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.     

Monotonic and Cyclic Deformations of Case‐Hardened Steels Including Residual Stress Effects

Abstract: Monotonic and cyclic deformations of case‐hardened steel specimens under axial loading were investigated experimentally and analytically. A finite element (FE) model for the case‐hardened specimens was constructed to study multiaxial stresses due to different plastic flow behaviour between the case and the core, as well as to evaluate residual stress relaxation and redistribution subsequent to cyclic loading. The multiaxial stress is shown to increase the effective stress on the surface, and, therefore, unfavourable to yielding or fatigue crack nucleation. The residual stresses are shown to relax or redistribute, even in the elastic‐behaving region, when any part of a case‐hardened specimen or component undergoes plastic deformation. Multi‐layer models were used to analyse and predict monotonic and cyclic deformation behaviours of the case‐hardened specimen based on the core and case material properties, and the results are compared with the experimental as well as FE model results. The predicted monotonic stress–strain curves were close to the experimental curves, but the predicted cyclic stress–strain curves were higher than the experimental curves.     

Numerical analysis of low cycle fatigue for welded joints considering welding residual stress and plastic damage under combined bending and local compressive loads

The numerical analysis of low cycle fatigue of HTS‐A steel welded joints under combined bending and local compressive loads are implemented using the damage mechanics approach. First, a finite element numerical simulation of the welding process is employed to extract the welding residual stresses, which are then imported as initial stresses in the subsequent fatigue analysis. Second, a multiaxial fatigue damage model including damage coupled elasto‐plastic constitutive equations and plastic damage evolution formulation is applied to evaluate the mechanical degradation of the material under biaxial fatigue loads. Further, the fatigue lives of the HTS‐A steel welded joints are computed and compared with the experimental results from literature. A series of predicted load‐life curves clearly illustrates the variation of fatigue lives along with the combined loadings. Finally, the effects of local compression on accumulated plastic strain and fatigue damage are studied in detail. It is revealed that the local compression induces a damage competition between two critical zones.     

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.     

Numerical modeling and simulation of wheel radial fatigue tests

A computational methodology is proposed for fatigue damage assessment of metallic automotive components and its application is presented with numerical simulations of wheel radial fatigue tests. The technique is based on the local strain approach in conjunction with linear elastic FE stress analyses. The stress–strain response at a material point is computed with a cyclic plasticity model coupled with a notch stress–strain approximation scheme. Critical plane damage parameters are used in the characterization of fatigue damage under multiaxial loading conditions. All computational modules are implemented into a software tool and used in the simulation of radial fatigue tests of a disk-type truck wheel. In numerical models, the wheel rotation is included with a nonproportional cyclic loading history, and dynamic effects due to wheel–tire interaction are neglected. The fatigue lives and potential crack locations are predicted using effective strain, Smith–Watson–Topper and Fatemi–Socie parameters using computed stress–strain histories. Three-different test conditions are simulated, and both number of test cycles and crack initiation sites are estimated. Comparisons with the actual tests proved the applicability of the proposed approach.     

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.     

Deformation behaviour,short crack growth and fatigue livesunder multiaxial nonproportional loading

Experimental results of a research project on short crack growth under multiaxial nonproportional loading are presented. Fatigue lives, crack growth curves and the deformation behaviour of hollow tube specimens and notched specimens were investigated under combined tension and torsion loading. The results served as basis for the development of a cyclic plasticity model [Döring R, Hoffmeyer J, Vormwald M, Seeger T. A plasticity model for calculating stress–strain sequences under multiaxial nonproportional cyclic loading. In: Comput Mater Sci. 28(3–4);2003:587–96; Döring R, Hoffmeyer J, Seeger T, Vormwald M. Constitutive modelling of nonproportional hardening, cyclic hardening and ratchetting. In: Proceedings of the seventh international conference on biaxial/multiaxial fatigue and fracture, DVM, Berlin; 2004. p. 291–6; Hoffmeyer J. Anrisslebensdauervorhersage bei mehrachsiger Beanspruchung auf Basis des Kurzrisskonzepts. PhD-Thesis, TU Darmstadt; 2004.] and a short crack model [Hoffmeyer J. Anrisslebensdauervorhersage bei mehrachsiger Beanspruchung auf Basis des Kurzrisskonzepts. PhD-Thesis, TU Darmstadt; 2004; Döring R, Hoffmeyer J, Seeger T, Vormwald M. Fatigue lifetime prediction based on a short crack growth model for multiaxial nonproportional loading. In: Proceedings of the seventh international conference on biaxial and multiaxial fatigue and fracture, DVM, Berlin; 2004. p. 253–8].Stress–strain paths including nonproportional hardening and experimental fatigue lives of the unnotched specimens under different loading cases are discussed and compared with calculations. Load-time-sequences were in-phase, 45° and 90° out-of-phase loading with constant and variable amplitudes, torsion without and with superimposed static normal stress, and strain paths like box, butterfly, diamond and cross path. For the notched specimens fatigue lives under 0° and 90° out-of-phase loading are compared with calculations based on finite element results and the short crack model. During some tests the initiation, growth and orientation of short cracks was studied using the plastic replica technique.     

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%.     

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.     

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.     

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.     

On the anelasticity and fatigue fracture entropy in high-cycle metal fatigue

The concept of thermodynamic entropy generation in a degradation process is utilized to study the high-cycle fatigue of medium carbon steel 1018. Uniaxial tension–compression fatigue tests are carried out with tubular dogbone specimens at different stress levels and loading frequencies. It is shown that a phase lag between the stress and the strain caused by the internal friction includes a considerable amount of non-damaging anelastic energy in a hysteresis loop when the amplitude of cyclic load is substantially smaller than the yield strength of the material. A methodology is proposed to determine the anelastic energy associated with metal fatigue at a stress level lower than the yield strength of a material. Finite element simulations are carried out with a 3-D model of the specimen to determine the validity of the proposed methodology. The evolutions of the plastic strain energy and temperature are discussed and utilized to calculate the entropy accumulation. It is shown that the accumulation of entropy generation in the HCF of the material—beginning with a pristine specimen and ending at fatigue fracture—is nearly constant within the experimental and loading conditions considered. The concept of tallying entropy is useful for the prediction of the fatigue life evolution of a material undergoing cyclic loading.     

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.     

Material characterization of SS 316 in low-cycle fatigue loading

This study deals with simulation of low-cycle fatigue (LCF), followed by evaluation of fatigue parameters, which would be suitable for estimating fatigue lives under uniaxial loading. The cyclic elastic–plastic stress–strain responses were analyzed using the incremental plasticity procedures. Finite-element (FE) simulation in elastic–plastic regime was carried out in FE package ABAQUS. Emphasis has been laid on calibration of SS 316 stainless steel for LCF behavior. For experimental verifications, a series of low-cycle fatigue tests were conducted using smooth, cylindrical specimens under strain-controlled, fully reversed condition in INSTRON UTM (Universal Testing Machine) with 8,800 controller at room temperature. The comparisons between numerical simulations and experimental observations reveal the matching to be satisfactory in engineering sense. Based on the cyclic elastic–plastic stress–strain response, both from experiments and simulation, loop areas, computed for various strain amplitude, have been identified as fatigue damage parameter. Fatigue strain life curves are generated for fatigue life prediction using Coffin–Manson relation, Smith–Watson–Topper model, and plastic energy dissipated per cycle (loop area). Life prediction for LCF has been found out to be almost identical for all these three criteria and correlations between predicted and 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 elastic–plastic stress/strain responses.     

Fatigue life estimation of bolt clamped and interference fitted-bolt clamped double shear lap joints using multiaxial fatigue criteria

In this paper seven different multiaxial fatigue criteria based on stress, strain and energy were employed to estimate the fatigue lives of double shear lap joint specimens of aluminum 2024-T3 with bolt clamped and interference fitted-bolt clamped fastener holes. Detailed finite element (FE) simulations were conducted to obtain the stress and strain distributions in the joint to be used to as basic data in estimating the fatigue lives using multiaxial fatigue criteria. The estimated lives were compared with available experimental fatigue test results to investigate the capability of the criteria in predicting the fatigue lives. The results showed that the accuracy of life estimation for any criterion varies for different batches of specimens and applied load ranges. However, including the fatigue crack growth life can improve the fatigue estimation life and reduce the absolute error of multiaxial fatigue criteria.     

A total strain energy density model of metal fatigue

In this paper a total cyclic strain energy density equal to the sum of plastic strain energy and tensile elastic strain energy densities is used as a damage parameter for metal fatigue. It is shown that the total cyclic strain energy density is a consistent damage parameter for low- and high-cycle fatigue in the conditions of both uniaxial and multiaxial cyclic loading. This parameter is also consistent with the concept of crack initiation and subsequent propagation. The approach described here is applicable for both ideal Masing and non-Masing material response. The predictions of the proposed criterion are compared with the experimental data for medium carbon steel St5. The comparison has shown good agreement.Published inProblemy Prochnosti, Nos. 1–2, pp. 53–64, January–February, 1995.     

Continuous fatigue damage prediction of a rubber fibre composite structure using multiaxial energy‐based approach

This paper details an advanced method of continuous fatigue damage prediction of rubber fibre composite structures. A novel multiaxial energy‐based approach incorporating a mean stress correction is presented and also used to predict the fatigue life of a commercial vehicle air spring. The variations of elastic strain and complementary energies are joined to form the energy damage parameter. Material parameter α is introduced to adapt for any observed mean stress effect as well as being able to reproduce the well‐known Smith‐Watson‐Topper criterion. Since integration to calculate the energies is simplified, the approach can be employed regardless of the complexity of the thermo‐mechanical load history. Several numerical simulations and experimental tests were performed in order to obtain the required stress‐strain tensors and the corresponding fatigue lives, respectively. In simulations, the rubber material of the air spring was simulated as nonlinear elastic. The mean stress parameter α , which controls the influence of the mean stress on fatigue life, was adjusted with respect to those energy life curves obtained experimentally. The predicted fatigue life and the location of failure are in very good agreement with experimental observations.     

Einfluß von last- und verformungsgesteuerten mehrachsigen Beanspruchungen auf die Anrißlebensdauer

Influence of load- and deformation-controlled multiaxial tests on fatigue life to crack initiation Generally, areas of components with notches or geometrical transitions are critical because of the resulting stress/strain concentrations. In these areas due to the stress-gradients and constraint local deformations are displacement controlled even if the material's yield stress is exceeded, as long as the deformations are below the structural yield point. Therefore, load controlled tests in the elasto-plastic region with unnotched specimens from ductile materials under combined axial loading and torsion are not suitable for the interpretation of component's behaviour because of uncontrolled local deformations. Thus, the influence of multiaxial stress/strain states on the fatigue behaviour of a component under elasto-plastic deformations can be determined reliably with unnotched specimens only by deformation controlled tests, if cyclic creep is not expected in critical areas.     

弹塑性随机有限元在低周疲劳分析中的应用

推导了交变载荷下弹塑性随机有限元的迭代格式,计算了局部多轴应力应变的随机响应。迭代格式中,针对复杂的交变载荷,采用运动强化模型反映塑性变形引起的各向异性和包辛格效应,运用Jhansale模型描述材料的瞬态应力应变关系。弹塑性有限元分析,克服了以往近似方法只能计算单轴局部应力应变响应的缺陷,为多轴疲劳分析奠定了基础。考虑零构件的随机因素,将随机有限元方法引入到交变载荷下弹塑性有限元的迭代格式中,得到局部应力应变的随机响应,为低周疲劳可靠性分析提供了更精确的依据。MontCarlo模拟结果证实了提出的弹塑性随机有限元方法是可靠的。     

Fatigue behavior of an epoxy polymer subjected to cyclic shear loading

Strain-range-controlled fully reversed cyclic shearing fatigue tests have been performed on thin-walled tubular specimens made of an epoxy polymer. The engineering shear strain was measured by a non-contact real-time strain measurement and control system recently developed in our lab. The synchronized stress–strain data were recorded by the system for full lives of the specimens. Therefore evolutions of mechanical properties of the epoxy polymer during fatigue process could be analyzed based on the retrieved stress–strain data. It was found that life data of the shearing fatigue tests were well correlated with the uniaxial fatigue test data of the material by using the suggested stress-, strain- or strain-energy-density-based multiaxial fatigue criteria.