Micromechanical creep model for pure copper

A Unit Cell made of copper is simulated and investigated under creep conditions within the framework of micromechanics. Geometrical 3D model of the copper microstructure is represented as a Unit Cell with grains of random crystallographical orientation and geometry. Such simulation enables algorithm of Voronoi tessellation. The stress-strain behavior of grains in the general case is anisotropic due to the ordered crystalline structure. The anisotropic model for a material with a cubic symmetry is implemented in Abaqus and used to assign behavior of grain interior in elastic and creep regions. Material parameters for elastic model are taken from elastic tests of single crystal copper [1]. Power law material parameters for creep model are taken from creep test performed for single crystal copper [2]. The model parameter ξ is validated numerically. Creep results are presented for the case of proportional loading during the primary and secondary creep. Statistical analysis of creep curves received for 55 different realizations of Unit Cell geometry is carried out. As a result confident interval and mathematical expectation of creep data are calculated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于有限元的金属基短纤维复合材料MMC的一种统计蠕变模型

在有限元分析的基础上建立了一个单向应力状态下金属基短纤维复合材料(MMC)的统计蠕变模型.首先建立细胞模型并进行有限元分析,得到了单向应力状态下材料细观尺寸及载荷方向对宏观蠕变响应的影响规律.通过在细胞模型中增加一界面层(考虑材料特性和厚度)来研究基体和纤维的界面对MMC宏观蠕变响应的影响.基于细胞模型的数值结果,提出了一适用于纤维平面随机分布的随机统计模型,该模型考虑了纤维的断裂.通过试验获得纤维的统计分布规律.分析结果表明随机统计模型可以满意地描述试验结果.进一步讨论了材料细观尺寸,纤维的断裂特性以及界面层的材料特性和厚度对MMC宏观蠕变响应的影响.     

2014“高教社杯”全国大学生数学建模竞赛颁奖仪式在海军航空工程学院青岛校区举行

<正>2014年12月20日,2014"高教社杯"全国大学生数学建模竞赛颁奖仪式暨工作会议在海军航空工程学院青岛校区隆重举行。全国大学生数学建模竞赛组委会主任、复旦大学李大潜院士,海军航空工程学院政委龚理华少将,山东省教育厅宋承祥副厅长,高等教育出版社林金安副总编辑,中国科学院袁亚湘院士,全国大学生数学建模竞赛组委会副主任、专家组组长、浙江大学陈叔平教授等160余人出席了颁奖仪式。颁奖仪式由全国组委会秘书长、清华大学谢金星教授主持。颁奖仪式上,学院龚理华     

2014全国大学生数学建模竞赛“高教社杯”获奖感言

<正>尊敬的各位领导、老师,亲爱的同学们:大家好!室外数九隆冬,室内春意阵阵。在这温暖如春的颁奖仪式现场,我的内心既高兴又激动。让我高兴的是,我能参加"高教社杯"全国大学生数学建模竞赛;让我激动的是,自己能作为获奖者的代表在此发言。我是来自信阳师范学院数学与信息科学学院2012级的学生程双泽,我们能获得今年的高教社杯,是和无数人的关心和帮助分不开的。所以我想真诚地对他们说声-谢谢。感谢全国数学建模竞赛组委会及所有为数学建模付出心血的领导和老师们,是你们为全国广大学子提供了一个展现自我风采的平     

纳米单晶与多晶铜薄膜力学行为的数值模拟研究

通过对不同温度下单晶薄膜的拉伸性能的分子动力学模拟，从微观角度揭示了温度效应对材料性能的影响. 结果表明温度效应对材料的变形机理影响很大.0K温度下由于缺乏热激活软化的影响, 粒子运动所受到的阻碍较大, 薄膜的强度较高, 塑性变形主要来自于粒子的短程滑移.温度升高，粒子的热运动加剧，屈服强度降低, 塑性变形将主要来自于大范围的位错长程扩展.多晶薄膜的模拟结果表明, 虽然其晶粒形状较为特殊, 但是它仍然遵循反Hall-Petch关系.在模拟过程中，侧向应力最大值比拉伸方向应力的最大值滞后出现.位错只会从晶界产生并向晶粒内部传播，晶粒间界滑移是多晶薄膜塑性变形的主要来源.     

Micro-mechanical analysis of creep behavior in a multipass weld

A method of evaluating creep response of the multipass weld based on the micro-macro mechanics approach is introduced. Multipass weld microstructure that consists from columnar, coarse and fine grained zones is considered. Materials of these constituents assumed to be isotropic. Weld metal properties of inelastic behavior have general type of symmetry and are described by the anisotropic creep constitutive model. To model the microstructure of the multipass weld metal the representative volume element (RVE) is created for CAE Abaqus. Material properties of weld metal grain type zones are taken from the experiments. Numerical tests on uniform loading of the RVE are performed. Creep material properties for equivalent weld material are found for welds with different number of passes. The symmetry type of the creep material properties of multi-pass weld are evaluated for the equivalent weld material. As an example of macro model analysis of the welding, the creep calculation of the cylindrical shell with the welding under the uniform inner pressure is performed. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An exact determination of the effective moduli of elasticity of micro-inhomogeneous medial

An exact solution is obtained of the problem of determining all the macroscopic elastic constants of an anisotropic textured polycrystalline system comprising grains with cubic symmetry of the elastic properties and a discrete distribution of those properties in two equivalent orientations, differing by a rotation about the fourth-order axis through an angle of π/4.     

A meso elastoplastic constitutive model for polycrystalline metals based on equivalent slip systems with latent hardening

A meso material model for polycrystalline metals is proposed, in which the tiny slip systems distributing randomly between crystal slices in micro-grains or on grain boundaries are replaced by macro equivalent slip systems determined by the work-conjugate principle. The elastoplastic constitutive equation of this model is formulated for the active hardening, latent hardening and Bauschinger effect to predict macro elastoplastic stress-strain responses of polycrystalline metals under complex loading conditions. The influence of the material property parameters on size and shape of the subsequent yield surfaces is numerically investigated to demonstrate the fundamental features of the proposed material model. The derived constitutive equation is proved accurate and efficient in numerical analysis. Compared with the self-consistent theories with crystal grains as their basic components, the present theory is much simpler in mathematical treatment. Project supported by the National Natural Science Foundation of China (Grant No. 19732006).     

A finite element model based on statistical two-scale analysis for equivalent heat transfer parameters of composite material with random grains

In this paper, a new finite element model based on statistical two-scale analysis for predicting the equivalent heat transfer parameters of the composite material with random grains is presented and its convergence, its error result and the symmetry, positive property of equivalent heat transfer parameters matrix are also proved. Firstly, some definitions of the probability space and the composite material with random grains are described and the STSA formulation predicting the equivalent heat transfer parameters of the composite material are briefly reviewed. Next, a finite element formulation and its corresponding procedure for the composite material with random grains is described. Then, the convergence, the error estimate and the symmetry, positive property of the equivalent heat transfer parameters matrix computed by FE based on STSA are proved. The numerical result shows the validity of the FE model based on STSA and the convergence and the symmetry, positive property of the equivalent heat transfer parameter matrix of the composite material with random grains by the FE model.     

Multiscale Modeling of Nanocrystalline Materials: A Variational Approach

This paper presents a variational multi-scale constitutive model in the finite deformation regime capable of capturing the mechanical behavior of nanocrystalline (nc) fcc metals. The nc-material is modeled as a two-phase material consisting of a grain interior (GI) phase and a grain boundary (GB) phase. A rate-independent isotropic porous plasticity model is employed to describe the GB phase, whereas a crystal-plasticity model which accounts for the transition from partial dislocation to full dislocation mediated plasticity is employed for the GI phase. Assuming the rule of mixtures, the overall behavior of a given grain is obtained via volume averaging. The scale transition from a single grain to a polycrystal is achieved by Taylor-type homogenization. It is shown that the proposed model is able to capture the inverse Hall-Petch effect. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application of the Green Tensor to the Modeling of Solution-Precipitation Creep

Our aim is to present a mechanical model for solution-precipitation creep, a diffusive deformation process occurring in polycrystalline and granular materials. Within the scope of the model, a Lagrangian consisting of the elastic power and dissipation is proposed. The former is kept in a standard form typical for linear material behavior while the latter is assumed as a surface integral depending on the velocity of the material transport and the velocity of the motion of the boundary. The minimization with respect to the total deformations leads to the equilibrium equation which is solved analytically, by using Green's function. The evolution equations are obtained as the result of the minimization with respect to the internal variables and are solved via finite element method. The contribution closes with a numerical example showing the deformation of a polycrystal consisting of hexagonal crystals. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

镍基定向结晶合金蠕变损伤的细观模型

针对镍基定向结晶合金的蠕变变形和损伤,本文建立了有限元和自洽两种晶体滑移细观模型。在这两种模型中同时考虑了晶粒滑移损伤和晶界损伤。通过一组镍基单晶合金和一组特殊结晶取向的定向结晶合金标定了模型参数。数值分析结果表明,这两种模型都可以比较准确地描述定向结晶合金的蠕变损伤变形和失效规律,尤其是定向结晶合金蠕变性能的结晶取向相关性。     

Computational mechanics-based modeling of size-dependent hardening in polycrystals

It has been well-known for a number of years that the macroscopic material response of polycrystalline metals is influenced by the size and morphology of grains. Different size effects may occur, one of which is the Hall-Petch effect. The key aim of this contribution is the computational modeling of grain-size-dependent hardening in polycrystals using a microstructural approach. Here, the focus is on the influence of the microscopic grain boundary conditions on the simulation results. In particular, micro-flexible boundary conditions are discussed and compared to micro-hard and micro-free assumptions. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Creep-fatigue analysis of the steel AISI type 316 component failure

The purpose of this work is to extend a typical creep-damage model in order to describe material behavior under variable thermal and mechanical loading in wide stress range. The model basis is creep constitutive law in form of hyperbolic sine stress response function proposed by Nadai. The constitutive law is extended to assume the damage process under creep and fatigue by the introduction of scalar damage parameters and appropriate evolution equations according to Kachanov-Rabotnov concept. The material constants for model are identified by fitting the experimental creep and low-cycle fatigue data for the steel AISI type 316 at the range of temperatures 500°C – 750°C. The development of such model is motivated by the well described failure case study of high-temperature components at unit 1 of Eddystone power plant, which have operated during 130520 hours under creep-fatigue interaction conditions. The main steam piping (MSP) from this power plant is selected for thermo-mechanical creep-fatigue analysis applying the proposed material model. The estimated values of damage parameters comply with the real location of the component failure and a scatter of experimental data on creep-fatigue interaction diagram. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the geometric autocorrelation function of polycrystalline materials

Herein we derive an expression for direct determination of the geometric autocorrelation function W of a polycrystalline material from images of its grain boundary network (e.g., those delivered by orientation imaging microscopy). We also obtain an identity that relates the mean linear intercept function to a directional derivative of the geometric autocorrelation function. These formulae were applied to examine whether a widely-used formula for W, particularly in theoretical studies of attenuation of elastic waves in polycrystalline media, would be valid for the grain boundary structure of a commercial aluminum alloy. The conclusion was negative.     

Analysis of nanoindentation experiments by means of rheological models

The nanoindentation technique is established in the field of material characterization at small dimensions. It is daily practice to analyze nanoindentation data with an almost “classical” formula based on the publications by Oliver and Pharr and Fischer-Cripps. The procedure works well for elastic-time independent plastic material behavior, for example copper and the calibration material fused silica, even at higher test temperatures. However, low melting solder materials are susceptible to creep behavior. For this reason, additional analysis procedures are required to determine the material parameters more precisely. In this paper the authors want to give an introduction to an “enhanced” analysis of nanoindentation data based on rheological models, which are often used to describe the time-dependence of material response. Two examples of such models are the MAXWELL- and the KELVIN-body. The authors present a rheological model, published by Mencik in 2011 [1], in context with the corresponding equation which is used to extract the material properties from the recorded data. Results of the analysis at the calibration material fused silica are presented and discussed together with the material parameters published in the literature. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

单位圆到任意曲线保角变换的近似计算方法

本文讨论了将单位圆内部映射成由任意曲线(包括任意曲线割缝)边界围成的单连通域内部或外部的保角变换问题.以多边形逼近单连通域的边界,采用Schwartz-Christoffel积分建立单位圆与该多边形的映射函数.给出了确定Schwartz-Christoffel积分中未知参数的数值计算方法.