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.     

Threshold stress intensity factor and crack growth rate prediction under mixed-mode loading

A new mixed-mode threshold stress intensity factor is developed using a critical plane-based multiaxial fatigue theory and the Kitagawa diagram. The proposed method is a nominal approach since the fatigue damage is evaluated using remote stresses acting on a cracked component rather than stresses near the crack tip. An equivalent stress intensity factor defined on the critical plane is proposed to predict the fatigue crack growth rate under mixed-mode loading. A major advantage is the applicability of the proposed model to many different materials, which experience either shear or tensile dominated crack growth. The proposed model is also capable to nonproportional fatigue loading since the critical plane explicitly considers the influence of the load path. The predictions of the proposed fatigue crack growth model under constant amplitude loading are compared with a wide range of fatigue results in the literature. Excellent agreements between experimental data and model predictions are observed.     

Crack initiation and growth path under multiaxial fatigue loading in structural steels

In real engineering components and structures many accidental failures occur due to unexpected or additional loadings, such as additional bending or torsion. There are many factors influencing the fatigue crack paths, such as the material type (microstructure), structural geometry and loading path. It is widely believed that fatigue crack nucleation and early crack growth are caused by cyclic plasticity. This paper studies the effects of multiaxial loading paths on the cyclic deformation behaviour, crack initiation and crack path. Three types of structural steels are studied: Ck45, medium carbon steel, 42CrMo4, low alloy steel and the AISI 303 stainless steel. Four biaxial loading paths were applied in the tests to observe the effects of multiaxial loading paths on the additional hardening, fatigue crack initiation and crack propagation orientation. Fractographic analyses of the plane orientations of crack initiation and propagation were carried out by optical microscope and SEM approaches. It is shown that these materials have different crack orientations under the same loading path, due to their different cyclic plasticity behaviour and different sensitivity to non-proportional loading. Theoretical predictions of the damage plane were conducted using the critical plane approaches, either based on stress analysis or strain analysis (Findley, Smith–Watson–Topper, Fatemi–Socie, Wang–Brown–Miller, etc). Comparisons of the predicted crack orientation based on the critical plane approaches with the experimental observations for the wide range of loading paths and the three structural materials are shown and discussed. Results show the applicability of the critical plane approaches to predict the fatigue life and crack initial orientation in structural steels.     

Multiaxial fatigue and life prediction of elastomeric components

Elastomeric components have wide usage in many industries. The typical service loading for most of these components is variable amplitude and multiaxial. In this study a general methodology for life prediction of elastomeric components under these typical loading conditions was developed and illustrated for a passenger vehicle cradle mount. Crack initiation life prediction was performed using different damage criteria. The methodology was validated with component testing under different loading conditions including constant and variable amplitude in-phase and out-of-phase axial–torsion experiments. The optimum method for crack initiation life prediction for complex multiaxial variable amplitude loading was found to be a critical plane approach based on maximum normal strain plane and damage quantification by cracking energy density on that plane. Rainflow cycle counting method and Miner’s linear damage rule were used for predicting fatigue life under variable amplitude loadings. The fracture mechanics approach was used for total fatigue life prediction of the component based on specimen crack growth data and FE simulation results. Total fatigue life prediction results showed good agreement with experiments for all of the loading conditions considered.     

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.     

Multiaxial fatigue and failure analysis of helical compression springs

Multiaxial fatigue criteria are applied to the analysis of helical compression springs. The critical plane approaches, Fatemi–Socie and Wang–Brown, and the Coffin–Manson method based on shear deformation, were used to predict fatigue lives of the springs under constant amplitude loading. Experimental fatigue lives are compared with the multiaxial fatigue criteria predictions. The stress analysis was carried out in the finite element code ANSYS, and the multiaxial fatigue study was performed using the fatigue software nCode. A failure analysis was conducted in order to determine the fatigue crack initiation point and a comparison of that location with the most damaged zone predicted by the numerical analysis is made. The Fatemi–Socie critical plane approach gives a good prediction of fatigue life. While the Wang–Brown criterion overestimates spring fatigue life, the Coffin–Mason model gives conservative results.     

Kurzrisswachstum bei mehrachsig nichtproportionaler Beanspruchung

Short fatigue crack growth under multiaxial nonproportional loading Initiation and short fatigue crack growth have been investigated under nonproportional cyclic loading. A critical plane approach based on fracture mechanics is used for modelling the fatigue process. A Paris‐type crack growth law, formulated using the effective cyclic J‐integral as crack driving force parameter, is integrated to give crack growth curves. Crack opening stresses and strains are calculated with approximation equations. Jiang's plasticity model is used to predict the stress‐strain path. The good agreement between model and real damage evolution is shown comparing experimentally determined crack growth curves, crack orientations, and life curves.     

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.     

On the expression of fatigue crack initiation life considering the factor of overloading effect

In the present study attempts are made to give an expression of the fatigue crack initiation life of notched elements with the consideration of overloading effects. This expression may be used to predict the fatigue crack initiation life of notched element under variable amplitude loading. Experimental work on LY12CZ alloy show that the test results of fatigue crack initiation life after tension overloading can be well fitted by the formula developed before for fatigue crack initiation life. Tension overloading increases the fatigue crack initiation threshold but has no effect on the coefficient of the resistance to fatigue crack initiation. The overloading ratio has no markable effect on crack initiation life. The increase of the crack initiation threshold results in the increase of crack initiation life, in particular, in long life range. The same results are also obtained by reanalysing some existing test results of overloading effect on crack initiation life given in literature. Consequently, the expression of the fatigue crack initiation life can be obtained by the method given in this paper. However, the overloading stress should be determined from the theoretical stress concentration factor of notched element and the maximum nominal stress in the load spectrum of elements.     

A structural stress‐based critical plane method for multiaxial fatigue life estimation in welded joints

This paper aims at proposing a new fatigue life estimation model that is preferably adapted to welded joints subjected to multiaxial loading. First, a mesh‐size insensitive structural stress is defined that enables to characterize the stress concentration effect appropriately. Second, the multiaxial stress state and loading path influence are taken into account in the lifetime prediction model by adopting a suitable critical plane method, originally proposed by Carpinteri and co‐authors. Experimental verification is conducted for a given welded joint geometry under different loading conditions, including uniaxial, torsional and multiaxial loads. The reliability and effectiveness of the new method are validated through substantive fatigue testing data.     

FATIGUE LIFE PREDICTION OF NOTCHED COMPOSITE COMPONENTS

Abstract— The local stress/strain approach has been used to predict the fatigue lives of notched composite components. The method was based on a microstress analysis and the application of a multiaxial fatigue parameter incorporating the alternating strain components on the critical plane. This parameter was able to correlate the fatigue lives obtained under a variety of multiaxial loading and geometrical configurations, enabling a generalized fatigue life curve to be determined on the basis of limited experimental data.
The ability of the multiaxial fatigue parameter to relate the fatigue behaviour of composites was illustrated by predicting the locations of crack initiation sites in a unidirectional silicon carbide fibre reinforced titanium plate containing a circular hole tested under constant amplitude cyclic loading. The same approach was also successfully employed to predict the fatigue lives of graphite reinforced epoxy composite tubes with circular holes tested under several combinations of cyclic tension and torsion.     

2A12铝合金的多轴加载疲劳行为

采用SDN100/1000电液伺服拉扭复合疲劳试验机对2A12铝合金进行多关键参数的多轴疲劳性能研究,通过对断口的微观分析探究疲劳失效机理。结果表明:等效应力加载条件下,随拉扭相位差的增加疲劳寿命降低,0°相位差下断面裂纹源区能观察到轮胎状、鱼骨状以及钟乳石状的特殊形貌,裂纹扩展区存在二次裂纹和模糊的疲劳条带;分别改变拉、扭平均应力,多轴疲劳寿命均降低,裂纹源区能看到白色絮状的氧化物,瞬断区存在二次裂纹和剪切型韧窝;不同加载波形条件下,正弦波对应最长的多轴疲劳寿命,三角波次之,方波时最短且体现出最大的结构耗能。低-高两级加载条件下,材料产生"锻炼效应"。     

Fatigue life analysis and predictions for NR and SBR under variable amplitude and multiaxial loading conditions

This paper investigates the effects of variable amplitude loading conditions on the fatigue lives of multiaxial rubber specimens. Two filled rubber materials were used and compared to investigate the effects of strain-crystallization on crack development NR, which strain crystallizes, and SBR, which does not. The applicability of Miner’s linear damage rule for predicting fatigue lives of variable amplitude tests in rubber and the use of both scalar and plane-specific equivalence parameters to characterize fatigue life results were also investigated. A fatigue life prediction approach that utilizes normal strain to find the critical plane and the cracking energy density on that plane to determine fatigue life is introduced and compared to other approaches. The effects of load sequence and temperature on fatigue life, as well as differences in fatigue lives using both stiffness and critical crack length failure criteria are discussed.     

On the interaction of normal and shear stresses in multiaxial fatigue damage

One of the important issues in assessing multiaxial fatigue damage is interactions between different components of stress such as normal and shear stresses. The present study investigated this interaction effect on the fatigue behavior of materials with shear failure mode when subjected to multiaxial loading conditions. A method is introduced to model this interaction based on the idea that two types of influence are caused by the normal stress acting on the critical plane orientation. These two types of influence are affecting roughness induced closure, as well as fluctuating normal stress which affects the growth of small cracks in mode II. Shear‐based critical plane damage models which use normal stress as a secondary input, such as FS damage model, could then use the summation of these terms. In order to investigate the effect of the method, constant amplitude load paths with different levels of interaction between the normal and shear stresses, as well as variable amplitude tests with histories both taken from service loading conditions and generated using random numbers were designed for an experimental program. The proposed method was observed to result in improved fatigue life estimations where significant interactions between normal and shear stresses exist.     

Multiaxial fatigue life assessment of welded structures

Welded structures, such as welded pressure vessel components subjected to multiaxial cyclic loading, are particularly susceptible to fatigue damage. In this paper, a new path-length-based effective stress range is proposed to assess the fatigue life of weld joints under multiaxial fatigue loading. The path-length measure, a function of both normal and shear components on a critical crack plane, has a solid root in classic fracture mechanics and its application is validated by correlating nominal fatigue data including pure-bending, pure-torsion, in-phase, and out-of-phase loading. Path-Dependent Maximum Range (PDMR), a unique general-purpose fatigue life assessment package for multiaxial variable-amplitude loading, is introduced in this paper. Finally, the application of PDMR to multiaxial fatigue life assessment of complex loading cases is also discussed.     

Short crack approach for multiaxial fatigue assessment

A significant part of the fatigue life is spent during short crack growth. Therefore, modelling of short fatigue crack growth offers an opportunity to improve the accuracy of numerical life assessment. Besides stating some general remarks on the short crack approach itself and on multiaxial fatigue criteria, a short crack growth based fatigue life prediction approach for multiaxial non‐proportional loading is presented. This approach accounts for the geometrical size effect by considering the geometry correction functions for semi‐elliptical surface cracks in inhomogeneous gradient stress fields. The geometrical size effect is becoming significant for notch radii smaller than four times the defined technical crack size. Additionally, life influencing factors due to the statistical size effect have been taken into account. The comparison of calculated and experimentally observed fatigue lives of shouldered shafts made of S460N with notch radii of 0.2 to 4.0 mm under non‐proportional tension and torsion loading yields a satisfying accuracy.     

Biaxial fatigue for proportional and non‐proportional loading paths

In order to study the use of a local approach to predict crack‐initiation life on notches in mechanical components under multiaxial fatigue conditions, the study of the local cyclic elasto‐plastic behaviour and the selection of an appropriate multiaxial fatigue model are essential steps in fatigue‐life prediction. The evolution of stress–strain fields from the initial state to the stabilized state depends on the material type, loading amplitude and loading paths. A series of biaxial tension–compression tests with static or cyclic torsion were carried out on a biaxial servo‐hydraulic testing machine. Specimens were made of an alloy steel 42CrMo4 quenched and tempered. The shear stress relaxations of the cyclic tension–compression with a steady torsion angle were observed for various loading levels. Finite element analyses were used to simulate the cyclic behaviour and good agreement was found. Based on the local stabilized cyclic elastic–plastic stress–strain responses, the strain‐based multiaxial fatigue damage parameters were applied and correlated with the experimentally obtained lives. As a comparison, a stress‐invariant‐based approach with the minimum circumscribed ellipse (MCE) approach for evaluating the effective shear stress amplitude was also applied for fatigue life prediction. The comparison showed that both the equivalent strain range and the stress‐invariant parameter with non‐proportional factors correlated well with the experimental results obtained in this study.     

Multiaxial high-cycle fatigue criterion considering crack initiation and non-propagation

A new criterion for multiaxial high-cycle fatigue limit is proposed using two parameters: one governing crack initiation and the other governing initial crack growth. The axial fatigue limit and the true fracture strength are used as the material properties required in estimations. The prediction accuracies using conventional criteria and the proposed criterion were compared using known data about fatigue limits under different loading conditions. The comparison was made for the effects of phase difference, mean stress, and the combination of phase difference and mean stress. The estimation error of the proposed criterion was approximately 10%, which is better than that of the other criteria used for comparison.     

Low-cycle fatigue model of damage accumulation - The strain approach

The paper presents a model of damage accumulation designed to analyse fatigue life of structural elements exploited in multiaxial, non-proportional, low-cycle loading conditions. The discussed approach consists of two calculation blocs. In the first bloc the components of stress and strain tensor are determined. This module, in which Mroz’s multisurface model was used, contains constitutive relations and the law of kinematic hardening. The second bloc contains the dependencies which determine the growth of anisotropic measure of damage accumulation (associated with the physical plane) and crack initiation criterion. The growth of the damage accumulation measure was associated with the loading damage accumulation function and the increment of non-dilatational plastic strain on the physical plane. It was assumed that crack initiation occurs when stress or a measure of damage accumulation on any physical plane reaches critical values.     

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.