dimensional finite element simulation with the steady‐state transport analysis technique. The capability of the SWT method to predict fatigue crack initiation in the rail head is confirmed in the case study. Analogous to von Mises stress for strength analysis, the maximum SWT parameter can be applied to evaluate the fatigue loading state not only in rail head due to rolling contact fatigue but also in a generic structure subjected to a cyclic loading.     

Prediction of crack initiation plane direction in high‐cycle multiaxial fatigue with in‐phase and out‐of‐phase loading

A new method for predicting crack plane direction in high‐cycle multiaxial fatigue is proposed. This method considers material properties and loading conditions. Two situations are considered: (i) in‐phase loading, where the crack plane direction only depends on the loading condition and material properties have little influence on it, and (ii) out‐of‐phase loading, where the crack plane direction is affected by both loading conditions and material properties. The prediction accuracy is assessed by comparison with several experimental results, including different loading conditions and materials. The results show that the proposed method provides a good prediction capability for these experiments.     

Use of an energy‐based/critical plane model to assess fatigue life under low‐cycle multiaxial cycles

For engineering components subjected to multiaxial loading, fatigue life prediction is crucial for guaranteeing their structural security and economic feasibility. In this respect, energy‐based models, integrating the stress and strain components, are widely used because of their availability in fatigue prediction. Through employing the plastic strain energy concept and critical plane approach, a new energy‐based model is proposed in this paper to evaluate the low‐cycle fatigue life, in which the critical plane is defined as the maximum damage plane. In the proposed model, a newly defined NP factor κ^*  is used to quantify the nonproportional (NP) effect so that the damage parameter can be conveniently calculated. Moreover, a simple estimation method of weight coefficient is developed, which can reflect different contributions of shear and normal plastic strain energy on total fatigue damage. Experimental data of 10 kinds of materials are employed to assess the effectiveness of this model as well as three other energy‐based 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.     

Online multiaxial fatigue damage evaluation method by real‐time cycle counting and energy‐based critical plane criterion

To realize online multiaxial fatigue damage assessment for the mechanical components in service, an online multiaxial cycle counting method is proposed coupled with the segment processing technique and Wang‐Brow's relative equivalent strain concept. Meanwhile, considering all the stress and strain components, which contribute to the fatigue damage on the critical plane, a multiaxial fatigue damage model without any weight coefficients is also proposed in an equivalent form of shear strain energy. Then, an online fatigue damage evaluation method for multiaxial random loading is developed by combining with the proposed damage model and online cycle counting method. The experimental results showed that the proposed online cycle counting method can be successfully applied to the calculation of multiaxial fatigue damage under random loading. Moreover, the proposed online multiaxial fatigue damage evaluation method can provide satisfactory predictions.     

Multiaxial notch fatigue life prediction based on pseudo stress correction and finite element analysis under variable amplitude loading

A new computational methodology is proposed for fatigue life prediction of notched components subjected to variable amplitude multiaxial loading. In the proposed methodology, an estimation method of non‐proportionality factor (F) proposed by authors in the case of constant amplitude multiaxial loading is extended and applied to variable amplitude multiaxial loading by using Wang‐Brown's reversal counting approach. The pseudo stress correction method integrated with linear elastic finite element analysis is utilized to calculate the local elastic‐plastic stress and strain responses at the notch root. For whole local strain history, the plane with weight‐averaged maximum shear strain range is defined as the critical plane in this study. Based on the defined critical plane, a multiaxial fatigue damage model combined with Miner's linear cumulative damage law is used to predict fatigue life. The experimentally obtained fatigue data for 7050‐T7451 aluminium alloy notched shaft specimens under constant and variable amplitude multiaxial loadings are used to verify the proposed methodology and equivalent strain‐based methodology. The results show that the proposed methodology is superior to equivalent strain‐based methodology.     

Evaluation of temperature‐sensitive fatigue crack propagation of a high‐speed railway wheel rim material

The fatigue crack growth rate (FCGR) of ER8C high‐speed railway wheel rim material was tested at various service temperatures. The temperature sensitivity of fatigue crack propagation was evaluated, and the effect of temperature on the crack propagation mechanism was analyzed. The obtained results indicate a fatigue ductile‐to‐brittle transition (FDBT) point at ?20°C for the ER8C wheel rim materials. A reverse relationship was found between FCGR and temperature for the near threshold and Paris regimes when the temperature was below the FDBT point. However, no evident changing rule was found when the temperature was above this transition point. An evident fatigue crack propagation mode transition was found from lamellar tearing to intergranular cracks, which was related to the FDBT for the near‐threshold regime.     

A critical plane‐energy model for multiaxial fatigue life prediction

A new critical plane‐energy model is proposed in this paper for multiaxial fatigue life prediction of metals. A brief review of existing methods, especially on the critical plane‐based and energy‐based methods, is given first. Special focus is on the Liu–Mahadevan critical plane approach, which has been shown to work for both brittle and ductile metals. One potential drawback of the Liu–Mahadevan model is that it needs an empirical calibration parameter for non‐proportional multiaxial loadings because only the strain terms are used and the out‐of‐phase hardening cannot be explicitly considered. An energy‐based model using the Liu–Mahadevan concept is proposed with the help of the Mróz–Garud plasticity model. Thus, the empirical calibration for non‐proportional loading is not needed because the out‐of‐phase hardening is naturally included in the stress calculation. The model predictions are compared with experimental data from open literature, and the proposed model is shown to work for both proportional and non‐proportional multiaxial loadings without the empirical calibration.