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.     

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.     

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.     

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.     

On the estimation of the material fatigue properties required to perform the multiaxial fatigue assessment

To accurately perform the fatigue assessment of engineering components subjected to in‐service multiaxial fatigue loading, the adopted design criterion must properly be calibrated, the used information usually being the fatigue strength under both pure uniaxial and pure torsional fatigue loading. Because of the complex fatigue response of metallic materials to multiaxial loading paths, the only reliable way to generate the necessary pieces of calibration information is by running appropriate experiments. Unfortunately, because of a lack of both time and resources, very often, structural engineers are requested to perform the multiaxial fatigue assessment by guessing the necessary fatigue properties. In this complex scenario, initially, the available empirical rules suitable for estimating fatigue strength under both pure axial and pure torsional fatigue loading are reviewed in detail. Subsequently, several experimental results taken from the literature and generated by testing metallic materials under a variety of proportional and non‐proportional multiaxial loading paths are used to investigate the way such empirical rules affect the accuracy in estimating fatigue strength, the damage extent being evaluated according to the modified Wöhler curve method. Such a systematic validation exercise allowed us to prove that under proportional loading (with both zero and non‐zero mean stresses), an adequate margin of safety can be reached even when the necessary calibration information is directly estimated from the material ultimate tensile strength. On the contrary, in the presence of non‐proportional loading, the use of the empirical rules reviewed in the present paper can result, under particular circumstances, in a non‐conservative fatigue design.     

A new model for describing a stable cyclic stress–strain relationship under non-proportional loading based on activation state of slip systems

This paper proposes a new simple model for cyclic incremental plasticity based on activation states of slip systems describing stable cyclic stress–strain relationships under non‐proportional loading. In the model, the magnitude and the direction of incremental plastic strain are estimated by (1+αf_NP) and Q , respectively. Here, α is the constant related to the dependence of material on additional hardening and f_NP the intensity factor expressing the severity of non‐proportional loading. Q is the second‐order tensor describing the activation states of slip systems in polycrystalline metals and is given by the calculation using a virtual specimen. The model was examined by application to the prediction of the stable cyclic stress–strain relationship in extensive non‐proportional low cycle fatigue tests for type 304 stainless steel and 6061 aluminium alloy. The simulated results showed that the model gave a satisfactory prediction of the stable cyclic stress–strain relationship under complex non‐proportional multiaxial loadings for the two materials.     

The choice of cyclic plasticity models in fatigue life assessment of 304 and 1045 steel alloys based on the critical plane-energy fatigue damage approach

The present study intends to examine various cyclic plasticity models in fatigue assessment of 304 and 1045 steels based on the critical plane-energy damage approach developed earlier. Cyclic plasticity models of linear hardening, nonlinear, multi-surface, and two-surface were chosen to study fatigue damage and life of materials under proportional and non-proportional loading conditions. The effect of additional hardening induced due to non-proportional loading in 1045 steel and particularly in 304 steel was further evaluated as different constitutive models were employed. In the present study, the plasticity models were calibrated by the equivalent cyclic stress–strain curves. The merits of the models were then investigated to assess materials deformation under proportional and non-proportional loading conditions. Under non-proportional loading, the cyclic plasticity models were found to be highly dependent upon the employed hardening rule as well as the materials properties/coefficients.The stress and strain components calculated through constitutive laws were then used as input parameters to evaluate fatigue damage and assess the fatigue life of materials based on the critical plane-energy approach.The calculated values of stress components based on constitutive laws resulted in a good agreement with those of experimentally obtained under various loading paths of proportional and non-proportional conditions in 1045 steels. In 304 steel, the calculated stress components were however found in good agreement when plasticity models were employed for proportional loading conditions. Under non-proportional loading, the application of the multi-surface plasticity model in conjunction with the fatigue damage approach resulted in more reasonable results as compared with other plasticity models. This can be attributed to the motion of the yield surface in deviatoric stress space in the multi-surface model encountering additional hardening effect through estimated higher stress values under non-proportional loading conditions.Predicted fatigue lives based on the critical plane-energy damage approach showed such range of agreements as ±1.05–±3.0 factors in 1045 and 304 steels as compared with experimental life data when various constitutive plasticity models were employed.     

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.     

一种基于临界平面法的多轴疲劳寿命预测模型

在多轴交变应力作用下,由于非比例循环附加强化效应导致疲劳寿命降低。针对这一问题,以薄壁圆管疲劳试件为研究对象,在分析临界平面上剪应变和正应变随相位角变化特征的基础上,引入了一个新的有效循环变量———临界平面上的等效应力,提出了一种新的多轴疲劳预测模型。新的损伤参量不含经验常数,便于工程实际的运用。通过和铝合金7075-T651多轴疲劳实验数据比较,结果表明,所提出的多轴寿命预测模型具有更好的预测精度,适用于比例与非比例加载条件。     

Analytical and experimental studies on fatigue crack path under complex multi-axial loading

In real engineering components and structures, many accidental failures are due to unexpected or additional loadings, such as additional bending or torsion, etc. Fractographical analyses of the failure surface and the crack orientation are helpful for identifying the effects of the non‐proportional multi‐axial loading. There are many factors that influence fatigue crack paths. This paper studies the effects of multi‐axial loading path on the crack path. Two kinds of materials were studied and compared in this paper: AISI 303 stainless steel and 42CrMo4 steel. Experiments were conducted in a biaxial testing machine INSTRON 8800. Six different biaxial loading paths were selected and applied in the tests to observe the effects of multi‐axial loading paths on the additional hardening, fatigue life and the crack propagation orientation. Fractographic analyses of the plane orientations of crack initiation and propagation were carried out by optical microscope and SEM approaches. It was shown that the two materials studied had 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 made using the critical plane approaches such as the Brown–Miller, the Findley, the Wang–Brown, the Fatemi–Socie, the Smith–Watson–Topper and the Liu's criteria. Comparisons of the predicted orientation of the damage plane with the experimental observations show that the critical plane models give satisfactory predictions for the orientations of early crack growth of the 42CrMo4 steel, but less accurate predictions were obtained for the AISI 303 stainless steel. This observation appears to show that the applicability of the fatigue models is dependent on the material type and multi‐axial microstructure characteristics.     

Prediction methods of fatigue critical point for notched components under multiaxial fatigue loading

Two methods based on local stress responses are proposed to locate fatigue critical point of metallic notched components under non‐proportional loading. The points on the notch edge maintain a state of uniaxial stress even when the far‐field fatigue loading is multiaxial. The point bearing the maximum stress amplitude is recognized as fatigue critical point under the condition of non‐mean stress; otherwise, the Goodman's empirical formula is adopted to amend mean stress effect prior to the determination of fatigue critical point. Furthermore, the uniaxial stress state can be treated as a special multiaxial stress state. The Susmel's fatigue damage parameter is employed to evaluate the fatigue damage of these points on the notch edge. Multiaxial fatigue tests on thin‐walled round tube notched specimens made of GH4169 nickel‐base alloy and 2297 aluminium‐lithium alloy are carried out to verify the two methods. The prediction results show that both the stress amplitude method and the Susmel's parameter method can accurately locate the fatigue critical point of metallic notched components under multiaxial fatigue loading.     

Enhanced assessment of ageing phenomena in steel structures based on materials data and non‐destructive testing

The increasing amount of ageing civil steel infrastructure requests an enhanced assessment of this infrastructure in terms of determining its residual fatigue life in a more realistic way than this has been done in the past. Often the relevant materials data for cyclic loading of such an ageing infrastructure is not available and its retrieval turns out to be relatively cumbersome bearing the urgency in data availability and continuous cost pressure in mind. This article addresses different approaches and techniques on how materials data for cyclic loading can be obtained at a fraction of the effort compared to state‐of‐the‐art techniques, considering load increase tests, non‐destructive testing techniques and finally even a stepped bar specimen allowing a complete set of materials data (stress‐strain behaviour and stress‐ and strain‐life curve) to be obtained with a single specimen in the end only. Options for ’digitizing’ materials data evaluation are discussed and some prospect on application of those novel approaches and techniques in damage accumulation assessments on real steel infrastructure is provided.     

Fatigue life assessment under a complex multiaxial load history: an approach based on damage mechanics

In order to assess the fatigue behaviour of structural components under a complex (cyclic or random) multiaxial stress history, methods based on damage mechanics concepts can be employed. In this paper, a model for fatigue damage evaluation in the case of an arbitrary multiaxial loading history is proposed by using an endurance function which allows us to determine the damage accumulation up to the final failure of the material. By introducing an evolution equation for the endurance function, the final collapse can be assumed to occur when the damage D is complete, that is when D reaches the unity. The parameters of this model, which adopts the stress invariants and the deviatoric stress invariants to quantify the damage phenomenon, are determined through a Genetic Algorithm once experimental data on the fatigue behaviour of the material being examined are known for some complex stress histories. With respect to traditional approaches to multiaxial fatigue assessment, the proposed model presents the following advantages: (1) the evaluation of a critical plane is not necessary; (2) no cycle counting algorithm to determine the fatigue life is required, because it considers the progressive damage process during the fatigue load history; (3) the model can be applied to any kind of stress history (uniaxial cyclic loading, multiaxial in‐phase or out‐of‐phase cyclic loading, uniaxial or multiaxial random loading).     

Cyclic strain rate effect on martensitic transformation and fatigue behaviour of an austenitic stainless steel

In this study, the effect of strain rate on the cyclic behaviour of 304L stainless steel is investigated to unveil the complex interrelationship between martensitic phase transformation, secondary hardening, cyclic deformation and fatigue behaviour of this alloy. A series of uniaxial strain controlled fatigue tests with varying cyclic strain rates were conducted at zero and non‐zero mean strain conditions. Secondary hardening was found to be closely related to the volume fraction of strain‐induced martensite which was affected by adiabatic heating due to increasing cyclic strain rates. Tests with lower secondary hardening rates maintained lower stress amplitudes during cyclic loading which resulted in longer fatigue lives for similar strain amplitudes. Fatigue resistance of 304L stainless steel was found to be more sensitive to changes in strain rate than the presence of mean strain. The mean strain effect was minimal due to the significant mean stress relaxation in this material.     

Simulation des Mikrorisswachstums unter Schwingbeanspruchung. Teil 2: Simulationsergebnisse – Einfluss des Spannungszustandes und Reihenfolgeeffekte

Simulation of fatigue micro crack growth. Part 2: Results of simulation – influence of stress state and sequence effects In part one the modelling of micro crack growth due to alternating loading has been presented. Simulation results for tension/compression, torsion and proportional multiaxial loading, the scatter of the simulated lifetimes to a macroscopic crack length of 500 μm as well as the influence of the density of crack seeds and the grain size have been presented. In part two the influence of the stress state under proportional and non‐proportional loading is examined. Additionally the sequence effect of High‐Low and Low‐High as well as consecutive load sequences will be discussed. The comparison of the simulation results to experimental results shows that the influences of multiaxial loading and sequences can be simulated qualitatively correctly. The simplifications of the modelling have been to be considered. If the length of the maximum crack is interpreted as a measure of the damage, it can be concluded that the damage accumulation is non linear and non continuous. The main proportion of lifetime from the crack seed to the macro crack is contributed in the phase in which the length of the maximum micro crack comes close to the size of the grain size.     

Investigation of fatigue damage accumulation in steels using the Fourier transform of the structure image

Studies of fatigue strength of steels 45 and Kh18N10T and the structure changes during cyclic loading are reported. The fatigue damage accumulation was evaluated by the statistical processing of microstructure images. The value of the ellipse eccentricity in the Fourier transform of the microstructure is used as a parameter characterizing the material state, while the damage accumulation factor, which is integral and invariant with respect to the amplitude of cyclic loading and cycle stress ratio, is used as a quantitative characteristic of changes in the material structure under cyclic loading. In the state prior to the fatigue fracture, the material damage accumulation factor attains a specific value irrespective of the stress amplitude and the cycle stress ratio, and serves as the criterion of fracture under cyclic loading.     

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.     

Modelling of fatigue damage progression and life of CFRP laminates

A progressive fatigue damage model has been developed for predicting damage accumulation and life of carbon fibre‐reinforced plastics (CFRP) laminates with arbitrary geometry and stacking sequence subjected to constant amplitude cyclic loading. The model comprises the components of stress analysis, fatigue failure analysis and fatigue material property degradation. Stress analysis of the composite laminate was performed by creating a three‐dimensional finite element model in the ANSYS FE code. Fatigue failure analysis was performed by using a set of Hashin‐type failure criteria and the Ye‐delamination criterion. Two types of material property degradations on the basis of element stiffness and strength were applied: a sudden degradation because of sudden failure detected by the fatigue failure criteria and a gradual degradation because of the nature of cyclic loading, which is driven by the increased number of cycles. The gradual degradation of the composite material was modelled by using functions relating the residual stiffness and residual strength of the laminate to the number of cycles. All model components have been programmed in the ANSYS FE code in order to create a user‐friendly macro‐routine. The model has been applied in two different quasi‐isotropic CFRP laminates subjected to tension–compression (T–C) fatigue and the predictions of fatigue life and damage accumulation as a function of the number of cycles were compared with experimental data available in the literature. A very good agreement was obtained.     

Ratcheting‐fatigue behaviour of bainite 2.25Cr1MoV steel with tensile and compressed hold loading at 455°C

The ratcheting behaviour of a bainite 2.25Cr1MoV steel was studied with various hold periods at 455°C. Particular attention was paid to the effect of stress hold on whole‐life ratcheting deformation, fatigue life, and failure mechanism. Results indicate that longer peak hold periods stimulate a faster accumulation of ratcheting strain by contribution of creep strain, while double hold at peak and valley stress has an even stronger influence. Creep strains produced in peak and valley hold periods are noticeable and result in higher cyclic strain amplitudes. Dimples and acquired defects are found in failed specimen by microstructure observation, and their number and size increase under creep‐fatigue loading. Enlarged cyclic strain amplitude and material deterioration caused by creep lead to fatigue life reduction under creep‐fatigue loading. A life prediction model suitable for asymmetric cycling is proposed based on the linear damage summation rule.     

Low-cycle fatigue of 1Cr–18Ni–9Ti stainless steel and related weld metal under axial, torsional and 90° out-of-phase loading

The fatigue behaviour of base metal and weld joints of 1Cr–18Ni–9Ti stainless steel has been studied under uniaxial, torsional and 90° out‐of‐phase loading. A significant degree of additional hardening is found for both base metal and weld metal under 90° out‐of‐phase loading. Both base metal and weld metal have the same cyclic stable stress–strain relationship under torsional cyclic loading and 90° out‐of‐phase cyclic loading. Base metal exhibits higher cyclic stress than weld metal under uniaxial loading, and Young's modulus and yield stress of weld metal are smaller than those of base metal. Weld metal exhibited lower fatigue resistance than base metal under uniaxial and torsional loading, but no significant difference was found between the two materials under 90° out‐of‐phase loading. A large scatter of fatigue life is observed for weld metal, perhaps because of heterogeneity of the microstructure. The Wang–Brown (WB) damage parameter and the Fatemi–Socie (FS) damage parameter, both based on the shear critical plane approach, were evaluated relative to the fatigue data obtained.