A micromechanical model for polycrystalline creep with grain boundary cavitation

Summary  A micromechanical model is developed to describe effects such as combined power-law creep and diffusion, grain boundary sliding and cavitation in polycrystals. Several aspects of creep-constrained cavitation are taken into account such as diffusion in a cage of creeping matrix material and cavitating facets in a cage of creeping grains. Grain boundary sliding is modelled by distributed micro-shearcracks. It is shown that the different physical mechanisms and their interactions are functions of a well-defined material parameter λ, which can be related to the material length scale L introduced by Rice. Received 18 January 2000; accepted for publication 17 May 2000     

Creep cavitation in metals

This review concisely describes the state-of-the-art of the understanding of cavity, or r-type void, formation during stages I and II (primary and secondary) creep in polycrystalline metals and alloys, particularly at elevated temperatures. These cavities can directly lead to Stage III, or tertiary, creep and the eventual failure of metals. There have been, in the past, a variety of creep fracture reviews that omitted important developments relevant to creep cavitation or are less than balanced in their discussions of conflicting ideas or theories regarding various aspects of cavity nucleation and growth. This concise, comprehensive, review discusses all of the important developments over the past several decades relating to both the nucleation and growth of cavities. The nucleation section discusses the details and limitations of the approaches based on “classic” nucleation theory, slip-induced nucleation as well as grain boundary sliding effects. Growth is discussed starting from the Hull–Rimmer diffusion controlled cavity growth (DCCG) model. This will be followed by refinements to DCCG by others. Next, there will be a discussion of plastic cavity growth and diffusion-plasticity coupling theories. This will be followed by the particularly important development of constrained cavity growth, initially proposed by Dyson, and probably under-appreciated. Other growth effects by grain boundary sliding will also be discussed. All of these mechanisms will be compared with their predictions in terms of creep fracture phenomenology such as the Monkman–Grant relationship. Finally, there will be a discussion of creep crack propagation by cavitation ahead of the crack tip.     

A homogenized microstructural approach to creep fracture

A two-dimensional nonlocal continuum model is proposed in this paper for creep damage in polycrystalline materials. Starting from previous micromechanical modeling, a heuristic homogenization approach is adopted to derive a theory for the macroscopic response. The model accounts for the main damage mechanisms (grain boundary sliding, nucleation, growth and coalescence of cavities along the grain boundaries) responsible for the creep fracture process. The resulting constitutive law takes into account the nonlocalities expressed through the gradients of the stresses and the damage variables.     

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。     

Recoverable creep deformation and transient local stress concentration due to heterogeneous grain-boundary diffusion and sliding in polycrystalline solids

Numerical simulations are used to investigate the influence of heterogeneity in grain-boundary diffusivity and sliding resistance on the creep response of a polycrystal. We model a polycrystal as a two-dimensional assembly of elastic grains, separated by sharp grain boundaries. The crystal deforms plastically by stress driven mass transport along the grain boundaries, together with grain-boundary sliding. Heterogeneity is idealized by assigning each grain boundary one of two possible values of diffusivity and sliding viscosity. We compute steady state and transient creep rates as functions of the diffusivity mismatch and relative fractions of grain boundaries with fast and slow diffusion. In addition, our results show that under transient conditions, flux divergences develop at the intersection between grain boundaries with fast and slow diffusivity, which generate high local stress concentrations. The stress concentrations develop at a rate determined by the fast diffusion coefficient, and subsequently relax at a rate determined by the slow diffusion coefficient. The influence of the mismatch in diffusion coefficient, loading conditions, and material properties on the magnitude of this stress concentration is investigated in detail using a simple model problem with a planar grain boundary. The strain energy associated with these stress concentrations also makes a small fraction of the plastic strain due to diffusion and sliding recoverable on unloading. We discuss the implications of these results for conventional polycrystalline solids at high temperatures and for nanostructured materials where grain-boundary diffusion becomes one of the primary inelastic deformation mechanisms even at room temperature.     

A solution to the hydrodynamic lubrication of a circular point contact sliding over a flat surface with cavitation

This letter presents an analytical solution to the hydrodynamic lubrication of a circular point contact sliding over a flat surface with cavitation. The solution is found by solving the Reynolds equation with Reynolds boundary condition for cavitation. The cavitation boundary is shown to be straight lines directed 108.4° against the sliding direction. The result is experimentally verified in the limit of large values of viscosity, sliding velocity and radius of a spherical ball. The solution raises questions about the coupling between cavitation and film rupture and can be used as an independent check on the validity of numerical solutions.     

A two-dimensional finite element method for simulating the constitutive response and microstructure of polycrystals during high temperature plastic deformation

We describe a finite element method designed to model the mechanisms that cause superplastic deformation. Our computations account for grain boundary sliding, grain boundary diffusion, grain boundary migration, and surface diffusion, as well as thermally activated dislocation creep within the grains themselves. Front tracking and adaptive mesh generation are used to follow changes in the grain structure. The method is used to solve representative boundary value problems to illustrate its capabilities.     

A crack on the grain boundary — An analysis based on crystal plasticity theory

The influence of the mismatch of the lattice orientation on the deformation and stress fields of a crack located on the grain boundary is studied by means of the finite-element analysis taking account of finite deformatio and finite lattice rotation. The plane strain calculations for an fcc crystal subjected to mode I loading are performed on the basis of the crystalline plasticity described by a planar three-slip model. For the crack-tip shapes and the dominant deformation modes on slip systems, results of all the cases analysed here are in qualitative agreement with the earlier analytical and numerical solutions. Our results indicate that the lattice orientation difference may greatly influence the shear stress along the grain boundary which is related to grain-boundary sliding, while the normal stress along the grain boundary, which may induce cleavage fracture, is virtually insensitive to it. The influence of the lattice orientations on the crack-tip fields is also investigated under small-scale-yielding conditions and the comparison with the results of finite deformation is made.     

Analysis of deformation mechanisms in superplastic yttria-stabilized tetragonal zirconia

There have been extensive experimental observations of changes in the apparent rate controlling creep parameters in studies on superplastic materials. The three most common explanations associated with these changes in the stress exponent, n, the activation energy Q and the inverse grain size exponent, p involve the effect of concurrent grain growth, the operation of a threshold stress or transitions in creep mechanisms. Each of these factors may influence experimental creep data in a similar manner. Therefore, a careful analysis of the consequences of all three factors must involve the development of a consistent set of experimental observations in order to adequately distinguish the effects of each. This paper discusses the role of concurrent grain growth, a threshold stress and transitions in creep mechanisms in superplastic materials. Specific attention is given to the analysis of data on superplastic yttria-stabilized zirconia ceramics for which an increase in n has been observed at low applied stresses. It is demonstrated that neither concurrent grain growth nor a threshold stress can account for all the relevant experimental observations in this material. It is concluded that the changes in rate controlling creep parameters are associated with the operation of two distinct sequential mechanisms as part of a grain boundary sliding process.     

Elastoplastic contact of rough surfaces: a line contact model for boundary regime of lubrication

This paper introduces an improved friction model accounting for elastoplastic behavior of interacting asperities along contiguous rough surfaces for a line contact solution. It is based on Greenwood and Tripp’s original boundary friction model and specifically tailored for a boundary regime of lubrication. The numerical solution of Reynolds’ equation is achieved by implementing Elrod’s cavitation algorithm for a one dimensional line contact. The transience in the numerical solution is retained by accounting for the squeeze film term in Reynolds’ equation under fixed loading conditions and varying sliding motion. A sliding bearing rig is used to measure friction and compare the results with the prediction made using the approach highlighted above. The numerical/experimental results show good agreement.     

FCC晶体中不均匀变形对空洞长大的影响

通过编制率相关有限元用户子程序,采用一个单胞模型研究了FCC晶体中孔洞在单晶及晶界的长大行为,分析了由于晶体取向及变形失配对孔洞长大和聚合的影响。研究结果表明：孔洞的形状和长大方向与晶体取向密切相关;晶界上孔洞的长大速度大于单晶中孔洞的长大速度;晶粒间的变形失配加速了晶界上孔洞的长大趋势,因而使材料易发生沿晶断裂,随着晶粒间取向因子差异的增加,孔洞越易沿着晶界长大。     

镍基单晶高温合金定向粗化行为及高温蠕变力学性能研究进展

镍基单晶高温合金是一种广泛应用于航空发动机和工业燃气轮机的两相叶片材料,由软的$\gamma $ 基体相和均匀镶嵌在其中的立方状 $\gamma'$ 沉淀强化相组成.它有个显著的特征,即在高温施加应力条件下, $\gamma '$沉淀相会发生定向粗化, 形成筏状.这种筏化行为直接影响了合金的蠕变疲劳寿命,是镍基单晶高温合金强化机制研究的重点. 此外,镍基单晶高温合金无晶界, 不存在高温晶界弱化、纵向晶界裂纹等问题.因此, $\gamma$/$\gamma'$相界面的位错运动、微观结构以及在载荷和温度作用下的演化决定了其蠕变力学性能.本文从镍基单晶高温合金的微观强化机制出发对定向粗化行为及蠕变力学性能进行了综述.重点介绍了定向粗化行为发生的微观机理、驱动力、影响因素和蠕变过程中界面微结构演化、蠕变力学模型以及定向粗化对高温蠕变力学性能的影响,指出了高温蠕变力学性能研究的发展方向和仍待解决的问题.      

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.     

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

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

基于纳米压入法Sn-Ag-Cu无铅焊料高温力学性能的研究

无铅化和微型化已经成为电子封装的发展趋势,温度对无铅焊点的可靠性产生了不可忽视的影响。本文对Sn96.5Ag3Cu0.5无铅焊料进行回流处理,采用纳米压入法研究其在实际工况下的高温力学性能。结果表明,温度对焊料试样的力学性能影响显著。随着温度的升高,弹性模量和硬度逐渐降低,焊料发生软化;较高温度下的蠕变应力指数较小,焊料的蠕变抗力降低,其相应的蠕变激活能为76kJ/mol。由此可知,随温度的升高,焊料的蠕变机制由位错攀移逐渐转变为晶界滑移。     

超塑性变形晶界效应研究综述

自1934年超塑性现象被发现, 一直以其特殊的塑性变形机制而备受关注.本文以对超塑性变形晶界研究为主线, 从力学角度总结了近年来研究成果. 包括: 基于晶界拓扑构造、统计规律以及能量耗散的力学模型; 论述了由孔洞损伤导致的超塑性沿晶破坏、晶界结构演化与宏观率敏感性之间的关系; 列举了考虑晶界效应的典型超塑性数值模型; 总结并讨论了晶界滑移定量表征的重要实验手段, 指出超塑性研究中需进一步拓展的领域: 多尺度耦合的超塑性力学、材料制备及组合工艺中利用超塑性.      

磁电弹复合材料和刚性导电导磁圆柱压头的二维微动接触分析

本文求解平面应变状态下磁电弹复合材料半平面和刚性导电导磁圆柱压头的二维微动接触问题。假设压头具有良好的导电导磁性,且表面电势和磁势是常数。微动接触依赖载荷的加载历史,所以首先求解单独的法向加载问题,然后在法向加载问题的基础上求解循环变化的切向加载问题。整个接触区可以分为内部的中心粘着区和两个外部的滑移区,其中滑移区满足Coulomb摩擦法则。利用Fourier积分变换,磁电弹半平面的微动接触问题将简化为耦合的Cauchy奇异积分方程组,然后数值离散为线性代数方程组,利用迭代法求解未知的粘着/滑移区尺寸、电荷分布、磁感应强度、法向接触压力和切向接触力。数值算例给出了摩擦系数、总电荷和总磁感应强度对各加载阶段的表面接触应力、电位移和磁感应强度的影响。     

Micromechanics modeling of strength for nanocrystalline copper

We present a model in this paper for predicting the inverse Hall–Petch phenomenon in nanocrystalline (NC) materials which are assumed to consist of two phases: grain phase of spherical or spheroidal shapes and grain boundary phase. The deformation of the grain phase has an elasto-viscoplastic behavior, which includes dislocation glide mechanism, Coble creep and Nabarro–Herring creep. However the deformation of grain boundary phase is assumed to be the mechanism of grain boundary diffusion. A Hill self-consistent method is used to describe the behavior of nanocrystalline pure copper subjected to uniaxial tension. Finally, the effects of grain size and its distribution, grain shape and strain rate on the yield strength and stress–strain curve of the pure copper are investigated. The obtained results are compared with relevant experimental data in the literature.