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A continuum approach to the modeling of microstructural evolution in polycrystalline solids.

机译:多晶固体微观结构演化建模的连续方法。

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摘要

Interest in microstructural evolution of polycrystalline materials stems from the multiplicity of interrelated phenomena that contribute to this evolution, and from the impact that such phenomena have on the performance and reliability of these materials, especially in applications such as microelectronic devices.; In this work, a continuum field formulation developed to study this type of phenomena is presented. The formulation accounts fully for the coupling between mechanical behavior, self diffusion, electric effects and interface migration. Each phenomenon being modeled is treated as a coupled initial and boundary value problem, consisting of these four component problems. Atomic-level mechanisms are taken into consideration while developing the thermodynamic basis of the formulation, from which the constitutive relations are derived.; The computational framework used to solve the resulting coupled field equations is described in detail. This framework is built around a staggered solution scheme in which the finite element method is used to solve each governing differential equation individually. Additional computational techniques utilized in the implementation are also discussed. Examples of these include the level set method, a least-squares projection/smoothing technique and a modified form of the Galerkin/least-squares stabilization method.; To study the problem of void nucleation in polycrystals, the stability of the atom-vacancy system is examined closely. A thermodynamic instability which could lead to spinodal decomposition of this system is identified. The amplications of this result in the context of void nucleation are explored and its relation to classical nucleation theory is realized. All quantities needed to calculate void formation rates are obtained from the coupled field calculations in a consistent mannen As expected, the results indicate that a high tensile stress can lead to void nucleation in the presence of impurities.; The problem of grain-boundary migration is also treated. The level set method is used successfully to track the moving boundary without remeshing. Thermodynamic driving forces for boundary migration arising from boundary curvature, stress-driven diffusion and electromigration are accounted for. In this case also, the strongly coupled nature of the problem is captured, the calculations remain stable and physically-meaningful results are obtained.
机译:对多晶材料的微结构演化的兴趣来自于促成这种演化的多种相互关联的现象,以及这种现象对这些材料的性能和可靠性的影响,特别是在微电子设备等应用中。在这项工作中,提出了研究这种现象的连续场公式。该公式充分说明了机械行为,自扩散,电效应和界面迁移之间的耦合。每个被建模的现象都被视为耦合的初始值和边值问题,由这四个组成部分问题组成。在开发配方的热力学基础时要考虑到原子级机理,由此可以得出本构关系。详细介绍了用于求解所得耦合场方程的计算框架。该框架围绕交错求解方案构建,其中使用有限元方法分别求解每个控制微分方程。还讨论了实现中使用的其他计算技术。这些示例包括水平设置方法,最小二乘投影/平滑技术和Galerkin /最小二乘稳定方法的改进形式。为了研究多晶中空核的问题,我们仔细研究了原子-空位系统的稳定性。确定了可能导致该系统旋节线分解的热力学不稳定性。探索了该结果在空隙形核中的意义,并实现了其与经典形核理论的关系。如所期望的,结果表明,高拉伸应力可导致在存在杂质的情况下空洞形核,从而计算出空洞形成速率所需的所有量。也解决了晶界迁移的问题。水平集方法可以成功地跟踪移动边界,而无需重新设置网格。考虑了由边界曲率,应力驱动的扩散和电迁移引起的边界迁移的热力学驱动力。同样在这种情况下,问题的强耦合性质得以捕获,计算保持稳定并获得了具有物理意义的结果。

著录项

  • 作者

    Mourad, Hashem M.;

  • 作者单位

    University of Michigan.;

  • 授予单位 University of Michigan.;
  • 学科 Engineering Mechanical.; Applied Mechanics.; Engineering Materials Science.
  • 学位 Ph.D.
  • 年度 2004
  • 页码 135 p.
  • 总页数 135
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 机械、仪表工业;应用力学;工程材料学;
  • 关键词

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