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.     

多孔材料在三向载荷作用下的力学模型

为更全面掌握三维网状多孔材料在工程应用中的安全承载问题,分析了各向同性的该类材料在三向载荷(多向载荷)作用下的力学性能.在其结构简化的基础上,提出了该类材料在三向载荷作用下相应的承载力学模型,其中三向载荷中的任何一个载荷都可以任意为拉伸和压缩.运用这一模型,可以判断当该类材料在承受上述载荷条件时是否会发生破坏,其用来判断的材料固有指标即是多孔体的孔率,该指标是多孔材料最基本的参量.     

A damage gradient model for fatigue life prediction of notched metallic structures under multiaxial random vibrations

In the present paper, a damage gradient model combing the damage concept with the theory of critical distance (TCD) is established to estimate the fatigue lives of notched metallic structures under multiaxial random vibrations. Firstly, a kind of notched metallic structure is designed, and the biaxial random vibration fatigue tests of the notched metallic structures are carried out under different correlation coefficients and phase differences between two vibration axes. Then, the fatigue lives of the notched metallic structures are evaluated utilizing the proposed model with the numerical simulations. Finally, the proposed model is validated by the experiment results of the biaxial random vibration fatigue tests. The comparison results demonstrate that the proposed model can provide fatigue life estimation with high accuracy.     

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.     

A method for low-cycle fatigue life assessment of metallic materials under multiaxial loading

A new method of fatigue life assessment under multiaxial low-cycle regular and irregular loading is proposed, which is based on the modified Pisarenko-Lebedev criterion, the linear damage accumulation hypothesis, and the nonlinear Manson approach. The results of low-cycle fatigue tests of titanium alloy VT9 under irregular proportional and non-proportional biaxial loading are given. The tests were carried out at three Mises strain levels (0.6, 0.8, and 1.0%) with various combinations of proportional and non-proportional strain paths. All the tests were carried out at room temperature. The proposed method turned out to be effective and to allow for such factors as strain state type, strain path type and loading irregularity. __________ Translated from Problemy Prochnosti, No. 1, pp. 56–59, January–February, 2008.     

A survey on multiaxial fatigue damage parameters under non‐proportional loadings

In this paper, several multiaxial fatigue damage parameters taking into account nonproportional additional hardening are reviewed. According to the way nonproportional additional hardening is considered in the model, the damage parameters are classified into 2 categories: (1) equivalent damage parameters and (2) direct damage parameters. The equivalent damage parameters usually define a nonproportional coefficient to consider nonproportional additional cyclic hardening, and make a combination of this nonproportional coefficient with stress and/or strain quantities to calculate the equivalent damage parameters. In contrast, the direct damage parameters are directly estimated from the stress and strain quantities of interest. The accuracy of 4 multiaxial fatigue damage parameters in predicting fatigue lifetime is checked against about 150 groups of experimental data for 10 different metallic materials under multiaxial fatigue loading. The results revealed that both Itoh's model, one of equivalent damage parameters, and Susmel's model, which belong to direct damage parameters, could provide a better correlation with the experimental results than others assessed in this paper. So direct damage parameters are not better than the equivalent damage parameters in predicting fatigue lifetime.     

A stress-based method to predict lifetime under multiaxial fatigue loadings

This paper extends to low/medium‐cycle fatigue a stress‐based method recently proposed by the same authors for high‐cycle multiaxial fatigue assessments. By considering the plane of maximum shear stress amplitude coincident with the microcrack initiation plane, the method requires the calculation both of the maximum shear stress amplitude and the maximum normal stress relative to the same plane. Multiaxial fatigue life estimates are made by means of bi‐parametric modified Wöhler curves, which take into account the mean stress effect, the influence of the out‐of‐phase angle and the presence of notches by using a generalization to multiaxial fatigue of the fatigue strength reduction factor K_f. Approximately 700 experimental data taken from the literature are used to demonstrate that the method is a useful tool to summarize fatigue strength data of both smooth and notched components, subjected to either in‐phase or out‐of‐phase loads. Finally, a simple practical rule for the calculation of the multiaxial fatigue strength reduction factor is proposed.     

Energy-based time derivative damage accumulation model under uniaxial and multiaxial random loadings

A new fatigue life prediction method using the energy-based approach under uniaxial and multiaxial random loadings is proposed. The uniqueness of the proposed model is based on a time-derivative damage accumulation unlike classical cycle-based damage accumulation models. Thus, damage under arbitrary random loading can be directly obtained using time-domain integration without cycle counting. First, a brief review of existing models is given focusing on their applicability to uniaxial/multiaxial, constant/random, and high cycle fatigue/low cycle fatigue loading regimes. Next, formulation of time-derivative damage model is discussed in detail under uniaxial random loadings. Then, an equivalent energy concept for general multiaxial loading conditions is used to convert the random multiaxial loading to an equivalent random uniaxial loading, where the time-derivative damage model can be used. Finally, the proposed model is validated with extensive experimental data from open literature and in-house testing under various constant and random spectrum loadings.     

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.     

Model of damage cumulation in metallic materials under static tension

The article deals with a new phenomenological model of damage cumulation in metallic materials subjected to static tension. The main parameter of the running state of the material, which is put in correspondence with the degree of loosening, is the Poisson ratio at the stage of loss of strength (the descending part of the stress-strain curve). The suggested model describes satisfactorily the results of specially arranged experiments.Translated from Problemy Prochnosti, No. 7, pp. 31–40, July, 1995.     

A non-linear model for the fatigue assessment of notched components under fatigue loadings

This paper presents a general theory for the estimations of an entire fatigue curve in ductile materials based on the implicit gradient approach. In order to modify the slope of the Woehler curves, the material was considered non-linear. The average stress of the hysteresis loop was taken into account by means of Walker’s model. Subsequently, the implicit gradient method was adopted for the numerical evaluation of the effective stress and strain at low- and medium-cycle fatigue life and was then related to the fatigue strength of the material. The characteristic length, relating to the fatigue behaviour of the material, was considered constant for the fatigue lifetime. In order to confirm the proposed method, new experimental data were obtained, relating to axisymmetric notched specimens loaded with nominal stress ratio R = −1 and R = 0. In terms of the effective strain amplitude, evaluated by means of the implicit gradient approach, the different Woehler curves of notched specimens were summarised in a unique fatigue curve as a function of Walker’s cycle parameter.     

A fatigue damage accumulation model for reliability analysis of engine components under combined cycle loadings

Rotor components of an aircraft engine in service are usually subjected to combined high and low cycle fatigue (CCF) loadings. In this work, combining with the load spectrum of CCF, a modified damage accumulation model for CCF life prediction of turbine blades is first put forward to take into account the effects of load consequence and load interaction caused by high‐cycle fatigue (HCF) loads and low‐cycle fatigue (LCF) loads under CCF loading conditions. The predicted results demonstrate that the proposed model presents a higher prediction accuracy than Miner, Manson‐Halford model does. Moreover, to evaluate the fatigue reliability of rotor components, reliability model with the failure mode of CCF is proposed on the basis of the stress‐strength interference method when considering the strength degeneration, and its results show that the reliability model with CCF is more suitable for aero‐engine components than that with the failure mode of single fatigue.     

Numerical methods of multiaxial fatigue life prediction for elastomers under variable amplitude loadings

In this paper, numerical methods of fatigue life prediction for elastomers subjected to multidirectional, variable amplitude loadings are presented. Because experiments and numerical methods use different stress measures in large deformation, transformation between nominal stress and the second Piola–Kirchhoff stress is performed before fatigue life calculation. In order to incorporate the Mullins effect, the material properties of elastomers are calculated after an initial transition period. An efficient interpolation scheme using load stress/strain curves under unidirectional loading is proposed based on the fatigue characteristic of elastomers. A rainflow counting method with multi‐stress components is developed for variable amplitude loadings, and the critical plane method is applied to find the plane with the maximum damage parameter. Fatigue life predictions using the proposed numerical method are validated against experimental results. As a practical example, the fatigue life of a rubber engine mount is predicted using the proposed numerical method.     

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.     

Cumulative damage model based on equivalent fatigue under multiaxial thermomechanical random loading

A new creep–fatigue damage cumulative model is proposed under multiaxial thermomechanical random loading, in which the damage at high temperature can be divided into the pure fatigue damage and the equivalent fatigue damage from creep. During the damage accumulation process, the elementary percentage of the equivalent fatigue damage increment is proportional to that of the creep damage increment, and the creep damage is converted to the equivalent fatigue damage. Moreover, combined with a multiaxial cyclic counting method, a life prediction method is developed based on the proposed creep–fatigue damage cumulative model. In the developed life prediction method, the effects of nonproportional hardening on the fatigue and creep damages are considered, and the influence of mean stress on damage is also taken into account. The thermomechanical fatigue experimental data for thin‐walled tubular specimen of superalloy GH4169 under multiaxial constant amplitude and variable amplitude loadings were used to verify the proposed model. The results showed that the proposed method can obtain satisfactory life prediction results.     

How to reduce the duration of multiaxial fatigue tests under proportional service loadings

This paper deals with a technique to transform a multiaxial stress and strain-time sequence (in service recorded) in a simplified sequence. This simplified sequence is shorter than the original one and equivalent in terms of damage and lifetime: the number of simplified sequences to crack initiation is equal to the number of original sequences. The proposal is based on an energy threshold, below which no micro-crack can initiate or grow in the material. This technique was validated with real loading sequences recorded by strain gauges pasted on a car suspension arm. Fatigue tests were carried out on smooth specimens made of spheroidal graphite cast iron loaded in bending, in torsion and in combined bending and torsion. Experimental fatigue lives under the original sequence and under the simplified one are in very good correlation. Fatigue test duration is reduced up to a factor of 10 for the severe stress–strain sequences tested in this study.     

An application of the implicit gradient method to welded structures under multiaxial fatigue loadings

This paper deals with the problem of fatigue strength assessment of welded joints subjected to multiaxial loading. Three-dimensional solid modelling and linear elastic stress analysis, by means of numerical methods, are used to investigate the local stress field at weld toes and roots, geometrically regarded as sharp notches. Starting from the stress field obtained from a linear elastic analysis and taking advantage of the so-called implicit gradient approximation, an effective stress index connected with the material strength is calculated. In particular, there will be an investigation into the possibility of applying the implicit gradient approach to welded structures, under both uniaxial and multiaxial loading conditions, by introducing a multiaxial criterion into the implicit gradient framework. The multiaxial criterion consists of an improvement of the well-established Crossland-like criteria. It will deal with multiaxiality caused by external loadings as well as multiaxial stress fields caused by severe stress raisers. In order to validate the devised approach, theoretical fatigue damage estimations are compared with experimental data. In particular, the proposed approach is applied to a series of applicative examples taken from scientific literature and related to welded joints subjected to uniaxial or in-phase multiaxial fatigue loading.     

A fatigue damage model of composite materials

The mechanical properties of composite materials degrade progressively with the increasing of the number of cyclic loadings. Based on the stiffness degradation rule of composites, a phenomenological fatigue damage model is presented in this paper, which contains two material parameters. They are proportional to the fatigue life of materials and inversely proportional to the fatigue loading level. Thirteen sets of experimental data of composite stiffness degradation were employed to verify the presented model, and the statistical results showed that this model is capable of describing the damage evolution of composite materials. The characteristics of damage development and accumulation of composite materials subjected to variable loading were studied in this paper. Four sets of two-level loading experimental data were cited to verify the damage model, and the results showed that the predicted life is in good agreement with the experimental ones.     

Comparative study of multiaxial fatigue damage models for ductile structural steels and brittle materials

Fatigue damage prediction under a general multiaxial service loading consists of three main steps: multiaxial cycle counting, damage evaluation for an identified cycle (or reversal), and damage accumulations. The accuracy of fatigue life predictions depends on all the above steps. This paper reviews the evolutions of various multiaxial fatigue damage models, a comparative study is conducted about the physical basis, the computational efficiency, and the application range of the approaches. Based on the comparative studies, a new procedure is proposed to evaluate fatigue damage under general multiaxial random loading, which uses the Wang and Brown´s multiaxial cycle counting method for identifying cycles (or reversals), the modified procedure of the minimum circumscribed ellipse (MCE) approach for fatigue damage evaluation for an identified cycle (or reversal), and the Miner´s linear damage law for fatigue damage accumulations. By comparisons of the predicted life results with experimental results and with other approaches, it is shown that the proposed procedure is very efficient and suitable for computer aided structural optimization against fatigue.