A multi‐axial low‐cycle fatigue life prediction model considering effects of additional hardening

It is generally accepted that the additional hardening of materials could largely shorten multi‐axis fatigue life of engineering components. To consider the effects of additional hardening under multi‐axial loading, this paper summarizes a new multi‐axial low‐cycle fatigue life prediction model based on the critical plane approach. In the new model, while critical plane is adopted to calculate principal equivalent strain, a new plane, subcritical plane, is also defined to calculate a correction parameter due to the effects of additional hardening. The proposed fatigue damage parameter of the new model combines the material properties and the angle of the loading orientation with respect to the principal axis and can be established with Coffin‐Manson equation directly. According to experimental verification and comparison with other traditional models, it is clear that the new model has satisfactory reliability and accuracy in multi‐axial fatigue life prediction.     

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.     

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.     

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 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.     

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.     

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.     

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.     

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.     

EVICD – eine Lebensdauermethode für komplexe mehrachsige Betriebsbelastungen für die Praxis

EVICD – an advanced crack intiation life prediction method for engineering application In the present paper an overview of the latest stand in the development of EVICD, a crack initiation life prediction method for arbitrary multiaxial loading, is given. The incremental prediction method which was originally proposed by W. Ott and which was later extended by the introduction of a secondary damage parameter either based on the normal stress on the planes with maximum shear stresses (EVICD‐N) or the normal stress on the octahedral planes (EVICD‐J1) has been further developed: A special Input Section was created, which is open to all important types and formats of engineering input data for fatigue calculations. The results of strain measurements can also be taken. Further on, the multiaxial Neuber‐Method has been worked in for a fast determination of the elastic plastic stresses and strains at fatigue critical locations of components. At the end of the Input Section the elastic plastic stress or strain path at the fatigue critical location is transferred to the damage evaluation modul of EVICD for an evaluation of the crack initiation life. The Mróz‐Garud plasticity model has been worked in the damage evaluation model. The fatigue damage evaluation does occur after a transparent flow diagram and has been realized as a FORTRAN Code. This is important for a general use of EVICD in practice. Meanwhile EVICD has been verified on a broader basis. A representation of the prediction results after EVICD vs. the corresponding experimental results after a proposal of E. Haibach shows, that the prediction capability of EVICD has become better than that of conventional fatigue prediction methods.     

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.     

A generalized frequency separation–strain energy damage function model for low cycle fatigue–creep life prediction

Fatigue–creep interaction is a key factor for the failures of many engineering components and structures under high temperature and cyclic loading. These fatigue–creep life prediction issues are significant in selection, design and safety assessments of those components. Based on the frequency‐modified Manson–Coffin equation and Ostergren's model, a new model for high temperature low cycle fatigue (HTLCF), a generalized frequency separation–strain energy damage function model is developed. The approach used in this model to reflect the effects of time‐dependent damaging mechanisms on HTLCF life is different from those used in all the earlier models. A new strain energy damage function is used to reduce the difference between the approximate strain energy and real strain energy absorbed during the damage process. This proposed model can describe the effects of different time‐dependent damaging mechanisms on HTLCF life more accurately than others. Comparing traditional frequency separation technique (FS) and strain energy frequency‐modified approach (SEFS), the proposed model is widely applicable and more precise in predicting the life of fatigue–creep interaction. Experimental data from existing literature are used to demonstrate the feasibility and applicability of the proposed model. A good agreement is found between the predicted results and experimental data.     

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.     

A method to develop a unified fatigue life prediction model for filled natural rubbers under uniaxial loads

Rubber components are widely used in many fields because of their superior elastic properties. Fatigue failures, commonly encountered in rubber components, however, remain a critical issue. In this study, the effect of strain ratio R on the fatigue life of filled natural rubbers used in automotive mounts is investigated experimentally and numerically. A uniaxial tension/compression fatigue experiment was conducted on dumb‐bell cylindrical rubber specimens subject to loads representing different R ratios. The experimental fatigue data are used to formulate two preliminary fatigue models based on peak strain and strain amplitude as the damage parameters. The deficiencies of these two models in predicting fatigue life over a wide range of R ratios are discussed, and an alternative life prediction model is proposed. The proposed model incorporates the effect of R ratio using an equivalent strain amplitude. It is shown that the proposed model could effectively predict fatigue life over a wide range of R ratios with an improved accuracy.     

An energy‐based critical fatigue life prediction method for AL6061‐T6

An energy‐based critical fatigue life prediction method is developed and analysed. The original energy‐based fatigue life prediction theory states that the number of cycles to failure is estimated by dividing the total energy accumulated during a monotonic fracture by the strain energy per cycle. Because the accuracy of this concept is heavily dependent on the cyclic behaviour of the material, a precise understanding of the strain energy behaviour throughout each failure process is necessary. Examination of the stress and strain during fatigue tests shows that the cyclic strain energy behaviour is not perfectly stable as initially presumed. It was discovered that fatigue hysteresis energy always accumulates to the same amount of energy by the end of the stable energy region, which has led to a new ‘critical energy’ material property. Characterization of strain energy throughout the fatigue process has thus improved the understanding of an energy‐based fatigue life prediction method.     

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.     

Multiaxial fatigue life prediction of a high temperature steam turbine rotor using a critical plane approach

This paper deals with the problem of multiaxial fatigue life assessment of engineering components. A computer-based procedure for multiaxial fatigue life assessment incorporating critical plane multiaxial damage models, suitable for use in design evaluations of engineering components based on finite element analysis results, is presented and applied to correlate results from tests conducted on SAE 1045 steel notched shaft specimens. The results from the two variants of critical plane models are compared vis-a-vis the results from the conventional local strain based life prediction method. Fatigue life prediction of a high temperature steam turbine rotor is also carried out using the above procedure.     

A modified normal strain ratio fatigue life model based on the hybrid approach of critical plane and crystallographic slip theory

Based on the method combining the critical plane with crystallographic slip theory, an anisotropic low cycle fatigue life model is proposed to reflect the effects of orientation dependence and damage factors on fatigue life. According to this method, the crystallographic slip plane is adopted as the critical plane by searching for 30 potential slip systems. In addition, considering the effects of normal strain and strain ratio on fatigue failure, the normal strain ratio is introduced into model and regression model is obtained by fitting method. The proposed model is verified by estimating the low cycle fatigue lives of single crystal nickel–based superalloys PWA1480, CMSX‐2 and DD3 for different loading conditions. The results show that the proposed model is applicable for more complicated loading situations and give a higher prediction accuracy compared to Sun's model.     

An energy‐based damage parameter for the life prediction of AISI 304 stainless steel subjected to mean strain

Abstract

This study extends the plastic strain energy approach to predict the fatigue life of AISI 304 stainless steel. A modified energy parameter based on the stable plastic strain energy density under tension conditions is proposed to account for the mean strain and stress effects in a low cycle fatigue regime. The fatigue life curve based on the proposed energy parameter can be obtained directly by modifying the parameters in the fatigue life curve based on the stable plastic strain energy pertaining to fully reversed cyclic loading. Hence, the proposed damage parameter provides a convenient means of evaluating fatigue life on the mean strain or stress effect. The modified energy parameter can also be used to explain the combined effect of alternating and mean strain/stress on the fatigue life. In this study, the mean strain effects on the fatigue life of AISI 304 stainless steel are examined by performing fatigue tests at different mean strain levels. The experimental results indicate that the combination of an alternating strain and a mean strain strongly influences the fatigue life. Meanwhile, it is found that the change in fatigue life is sensitive to changes in the proposed damage parameter under the condition of a constant strain amplitude at various mean strain levels. A good agreement is observed between the experimental fatigue life and the fatigue life predicted by the proposed damage parameter. The damage parameter proposed by Smith et al. (1970) is also employed to quantify the mean strain effect. The results indicate that this parameter also provides a reasonable estimate of the fatigue life of AISI 304 stainless steel. However, a simple statistical analysis confirms that the proposed damage parameter provides a better prediction of the fatigue life of AISI 304 stainless steel than the SWT parameter.