An improved multiaxial high‐cycle fatigue criterion based on critical plane approach

Several groups of fatigue damage parameters are discussed and then an improved multiaxial high‐cycle fatigue criterion based on critical plane defined by the plane of maximum shear stress range is presented in this paper. A compromising solution to consider the mean normal stress acting on the critical plane is also proposed. The new fatigue criterion extends the range of metallic materials which is valid for the ratio 1.25 < f_?1/t_?1 < 2. The predictions based on the presented model show a good agreement with test data.     

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.     

Fatigue behaviour of a box-welded joint under biaxial cyclic loading: effects of biaxial load range ratio and cyclic compressive loads in the lateral direction

ABSTRACT The biaxial fatigue of a steel plate (JIS SM400B) having a box‐welded (wrap‐around) joint was experimentally studied. Special concerns were focused on the effects of the biaxial load range ratio and compressive cyclic loading in the lateral direction. The direction of fatigue crack propagation under biaxial cyclic tensile loading, which has a phase difference of π, changed according to the biaxial load range ratio, R_xy = ΔP_x/ΔP_y. When R_xy was less than 0.56, fatigue cracks propagated along the toe of the weld in the x‐direction because the principal tensile stress range Δσ_y at that location exceeded the orthogonal value Δσ_x at the box‐weld toe. The fatigue lives in biaxial tests related well to the data from uniaxial tests when invoking the Δσ₅ criterion. However, the location and direction of Δσ₅ should be chosen according to the R_xy value and the failure crack direction. An increase in Δσ₅, as induced by the Poisson's ratio effect from either the out‐of‐phase tensile loading or the in‐phase compressive loading in the y‐direction, leads to an increase in fatigue damage (decrease in fatigue resistance or specifically a faster crack propagation rate), and this effect can be successfully estimated from uniaxial fatigue test data.     

Fatigue of vulcanized natural rubber under proportional and non‐proportional loading

Two natural rubber (NR) compounds of hardness shore A 60 and 70 with 10 different biaxial displacement/twist paths were investigated using an axisymmetric cylindrical hollow dumbbell specimen. The effects of the proportional and non‐proportional loading modes on the fatigue life are discussed. In total, 52 fatigue test results are reported with fatigue life results of 3,918 to 488,000 cycles. The effect of the channel phase on the fatigue life is discussed.     

A convex hull‐based approach for multiaxial high‐cycle fatigue criteria

Design methods against multiaxial high‐cycle fatigue require the formulation of appropriate criteria that differ in the definition of critical measures introduced to quantify damage, as the amplitude of shear stress. The present paper proposes a novel approach to compute the amplitude of shear stress in multiaxial high‐cycle fatigue. The approach is based on the computation of the convex hull enclosing the stress history under investigation and is validated on proportional and non‐proportional paths in several dimensions and for different materials. High accuracy is achieved when compared with alternative methods from the literature.     

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.     

Investigation of the multiaxial fatigue behaviour of 316 stainless steel based on critical plane method

In this work, the multiaxial behaviour of 316 stainless steel is studied under the lens of critical plane approach. A series of experiments were developed on dog bone–shaped hollow cylindrical specimens made of type 316 stainless steel. Five different loading conditions were assessed with (a) only tensile axial stress, (b) only hoop stress, (c) combination of axial and hoop stresses with square shape, (d) combination of tensile axial and hoop stresses with L shape, and (e) combination of compressive axial and hoop stresses with L shape. The fatigue analysis is performed with four different critical plane theories, namely, Wang‐Brown, Fatemi‐Socie, Liu I, and Liu II. The efficiency of all four theories is studied in terms of the accuracy of their life predictions and crack failure plane angle. The best fatigue life predictions were obtained with Liu II model, and the best predictions of the failure plane were obtained with Liu I model.     

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.     

Low‐cycle fatigue of 316L stainless steel under proportional and nonproportional loadings

This paper discusses low‐cycle fatigue characteristics of 316L stainless steel under proportional and nonproportional loadings. Tension–torsion multiaxial low‐cycle fatigue tests were performed using five strain paths. Additional hardening was observed under nonproportional loadings and was more significant in tests with larger nonproportionality. Mises equivalent strain, Smith–Watson–Topper, Fatemi–Socie, Kandil–Brown–Miller and nonproportional strain parameters were applied to the experimental data to evaluate the multiaxial low‐cycle fatigue damage. The applicability of the damage laws to practical design was discussed.     

Comparative analysis of three thermal fatigue experiments

This paper presents an analysis of the ability of different criteria to predict fatigue crack initiation under thermal loading. More precisely the predictions of the number of cycles to crack initiation are compared with experimental results obtained using five different fatigue criteria in three types of thermal fatigue tests (namely the FAT3D, JRC and SPLASH test campaigns). This analysis has revealed that:

• ? The conventional criteria based on equivalent strain variation substantially overestimate the lifespan of a structure subjected to thermal loading.
• ? A criterion making account for loading multiaxiality is required to estimate thermal fatigue life.

Three of the criteria studied give satisfactory results: the Zamrik criterion, the Park and Nelson criterion and a criterion taking hydrostatic pressure into consideration proposed by Amiable et al. The latter should be preferred for the accuracy of its results and the Zamrik criterion for its simplicity.     

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.     

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.     

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.     

Effect of hardness on multiaxial fatigue behaviour and some simple approximations for steels

Constant-amplitude in-phase and 90° out-of-phase axial-torsional fatigue tests were conducted on tubular specimens made from a medium-carbon steel with three hardness levels obtained from normalizing, quenching and tempering and induction hardening to find the effect of hardness on multiaxial fatigue behaviour. In addition, the same loadings were applied on the normalized solid specimens to investigate the effect of specimen geometry on multiaxial fatigue life. Similar fatigue life variation as a function of hardness was found for in-phase and out-of-phase loadings, with higher ductility beneficial in low-cycle fatigue (LCF) and higher strength beneficial in high-cycle fatigue (HCF). Multiaxial fatigue data were satisfactorily correlated for all hardness levels with the Fatemi–Socie parameter. Furthermore, in order to predict multiaxial fatigue life of steels in the absence of any fatigue data, the Roessle–Fatemi hardness method was used. Multiaxial fatigue lives were predicted fairly accurately using the Fatemi–Socie multiaxial model based on only the hardness level of the material. The applicability of the prediction method based on hardness was also examined for Inconel 718 and a stainless steel under a wide range of loading conditions. The great majority of the observed fatigue lives were found to be in good agreement with predicted lives.     

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.     

Evaluation of fatigue life for titanium alloy TC4 under variable amplitude multiaxial loading

Fatigue tests under variable amplitude multiaxial loading were conducted on titanium alloy TC4 tubular specimens. A method to estimate the fatigue life under variable amplitude multiaxial loading has been proposed. Multiaxial fatigue parameter based on Wu–Hu–Song approach and rainflow cycle counting and Miner–Palmgren rule were applied in this method. The capability of fatigue life prediction for the proposed method was checked against the test data of TC4 alloy under variable amplitude multiaxial loading. The prediction results are all within a factor of two scatter band of the test results.     

A weight function-critical plane approach for low-cycle fatigue under variable amplitude multiaxial loading

Low‐cycle fatigue data of type 304 stainless steel obtained under axial‐torsional loading of variable amplitudes are analyzed using four multiaxial fatigue parameters: SWT, KBM, FS and LKN. Rainflow cycle counting and Morrow's plastic work interaction rule are used to calculate fatigue damage. The performance of a fatigue model is dependent on the fatigue parameter, the critical plane and the damage accumulation rule employed in the model. The conservatism and non‐conservatism of predicted lives are examined for some combinations of these variables. A new critical plane called the weight function‐critical plane is introduced for variable amplitude loading. This approach is found to improve the KBM‐based life predictions.     

Room-temperature low-cycle fatigue behaviour of Ti-27Al-15Nb alloy

Low-cycle fatigue (LCF) behaviour of the alloy Ti-27Al-15Nb, in (α ₂+B2) heat-treated condition was studied in total axial strain control mode at different total strain amplitudes (Δɛ ₁/2) from ±0·65 to ±1·0% and room temperature. While there was little hardening of the material at the lowest strain amplitude (Δɛ _t/2: ±0·65%), pronounced hardening was observed at the higher strain amplitudes (Δɛ _t/2⩾0·83%). The cyclic stress, at high strain amplitudes, continuously increased from the beginning till fracture of the specimens. The LCF resistance of the material was found to be low and this was due to its poor ductility at room temperature. Dual slope was observed in the Coffin-Manson plot, with less slope of the upper segment than that of the lower one, as observed in several alloys. The fracture behaviour pointed to brittleness and faceted features were observed.     

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 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.