Lattice Curvature and Crystal Plasticity: Theory and Computation

晶格曲率和晶体可塑性：理论与计算

• 批准号: 9700358
• 负责人: David Parks
• 金额: $ 23.39万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-06-01 至 2001-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9700358&HistoricalAwards=false
• 关键词: Lattice; Curvature; Crystal; Plasticity; Theory

9700358 Parks A program of constitutive and computational research in crystal plasticity is proposed which is based on the concept of geometrically necessary dislocation density, proportional to certain spatial gradients of crystal shear strain, as providing a physical means to introduce size- dependent plastic response in crystals. The proposed formulation fits nicely with the underlying physical concepts, most clearly described by Ashby over 20 years ago. Among the host of applications where scale-dependent plasticity driven by this mechanism is encountered are the grain-size dependence of flow strength and work-hardening in polycrystals (Hall-Petch effect), size dependence of indentation microhardness, particle-size effects in the dispersion strengthening crystals. and others. In each case, the attainment of locally inhomogeneous shear strain,,over a characteristic geometric length scale,,results approximately in the storage of a geometrically necessary dislocations, where b is the crystal lattice constant. These "geometric" dislocations, which relieve the lattice incompatibility which would otherwise be introduced by conservative dislocation movement in producing the strain gradient, act as obstacles to other (glissile) dislocations, producing very enhanced local hardening. A review of the field shows that the computational methods proposed for dealing with this class of problems are both feasible to implement and are methodologically in good agreement with the materials science understanding. Preliminary computational results on a multi-crystalline aggregate have shown a clear Hall-Petch effect, based on "first principles." The effects of the extra dislocation density, which is concentrated near grain boundaries struggling to deform compatibly, also give rise to distinct patterning of strain within the grain. The proposed extensions of the work will address less idealized versions of the Hall-Petch phenomenon, the deformation of thin metallic layers constrained between ceramics, including thermally-induced misfit strain, and particle size effects in the dispersion strengthening of crystals. The results will be of fundamental scientific value, being a first computational thrust into quantifying scale effects in crystal plasticity and the interactions of statistically stored and geometrically necessary dislocations. Among the industrial applications which could benefit from a robust computational capability to account for scale-dependent plasticity are the mechanical behavior of multi-layer electronic devices and thin films.

本文提出了晶体塑性的本构和计算研究方案，该方案基于几何必要位错密度的概念，与晶体剪切应变的一定空间梯度成正比，为引入晶体中尺寸相关的塑性响应提供了一种物理手段。所提出的公式与Ashby在20多年前最清晰地描述的基本物理概念非常吻合。在由该机制驱动的尺度相关塑性的众多应用中，包括多晶体中流动强度和加工硬化的晶粒尺寸依赖性（霍尔-佩奇效应），压痕显微硬度的尺寸依赖性，分散强化晶体中的粒度效应。和其他人。在每一种情况下，局部不均匀剪切应变的实现，在一个特征几何长度尺度上，近似地导致了一个几何上必要的位错的存储，其中b是晶格常数。这些“几何”位错缓解了晶格不相容，否则，在产生应变梯度时，保守位错运动将引入晶格不相容，作为其他（滑块）位错的障碍，产生非常增强的局部硬化。对这一领域的回顾表明，所提出的处理这类问题的计算方法是可行的，而且在方法上与材料科学的理解是一致的。基于“第一性原理”的多晶聚集体的初步计算结果显示出清晰的霍尔-佩奇效应。额外的位错密度的影响，集中在晶界附近，难以协调变形，也会在晶粒内产生明显的应变模式。提出的工作扩展将解决不太理想的Hall-Petch现象，陶瓷之间约束的薄金属层的变形，包括热诱导的失配应变，以及晶体弥散强化中的粒度效应。这些结果将具有基本的科学价值，是对晶体塑性的尺度效应以及统计上存储的和几何上必要的位错的相互作用进行量化的第一次计算推进。在工业应用中，可以从强大的计算能力中受益，以解释尺度相关的塑性，包括多层电子器件和薄膜的机械行为。