The Morphological Evolution of Particles in Elastically Stressed Solids

许多具有工程意义的合金的性能与相干第二相粒子的形貌和空间分布有关。在许多情况下，弹性应力存在于这些两相体系中，这要么是由于少数相颗粒和基体之间晶格参数的差异，要么是由于外加应力。由于对控制应力结晶固体中颗粒形态的因素的了解尚不清楚，因此很难预测这些多相材料的性能。这种理解的缺乏可以追溯到有限数量的研究，这些研究调查了控制相干错配粒子的平衡形状的因素，即在粒子形态的所有可能变化下，使系统总能量最小化的形状。然而，这些少数研究表明，弹性应力的存在可以导致与没有应力时质的不同现象，例如给定一组材料参数的多个平衡形状，颗粒分裂和非凸，沙漏状平衡形状。%%%%该项目的一个主要目标是提供弹性应力在不拟合的三维粒子的平衡形态发展中的一般作用的图片。由于确定错拟合粒子平衡形状的方程是高度非线性的，因此在三维中存在比以往在二维中观察到的粒子平衡形状复杂得多的粒子形状分岔结构。尽管研究的数值性质和工作中每个部分采用的具体假设，但将提供理解和预测应力固体中颗粒形态演变的一般框架。最后，该理论将与实验一起用于研究非膨胀失配对弹性各向异性系统中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. ***