Physics of Dislocation Patterning and Size Effects in Plasticity

该基金支持晶体固体弹塑性响应的理论研究。 该项目的目标包括：（1）表征和理解驱动位错聚合成二维有序结构的热力学，（2）研究塑性中尺寸效应的起源。位错图案化被广泛地模拟为受竞争动力学支配的非平衡过程，但驱动位错聚合成有序结构的热力学还没有得到很好的理解。 这个项目考虑了简单的情况下，在两个维度的剪切螺旋位错，并使用模拟和理论模型，他们合并成滑移带。 模拟研究进行了使用一个理想化的模型下的晶体反平面剪切与恒定的应变率，一个系统，是一个密切的模拟驱动边界条件下的二维XY转子模型。 结果表明，二维滑移带的形成代表了富缺陷相和贫缺陷相两相共存的非平衡淬火过程。 基本的平衡相图，标度行为和流动特性的缺陷丰富的相的表征将被用来推导塑性在两个维度的本构关系。 三维晶体中的位错图案要复杂得多，涉及位错缠结和许多固有的3D机制。 虽然没有二维模型可以准确地描述一个真实的三维材料，这项工作将提供至少定性的洞察力之间的竞争的能量和熵的位错微观结构的演变。该项目的第二个目标是深入了解塑性中尺寸效应的起源。 最近的实验表明，结晶固体的一些机械性能随样品尺寸在~100微米以下的范围内变化。 在扭转和弯曲中观察到尺寸效应，但在简单拉伸中没有观察到尺寸效应，这表明应变梯度起着重要作用。 在连续塑性理论中建立应变梯度效应的努力指出了特征长度尺度的重要性，其起源尚未完全理解。 为了找出所涉及的机制，位错图案化的模拟研究将使用理想化的二维模型和更现实的二维和三维分子动力学进行。 几何形状将包括（1）剪切载荷下的韧性狭缝裂纹，（2）梁的扭转/弯曲，以及（3）从软金属基质中拔出薄纤维。 在每种情况下，将对不同尺寸的样品进行多次模拟，并将结果与连续应变梯度理论的预测进行比较。%该基金支持晶体固体弹塑性响应的理论研究。 该项目的目标包括：（1）表征和理解驱动位错合并成二维有序结构的热力学，以及（2）研究塑性中尺寸效应的起源。 本项目的成功完成将增加我们对材料的机械性能的了解，包括它们的失效。*

This grant supports theoretical research on the elastic-plastic response of crystalline solids. The objectives of the project include: (1) characterizing and understanding the thermodynamics driving coalescence of dislocations into ordered structures in two dimensions, and (2) investigating the origins of size effects in plasticity.Dislocation patterning has been extensively modeled as a non-equilibrium process governed by competing kinetics, but the thermodynamics driving the coalescence of dislocations into ordered structures is not well understood. This project considers the simple case of screw dislocations under shear in two dimensions, and models their coalescence into slip bands using both simulation and theory. Simulation studies are carried out using an idealized model of a crystal under anti-plane shear with constant strain rate, a system that is a close analog of the two-dimensional XY rotor model under driving boundary conditions. It is conjectured that slip-band formation in 2D represents a non-equilibrium quench into two-phase coexistence between defect-rich and defect-poor phases. Characterization of the underlying equilibrium phase diagram, scaling behavior, and flow properties of the defect-rich phase will be used to derive constitutive laws for plasticity in two dimensions. Dislocation patterning in three-dimensional crystalline solids is far more complex, involving dislocation entanglement and a host of inherently 3D mechanisms. While no 2D model can accurately describe a real 3D material, this work will provide at least qualitative insight into the competition between energy and entropy in evolution of dislocation microstructures. The project's second goal is to gain insight into the origin of size effects in plasticity. Recent experiments show that some mechanical properties of crystalline solids vary with sample size in the range below ~ 100 microns. Size effects are observed in torsion and bending but not in simple tension, suggesting that strain gradients play an important role. Efforts to build strain gradient effects in continuum plasticity theory point to the importance of a characteristic length scale whose origin is not fully understood. To find out what mechanisms are involved, simulation studies of dislocation patterning will be carried out using both the idelaized two-dimensional model and more realistic molecular dynamics in two and three dimensions. Geometries will include (1) a ductile slit crack loaded in shear, (2) torsion/bending of a beam, and (3) pullout of a thin fiber from a soft metal matrix. In each case multiple simulations will be preformed for samples of different sizes and the results will be compared to the predictions of continuum strain gradient theories.%%%This grant supports theoretical research on the elastic-plastic response of crystalline solids. The objectives of the project include: (1) characterizing and understanding the thermodynamics driving coalescence of dislocations into ordered structures in two dimensions, and (2) investigating the origins of size effects in plasticity. Successful completion of this project will increase our knowledge of the mechanical propoerties of materials, including their failure.***