The application of endochronic plasticity theory in modeling the dynamic inelastic response of structural systems

The endochronic theory of plasticity proposed by Valanis has been applied in predicting the inelastic responses of structural systems. A recently developed convected coordinates finite-element program has been modified to use an endochronic constitutive law. A series of sample problems for a variety of dynamic loadings are presented. The calculations that have been performed comparing classical and endochronic plasticity theories have revealed that the endochronic approach can result in a substantial reduction in computer time for equivalent solution accuracy. This result, combined with the apparent accuracy of material representation indicate that the use of endochronic plasticity has great potential in evaluating the dynamic response of structural systems.     

Modelization of ratcheting in biaxial experiments

A new constitutive equation has been developed on a purely phenomenological basis in order to interpret ratcheting experiments. The model is based on a generalized Armstrong-Frederick equation for the kinematic variable; the coefficients of this equation are functions of both instantaneous and accumulated plastic strain. The experiments described relate to austenitic stainless steel (17-12 SPH) tubular specimens subjected to cyclic torsional loading under constant tensile stress at 600°C. Comparisons between experimental and theoretical results show that the model reasonably well predicts not only ratcheting but also hysteresis loops and the cyclic hardening curve.     

Determination of internal state variables and constitutive modeling for Type 316 stainless steel

The purpose of this study is to develop an approach for unified constitutive modeling based on experimentally determined back stress and overstress. Back stress and overstress were experimentally determined for Type 316 stainless steel at 600°C, by analyzing the unloading curve for the stress-strain response of cyclic strain tests. The result has indicated that the cyclic strain hardening behavior is mainly caused by hardening in the back stress. A phenomenological unified constitutive model in which the back stress and drag stress are taken as the internal state variables is proposed, and has been shown that this model is able to simulate the cyclic inelastic behavior.     

Description of creep-plasticity interaction with non-unified constitutive equations: application to an austenitic stainless steel

We present constitutive equations able to account for time independent plasticity together with creep and creep-plasticity interaction. A classical decomposition of the inelastic strain into a time independent plastic strain and a time dependent viscoplastic part is assumed. The coupling between both deformation modes (i.e. creep and plasticity) is obtained through an interaction between the plastic and viscoplastic state variables. In a first part, the capabilities of the model are described, and qualitative identifications are given in order to characterize the behaviour of the model. The practical applicability of the model is then tested, mainly using test results from the literature, but also specific data including creep, relaxation and tensile tests with various loading rates, as reported in the paper. The model is found able to discriminate between the increase of hardening produced by plasticity or creep. The effect of the loading rate on the subsequent amount of relaxation is correctly described and a good general agreement is observed between experiment and model predictions, even for complex loading paths (monotonic with temporary unloading periods, multiaxial loading paths in the stress space).     

A two-surface cyclic plasticity model consistent with fundamental stress-strain equations of the power-law type

A plasticity constitutive model which can describe primary features of stress-strain behaviors of cyclically loaded metallic materials under isothermal conditions is developed in the framework of the two-surface plasticity theory. A special plastic hardening modulus function, which is consistent with the power-law type stress-strain expressions frequently used for both monotonic and cyclic stable stress-strain curves, is introduced to represent cyclic hardening as well as saturated behaviors more realistically. The model is validated through its application to the simulation of uniaxial cyclic and biaxial behaviors of cyclic hardening materials. This model is then implemented into a general purpose finite element computer program and applied to the analysis of a notched plate subjected to cyclic loading.     

The viscoplasticity theory based on overstress applied to the analysis of beams under monotonic and cyclic creep loading

The viscoplasticity theory based on total strain and overstress can reproduce rate-dependent inelastic deformation without distinction between plastic and creep strain using two material functions. A viscosity function and an equilibrium stress-strain curve characterize rate-dependency and work hardening, respectively. The theory is used to analyze the creep and cyclic creep behavior of a beam subjected to a linearly increasing moment which is subsequently held constant.The analysis shows the existence of two possible states of equilibrium for creep deformation: termination of primary creep or secondary creep. They occur when the equilibrium stress-strain curve has positive or zero slope in the plastic range.The numerical experiments illustrate that the stress distribution at the end of the moment increase depends on the moment rate. The rate effects disappear with time when stress is redistributed. For practical purposes the equilibrium solution is obtained before 10⁷ s, when the material functions representing AISI Type 304 Stainless Steel at room temperature are used. The other equilibrium solution (secondary creep) is reached after primary creep when the constant moment is above the limiting equilibrium moment which corresponds to the plastic hinge moment of plasticity theory. The stress distribution during stationary creep is shown to be the solution corresponding to the Norton law of creep theory. The numerical experiments also illustrate the influence of various viscosity functions and equilibrium stress levels. A growth law for the equilibrium stress-strain curve is postulated and reversed loading as well as repeated loading are investigated.     

Cyclic softening as a parameter for prediction of remnant creep rupture life of a Indian reduced activation ferritic–martensitic (IN-RAFM) steel subjected to fatigue exposures

Sequential fatigue-creep tests were conducted on Indian reduced activation ferritic–martensitic steel at 823 K leading to sharp decrease in residual creep life with increase in prior fatigue exposures. Extensive recovery of martensitic-lath structure taking place during fatigue deformation, manifested as cyclic softening in the cyclic stress response, shortens the residual creep life. Based on the experimental results, cyclic softening occurring during fatigue stage can be correlated with residual creep life, evolving in an empirical model which predicts residual creep life as a function of cyclic softening. Predicted creep lives for specimens pre-cycled at various strain amplitudes are explained on the basis of mechanism of cyclic softening.     

Void swelling and irradiation creep relationships

Recent analytical and theoretical work on swelling enhanced irradiation creep and stress effects on swelling is reviewed. A proposed explanation for swelling enhanced irradiation creep involves consideration of the role of vacancy loops. Theoretical work leads to the development of a new relationship for swelling enhanced creep which predicts larger irradiation creep rates at high levels of swelling (>5%) than the original formulation. Consideration is given to an additional effect of stress on swelling which involves a stress effect on the incubation dose. A constitutive equation is presented to describe this phenomenon. Design related illustrations are presented for these high fluence irradiation induced phenomena.     

High temperature creep and cyclic deformation behaviour of AISI 316 L(N) austenitic steel and its modelling with unified constitutive equations

Creep tests at constant stress and low cycle fatigue (LCF) tests were performed with a view to investigating and modelling the deformation behaviour of AISI 316 L(N) austenitic stainless steel at 700 °C. All experiments were done on samples taken from two different sheets of the same batch of material.The creep stresses were selected from the high stress range. The results obtained from creep tests on samples from different sheets are compared with each other. The differences between them and the results of a creep test carried out at constant load are indicated.The LCF experiments were strain controlled. The effects of strain rate and strain amplitude on the cyclic hardening behaviour were investigated.The parameters of a set of constitutive equations are determined from these data. The quality of the parameter fit is discussed.     

304不锈钢的非饱和循环硬化行为及其本构描述

针对循环硬化行为的应变幅值依赖性和相对大应变幅值下的非饱和特性．建立了新的粘塑性循环本构模型,在本构模型中．引入新的变量来表征材料的循环硬化特性,该变量的演变方程中引入一个临界状态来反映循环硬化对应变幅值的依赖性：同时,将该变量分解为2个具有不同演变规律的分量．以此来描述相对大应变幅值下的非饱和循环硬化特性．结果表明．新建模型能够很好地描述304不锈钢循环硬化行为的应变幅值依赖性和非饱和特性．     

Elastic-plastic creep response of structures under composite time history of loading

High temperature nuclear reactor components are subject to a complex history of thermal and mechanical loading cycles. To evaluate the adequacy of such components, detailed information on the accumulated inelastic strains and strain cycling is required. This paper presents the theory, describes efficient numerical techniques accounting for plasticity, creep and overall equilibrium, describes the overall structure of the resulting computer program, and demonstrates the capability of the analysis method on a real three-dimensional structure. Starting with the principle of virtual work, exact equilibrium equations are derived for a stepwise Lagrangian formulation. The resulting equilibrium equations are then specialized to the incremental Piola-Kirchhoff stress computation and to small incremental strain formulation. Classical plasticity theory is used to develop a novel method based on the concept of ‘plastic stress’ for consideration of inelastic behavior. It is shown that the material's stress-strain curves can be followed to any desired degree of accuracy both for isotropic and kinematic hardening. It is further shown that for kinematic hardening it is necessary to base the incremental change on the state corresponding to the mean of the initial and the final states to satisfy the yield condition at the final state. The equation of state and strain hardening is used to describe the creep behavior. A novel numerical technique to describe a complex load history is developed by using time as a parameter, history breakpoint determination by scanning of various load vectors, and by linear interpolation between any two breakpoints in the load history. Efficient criteria for load incrementation in the form of a fraction of the total ‘plastic stress’ for any sequence of two load history break points are developed and made an internal function of the program. This saves the user significant hardship when faced with guessing the load increment for an unknown state of the solution at any of the load history breakpoints. The ‘plastic stress’ load vector concept is utilized with interation and extrapolation to converge to the equilibrium states with simultaneous satisfaction of the stress-strain relations for each of the iterated states. The essential features of the computer program DYPLAS-FSH, based on the theory and techniques described above, and a postprocessor program POR-FSH, based on RDT F9-5T for ratcheting and fatigue evaluation, are identified and discussed. In summary, the new results of this work are the efficient handling of an arbitrary load history, introduction of the ‘plastic stress’ concept for inelastic computation, novel implementation of classical plasticity with recognition of incrementation conditions for the kinematic hardening, use of the load incrementation algorithm based on the ‘plastic stress’ concept, and development of a computer code capable of solving practical three-dimensional problems.     

锆合金薄壁细管的单调拉伸与低周疲劳试验研究

利用自行研制的高温夹具完成了Zr-1Nb合金和Zr-4合金薄壁短管试样不同温度下的单调拉伸和375℃下的等幅低周疲劳试验,获得了两种锆合金的单调和循环本构关系及Manson-Coffin寿命估算模型。研究结果表明：Zr-1Nb合金和Zr-4合金的弹性模量、屈服强度、抗拉强度以及应变硬化程度明显下降。随着温度的升高,温度对Zr-4合金的应变硬化程度的影响逐渐减弱;应变速率对Zr-4合金的拉伸性能的影响微弱。在等幅应变循环过程中,Zr-4合金表现为循环硬化,应变幅越低,硬化现象越明显;Zr-1Nb在较低应变幅下表现为循环硬化特性,而在较高应变幅下表现为循环软化。相对于单调拉伸行为,Zr-4合金在不同温度下的循环行为均表现出明显的强化特性。     

Application of endochronic theory in dynamic viscoplasticity

This paper summarizes the work completed on a project concerned with engineering models in dynamic plasticity. The concept of the endochronic theory of viscoplasticity and its subsequent improvement are discussed briefly. Applications and extensions of the theory to various dynamic problems are presented. In particular, the strain-rate effect in the improved endochronic theory and its application to wave propagation problems are discussed. Comparing the numerical results with other calculations and experimental data, it appears that endochronic theory provides a promising representation of realistic material behavior. At the same time endochronic theory is often numerically more efficient than other formulations.     

Strain-rate dependent plasticity in thermo-mechanical transient analysis

The thermo-mechanical transient behavior of fuel element cladding and other reactor components is generally governed by the strain-rate properties of the material. Relevant constitutive modeling requires extensive material data in the form of strain-rate response as function of true-stress, temperature, time and environmental conditions, which can then be fitted within a theoretical framework of an inelastic constitutive model. In this paper, we present a constitutive formulation that deals continuously with the entire strain-rate range and has the desirable advantage of utilizing existing material data. The derivation makes use of strain-rate sensitive stress-strain curve and strain-rate dependent yield surface. By postulating a strain-rate dependent von Mises yield function and a strain-rate dependent kinematic hardening rule, we are able to derive incremental stress-strain relations that describe the strain-rate behavior in the entire deformation range spanning high strain-rate plasticity and creep. The model is sufficiently general as to apply to any materials and loading histories for which data is available.     

Creep analysis of zircaloy-4 and its application in the prediction of residual stress relaxation

Creep tests of zircaloy-4 were conducted in argon at 400, 500 and 600°C. A graphical analysis yielded a creep equation at each temperature to describe the creep curves for strains up to about 10%. A general equation incorporating temperature was also developed and shown to predict experimental strains within a factor of 2 in time over this temperature range for most of the creep curve. Using the creep analysis, together with a strain hardening history dependence, stress relaxation from various initial stresses was calculated. These calculations compared favorably with the results of some manual unloading tests. It was, therefore, possible to make some qualitative predictions to apply to the analysis of dimensional stability of reactor components in cases where residual stresses are present. These predictions were consistent with reported measurements on actual BWR channels, tested after fabrication.     

N18合金薄壁管高温应变循环与疲劳行为研究

应用新型自研夹具对N18合金薄壁短管进行400℃下的单轴拉伸和等幅低周应变疲劳试验。试验结果表明：N18短管高温循环应力应变滞回线有良好对称性；等幅循环下短管试样在较低应变幅下表现出循环硬化特性，而在较高应变幅下表现出循环软化；在多级应变循环加载下短管试样应力幅在循环中均保持稳定，循环本构关系不受多级应变循环工况差异的影响；材料循环特性不符合Manson律。获得了用于N18合金在400℃高温下的几个寿命估算式。