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.     

Development of new cyclic plasticity model for 304LN stainless steel through simulation and experimental investigation

Cyclic plastic deformation characteristics of 304LN stainless steel material have been studied with two proposed cyclic plasticity models. Model MM-I has been proposed to improve the simulation of ratcheting phenomenon and model MM-II has the capability to simulate both cyclic hardening and softening characteristics of the material at various strain ranges. In the present paper, strain controlled simulations are performed with constant, increasing and decreasing strain amplitudes to verify the influences of loading schemes on cyclic plasticity behaviors through simulations and experiments. It is observed that the material 304LN exhibits non Masing characteristics under cyclic plastic deformation. The measured deviation from Masing is well established from the simulation as well as from experiment. Simulation result shows that the assumption of only isotropic hardening is unable to explain the hardening or softening characteristics of the material in low cycle fatigue test. The introduction of memory stress based cyclic hardening coefficient and an exponentially varying ratcheting parameter in the recall term of kinematic hardening rule, have resulted in exceptional improvement in the ratcheting simulation with the proposed model, MM-II. Plastic energy, shape and size of the hysteresis loops are additionally used to verify the nature of cyclic plasticity deformations. Ratcheting test and simulation have been performed to estimate the accumulated plastic strain with different mean and amplitude stresses. In the proposed model MM-I, a new proposition is incorporated for yield stress variation based on the memory stress of loading history along with the evolution of ratcheting parameter with an exponential function of plastic strain. These formulations lead to better realization of ratcheting rate in the transient cycles for all loading schemes. Effect of mean stress on the plastic energy is examined by the simulation model, MM-I. Finally, the micro structural investigation from transmission electronic microscopy is used to correlate the macroscopic and microscopic non Masing behavior of the material.     

A finite element algorithm to study creep cracks based on the creep hardening surface

This work addresses finite element (FE) modelling of creep cracks under reversed and cyclic loads in steels. A constitutive model based on the creep hardening surface developed by Murakami and Ohno has been selected for this purpose. This model is particularly accurate for describing creep under reversed and cyclic loads and requires no additional material constants. An FE algorithm for this model has been derived and implemented into a research code FVP. The algorithm is verified by comparing the numerical predictions with closed form solutions for simple geometries and loading configurations. FE predictions are compared with experimental data for a stationary crack in a compact tension specimen. The stress and strain fields in the vicinity of a crack under a sustained load are compared with those for the intermediate unloading case. Several integral fracture parameters are investigated as to their appropriateness for describing creep cracks under reversed and cyclic loads.     

Prediction of crack growth in a nickel-based superalloy under fatigue-oxidation conditions

Prediction of oxidation-assisted crack growth has been carried out for a nickel-based superalloy at elevated temperature based on finite element analyses of oxygen diffusion, coupled with viscoplastic deformation, near a fatigue crack tip. The material constitutive behaviour, implemented in the finite element code ABAQUS via a user-defined material subroutine (UMAT), was described by a unified viscoplastic model with non-linear kinematic and isotropic hardening rules. Diffusion of oxygen was assumed to be controlled by two parameters, the oxygen diffusivity and deformation-assisted oxygen mobility. Low frequencies and superimposed hold periods at peak loads significantly enhanced oxygen concentration near the crack tip. Evaluations of near-tip deformation and oxygen concentration were performed, which led to the construction of a failure envelop for crack growth based on the consideration of both oxygen concentration and accumulated inelastic strain near the crack tip. The failure envelop was then utilised to predict crack growth rates in a compact tension (CT) specimen under fatigue-oxidation conditions for selected loading ranges, frequencies and dwell periods. The predictions from the fatigue-oxidation failure envelop compared well with the experimental results for triangular and dwell loading waveforms, with marked improvements achieved over those predicted from the viscoplastic model alone. The fatigue-oxidation predictions also agree well with the experimental results for slow-fast loading waveforms, but not for fast-slow waveforms where the effect of oxidation is much reduced.     

Lateral behavior of concrete under uniaxial compressive cyclic loading

In reinforced concrete structures under seismic loading, concrete is subjected to compressive cyclic stress. Although cyclic stress–strain response has been described before, the cyclic behavior of strains in the direction orthogonal to loading has not been characterized yet. Such behavior can be of great importance for evaluating the efficiency of the confinement under cyclic loading. For this purpose an experimental program on cylindrical specimens of concrete strength from 35 to 80 MPa subjected to uniaxial cyclic compression was carried out. Stress versus longitudinal and lateral strains curves have been obtained both for the hardening and softening branches under monotonic and cyclic loading. Governing parameters of the lateral behavior are identified and correlated to describe the response of the lateral strain. Additionally, an analytical model to obtain the lateral deformations of concrete under cyclic uniaxial compression has been formulated and verified experimentally. Finally, some examples are presented in order to illustrate the applicability of the proposed model and its possible incorporation into a 3D constitutive cyclic model.     

考虑应变率影响的厚壁筒残余应力场分析

本文针对弹塑性拉压循环加卸载条件下，不同的应变率（１０－４－１０－２ｓ－１）变化，对高强钢（ＰＣｒＮｉ３ＭｏＶ）材料的屈服应力、应变硬化参数和反向屈服应力等参量的影响进行了实验研究，提出了便于理论计算的简化弹塑性本构模型，并假设拉屈服应力与压屈服应力的差值不随应变率的不同而发生变化，这一假定与实验结果相符合，且便于工程计算。针对厚壁筒自紧加工工艺的残余应力场分析问题，用本文提出的模型对厚壁筒在四种不同的应变率条件下进行自紧加工时残余应力场的变化及不同的自紧效果进行了详细的分析和比较，并提出了改进工艺过程和提高自紧效果的建设性意见。     

The application of a three-surface kinematic hardening model to repeated loading of thinly surfaced pavements

This paper examines the application of kinematic hardening to modelling the behaviour of thinly surfaced pavements dominated by the clay subgrade. An existing three-surface kinematic hardening model has been found to predict too much shear strain and therefore too much settlement under repeated loading for certain stress conditions. Under some stress conditions, the model also predicts an accumulation of negative shear strain with increasing number of cycles of load, leading to a pavement rut depth which decreases with increasing numbers of cycles. Consequently, a new model has been developed by modifying the flow rule and hardening modulus. The new model requires 10 parameters, most of which can be determined directly from simple triaxial tests. The new model is validated against drained cyclic triaxial results in order to determine model parameters, and it is shown that the new model predicts better the accumulation of shear strain and the problem of accumulation of negative shear strain is eliminated. This new model is applied to the repeated loading of a thinly surfaced pavement and is seen to predict realistic resilient and permanent deformations.This revised version was published online in September 2005 with a corrected sequence of authors.     

Applying viscoplastic constitutive models to predict ratcheting behavior of sintered nanosilver lap-shear joint

A series of displacement-controlled tests were conducted for sintered nanosilver lap-shear joints at different loading rates and temperatures. The relationship between force and displacement was studied. It was found that higher loading rate or lower temperature caused higher stress–strain response of the sintered nanosilver joint. Force-controlled cyclic tests were also performed at different mean forces, force amplitudes, dwell time at peak force, and temperatures. The mean force, the force amplitude, and the temperature played key roles in the shear ratcheting strain accumulation. The ratcheting strain rate could be enhanced with increasing the dwell time at peak force as well. A viscoplastic constitutive model based on Ohno–Wang and Armstrong–Fedrick (OW–AF) non-linear kinematic hardening rule, and Anand model were separately embedded in ABAQUS to simulate the shear and the ratcheting behavior of the sintered nanosilver joint. It was concluded that OW–AF model could predict the ratcheting behavior of the sintered nanosilver joint better than Anand model, especially at high temperatures.     

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.     

INTERACTIONS BETWEEN TIME AND CYCLIC DEFORMATION PROCESSES IN A NIMONIC ALLOY

Interactive creep–fatigue behaviour of a nickel-base superalloy (IN 597) has been examined at 850 °C under various strain-limited, cyclic torsional loading conditions. In one test, forward creep deformation was reversed by creep under equal magnitude stress levels and strain limits. In other tests, forward creep strain was reversed by fast monotonic plasticity with and without a subsequent period of relaxation. These cycles were repeated within each test until fracture. This paper examines empirically the influence of a number of test variables upon cyclic creep curves, and demonstrates the usefulness of predictions based upon continuous low cycle fatigue and simple creep data when used in conjunction with a mechanical equation of state. A cyclic equilibrium condition was not achieved from these tests. Instead, a progressive softening occurred giving reductions to the amount of creep strain, creep time interval and reversed peak stress with each new cycle. Such reductions are expressed from derived formulae that embrace the range of inelastic strain, cycle number, creep dwell stress, reversed peak stress, and times expended in creep and relaxation.
Observations made on accumulated creep strain reveal the contribution to a creep–fatigue fracture from cyclic creep. This has led to a modified form of the linear damage rule which can provide conservative life predictions for components operating in service under similar cyclic conditions.     

Experimental and numerical evaluations of stress relaxation in A356 aluminium alloy subjected to out-of-phase thermomechanical cyclic loadings

Abstract

In this study, the stress relaxation has been measured experimentally and has been also calculated numerically by the finite element method in the A356·0 aluminium–silicon–magnesium alloy, under out-of-phase thermomechanical cyclic loadings. To get this objective, strain based thermomechanical fatigue tests were performed on cylindrical specimens, at an out-of-phase condition. In this loading condition, when the temperature was maximum, the mechanical strain was compressive and vice versa. These fatigue experiments were repeated at various dwell times, in which the temperature was held at the maximum temperature. This hold time was considered as 5, 30, 60 and 180 s and then the stress relaxation was measured during the mid-life cycle of each test. Besides, the finite element analysis was also conducted on the material to simulate the stress relaxation numerically. A two-layer visco-plastic model was applied to simulate the high temperature cyclic behavior of the material. Finite element results showed a good agreement with experimental results, which were obtained from thermomechanical fatigue tests on the A356·0 aluminium alloy. The two-layer visco-plastic model could properly predict the stress relaxation at elevated temperatures, during various dwell times.     

Experimental and numerical analyses of mean stress relaxation in cold expanded plate of Al‐alloy 2024‐T3 in double shear lap joints

In this paper, the mean stress relaxation behavior of simple Al‐alloy 2024‐T3 specimens and also the mean stress relaxation around the hole of cold expanded specimen are studied. The analyses are performed through the combination of the nonlinear isotropic hardening and Chaboche nonlinear kinematic hardening model accompanied by the results of experimental tests. The strain‐controlled axial tests are performed at two different strain amplitudes, while the stress‐controlled tests of cold expanded specimens are performed for three different imposed load amplitudes. The constitutive equations of the hardening model are coded as a UMAT subroutine in FORTRAN programming language and implemented in the commercial finite element code of ABAQUS. The accuracy of the hardening model has been proved in two steps: first by simulations of mean stress relaxation during the uniaxial strain‐controlled cyclic tests and second by simulation of strain ratcheting during the stress‐controlled cyclic loading. The stress and strain distributions after cold expansion process are examined as well as the mean stress relaxation due to cyclic loading. The results show the influences of imposed stress amplitude on increasing mean stress relaxation and also the effect of cold expansion level on reducing the mean stress relaxation.     

Stabilized cyclic stress-strain calculation for metals under multiaxial loading

A simple plasticity model for modeling the stabilized cyclic stress-strain responses is developed to consider the effect of non-proportional additional hardening. In the proposed model, the plastic modulus for uniaxial loading is extended to multiaxial loading by introducing the non-proportionality factor and the additional hardening coefficient. The two introduced factors take into account the effects of non-proportional additional hardening, not only on the shape of the loading path, but also on the material and its microstructure. And then, the basic Armstrong-Frederick nonlinear hardening rule is modified to model the evolution of the back stress. The consistency condition is enforced to obtain the relationship between the back stress and plastic modulus. The proposed model requires only six material constants for estimating the stabilized responses. Comparisons between the test results (30CrNiMo8HH steel, SA 333 Gr.6 steel, and 1 %CrMoV steel) and model predictions show that the proposed model predicts relatively accurate stress responses under both proportional and non-proportional loading paths.     

Uniaxial and non-proportionally multiaxial ratcheting of U71Mn rail steel: experiments and simulations

The ratcheting and strain cyclic characteristics of U71Mn rail steel were experimentally researched under uniaxial and non-proportionally multiaxial cyclic loading at room temperature. The effects of cyclic strain, stress and their histories on strain cyclic characteristics and ratcheting were studied, respectively. It is shown that: U71Mn rail steel exhibits a cyclic stabilization and non-memorization for previous loading history under strain cycling; however, the ratcheting of the material depends greatly not only on the current values of mean stress and stress amplitude, but also on their histories; the non-proportionality of multiaxial loading path only causes a negligible additional hardening for the material. Based on the Ohno–Wang non-linear kinematic hardening model [Int. J. Plast. 9 (1993) 375, 391], the uniaxial and multiaxial ratcheting behaviours of the material were simulated by a visco-plastic constitutive model. The simulated results are in good consistence with the experimental ones.     

A temperature- and strain-rate-dependent isotropic elasto-viscoplastic model for glass-fiber-reinforced polyurethane foam

The primary aim of the present study is to provide a new constitutive model and its computational procedure for a glass-fiber-reinforced polyurethane foam (RPUF) subjected to various cryogenic temperatures and compressive loading rates. A Frank–Brockman-type isotropic elasto-viscoplastic model was introduced to describe the hardening and softening phenomena of RPUF under compressive loads. In addition, the increase of the yield strength and plateau according to the change of temperature and strain rates was demonstrated using the given constitutive model. The introduced numerical model was transformed as an implicit form and was implemented into a user-defined subroutine of commercial finite element analysis (FEA) code, i.e., ABAQUS UMAT. Based on the developed material library, the complex elasto-plastic behavior of RPUF under various cryogenic temperatures and strain rates was numerically estimated. The variation of material internal variables, such as hardening and softening control parameters, was quantitatively investigated, and the temperature- and strain-rate-dependent empirical formulae, namely, a polynomial multiple regression model, were proposed. Finally, the simulation results were compared with a series of compressive test results to validate the proposed method. On using the developed numerical method, it might be feasible to predict the unknown stress–strain behavior of RPUF under arbitrary severe environments.     

混凝土循环加卸载动态损伤特性研究

利用大型多功能动静力三轴仪对混凝土试件进行了5种应变速率下的动态循环加卸载压缩试验。对混凝土的物理力学参数的变化规律进行了统计分析。结果表明:峰值应力和弹性模量随加载速率的提高而增大,但峰值应变随加载速率的变化表现出较大的离散性。在此基础上,进一步研究了混凝土在不同加载速率下的刚度退化规律。最后,选用基于Weibull统计理论的分段式动态损伤本构模型对试验数据进行拟合。经验证,此模型能够较好的模拟混凝土材料的本构特性。     

Cyclic deformation behaviour of a nickel base alloy at elevated temperature

Low cycle fatigue tests for a hot extruded Nickel base alloy tube material have been performed at room temperature and at 204°C. The alloy shows a normal hardening and softening cyclic stress-strain response at room temperature. At 204°C, however, the cyclic stress-strain response shows a strain hardening first, followed by a relatively stable stress and finally a secondary cyclic strain hardening. This stable stress disappears with increasing strain amplitude. The mechanisms of the secondary cyclic strain hardening have also been investigated by transmission electron microscopy (TEM). Besides dislocation multiplication, interactions between stacking faults and moving dislocations and between interstitial atoms and moving dislocations could also contributed to this secondary cyclic strain hardening. The formation of micro-twins during cyclic loading at 204°C and its influence on the cyclic stress-strain response were also discussed.     

Assessment of fatigue response of thermally aged reduced activation ferritic-martensitic steel based on finite element analysis

Abstract

In the present investigation, effect of thermal ageing on low cycle fatigue (LCF) behaviour of Reduced Activation Ferritic Martensitic steel has been assessed by finite element analysis. The steel was thermally aged at 873 K for 3000 hour. Low cycle fatigue tests were carried out on both the as-received and thermally aged material at strain rate of 3×10^?3 s^?1 at 823 K, over strain amplitudes in the range of ± 0.25 to ± 0.8%. Continuous cyclic softening till final failure, except for initial few cycles especially at relatively lower strain amplitudes, was observed in both the material conditions. Thermal ageing resulted in marginally higher cyclic stress response accompanied by lower fatigue life. The differences in fatigue responses have been attributed to the coarsening of precipitates on thermal ageing. Finite element analysis has been carried out considering combined isotropic and kinematic hardening as material model to estimate the effect of thermal ageing on the response of material under LCF loading. Thermal ageing was found to decrease both the isotropic and kinematic hardening with appreciable effect on isotropic hardening. The predicted cyclic stress response and hysteresis loops were found to be in good agreement with the experimental data. The LCF life of the steel has been estimated based on the hysteresis energy approach.     

A 3D full‐field study of cracks in a nuclear graphite under mode I and mode II cyclic dwell loading conditions

Three‐dimensional (3D) full‐field deformation around crack tips in a nuclear graphite has been studied under mode I and mode II cyclic dwell loading conditions using digital volume correlation (DVC) and integrated finite element (FE) analysis. A cracked Brazilian disk specimen of Gilsocarbon graphite was tested at selected loading angles to achieve mode I and mode II cyclic dwell loading conditions. Integrated FE analysis was carried out with the 3D displacement fields measured by DVC injected into the FE model, from which the crack driving force J‐integral was obtained using a damaged plasticity material model. The evolution of near‐tip strains and the J‐integral during the cyclic dwell loading was examined. Under cyclic dwell, residual strain accumulation was observed for the first time. The results shed some light on the effect of dwell time on the 3D crack deformation and crack driving force in Gilsocarbon under cyclic mode I and II loading conditions.