An online‐offline prognosis model for fatigue life prediction under biaxial cyclic loading with overloads

This paper presents a robust online‐offline model for the prediction of crack propagation under complex in‐phase biaxial fatigue loading in the presence of overloads of different magnitudes. The online prognosis model comprises a combination of finite element analysis and data‐driven regression to predict the crack propagation under constant loading, while the offline model is trained using experimental data to inform the post‐overload crack growth retardation behavior to the online model. The developed methodology is validated by conducting biaxial fatigue experiments using aluminum AA7075‐T651 alloy cruciform specimens. A close correlation is observed between the experimental results and model predictions. The results show that the model successfully predicts the crack retardation behavior under the influence of overloads with different magnitudes occurring at different stages of fatigue crack growth. Error analysis is conducted to investigate the sensitivities of the number of training points and crack increments to the prediction accuracy. In addition, the error propagation with respect to the crack length is studied, which provides constructive suggestions for further model improvement.     

Multiaxial fatigue life prediction method based on path‐dependent cycle counting under tension/torsion random loading

A path‐dependent cycle counting method is proposed by applying the distance formula between two points on the tension‐shear equivalent strain plane for the identified half‐cycles first. The Shang–Wang multiaxial fatigue damage model for an identified half‐cycle and Miner's linear accumulation damage rule are used to calculate cumulative fatigue damage. Therefore, a multiaxial fatigue life prediction procedure is presented to predict conveniently fatigue life under a given tension and torsion random loading time history. The proposed method is evaluated by experimental data from tests on cylindrical thin‐walled tubes specimens of En15R steel subjected to combined tension/torsion random loading, and the prediction results of the proposed method are compared with those of the Wang–Brown method. The results showed that both methods provided satisfactory prediction.     

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.     

The prediction of fatigue life under random loading: a diffusion model

A diffusion model is used to analyze the growth of a fatigue crack under random loading. The randomness in loading is embedded in the coefficients of the diffusion equation, whose solution leads to the determination of fatigue life. To demonstrate the potential of this method, some calculations are made using typical values for material properties. The results show that fatigue life under random loading is governed, in addition to material properties, by such statistics as the mean and the mean square value of the loading.     

A simple energy‐based model for nonproportional low‐cycle multiaxial fatigue life prediction under constant‐amplitude loading

From the literature concerning the traditional nonproportional (NP) multiaxial cyclic fatigue prediction, special attentions are usually paid to multiaxial constitutive relations to quantify fatigue damage accumulation. As a result, estimation of NP hardening effect decided by the entire history path is always proposed, which is a challenging and complex task. To simplify the procedure of multiaxial fatigue life prediction of engineering components, in this paper, a novel effective energy parameter based on simple material properties is proposed. The parameter combines uniaxial cyclic plastic work and NP hardening effects. The fatigue life has been assessed based on traditional multiaxial fatigue criterion and the proposed parameter, which has been validated by experimental results of 316 L stainless steel under different low‐cycle loading paths.     

A general model for stress‐life fatigue prediction

From several factors that influence the fatigue behaviour of a particular material, the stress ratio or mean stress and the stress concentration factor are of great importance for the structural calculation. Since most components and structural members contain notches that could be sites of fatigue crack initiation, fatigue data from specimens with different forms of notches have to be collected. The collection of such data at various stress ratios or mean stresses is not economic and time‐consuming. Based on the Walker equivalent stress model, a general fatigue life model is presented and tested with 2024‐T3 fatigue data, available in the literature. The Walker model considered only the effect of stress ratio or mean stress on the fatigue behaviour. On the other hand, in the proposed model, the combined effect of mean stress and stress concentration factor on fatigue behaviour is demonstrated. The statistical analysis indicates that the presented model is very efficient to interpolate the fatigue life successfully, thereby reducing both time and cost.     

Notch fatigue life prediction considering nonproportionality of local loading path under multiaxial cyclic loading

An innovative numerical methodology is presented for fatigue lifetime estimation of notched bodies experiencing multiaxial cyclic loadings. In the presented methodology, an evaluation approach of the local nonproportionality factor F for notched specimens, which defines F as the ratio of the pseudoshear strain range at 45° to the maximum shear plane and the maximum shear strain range, is proposed and discussed deeply. The proposed evaluation method is incorporated into the material cyclic stress‐strain equation for purpose of describing the nonproportional hardening behavior for some material. The comparison between multiaxial elastic‐plastic finite element analysis (FEA) and experimentally measured strains for S460N steel notched specimens shows that the proposed nonproportionality factor estimation method is effective. Subsequently, the notch stresses and strains calculated utilizing multiaxial elastic‐plastic FEA are used as input data to the critical plane‐based fatigue life prediction methodology. The prediction results are satisfactory for the 7050‐T7451 aluminum alloy and GH4169 superalloy notched specimens under multiaxial cyclic loading.     

Application of an energy model for fatigue life prediction of construction steels under bending, torsion and synchronous bending and torsion

The paper contains a mathematical model of the material’s behaviour under cyclic loading taking into account the dynamics of the fatigue process, including the number of cycles to failure, induced by the mean stress value. The coefficients in the proposed model have been obtained from experimental tests under symmetrical and nonsymmetrical loading (with the stress ratio R=0). The proposed model has been used in order to modify an energy criterion with the aim of accounting for the influence of the mean stress on the fatigue life. The fatigue tests have been performed for structural steels 10HNAP and 18G2A subjected to cyclic bending, torsion and synchronous bending with torsion, by considering different values of the mean stress. A good agreement between the calculated and experimental results has been obtained.     

Area and point approaches in fatigue life evaluation under combined bending and torsion loading

We present a new nonlocal approach to nonuniform stress distribution, consisting in reduction of stresses to representative local ones in the critical plane for fatigue life calculation. The shear and normal stresses are averaged in two overlapping areas of different sizes on the critical plane. The proposed method is compared with the point (in critical distance) method and both are verified by fatigue tests under combined bending and torsion. Verification is done for the experimental and calculated fatigue lives with use of two multiaxial fatigue failure criteria. __________ Translated from Problemy Prochnosti, No. 1, pp. 69–72, January–February, 2008.     

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.     

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.     

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.     

Long life fatigue under multiaxial loading

A life prediction model in the field of high-cycle (i.e. long-life) fatigue is presented in this paper. The proposed model applies in the case of constant amplitude multiaxial proportional and non-proportional loading. The problems of the fatigue limit criterion and of the fatigue life prediction are both addressed and comparisons with experimental data are shown. Some limited discussion of the stress gradient effect is also offered. Although the particular model developed here is better suited for ferritic steels, it is explained in the paper that the methodology used to obtain this model can be adequately adapted to derive mathematically consistent models for other classes of metallic materials.     

A new approach of fatigue life prediction for metallic materials under multiaxial loading

Based on experimental data found in literatures, four traditionally multiaxial fatigue life criteria are analyzed and verified. It is discovered that these conventional criteria cannot reflect well the combined effect both under tension and torsion loadings for some materials, such as 6082-T6 and AlCu4Mg1, due to lack of enough consideration about the influence of stress amplitude ratio and stress level on fatigue life even under proportional loading. In order to solve this problem, a new approach of fatigue life prediction, based on the equal-life curve, is proposed and it is composed of three parts: the multiaxial fatigue life surface, a new path-dependent factor for multiaxial high-cycle fatigue and a material parameter describing material sensitivity to non-proportional loading. Finally, the precision of the presented approach is systematically checked against the experimental data found in literatures for four different materials under proportional and non-proportional loadings.     

Multiaxial fatigue life prediction of composite bolted joint under constant amplitude cycle loading

In this paper, a fatigue model of composite is established to predict multiaxial fatigue life of composite bolted joint under constant amplitude cycle loading. Firstly, finite element model is adopted to investigate stress state of composite bolted joint under constant amplitude cycle loading. Secondly, Tsai–Hill criterion is used to calculate equivalent stress of joint. At last, modified S–N fatigue life curve fitted by unidirectional laminate S–N curve which takes ply angle and stress ratio into consideration is adopted to determine fatigue life of composite. Calculation results of equivalent stress model show excellent agreement with experiments of composite bolted joint.     

Local stress–strain field intensity approach to fatigue life prediction under random cyclic loading

According to the characteristic of the local behavior of fatigue damage, on the basis of stress field intensity approach, a theory of local stress–strain field intensity for fatigue damage at the notch is developed in this paper, which can take account of the effects of the local stress–strain gradient on fatigue damage at the notch. In order to calculate the local stress–strain field intensity parameters, an incremental elastic-plastic finite element analysis under random cyclic loading is used to determine the local stress–strain response. A local stress–strain field intensity approach to fatigue life prediction is proposed by means of elastic-plastic finite element method for notched specimens. This approach is used to predict fatigue crack initiation life, and good correlation was observed with U-shape notched specimens for normalized 45 steel.     

A fatigue driving energy approach to high‐cycle fatigue life estimation under variable amplitude loading

In this paper, a concept of fatigue driving energy is formulated to describe the process of fatigue failure. The parameter is taken as a combination of the fatigue driving stress and strain energy density. By assessing the change of this parameter, a new non‐linear damage model is proposed for residual life estimation within high‐cycle fatigue regime under variable amplitude loading. In order to consider the effects of loading histories on damage accumulation under such condition, the load interaction effects are incorporated into the new model, and a modified version is thus developed. Life predictions by these two models and Miner rule are compared using experimental data from literature. The results show that the proposed model gives lower deviations than the Miner rule, while the modified model shows better prediction performances than the others. Moreover, the proposed model and its modifications are ease of implementation with the use of S–N curve.     

A model for predicting the creep-fatigue life under stepped-isothermal fatigue loading

A model is developed herein for predicting the fatigue life of creep-fatigue damage interaction, which is induced by combined high frequency mechanical loading and low frequency temperature variation, i.e. stepped-isothermal fatigue loading. The model is derived from continuum damage mechanics. In the model, the interaction between creep and fatigue damage is considered to be nonlinear. To validate the proposed model, a cast aluminum alloy is fatigue tested at 200–350 °C and 350–400 °C. The results show that good agreement can be achieved between predicted life and experimental data.     

Multiaxial notch fatigue life prediction based on the dominated loading control mode under variable amplitude loading

A new calculation approach is suggested to the fatigue life evaluation of notched specimens under multiaxial variable amplitude loading. Within this suggested approach, if the computed uniaxial fatigue damage by the pure torsional loading path is larger than that by the axial tension–compression loading path, a shear strain‐based multiaxial fatigue damage parameter is assigned to calculate multiaxial fatigue damage; otherwise, an axial strain‐based multiaxial fatigue damage parameter is assigned to calculate multiaxial fatigue damage. Furthermore, the presented method employs shear strain‐based and axial strain‐based multiaxial fatigue damage parameters in substitution of equivalent strain amplitude to consider the influence of nonproportional additional hardening. The experimental data of GH4169 superalloy and 7050‐T7451 aluminium alloy notched components are used to illustrate the presented multiaxial fatigue lifetime estimation approach for notched components, and the results reveal that estimations are accurate.     

A low-cycle fatigue life prediction model of ultrafine-grained metals

A (high strain) low‐cycle fatigue (LCF) life prediction model of ultrafine‐grained (UFG) metals has been proposed. The microstructure of a UFG metal is treated as a two‐phase ‘composite’ consisting of the ‘soft’ matrix (all the grain interiors) and the ‘hard’ reinforcement (all the grain boundaries). The dislocation strengthening of the grain interiors is considered as the major strengthening mechanism in the case of UFG metals. The proposed model is based upon the assumption that there is a fatigue‐damaged zone ahead of the crack tip within which the actual degradation of the UFG metal takes place. In high‐strain LCF conditions, the fatigue‐damaged zone is described as the region in which the local cyclic stress level approaches the ultimate tensile strength of the UFG metal, with the plastic strain localization caused by a dislocation sliding‐off process within it. The fatigue crack growth rate is directly correlated to the range of the crack‐tip opening displacement. The empirical Coffin–Manson and Basquin relationships are derived theoretically and compared with experimental fatigue data obtained on UFG copper (99.99%) at room temperature under both strain and stress control. Good agreement is found between the model and the experimental data. It is remarkable that, although the model is essentially formulated for high strains (LCF), it is also found to be applicable at low strains in the high‐cycle fatigue (HCF) regime.