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.     

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．     

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.     

Random cyclic stress–strain responses of a stainless steel pipe-weld metal II — a modeling

This paper pays special attention to an issue that there is a significant scatter of the stress–strain responses of a nuclear engineering material, 1Cr18Ni9Ti stainless steel pipe-weld metal. Efforts are made to reveal the random fatigue damage character by fracture surface observations and to model the random responses by introducing probability-based stress–strain curves of Ramberg–Osgood relation and its modified form. Results reveal that the fatigue damage is subjected to, 3-D interacting and involved microcracks. The three stages, namely microstructural short cracks (MSC), physical short cracks (PSC) and long cracks (LC) subdivided by Miller and de los Rios, can give a good characterization of the damage process. Both micro- and macro-behaviour of the material have the character of three stages. The 3-D effects are strong in the MSC stage, tend to a gradual decrease in the PSC stage, and then show saturation after going to the LC stage. Intrinsic causes of the random behaviour are the difference and evolution of the microstructural conditions ahead of the dominant crack tips. The ‘effectively short fatigue crack criterion’ introduced by Zhao et al. in observing the material surface short crack behaviour could facilitate an understanding of the mechanism of interaction and evolution. Based on the previous obtained appropriate assumed distribution, normal model, for the cyclic stress amplitude, the probability-based curves are approximated by the mean value and standard deviation cyclic stress–strain curves. Then, fatigue analysis at arbitrarily given reliability can be conveniently made according to the normal distribution function. To estimate these curves, a maximum likelihood method is developed. The analysis reveals that the curves could give a good modeling of the random responses of material.     

A micromechanical interpretation of the temperature dependence of Beremin model parameters for french RPV steel

Local approach to brittle fracture for low-alloyed steels is discussed in this paper. A bibliographical introduction intends to highlight general trends and consensual points of the topic and evokes debatable aspects. French RPV steel 16MND5 (equ. ASTM A508 Cl.3), is then used as a model material to study the influence of temperature on brittle fracture. A micromechanical modelling of brittle fracture at the elementary volume scale already used in previous work is then recalled. It involves a multiscale modelling of microstructural plasticity which has been tuned on experimental inter-phase and inter-granular stresses heterogeneities measurements. Fracture probability of the elementary volume can then be computed using a randomly attributed defect size distribution based on realistic carbides repartition. This defect distribution is then deterministically correlated to stress heterogeneities simulated within the microstructure using a weakest-link hypothesis on the elementary volume, which results in a deterministic stress to fracture. Repeating the process allows to compute Weibull parameters on the elementary volume. This tool is then used to investigate the physical mechanisms that could explain the already experimentally observed temperature dependence of Beremin’s parameter for 16MND5 steel. It is showed that, assuming that the hypothesis made in this work about cleavage micro-mechanisms are correct, effective equivalent surface energy (i.e. surface energy plus plastically dissipated energy when blunting the crack tip) for propagating a crack has to be temperature dependent to explain Beremin’s parameters temperature evolution.     

Shakedown analysis of elastoplastic structures: A review of recent developments

Classical shakedown analysis rests on the assumptions of perfectly plastic, associative temperature-independent constitutive laws, negligible inertia and damping forces and negligible geometric effects.This paper provides a survey of the recent literature on the structural behaviour under variable repeated loads, with emphasis on the developments which relaxed some of the above assumptions, but preserved the character of generalization of limit analysis typical of the ‘classical’ shakedown theory and methods of analysis and design (in contrast to evolutive, step-by-step approaches of incremental plasticity).     

Some recent developments of the endochronic theory with applications

In this paper we presented a comprehensive review of recent developments of the endochronic theory of plasticity. The endochronic theory was first proposed by Valanis in 1971 with the aim of circumventing some of the difficulties associated with classical theories of plasticity, such as the concept of a yield surface and its motion in the stress space, criteria for unloading, hardening rules, etc. The theory is developed by using irreversible thermodynamics of internal variables. In the early version of the theory the intrinsic time was defined as a measure of length in strain space. This version is now called the simple endochronic theory. The derived constitutive equations have been applied with success to a number of problems of practical interest, e.g. cyclic response, cross hardening, cross ratcheting, etc. However, it has been shown by the first author that the simple theory leads to an unloading response which is not elastic at its onset. As a consequence infinitesimal hysteresis loops in the first quadrant of the stress-strain space are open, in disagreement with observed behavior in metals. Recently Valanis introduced a new intrinsic time scale which is a measure of length in the plastic strain space. As a result, a new model of endochronic theory has been developed which leads to closure of hysteresis loops in the small as well as the large. It is also shown that the new model predicts the existence of a yield surface. Hardening rules proposed in the classical theory of plasticity appear as special results.It is also shown that the constitutive equations derived from the new model are very powerful in their quantitative prediction of steady cyclic response under constant strain amplitude conditions. In the case of cyclic creep the theory predicts the dependence of cumulative axial creep on the plastic shear strain amplitude but that it overestimates the dependence of the latter on the number of cycles. At the present time we think that this difficulty cannot be overcome on the basis of an isotropic theory. This suggests a future area of investigation and application of the endochronic theory.     

The interaction of rate and history-dependent effects and its significance for slow cyclic inelastic analysis at elevated temperature

Life prediction for creep and low-cycle fatigue interaction and the analysis of ratcheting phenomena are of great importance in the design of future high-temperature nuclear reactors. These problems involve slow cyclic load application, inelastic deformation, and are inherently nonlinear. Fortunately, finite element computer programs with their time following and nonlinear capabilities are now available for the efficient solution of these complicated problems. The task is now to ensure that a proper representation of the material deformation behavior, the constitutive equation, is used in these computer programs. A systematic study of structural metal deformation behavior in slow cyclic laboratory tests such as cyclic creep, cyclic relaxation, low-cycle fatigue with and without hold-time showed that rate and history dependence interact. A few examples of such interactions are given in this paper. It is further shown that constitutive equations based on the additive use of elastic, plastic, and creep strains are not capable of reproducing these interaction phenomena on principal grounds. New inelastic constitutive equations for metals must be developed and some presently pursued approaches are discussed briefly.     

Application of material models and assessment of strains in a surgeline under cyclic thermal loading

Inelastic constitutive models in commercial finite element (FE) programs are examined with respect to their capability of describing cyclic thermal loading. Neither isotropic nor linear kinematic hardening alone gives correct answers. Therefore, a model with combined isotropic and kinematic hardening based on Chaboche is implemented in an FE program and validated by appropriate experiments. This model is applied to assess the safety of a piping loop in a nuclear power plant subjected to cyclic loading. The numerical simulation shows a purely elastic behaviour of the surgeline after two cycles (elastic shakedown) as indicated by previous strain gauge measurements.     

On a simplified inelastic analysis of structures

In this paper two main problems are considered: the derivation of cyclic constitutive relations during inelastic regime where hardening, softening and creep can occur, and the development of the eventual periodical state in the structure during cyclic thermodynamical loadings.We give a very simple and practical framework to solve these problems in one unique manner.Its essential feature consists in the introduction of a family of internal parameters which characterize local inelastic mechanisms and the family of transformed internal parameters which are linearly linked to the previous ones through a symmetrical non-negative matrix and are indeed the opposite of the associated residual stresses. Thanks to that, the treatment of the local plastic or viscoplastic yield conditions can be easily made from only the classical simple purely elastic (or viscoelastic) analysis.This property allows important results during cyclic loadings: conditions for elastic shakedown, plastic shakedown, ratcheting and bounds for the limiting state.Several examples are given in the text.     

The influence of He/dpa ratio and displacement rate on microstructural evolution: a comparison of theory and experiment

A kinetic model was developed to investigate the influence of the displacement rate and helium generation rate on microstructural evolution in austenitic stainless steels. The model integrates the rate equations describing the evolution of point defects, small point defect clusters, helium-vacancy clusters, and the larger cavity size distribution that is responsible for observable swelling. Cavity (bubble) nucleation is accounted for by the helium-vacancy cluster evolution, while void formation occurs when bubbles grow beyond a critical size in the larger cavity distribution.

A series of ion irradiation experiments were used to both calibrate the model and to provide a comparison between model predictions and experimental observations. The experiments involved single and dual-beam irradiations of solution annealed AISI-316 stainless steel at 873 K. The displacement rates were in the range of 2 × 10⁻³ to 1 × 10⁻² dpa/s and the helium-to-dpa ratios were in the range of 0 to 50 appm He/dpa. The maximum displacement dose was 25 dpa. The experiments revealed a significant effect of helium on both the dislocation structure and the cavity distribution. The model predictions of helium effects over a broad range of He/dpa ratios and displacement rates were consistent with experimental observations.     

A flow rule based on Huddleston’s multiaxial rupture criterion as a yield function

An elastic–plastic constitutive equation is proposed to develop a continuum damage model for multiple flawed medium. The constitutive model takes into account the effect of hydrostatic stress to describe the decrease of rigidity and flow stress in tension and has an extended form of Huddleston’s equi-rupture function. The decrease of those properties due to an evolution of damage is described by a proper selection of parameters in the yield function in accordance with a state of damage. Some case studies are shown. The model can be extended to include the kinematic and combined hardening rules or incorporated in constitutive equations for finite element calculations such as unified models.     

1Cr18Ni9Ti不锈钢低周疲劳随动硬化实验研究

为了研究单调加载对1Cr18Ni9Ti不锈钢材料后继循环塑性硬化和流动特性的影响,对该材料进行了带平均应变的低周疲劳实验研究.对不同应变幅值的对称应变及非对称的应变循环进行了屈服面半径和背应力演化分析,揭示了材料的随动硬化和各向同性硬化演化对应变幅值和平均应变的依赖性.实验结果为建立循环加载和单调加载耦合的复杂加载条件下的本构模型提供了实验基础.     

应力循环下T225NG合金塑性累积行为研究

对应力循环下T225NG合金的塑性累积行为进行了试验研究,提出了预测棘轮饱和应变的本构关系及描述棘轮应变演化规律的指数型演化方程。讨论了蠕变效应对T225NG合金棘轮行为的影响．结果表明．应力幅越低,循环蠕变分量在塑性累积中的贡献越大。     

Modeling elasto-plastic behavior of polycrystalline grain structure of steels at mesoscopic level

The multiscale model is proposed to explicitly account for the inhomogeneous structure of polycrystalline materials. Grains and grain boundaries are modeled explicitly using Voronoi tessellation. The constitutive model of crystal grains utilizes anisotropic elasticity and crystal plasticity. Commercially available finite element code is applied to solve the boundary value problem defined at the macroscopic scale. No assumption regarding the distribution of the mesoscopic strain and stress fields is used, apart the finite element discretization. The proposed model is then used to estimate the minimum size of polycrystalline aggregate of selected reactor pressure vessel steel (22 NiMoCr 3 7), above which it can be considered macroscopically homogeneous. Elastic and rate-independent plastic deformation modes are considered. The results are validated by the experimental and simulation results from the literature.     

非均匀形核对辐照诱导钨内微结构演化行为影响的团簇动力学模拟

金属钨(W)及其合金作为未来聚变堆最具应用前景的面向等离子体结构材料(PFMs),其服役性能直接影响聚变堆长期服役的安全性,辐照诱导W及其合金内微结构演化导致的辐照脆化现象始终是限制其工程应用的关键因素。本文基于分子动力学计算结果,进一步完善了辐照诱导材料微结构演化行为的团簇动力学模型,采用更加完备的物理模型描述材料内辐照缺陷的产生行为,并进一步探讨了W基体内辐照缺陷产生过程对微结构演化行为的影响。模拟结果表明,高能初始离位原子(PKA)诱发级联碰撞直接产生的缺陷团簇是W内位错环、空洞演化中最重要的形核机制;非均匀形核所产生的间隙团簇的扩散行为对位错环的长大行为有重要影响,会导致位错环尺寸分布中出现亚尖峰与台阶状形貌。     

A simple approach for the modeling of an ODS steel mechanical behavior in pilgering conditions

The optimization of the forming of ODS tubes is linked to the choice of an appropriated constitutive model for modeling the metal forming process. In the framework of a unified plastic constitutive theory, the strain-controlled cyclic characteristics of a ferritic ODS steel were analyzed and modeled with two different tests. The first test is a classical tension–compression test, and leads to cyclic softening at low to intermediate strain amplitudes. The second test consists in alternated uniaxial compressions along two perpendicular axes, and is selected based on the similarities with the loading path induced by the Fe–14Cr–1W–Ti ODS cladding tube pilgering process. This second test exhibits cyclic hardening at all tested strain amplitudes. Since variable strain amplitudes prevail in pilgering conditions, the parameters of the considered constitutive law were identified based on a loading sequence including strain amplitude changes. A proposed semi automated inverse analysis methodology is shown to efficiently provide optimal sets of parameters for the considered loading sequences. When compared to classical approaches, the model involves a reduced number of parameters, while keeping a good ability to capture stress changes induced by strain amplitude changes. Furthermore, the methodology only requires one test, which is an advantage when the amount of available material is limited. As two distinct sets of parameters were identified for the two considered tests, it is recommended to consider the loading path when modeling cold forming of the ODS steel.     

高温气冷堆舱室抗商用飞机撞击的耦合数值分析

本文建立了大型商用飞机撞击典型高温气冷堆核电站反应堆舱室的非线性有限元模型,计算中混凝土舱室直接采用工程用钢筋混凝土的损伤塑性本构模型,飞机结构采用Johnson-Cook本构模型。对飞机高速撞击高温气冷堆核电站反应堆舱室非线性撞击过程进行模拟计算,得出正面和侧面撞击条件下的撞击载荷曲线、撞击位移云图、反应堆舱室混凝土破坏情况等结果。评估表明,反应堆舱室结构在撞击条件下的整体损伤微小,可为保护内部关键设备提供重要的屏障功能。     

Experimental study on uniaxial and nonproportionally multiaxial ratcheting of SS304 stainless steel at room and high temperatures

An experimental study was achieved for the cyclic properties of SS304 stainless steel subjected to uniaxial strain-controlled, uniaxial and nonproportionally multiaxial stress-controlled cyclic loading at room and high temperatures. The effects of cyclic strain amplitude, mean strain, temperature and their histories on the cyclic deformation behavior of the material were investigated under the uniaxial strain-controlled cyclic loading. The uniaxial and nonproportionally multiaxial ratcheting was researched under the asymmetrical stress-controlled cyclic loading with variable stress amplitudes, mean stresses, loading paths and their histories at room and high temperatures. It is shown that the uniaxial cyclic properties under strain-controlled cyclic loading and the ratcheting under asymmetric uniaxial and nonproportionally multiaxial stress-controlled cyclic loading depend not only on the current temperature and loading state, but also greatly on the previous loading history and the shape of loading path. The material presents much greater cyclic hardening and less ratcheting in the range of 400–600 °C than at room temperature, due to the strong dynamic strain aging taken place in this temperature range. Some significant results were obtained for the constitutive modeling of cyclic plastic deformation such as ratcheting.