Simulation of cyclic stress/strain evolutions for multiaxial fatigue life prediction

This study deals with simulation for cyclic stress/strain evolutions and redistributions, and evaluation of fatigue parameters suitable for estimating fatigue lives under multiaxial loadings. The local cyclic elastic–plastic stress–strain responses were analyzed using the incremental plasticity procedures of ABAQUS finite element code for both smooth and notched specimens made of three materials: a medium carbon steel in the normalized condition, an alloy steel quenched and tempered and a stainless steel, respectively. Emphasis is on the studying of ‘intelligent’ material behaviors to resist fracture, such as stress redistribution and relaxation through plastic deformations, etc. For experimental verifications, a series of tests of biaxial low cycle fatigue composed of tension/compression with static and cyclic torsion were carried out on a biaxial servo-hydraulic testing machine (Instron 8800). Different multiaxial loading paths were used to verify their effects on the additional cyclic hardening. The comparisons between numerical simulations and experimental observations show that the FEM simulations allow better understanding on the evolutions of the local cyclic stress–strain and it is shown that strong interactions exist between the most stressed material element and its neighboring material elements in the plastic deformations and stress redistributions. Based on the local cyclic elastic–plastic stress–strain responses, the energy-based multiaxial fatigue damage parameters are applied to correlating the experimentally obtained lives. Improved correlations between the predicted and the experimental results are shown. It is concluded that the improvement of fatigue life prediction depends not only on the fatigue damage models, but also on the accurate evaluations of the cyclic elasto-plastic stress/strain responses.     

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.     

Fatigue behaviour of tubular AlMgSi welded specimens subjected to bending–torsion loading

This paper is concerned with an experimental and numerical study of the fatigue behaviour of tubular AlMgSi welded specimens subjected to biaxial loading. In‐phase torsion–bending fatigue tests under constant amplitude loading were performed in a standard servo‐hydraulic machine with a suitable gripping system. Some tests in pure rotating bending with and without steady torsion were also performed. The influence of stress ratio R and bending–torsion stress ratio were analysed. Correlation of the fatigue lives was done using the distortion energy hypothesis (DEH), based on the local stresses and strains. The applicability of the local strain approach method to the prediction of the fatigue life of the welded tubular specimens was also investigated. Static torsion has only a slight detrimental influence on fatigue strength. The DEH (von Mises criterion) based on local stresses in the weld toes was shown to satisfactorily correlate fatigue lives for in‐phase multiaxial stress–strain states. The stress–strain field intensity predictions were shown to have less scatter and are in better agreement with the experimental results than the equivalent strain energy density approach.     

在多轴载荷下45钢的循环特性

通过多轴疲劳试验，研究了在多轴加载条件下45钢的循环特性变化规律，分析了非比例附加强化、多轴循环软化/硬化特性及疲劳寿命对加载路径参数的依赖性，结果表明，相位角主要影响非比例附加强化程度，幅值比主要影响多轴循环软化/硬化特性，二者都影响多轴疲劳寿命。     

EFFECT OF BIAXIAL MEAN STRESS ON CYCLIC STRESS-STRAIN RESPONSE AND BEHAVIOUR OF SHORT FATIGUE CRACKS IN A HIGH STRENGTH SPRING STEEL

Abstract— Biaxial fatigue tests were conducted on a high strength spring steel using hour-glass shaped smooth specimens. Four types of loading system were employed, i.e. (a) fully reversed cyclic torsion, (b) uniaxial push—pull, (c) fully reversed torsion with a superimposed axial static tension or compression stress, and (d) uniaxial push—pull with a superimposed static torque, to evaluate the effects of mean stress on the cyclic stress—strain response and short fatigue crack growth behaviour. Experimental results indicate that a biaxial mean stress has no apparent influence on the stress—strain response in torsion, however a superimposed tensile mean stress was detrimental to torsional fatigue strength. Similarly a superimposed static shear stress reduced the push—pull fatigue lifetime. A compressive mean stress was seen to be beneficial to torsion fatigue life. The role of mean stress on fatigue lifetime, under mixed mode loading, was investigated through experimental observations and theoretical analyses of short crack initiation and propagation. Using a plastic replication technique the effects of biaxial mean stress on both Stage I (mode II) and Stage II (mode I) short cracks were evaluated and analysed in detail. A two stage biaxial short fatigue crack growth model incorporating the influence of mean stress was subsequently developed and applied to correlate data of crack growth rate and fatigue life.     

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.     

Multiaxial fatigue of rubber: Part II: experimental observations and life predictions

Fatigue experiments were conducted with an axial‐torsion specimen covering a wide range of stretch biaxiality and a range of fatigue lives between 10³ and 2 × 10⁶ cycles. These experiments include combined torsion–compression, pure torsion, combined torsion–tension and pure axial tension. Both in‐phase and out‐of‐phase combinations of axial and torsion loading were considered. The multiaxial fatigue experiments described provide empirical evidence from which an understanding of the mechanics of the fatigue process in rubber can be developed. Each of the four equivalence parameters described in Part I has been applied to the axial‐torsion fatigue experiments described in this paper (Part II). These results provide the basis for an analysis of the effects of multiaxial loading on fatigue life, and an assessment of the degree to which the various equivalence parameters are able to rationalize the results in a unified way. For the combined axial and shear strain histories in this study, the maximum principal strain criterion gave the best correlation to fatigue life. Strain energy density gave the worst correlation. The cracking energy density criterion was generally found to give good correlation of fatigue crack nucleation lives from combined axial‐torsion tests. Because it provides a plane‐specific analysis, this criterion appears to be particularly well suited for use in crack nucleation analyses of multiaxial strain histories.     

Comparative study on biaxial low-cycle fatigue behaviour of three structural steels

In this study the uniaxial/biaxial low‐cycle fatigue behaviour of three structural steels (Ck45 normalized steel, 42CrMo4 quenched and tempered steel and AISI 303 stainless steel) are studied, evaluated and compared. Two parameters are considered for estimating non‐proportional fatigue lives: the coefficient of additional hardening and the factor of non‐proportionality. A series of tests of uniaxial/biaxial low‐cycle fatigue composed of tension/compression with cyclic torsion were carried out on a biaxial servo‐hydraulic testing machine. Several loading paths were carried out, including proportional and non‐proportional ones, in order to verify the additional hardening caused by different loading paths. The experiments showed that the three materials studied have very different additional hardening behaviour. Generally, the transient process from the initial loading cycle to stabilized loading cycle occurs in a few cycles. The stabilized cyclic stress/strain parameters are controlling parameters for fatigue damage. A factor of non‐proportionality of the loading paths is evaluated based on the Minimum Circumscribed Ellipse approach. It is shown that the microstructure has a great influence on the additional hardening and the hardening effect is dependent on the loading path and also the intensity of the loading.     

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.     

Multiaxial fatigue life prediction method in the ground vehicle industry

The extensive progress which has been made in the multiaxial fatigue area over the past 5 to 10 years has allowed wider application of the multiaxial fatigue method in component durability design in the ground vehicle industry. The method adopts the long established local strain–life approach and includes several new features. (1) A three-dimensional cyclic stress–strain model, used to simulate the elastic–plastic material behavior under complicated loadings. (2) The critical plane approach, which requires the fatigue analysis to be performed on various potential failure planes before determining the lowest fatigue life. (3) A biaxial damage criterion, to better quantify fatigue damage under various loading conditions. (4) A multiaxial Neuber equivalencing technique, used to estimate, from the elastic finite element stress results, the multiaxial stress and strain history of plastically deformed notch areas. This paper examines the application of the above features to the fatigue analyses of three generic service/test histories: a constant amplitude (baseline) test history, a history directly recorded by strain gages mounted on the critical location of a structural component, and a loading history recorded in multichannels for a complex structure.     

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.     

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.     

Notch fatigue life prediction considering nonproportionality of local loading path under multiaxial cyclic loading

An innovative numerical methodology is presented for fatigue lifetime estimation of notched bodies experiencing multiaxial cyclic loadings. In the presented methodology, an evaluation approach of the local nonproportionality factor F for notched specimens, which defines F as the ratio of the pseudoshear strain range at 45° to the maximum shear plane and the maximum shear strain range, is proposed and discussed deeply. The proposed evaluation method is incorporated into the material cyclic stress‐strain equation for purpose of describing the nonproportional hardening behavior for some material. The comparison between multiaxial elastic‐plastic finite element analysis (FEA) and experimentally measured strains for S460N steel notched specimens shows that the proposed nonproportionality factor estimation method is effective. Subsequently, the notch stresses and strains calculated utilizing multiaxial elastic‐plastic FEA are used as input data to the critical plane‐based fatigue life prediction methodology. The prediction results are satisfactory for the 7050‐T7451 aluminum alloy and GH4169 superalloy notched specimens under multiaxial cyclic loading.     

Selection of the critical plane orientation in two-parameter multiaxial fatigue failure criterion under combined bending and torsion

The present paper is focused on engineering application of the algorithm of fatigue life calculation under multiaxial fatigue loading. For that reason, simple two-parameter multiaxial fatigue failure criterion is proposed. The criterion is based on the normal and shear stresses on the critical plane. Experimental results obtained under multiaxial proportional, non-proportional cyclic loading and variable-amplitude bending and torsion were used to verify the proposed two-parameter criterion and other well-known multiaxial fatigue criteria. Elastic–plastic behaviour of the bulk material was taken into account in calculation of the stress/strain distribution across the specimen cross-section. It is shown that the proposed two-parameter multiaxial fatigue failure criterion gives the best correlation between the experimental and calculated fatigue lives.     

Fatigue life evaluation of tension‐compression asymmetric material using local stress–strain method

In this paper, the low‐cycle fatigue characteristics of cold‐drawn steel were investigated under strain‐controlled uniaxial fatigue load. Cyclic softening was observed throughout fatigue life except for the initial relatively short period which exhibited cyclic hardening. Positive mean stress was found under fully reversed strain loading, indicating that there was a significant cyclic asymmetry. A modified local stress–strain method was proposed to estimate fatigue life of notched tension‐compression asymmetric material. In order to verify this method, fatigue experiments on two kinds of notched specimens with different notch radius were carried out under constant and block load spectrum. It was found that the modified local stress–strain method was more accurate than the traditional ones, the maximum relative error between predicted and experimental fatigue life was less than 6%.     

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.     

Cyclic stress–strain response and crystal plasticity finite element analysis of AISI 9310 steel in biaxial fatigue loading

There are still many gaps in the research on the multiaxial fatigue failure mechanism of the gear shaft. In this paper, cyclic stress–strain response and biaxial fatigue damage characteristics of gear steel AISI 9310 were investigated. The specimens showed obvious cyclic softening characteristics at all phase angles, and the softening rate was directly associated with the initiation and propagation of cracks. The fractographies at different phase angles revealed that the specimens under out-of-phase loading suffered fatigue failure caused by a single crack source on the surface, while the fatigue crack under in-phase loading was gathered together by the propagation of different crack sources. Finally, the established crystal plastic finite element model showed a good prediction of the plastic strain energy density at different phase angles, and the maximum error was 13.03%. Furthermore, a biaxial fatigue life prediction method was proposed, with a maximum error of 39.5%.     

Corrosion fatigue behaviour of 304 stainless steel under proportional and non‐proportional multiaxial loading condition

Corrosion fatigue and electrochemical tests under proportional loading and non‐proportional loading were conducted on 304 stainless steel in 0.63 mol L^?1 NaCl solution at room temperature. Two biaxial loading paths were applied to study the effect of proportional loading and non‐proportional loading on corrosion fatigue behaviour. Surface and fractographic observations of multiaxial corrosion fatigue specimens were carried out by scanning electron microscopy. It was shown that proportional loading had a more significant effect on the occurrence of local corrosion compared with non‐proportional loading because the continuous rotation of the principal stress plane under non‐proportional loading inhibits the pit formation.     

Multiaxial fatigue of quenched and tempered U2 steel: Testing and fatigue life prediction

Tension‐compression, tension‐tension, torsional, and 90° out‐of‐phase axial‐torsional fatigue tests were performed on a quenched and tempered U2 steel. All tests were conducted under force/torque control because macroscopic plastic strains were insignificant in the life range of interest (from 10⁴ to 2 × 10⁶ loading cycles). Stress‐based versions of the Fatemi‐Socie critical plane parameter and of the Smith‐Watson‐Topper parameter with a critical plane interpretation were evaluated using the experimental data. The Smith‐Watson‐Topper parameter was not able to correlate the test data. The Fatemi‐Socie method correlated most of the test data within factor‐of‐three boundaries. A modified Crossland invariant‐based parameter made of two interaction rules between the shear stress amplitude and the maximum hydrostatic stress, and of a definition of shear stress amplitude based on the maximum prismatic hull method, yielded fatigue life estimates in reasonable agreement with the experimental observations.     

Behaviour of short cracks in alloy 800HT under biaxial fatigue

Biaxial in phase fatigue tests were carried out on thin walled tube specimens of alloy 800HT at ambient temperature. The loading modes included tension, torsion, and combined tension—torsion with a tensile/shear plastic strain range ratio Δ?p/Δγp = 3^1/2. The influence of effective strain amplitudes and biaxiality on the initial growth of fatigue cracks was investigated using the replica technique. The results indicated that the loading conditions strongly affected the growth rates of short cracks. In torsion the cracks grew significantly more slowly than under axial or biaxial loading. A mean tensile stress perpendicular to the shear crack promoted its growth and reduced the fatigue life. The growth of the cracks could be described by the ΔJ integral for axial and biaxial loading; the integration predicted the fatigue life under axial and biaxial loading correctly. However, significantly conservative lifetime predictions were obtained for pure torsional loading since ΔJ does not include crack closure and crack surface rubbing.

MST/3234