Lattice Curvature and Crystal Plasticity: Theory and Computation

9700358 Parks提出了晶体塑性本构和计算研究的程序，该程序基于几何必需的位错密度的概念，与晶体剪切应变的某些空间梯度成正比，为在晶体中引入尺寸相关的塑性响应提供了物理手段。提议的公式与阿什比在20多年前最清楚地描述的基本物理概念非常吻合。在许多应用中，遇到了由这种机制驱动的尺度相关塑性，包括多晶体中流动强度和加工硬化的颗粒尺寸依赖性(Hall-Petch效应)、压痕显微硬度的尺寸依赖性、弥散强化晶体中的颗粒尺寸效应。还有其他人。在每种情况下，局部非均匀剪切应变在特征几何长度尺度上的达到，大约导致几何上必要的位错的存储，其中b是晶格常数。这些“几何”位错缓解了在产生应变梯度时由保守的位错运动引入的晶格不相容，它们作为其他(滑性)位错的障碍，产生了非常强的局部硬化。对这一领域的回顾表明，为处理这类问题而提出的计算方法是可行的，并且在方法上与材料科学的理解很好地一致。对多晶聚集体的初步计算结果表明，基于“第一原理”，存在明显的霍尔-佩奇效应。额外的位错密度集中在晶界附近，努力协调变形，这也导致了晶内明显的应变图样。拟议的工作扩展将解决霍尔-佩奇现象的不太理想的版本，陶瓷之间约束的薄金属层的变形，包括热诱导失配应变，以及晶体弥散强化中的颗粒尺寸效应。这些结果将具有基本的科学价值，是量化晶体塑性中的尺度效应以及统计存储和几何上必要的位错相互作用的第一个计算推力。在工业应用中，可以受益于强大的计算能力来解释尺度相关的塑性，其中包括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.