The Morphological Evolution of Particles in Elastically Stressed Solids

9322687 Voorhees许多具有工程意义的合金的性能与共格第二相粒子的形态和空间分布有关。在许多情况下，这些两相系统中存在弹性应力，其原因要么是少数相粒子和基质之间的晶格参数不同，要么是外加应力。由于目前还不了解控制应力结晶固体中颗粒形态的因素，因此很难预测这些多相材料的性质。这种认识的缺乏可以追溯到研究控制相干失配粒子的平衡形状的因素的有限数量的研究，即使系统总能量最小化的形状受制于粒子形态的所有可能的变化。然而，这几项研究表明，弹性应力的存在可以导致与无应力情况下本质上不同的现象，例如给定一组材料参数的多种平衡形状、粒子分裂和非凸的沙漏状平衡形状。这个项目的一个主要目标是提供一幅图，说明弹性应力在发展失配三维粒子的平衡形态中所起的一般作用。由于决定失配粒子平衡形状的方程是高度非线性的，因此在三维空间中出现了比以往关于二维粒子平衡形状的工作复杂得多的粒子形状分叉结构。尽管这项研究的数值性质和工作的每一部分都采用了具体的假设，但仍将提供一个理解和预测受压固体中颗粒形态演变的一般框架。最后，这一理论将与实验相结合，研究弹性各向异性系统中非膨胀失配对失配粒子形态的影响。***

9322687 Voorhees The properties of many alloys of engineering significance are related to the morphology and spatial distribution of coherent second-phase particles. In many cases elastic stress is present in these two-phase systems resulting from either a difference in lattice parameters between the minority phase particles and the matrix, or an applied stress. As an understanding of the factors controlling the morphology of a particle in a stressed crystalline solid is not at hand, it is difficult to predict the properties of these multiphase materials. This lack of understanding can be traced to the limited number of studies that have investigated the factors controlling the equilibrium shape of a coherent misfitting particle, i.e. the shape that minimizes the total energy of the system subject to all possible variations in particle morphology. Nevertheless, these few studies have shown that the presence of elastic stress can lead to qualitatively different phenomena than in the absence of stress, such as multiple equilibrium shapes for a given set of materials parameters, particle splitting and non convex, hourglass-like, equilibrium shapes. %%%% A major goal of this project is to provide a picture of the generic role elastic stress plays in the development of the equilibrium morphology of a misfitting three-dimensional particle. As the equations which determine the equilibrium shape of a misfitting particle are highly nonlinear, a far more complex particle shape bifurcation structure is present in three-dimensions than observed in previous work on the equilibrium shape of a particle in two- dimensions. Despite the numerical nature of the study and the specific assumptions employed in each section of the work, a general framework for understanding and predicting the morphological evolution of particles in stressed solids will be provided. Finally, this theory will be used in concert with experiments to investigate the effects of a nondilation al misfit on the morphology of misfitting particles in an elastically anisotropic system. ***