非比例循环塑性内时本构关系研究

在Valanis的内时本构理论的框架中,引入内结构张量以反映由于非比例加载而引起金属材料的附加等向强化及异向强化效应,同时提出材料强化程度的度量采用沿路径法线方向的塑性应变分量来描述.这些考虑的有效性已经通过用所建模型对304不锈钢材料在一些典型非比例循环加载路径下的响应进行的理论预测得到了验证;将该模型应用于U71Mn材料室温单轴棘轮行为描述中,结果显示内结构张量的引入不仅能较好地反映应变控制下的非比例附加效应,而且也能较好地反映应力控制下塑性应变的累积及变化率.     

1Cr18Ni9Ti不锈钢的非比例循环强化性能

对1Cr18Ni9Ti不锈钢进行了各种比例和非比例循环本构实验,其中包括圆路径、正方形、正菱形、蝶形、三角形和两种十字形应变路径。表明其具有明显的非比例循环附加强化。在相同的等效应变幅值上,材料的附加强化与路径密切相关。对于圆路径,其附加强化度最大可达60％。通过对不同应变历史的实验研究表明,先前小的非比例度的加载历史对后继大的非比例度路径的强化没有影响;而先前大非比例度的加载路径对后继小非比例度路径的循环强化有较大影响。     

加载历史对循环硬化的影响

本文研究了45#钢和LY-12CZ铝合金在室温条件下拉扭复合比例及非比例加载时的循环硬化特性,其结果表明不同加载路径循环硬化程度不同,纯扭硬化程度最小,圆形路径硬化程度最大。着重研究了不同循环历史对后面循环稳定应力幅值的影响。     

Multiscale experimental investigations about the cyclic behavior of the 304L SS

This work follows a series of experiments carried out earlier at INSA of Rouen (Hassan, T., Taleb, L., Krishna, S., 2008. Influence of non-proportional loading paths on ratcheting responses and simulations by two recent cyclic plasticity models. Int. J. Plast. 24, 1863–1889). It investigates the elastoplastic cyclic behavior of a 304L stainless steel at room temperature. In a first step the cross path effect on ratcheting is confirmed, as well as the crucial role of the loading path non-proportionality. Strain controlled tests are also conducted for different strain amplitudes and loading paths. Cross-hardening effect appears more important when the shearing sequence is followed by the axial one. Moreover for alternating axial and shearing cycles, this phenomenon occurs after each crossing sequence leading to a very significant strain hardening, at least of the same order as the one obtained after a circular strain path. Yet, the magnitude of the observed over hardening does not necessarily seem a function of the cumulated plastic strain.     

Uniaxial and non-proportionally multiaxial ratcheting of SS304 stainless steel at room temperature: experiments and simulations

The uniaxial and non-proportionally multiaxial ratcheting behaviors of SS304 stainless steel at room temperature were initially researched by experiment and then were theoretically described by a cyclic constitutive model in the framework of unified visco-plasticity. The effects of cyclic stress amplitude, mean stress, and their histories on the ratcheting were experimentally investigated under uniaxial and different multiaxial loading paths. The shapes of non-proportional loading paths were linear, circular, elliptical and rhombic, respectively. In the constitutive model, the rate-dependent behavior of the material was reflected by a viscous term; the cyclic flow and cyclic hardening behaviors of the material under asymmetrical stress-controlled cycling were reflected by the evolution rules of kinematic hardening back stress and isotropic deforming resistance, respectively. The effect of loading history on the ratcheting was also considered by introducing two fading memorization functions for maximum inelastic strain amplitude and isotropic deformation resistance, respectively, into the constitutive model. The effect of multiaxial loading path on the ratcheting was reflected by a non-proportional factor defined in this work. The predicting ability of the developed model was proved to be good by comparing the simulations with corresponding experiments.     

An evaluation of a combined isotropic-kinematic hardening model for representation of complex strain-path changes in dual-phase steel

This paper aims at evaluating an elastoplastic constitutive model which accounts for combined isotropic-kinematic hardening for complex strain-path changes in a dual-phase steel, DP800. The capability of the model to reproduce the transient hardening phenomena under two-stage non-proportional loading has been assessed through numerical simulations of sequential uniaxial tension and notched tension/shear tests. Finite element simulations with shell elements were performed using the explicit non-linear FE code LS-DYNA. Numerical predictions of the stress–strain response were compared to the corresponding experimental data. The results from the experiments demonstrated that prior plastic deformation has certainly influenced the subsequent work-hardening behaviour of the material under biaxial or shear deformation modes. Furthermore, the numerical simulations from the two-stage uniaxial tension–notched tension and uniaxial tension–shear tests predicted the general trends of the experimental results such as transitory hardening and overall work hardening. However, some discrepancies were found in accurately describing the transient hardening behaviour subsequent to strain path changes between the experiments and numerical simulations.     

Effects of strain path shapes on non-proportional cyclic plasticity

The title problem was discussed to facilitate the formulation of constitutive models of cyclic plasticity under general states of loading. A series of plastic strain controlled cyclic tests was performed by applying combined axial force and torque to thin-walled tubular specimens of Type 316 stainless steel at room temperature. These tests consist of cyclic loading along uniaxial, torsional, cruciform, stellate in eight directions, square and circular plastic strain paths with a constant amplitude of equivalent plastic strain.The results of these tests showed that the strain-hardening depends markedly on the shape of the plastic strain path, and that the strain-hardening (measured by equivalent stress amplitudes) in the saturated state is significant in the order of circular, square, stellate, cruciform and proportional paths. It was also observed that these saturated values were independent of the less significant plastic strain cycles experienced in the past. Finally, the characteristic features of strain-hardening mechanisms under non-proportional loadings were discussed in some detail on the basis of the present results.     

考虑塑性应变记忆恢复的循环棘轮本构模型研究

在统一粘塑性循环本构理论框架下,以Ohno-Abdel-Karim非线性随动硬化模型为基础,建立了一个循环本构模型。模型通过引入塑性应变幅值记忆效应,并在塑性应变记忆项中加入恢复系数,提高了对循环硬化材料单轴棘轮行为的预言能力。将模型应用于316L不锈钢单轴棘轮行为的描述中,模拟不同平均应力、应力幅值下的棘轮应变,均与实验数据吻合较好,证明本文改进的本构模型能合理地描述循环硬化材料的单轴棘轮行为。     

A viscoplasticity theory applied to proportional and non-proportional cyclic loading at small strains

The small strain, isotropic, Viscoplasticity theory Based on Overstress (VBO) is modified so that the experimentally observed, complex cyclic hardening behavior under proportional and non-proportional loading with fixed as well as variable strain amplitude can be reproduced. This is accomplished by formulating a growth law for the isotropic, rate independent stress, a scalar valued state variable of VBO. The non-proportionality measure employed for modeling the effects of loading path, amplitude and prior history is Tanaka's fourth order tensor [Eur. J. Mech. Solids 13 (1994) 155]. Numerical experiments show the responses in step-up and down two amplitude tests and include further hardening after an increase in the strain amplitude. The differences in the responses to proportional and non-proportional loading including circular, square, one step and two steps are demonstrated. History dependence of the hardening is depicted. The cross hardening behavior, sudden increase in the stress level which is followed by softening after the path change are modeled well.     

循环软化45碳钢和循环硬化304不锈钢的棘轮行为实验研究

对循环软化45碳钢的单轴应力循环下的平均应力、应力幅值以及先前应变循环对棘轮效应的影响进行了实验研究;并对循环硬化的304不锈钢进行了多种非比例循环加载路径下路径形状、路径等效应力幅值、平均应变与平均应力对材料棘轮变形行为的影响实验．发现平均应力和应力幅值及其历史对于材料的棘轮行为都有很大的影响．     

Material effects during monotonic-cyclic loading

The effects commonly related with deformation caused by proportional and non-proportional loading types were identified experimentally. In the case of non-proportional cyclic loading along circular strain path the second order effects such as: phase shift between stress and strain signals was observed. An analysis of experimental data from tests under non-proportional cyclic loading along square strain path exhibited a significant reduction of stress independently on direction of deformation.The paper also presents experimental results concerning evaluation of an influence of cyclic loading on stress variations during monotonic deformation carried out on the pure copper and X10CrMoVNb9-1 steel. All strain controlled tests were performed at room temperature using thin-walled tubular specimens. The experimental programme contained selected combinations of monotonic and cyclic loadings, i.e. the torsion-reverse-torsion cycles were superimposed on the monotonic tension. It is shown that such cycles associated with monotonic tension caused essential variations of tensile stress. For both materials, a significant decrease of the axial stress was visible. The effects observed during monotonic and cyclic loading combinations were theoretically described using the Mróz and Maciejewski model.     

Cyclic plasticity modeling with the distribution of non-linear relaxations approach

Motivated by the distribution of non-linear relaxation (DNLR) approach, a phenomenological model is proposed in order to describe the cyclic plasticity behavior of metals under proportional and non-proportional loading paths with strain-controlled conditions. Such a model is based on the generalization of the Gibbs's relationship outside the equilibrium of uniform system and the use of the fluctuation theory to analyze the material dissipation due to its internal reorganization. The non-linear cyclic stress–strain behavior of metals notably under complex loading is of particular interest in this study. Since the hardening effects are described appropriately and implicitly by the model, thus, a host of inelastic behavior of metals under uniaxial and multiaxial cyclic loading paths are successfully predicted such as, Bauschinger, strain memory effects as well as additional hardening. After calibrating the model parameters for two metallic materials, the model has demonstrated obviously its ability to describe the cyclic elastic-inelastic behavior of the nickel base alloy Waspaloy and the stainless steel 316L. The model is then implemented in a commercial finite element code simulating the cyclic stress–strain response of a thin-walled tube specimen. The numerical responses are in good agreement with experimental results.     

镍基单晶合金多轴非比例加载低周疲劳研究

基于正交设计, 分别在680℃和850℃下进行DD3镍基单晶合金薄壁圆管试样([001]取向)拉/扭非比例加载低周疲劳试验, 研究等效应变范围、应变路径角、拉/扭载荷相位角、循环特性和温度诸因素对镍基单晶合金多轴低周疲劳寿命的影响作用. 疲劳试验数据的极差分析表明, 应变路径角、拉/扭载荷相位角和等效应变范围是影响疲劳寿命的主要因素. 将菱形应变加载路径区分为比例加载段和非比例加载段, 提出了表征非比例加载效应的等效应变参量, 并通过引入单晶应变三轴性因子反映拉/扭应变路径角对多轴疲劳寿命的影响. 用考虑非比例加载效应的等效应变范围和单晶应变三轴性因子构造循环塑性应变能损伤参量, 进行多元线性回归分析, 疲劳寿命回归模型与试验寿命具有很好的相关性, 所有试验数据都落在2.0倍的偏差分布带之内.      

Further application of endochronic constitutive equation to loading with non-proportional axial-torsional strain-path

A combined theoretical-experimental investigation of the stress response to complex, non-proportional strain-paths in the axial-torsional strain space is reported in this paper. Type 304 stainless steel tubular specimens have been tested at a constant strain rate of 5 × 10^?4 per second. Two strain-paths have been investigated. The first path involves a cyclic axial straining and unstraining following a shear prestraining, and the second strain-path is cyclic in shear after a prestraining in tension.The endochronic theory with a plastic strain defined intrinsic time has been shown to be capable of predicting the stress response to the two strain-paths considered.     

考虑路径相关性的非比例循环塑性本构模型

根据非比例加载下金属材料响应的延迟特性及加载路径相关性,选取沿应力迹法向的塑性应变的累积量作为非比例加载影响的度量,相应给出反映非比例附加强化的变量,并假设其模量和强化率与加载路径的几何参数相关．为反映由于非比例加载而引起的材料强化的异向效应,在Valanis的塑性内时响应方程中引入与加载路径几何性质有关的应力项,构成非比例循环塑性本构关系．对316和304不锈钢材料在一些典型非比例循环加载路径下的应力响应进行了理论预测,与Benallal等及McDowell的实验结果取得了良好的一致．     

Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheets

Magnesium alloy sheets have been extending their field of applications to automotive and electronic industries taking advantage of their excellent light weight property. In addition to well-known lower formability, magnesium alloys have unique mechanical properties which have not been thoroughly studied: high in-plane anisotropy/asymmetry of yield stress and hardening response. The reason of the unusual mechanical behavior of magnesium alloys has been understood by the limited symmetry crystal structure of HCP metals and thus by deformation twinning. In this paper, the phenomenological continuum plasticity models considering the unusual plastic behavior of magnesium alloy sheet were developed for a finite element analysis. A hardening law based on two-surface model was further extended to consider the general stress–strain response of metal sheets including Bauschinger effect, transient behavior and the unusual asymmetry. Three deformation modes observed during the continuous in-plane tension/compression tests were mathematically formulated with simplified relations between the state of deformation and their histories. In terms of the anisotropy and asymmetry of the initial yield stress, the Drucker–Prager’s pressure dependent yield surface was modified to include the anisotropy of magnesium alloy. The numerical formulations and characterization procedures were also presented and finally the correlation of simulation with measurements was performed to validate the proposed theory.     

An updated version of the multimechanism model for cyclic plasticity

In this paper we consider the elastoplastic behavior of the 304L stainless steel under cyclic loading at room temperature. After the experimental investigations presented in Taleb and Hauet (2009), the present work deals with modeling in the light of the new observations. An improved version of the multimechanism model is proposed in which the isotropic variable is revisited in order to take into account the non-proportional effect of the loading as well as the strain memory phenomenon. A particular attention has been paid to the identification process in order to capture the main important phenomena: relative parts of isotropic and kinematic hardening, time dependent effects, non-proportionality effect, strain amplitude dependence. Only strain controlled tests have been used for the identification process. The capabilities of the model with “only” 17 parameters are evaluated considering a number of proportional and non-proportional stress and strain controlled tests.     

Multiaxial cyclic deformation and non-proportional hardening employing discriminating load paths

Some novel discriminating multiaxial cyclic strain paths with incremental and random sequences were used to investigate cyclic deformation behavior of materials with low and high sensitivity to non-proportional loadings. Tubular specimens made of 1050 QT steel with no non-proportional hardening and 304L stainless steel with significant non-proportional hardening were used. 1050 QT steel was found to exhibit very similar behavior under various multiaxial loading paths, whereas significant effects of loading sequence were observed for 304L stainless steel. In-phase cycles with a random sequence of axial-torsion cycles on an equivalent strain circle were found to cause cyclic hardening levels similar to 90° out-of-phase loading of 304L stainless steel. In contrast, straining with a small increment of axial-torsion on an equivalent strain circle results in higher stress than for in-phase loading of 304L stainless steel, but the level of hardening is lower than for 90° out-of-phase loading. Tanaka’s non-proportionality parameter coupled with a Armstrong–Fredrick incremental plasticity model, and Kanazawa et al.’s empirical formulation as a representative of such empirical models were used to predict the stabilized stress response of the two materials under variable amplitude axial-torsion strain paths. Consistent results between experimental observations and predictions were obtained by employing the Tanaka’s non-proportionality parameter. In contrast, the empirical model resulted in significant over-prediction of stresses for 304L stainless steel.     

316L不锈钢随动强化模型改进研究

本文对316L不锈钢进行了单轴与多轴非比例路径下的应力控制棘轮试验,考察了应力幅值、平均应力和加载历程对棘轮特性的影响。同时进行了应变控制循环试验以研究材料的应力松弛特性。试验结果表明轴向棘轮效应在对称剪切荷载下效果明显,同时棘轮应变随应力幅值和平均应力的增加而增加。研究了Chen-Jiao随动强化模型与Jiang-Sehitoglu随动强化模型采用的单轴与多轴参数对背应力分量增量方向的影响,将Chen-Jiao模型中的多轴系数替换为界面饱和率,并在此基础上引入新的参数对塑性模量系数进行修正,计算结果表明修正后的模型能提升应力控制下多轴棘轮的预测精度,并能很好的预测应力松弛现象,表明了新模型的正确性与有效性。     

Constitutive modeling of strain range dependent cyclic hardening

In this paper, a new approach for constitutive modeling of strain range dependent cyclic hardening is proposed by extending the kinematic hardening model based on the critical state of dynamic recovery. It is assumed that isotropic, as well as kinematic, hardening consists of several parts, and that each part of isotropic hardening evolves when the corresponding part of kinematic hardening is in the critical state of dynamic recovery. The extended model is capable of simulating the cyclic hardening behavior in which different characteristics of cyclic hardening appear depending on strain range. The model is verified by simulating the relatively large cyclic straining tests of 304 stainless steel at ambient temperature, in which cyclic hardening does not stabilize before rupture if strain range exceeds a certain value. The model is further verified by predicting the history dependence of cyclic hardening under incremental cyclic loading and the maximum plastic strain dependence of strain hardening in cyclic tension.