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.     

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.     

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 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.     

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.     

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.     

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.     

Comparison of HCF life prediction methods based on different critical planes under multiaxial variable amplitude loading

High‐cycle fatigue life prediction methods based on different critical planes, including the maximum shear stress (MSS) plane, the weighted average shear stress plane and the Maximum Variance shear stress plane, are compared by two multiaxial cycle counting methods, i.e. the main and auxiliary channels (MAC) counting and the relative equivalent stress counting. A modified damage model is used to calculate the multiaxial fatigue damage. Compared with the experimental lives for 7075‐T651 aluminium alloy, the predicted results show that the MSS method together with MAC counting is suitable for the multiaxial fatigue life prediction.     

Validating generality of recently developed critical plane model for fatigue life assessments using multiaxial test database on seventeen different materials

The present studies are aimed at validation of a newly developed critical plane model with respect to large variety of engineering materials used for different applications. This newly developed model has been recently reported by present authors. To strengthen general applicability of this model, multiaxial test database consisting of a wide variety of multiaxial loading paths have been considered. The strain paths include pure axial, pure torsion, in‐phase axial‐torsion, out‐of‐phase axial‐torsion with phase shift angles varying from 30° to 180° having sine/trapezoidal/triangular strain waveforms, with/without mean axial/shear strains and asynchronous axial‐torsion strain paths of different frequency ratios etc. The materials covered in present study are mainly categorized as ferrous and nonferrous alloys. In ferrous alloy category, material grades from plain carbon steel (mild steel, 16MnR, SA333 Gr. 6, E235 and E355), low‐alloy steel (1Cr‐Mo‐V and S460 N) and austenitic stainless steel (SS304, SS316L and SS347) have been considered. In nonferrous alloy category, aluminium alloys (2024T3‐Al, 7075T651‐Al, and PA38‐T6‐Al), titanium (pure titanium and TC4 alloy), cobalt base super‐alloy (Haynes 188), and nickel alloy (Inconel‐718) have been considered. The predicted and test fatigue lives are found in good agreement for all these materials and complex multiaxial loading paths.     

An improved critical plane and cycle counting method to assess damage under variable amplitude multiaxial fatigue loading

The plane with the maximum variance of the resolved shear stress is taken as the critical plane. Two algorithms are used along with the maximum variance method (MVM) to determine the orientation of the critical plane. The maximum variance of the normal stress on the potential critical planes is calculated to determine the one experiencing the maximum extent of fatigue damage. A new multiaxial cycle counting method is proposed to count cycles on the critical plane. The modified Wöhler curve method is used to assess fatigue damage. About 200 experimental results were collected from the technical literature to validate the approaches being proposed. The results show that the improved design technique being proposed is successful in assessing fatigue damage under variable amplitude multiaxial cyclic loading.     

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.     

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.     

Criteria of multiaxial random fatigue based on stress,strain and energy parameters of damage in the critical plane

In this paper generalized criteria of multiaxial random fatigue based on stress, strain and strain energy density parameters in the critical plane have been discussed. The proposed criteria reduce multiaxial state of stress to the equivalent uniaxial tension–compression or alternating bending. Relations between the coefficients occurring in the considered criteria have been derived. Thus, it is possible to take into account fatigue properties of materials under simple loading states during determination of the multiaxial fatigue life. Presented models have successfully correlated fatigue lives of cast iron GGG40 and steel 18G2A specimens under constant amplitude in‐phase and out‐of‐phase loadings including different frequencies.     

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.     

Prediction of crack initiation plane direction in high‐cycle multiaxial fatigue with in‐phase and out‐of‐phase loading

A new method for predicting crack plane direction in high‐cycle multiaxial fatigue is proposed. This method considers material properties and loading conditions. Two situations are considered: (i) in‐phase loading, where the crack plane direction only depends on the loading condition and material properties have little influence on it, and (ii) out‐of‐phase loading, where the crack plane direction is affected by both loading conditions and material properties. The prediction accuracy is assessed by comparison with several experimental results, including different loading conditions and materials. The results show that the proposed method provides a good prediction capability for these experiments.     

A critical plane-strain energy density criterion for multiaxial low-cycle fatigue life under non-proportional loading

A series of multiaxial low-cycle fatigue experiments was performed on 45 steel under non-proportional loading. The present evaluations of multiaxial low-cycle fatigue life were systematically analysed. A combined energy density and critical plane concept is proposed that considers different failure mechanisms for a shear-type failure and a tensile-type failure, and from which different damage parameters for the critical plane-strain energy density are proposed. For tensile-type failures in material 45 steel and shear-type failures in material 42CrMo steel, the new damage parameters permit a good prediction for multiaxial low-cycle fatigue failure under non-proportional loading. The currently used critical plane models are a special and simple form of the new model.     

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.     

A non-local theory applied to high cycle multiaxial fatigue

ABSTRACT The stress gradient effect on the fatigue limit is an important factor which has to be taken into account for an efficient transfer of fatigue data from laboratory tests to design of industrial components. A short review of some multiaxial high cycle fatigue criteria considering this effect is presented. On the basis of the two local mesoscopic approaches of Papadopoulos, two new non‐local high cycle multiaxial fatigue criteria are developed. These proposals are based on the concept of volume influencing fatigue crack initiation. Their predictions are compared with experimental multiaxial fatigue data on four materials (a mild steel, two high strength steels and a spheroidal graphite cast iron). The accuracy of the two local Papadopoulos criteria and of the non‐local proposals are compared and discussed, together with the physical interpretation of the threshold defining the volume influencing fatigue crack initiation.     

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.     

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.