含与不含晶界空穴的双晶体蠕变行为研究

基于晶体滑移理论,建立了各向异性镍基合金双晶体的蠕变本构模型和蠕变寿命预测模型,通过MARC用户子程序CRPLAW将上述本构模型进行了有限元实现,并对双晶体蠕变行为进行了计算分析,考虑了:(1)晶体取向的影响;(2)垂直、倾斜和平行于外载方向的三种位向晶界情况;(3)晶界处引进空间空穴的影响。结果表明,双晶体上特别是微空穴和晶界附近区域的蠕变应力应变呈现不同的变化规律,对此晶粒晶体取向和晶界位向有较大的影响;微空穴的存在削弱了双晶体的承载能力,显著地影响了双晶体蠕变持久寿命;相同条件下,垂直晶界对双晶体模型的蠕变损伤影响最为强烈,倾斜晶界次之,平行晶界最小;微空穴的生长与晶界位向和晶体取向有强烈的依赖关系,其中垂直晶界更有利于晶体滑移和微空穴生长。     

Meso approaches for the creep damage behavior of nickel-base directionally solidified superalloys

IntroductionNickel-basehightemperatureresistancesuperalloysarsewidelyusedingasturbinesandjetengines.DireetionallysolidificationwasintroducedtoenhancecreepsbengthbyelindnahnggrainboundariesnormaltotheappliedstresswherevoidsarelikelytOoccurundercreepload.Inpractice,however,theappliedstressmaynotbeuniaxialnordirectedparalleltOthegrainboundaries.Singlecrystalswerethusdeveloped.CongregationoflowtempefAnremeltingelementsongrainboundaries,grainboundaryoxidation)etc.,areadditionalfactorsthatwoulddeg…     

Evaluation of creep damage behavior of nickel-base directionally solidified superalloys with different crystallographic orientations

A crystallographic creep damage constitutive model is developed for nickel-base directionally solidified superalloys. The rates of material degradation and grain boundary void growth are considered. The governing parameters are determined from the creep test data of single crystals and directionally solidified superalloys with a crystallographic orientation. A finite element program is used to analyze the creep damage behavior of nickel-base directionally solidified superalloys for different crystallographic orientations. The results depend on the number of grains modelled and compare well with the experimental data.     

Numerical investigation of grain boundary effects on elevated-temperature deformation and fracture

A three-dimensional (3D) polycrystal intergranular model that accounts for grain boundary deformation and intergranular weakening at elevated temperatures is presented. The effects of grain boundaries on the accumulated slip deformation of grain interiors and lattice rotation have been investigated through a comparison between results from a model including grain boundary region (GBM) and a model representing only the grain interiors not the grain boundary region directly (NGBM). It is found that the presence of grain boundaries seems to suppress the grain interior slip deformation, and this suppressive role is reduced with increased relative thickness of the grain boundaries. In addition, grain boundaries promote the lattice rotation of individual grains in shear bands but suppress that of individual grains within non-shear bands. Mutual rotation of grains in both shear and non-shear bands is caused by the introduction of grain boundary regions. Rate-dependence of high-temperature plasticity could be more accurately captured by the GBM than by the NGBM. By considering creep damage of grain boundary, when the damage variable reaches a critical value, the corresponding grain boundary element is eliminated to describe dynamic intergranular fracture processes. The volume-averaged stress–strain curve by a model considering grain boundary damage (DGBM) showed better agreement with experimental results than that by a model not considering grain boundary damage (GBM).     

Brittle versus ductile transition of nanocrystalline metals

The brittle versus ductile transition for conventional metals is dictated by the competition between dislocation emission and cleavage. For nanocrystalline metals with grain size below 25 nm, however, dislocation activities are suppressed and the classic theory fails to apply. In this paper, one of the competing mechanisms that control the brittle versus ductile transition of nanocrystalline metals is found to be the grain boundary dominated creep deformation versus the grain boundary decohesion. A model is proposed to quantify the crack propagation in nanocrystalline metals. The effects of material properties, initial configuration and applied loads on the property of crack propagation are addressed. It is concluded that either the increases in the initial crack length, the applied load and the grain boundary damage, or the deterrence in creep deformation, accelerate the crack propagation, and vice versa.     

基于Burgers模型考虑损伤的岩石蠕变全过程研究

岩石蠕变是一个显著的非线性问题，而经典的Burgers 模型是一种线性蠕变模型，必然不能全面地描述岩石蠕变的全过程．当岩石处于高应力水平下的加速蠕变阶段，岩石内部损伤会不断产生和累积，蠕变呈现出明显的非线性特征．为了更好地描述考虑损伤的岩石蠕变全过程，本文假定加速蠕变阶段的损伤演化方程，将损伤引入到Burgers 模型中，提出了一种非线性蠕变损伤模型．然后以乔后盐矿试件蠕变实测数据为分析案例，验证模型在应用于实际工程时的准确性和适用性．最后根据Origin 软件数值拟合的结果，表明本文所提出的非线性蠕变损伤模型能很好地描述岩石蠕变全过程，模型参数取值也在合理范围之内，模型拟合曲线与实验所得数据具有较好的一致性．     

A constitutive theory for creep behavior of initially isotropic materials sustaining unilateral damage

The goal of the present work is to modify structure of the creep constitutive equations existing in the literature, and simultaneously to incorporate both damage induced anisotropy and unilateral damage into the constitutive model. The proposed nonlinear-tensor constitutive equation for creep together with the damage evolution equation take into account the secondary and tertiary creep of the initially isotropic materials. The material parameters of the model are determined using basic experiments. It is shown that the creep model is capable of describing available experimental data for the lateral creep responses under uniaxial compression.     

On a damage law for creep rupture of clays with accumulated inelastic deviatoric strain as a damage measure

To avoid the dependency on origin of time, an improved damage law for creep rupture of clays is proposed considering the accumulated inelastic deviatoric strain as a measure of damage, instead of incorporating time directly. This law is incorporated into an existing anisotropic elastoplastic-viscoplastic bounding surface model for clays. The performance of the damage law was demonstrated via the simulations of creep rupture tests on undisturbed clays, and generally a good agreement between model simulations and test data was obtained. Discussions on the creep rupture parameters were followed and further improvement was suggested. At present when high quality test data for creep rupture is very limited, the proposed damage law could serve as a practical way to model creep rupture of clays.     

基于Lemaitre原理改进砂岩蠕变损伤模型研究

以煤矿巷道围岩（砂岩）为研究对象,采用MTS815.02岩石力学试验系统,对流固耦合蠕变过程中孔隙水压力作用机制展开研究,以伯格斯模型为基础,基于Lemaitre原理建立改进的伯格斯非线性蠕变损伤模型,可以得到如下主要结论：当围压越大,岩石蠕变最后一级荷载作用持续时间越长,相对经历衰减蠕变和稳定蠕变时间越长;且由最终一级破坏蠕变变形值可知,孔隙水压较小时,蠕变变形量相对较大,此时围压增大提升了岩石延性特性,但是孔隙水压增大却削弱了围压作用,由于孔隙水压使得岩石力学性能劣化,因而减少了岩石在破坏时蠕变变形量;随后基于Lemaitre原理建立的伯格斯非线性损伤蠕变模型,可以较好地描述岩石的衰减蠕变、稳定蠕变与加速蠕变阶段;且试验曲线与拟合曲线吻合度高,验证了本文所建立损伤流变模型的合理性．     

岩石材料的一种蠕变损伤方程

通过大量的岩石蠕变试验研究，总结出了以能描述损伤历史的蠕变模量为参数的岩石蠕变损伤方程，由该方程能方便地定出任意蠕变时刻的损伤状态和进行蠕变损伤的测定。     

Anisotropic continuum damage modeling for single crystals at high temperatures

In single crystals, the process of creep damage is generally anisotropic. Indeed, the damage evolution does not only depend on the loading conditions, but also on the lattice orientation. And the current state of damage has an anisotropic influence on the effective stress state, so that it is represented by a tensorial damage variable. Based on the continuum damage mechanics theory, a creep damage model for F.C.C. single crystals has been developed and implemented in a three-dimensional anisotropic creep model. It is shown that the resulting material model is capable of describing the orientation dependence of the creep and damage evolution of nickel-based superalloys in the high temperature regime.     

A CREEP DAMAGE EQUATION FOR ROCKS

In this paper,based on many experimental results,a creep damageequation for rocks with a creep modulus that can describe the history of damage hasbeen deduced.According to the equation,a creep damage model for rock materials isconstructed,and it is shown that the extent of their damage,or damage degree,duringcreep can be determined by means of simple experiments.     

Effect of grain boundary sliding on creep constrained diffusive cavitation

For polycrystalline metals undergoing creep at high temperatures the nucleation, growth and coalescence of grain boundary cavities is investigated, with main focus on the influence of grain boundary sliding. Both the local stress state and the average rate of opening of a cavitating facet can be rather strongly affected by sliding on the grain boundaries emanating from the edges of this facet. A number of numerical solutions of axisymmetric model problems are used to study the combined influence of sliding and cavitation. The time to creep rupture by cavity coalescence is significantly reduced by grain boundary sliding, as is seen by comparison with analyses that disregard sliding. The numerical results are compared with predictions of a set of constitutive relations for creep in polycrystals with grain boundary cavitation.     

动力损伤后的脆性岩石静力蠕变断裂模型研究

应力波动力扰动下脆性岩石的静力蠕变特性,对深部地下工程围岩变形的评价有重要的实践意义.动力载荷作用导致的局部细观裂纹损伤严重影响脆性岩石蠕变力学行为.基于细观裂纹扩展与应力关系模型、动力扰动损伤演化函数、静动力载荷演化路径函数与黏弹性本构模型,提出一种应力波动力扰动下脆性岩石蠕变断裂特性的宏细观力学模型.其中动力损伤通过控制岩石内部细观裂纹数量变化实现.模型描述了应力波动力扰动下岩石的应变时间演化曲线,解释了岩石动力扰动下蠕变失效特性.研究了不同应力波幅值及周期影响下的脆性岩石应变-时间关系曲线,并通过试验结果验证了模型的合理性.讨论了动力损伤变化形式,突变发生时刻,突变量的大小对岩石蠕变失效特性的影响.分析了应力波幅值、周期对岩石动态动力损伤效应以及蠕变失效特性的影响.主要研究结果:动力损伤的变化值越大,岩石蠕变失效发生时间越短.冲击载荷扰动期间,动力损伤发生的时刻及增加的形式,对动力扰动后的岩石应变及蠕变破坏时间影响很小.动力损伤变化量随应力波幅值增加、周期减小而加速增大.应力波幅值越大、周期越小,岩石发生蠕变失效时间越短.     

A model for high temperature creep of single crystal superalloys based on nonlocal damage and viscoplastic material behavior

A model for high temperature creep of single crystal superalloys is developed, which includes constitutive laws for nonlocal damage and viscoplasticity. It is based on a variational formulation, employing potentials for free energy, and dissipation originating from plasticity and damage. Evolution equations for plastic strain and damage variables are derived from the well-established minimum principle for the dissipation potential. The model is capable of describing the different stages of creep in a unified way. Plastic deformation in superalloys incorporates the evolution of dislocation densities of the different phases present. It results in a time dependence of the creep rate in primary and secondary creep. Tertiary creep is taken into account by introducing local and nonlocal damage. Herein, the nonlocal one is included in order to model strain localization as well as to remove mesh dependence of finite element calculations. Numerical results and comparisons with experimental data of the single crystal superalloy LEK94 are shown.     

Creep damage and life analysis of anisotropic materials

Summary  This paper provides a short survey of some recent advances in the mathematical modelling of materials behaviour under creep conditions. The tertiary creep phase is accompanied by the formation of microscopic cracks on the grain boundaries in such a way so that damage accumulation occurs. The paper is divided into three parts. Firstly, the damage state in a uniaxial tension specimen is discussed and the time to rupture calculated. The second part is concerned with the creep behaviour of materials in multiaxial stress. Because of its microscopic nature, damage generally has an anisotropic character even if the material was originally isotropic. The fissure's orientation and length cause anisotropic macroscopic behaviour. Therefore, damage in an isotropic or anisotropic material, which is in a state of multiaxial stress, can only be described in a tensorial form. Thus, tensorial constitutive and evolution equations have been developed. Some examples for practical use are discussed. Finally, some own experiments are mentioned which have been carried out in order to validate the mathematical modelling. Received 16 July 1999; accepted for publication 8 March 2000     

Modeling hydrogen attack effect on creep fracture toughness

The effect of high temperature hydrogen attack on creep crack growth rates in steels is studied by modeling the interaction between creep deformation and gaseous pressures generated by hydrogen and methane. The equilibrium methane pressure as a function of hydrogen pressure, temperature and carbide types for carbon steels and Cr–Mo steels is calculated. This gaseous driving force is incorporated into a micromechanics model for void growth along grain boundaries of a creeping solid. Growth and coalescence of voids along grain boundaries is modeled by a microporous strip of cell elements, referred to as the fracture process zone. The cell elements are governed by a nonlinear viscous constitutive relation for a voided material. Two rate sensitivities as well as two types of grain boundaries are considered in this computational study. Simulations of creep crack growth accelerated by gaseous pressures are performed under conditions of small-scale and extensive creep. The computed crack growth rates at elevated temperatures are able to reproduce the trends of experimental results.     

一种新的岩石非线性损伤蠕变模型

为描述岩石加速蠕变阶段的非线性变形规律,在广义开尔文体基础上串联一个村山体,基于Kachanov损伤率理论,建立了损伤变量D与蠕变时间的函数关系,并根据Lemaitre应变等效原理将村山体中的无损模型参数p用有效模型参数p(1-D)代替,以此来表征岩石加速蠕变阶段的非线性,建立了一种新的非线性损伤蠕变模型;根据广义塑性力学理论给出了该模型的三维蠕变方程;采用Levenberg-Marquardt非线性优化最小二乘法对红砂岩和绿片岩常规三轴压缩蠕变试验数据进行拟合,反演得到这两种岩石的蠕变模型参数。拟合结果表明:拟合曲线与试验曲线的拟合相关系数R2分别为0.999和0.992,说明该蠕变模型能较好地反映这两种岩石各阶段的蠕变曲线特征。     

岩石含水蠕变损伤模型的开发与应用

摘要：为研究岩石含水率对蠕变的影响,将含水开关与蠕变损伤阀值引入蠕变模型,实现了含水劣化与蠕变损伤在本构关系上的耦合,建立了岩石含水蠕变损伤模型。模型与某软岩的三轴压缩蠕变试验结果取得了较好的拟合效果,并由麦夸特法+通用全局优化（LM-UGO）算法反演出了模型参数随岩石含水率的变化规律。在C++语言和FLAC3D中Fish语言的环境下,通过推导模型本构方程的三维差分形式,并利用FLAC3D所提供的接口实现了模型的二次开发。通过对开发的岩石含水蠕变损伤模型进行算例验证和分析,验证了模型的可靠性,也得出了软岩巷道蠕变变形随围岩含水率增大而增加的结论,进一步反映出蠕变模拟计算中考虑岩石含水率的必要性。     

A phenomenological model for anisotropic creep in a multipass weld metal

Creep strength of welded joints can be estimated by continuum damage mechanics. In this case constitutive equations are required for different constituents of the welded joint: the weld metal, the heat-affected zone, and the parent material. The objective of this paper is to model the anisotropic creep behavior in a weld metal produced by multipass welding. To explain the origins of anisotropic creep, a mechanical model for a binary structure composed of fine-grained and coarse-grained constituents with different creep properties is introduced. The results illustrate the basic features of the stress redistribution and damage growth in the constituents of the weld metal and agree qualitatively with experimental observations. The structural analysis of a welded joint requires a model of creep for the weld metal under multiaxial stress states. For this purpose the engineering creep theory based on the creep potential hypothesis, the flow rule, and assumption of transverse isotropy is applied. The outcome is a coordinate-free equation for secondary creep formulated in terms of the Norton–Bailey–Odqvist creep potential and three invariants of the stress tensor. The material constants are identified according to the experimental data presented in the literature.