Lattice Curvature and Crystal Plasticity: Theory and Computation

小行星9700358 本文提出了一个晶体塑性本构和计算研究的程序，它是基于 几何 必要 脱位 密度，与晶体剪切应变的某些空间梯度成比例，作为一种物理手段，在晶体中引入尺寸相关的塑性响应。 的 拟定制剂 很好地符合了 物理概念，最清楚地描述了阿什比超过20年前。 在众多的应用中，遇到了由这种机制驱动的尺度相关塑性，其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），尺寸 依赖 压痕显微硬度、弥散强化晶体中的颗粒尺寸效应。 等人 在每种情况下， 的 局部非齐次性 剪应变，，超过 一 特性 几何 长度比例，结果 约 在 的 存储 的 几何上必要的位错， 其中B是 晶格常数。 这些“几何”位错， 减轻晶格不相容性，否则晶格不相容性将由产生应变梯度的保守位错运动引入，作为其他（滑动）位错的障碍，产生非常增强的 局部硬化 对该领域的回顾表明，为处理这类问题而提出的计算方法既可行，又在方法论上具有良好的一致性 与 的 材料科学 认识 基于“第一性原理”，对多晶聚集体的初步计算结果显示出明显的霍尔-佩奇效应。“额外位错密度的影响， 集中在谷物附近 努力相容地变形的边界也在晶粒内产生明显的应变图案。 这项工作的拟议扩展将解决霍尔-佩奇现象的不太理想化的版本，薄金属层之间的陶瓷，包括热致失配应变，和晶体的分散强化的颗粒尺寸效应约束的变形。 结果将是基本的科学价值，是第一个计算推力量化晶体塑性的尺度效应和统计存储和几何必要的位错的相互作用。 在工业应用中，可以从强大的计算能力中受益，以考虑尺度相关的塑性是多层电子器件和薄膜的机械行为。

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.