CAREER: Multi-Scale Experiments of Fracture in Elastic-Plastic Materials

摘要本课题的研究和教学工作包括建立一个多尺度的实验项目来研究弹塑性材料的断裂力学。本研究旨在补充和指导弹塑性材料断裂的多尺度模拟。实验将集中于理解沿纯铝或纯铜对称倾斜双晶晶界存在的裂纹行为。在这样一个标本中，有一个众所周知的，但知之甚少的现象，即断裂的方向依赖性。如果沿晶界引入裂纹，则裂纹在宏观上的扩展量取决于裂纹在晶界内扩展的方向。合理选择晶体取向和加载技术可以保证裂纹在宏观长度尺度上的力学性能相同，但宏观扩展量不同。因此，对方向依赖的解释必须依赖于较小长度尺度上的变形机制以及跨长度尺度的变形机制的相互作用。在实验中，裂纹将在对称倾斜双晶的晶界内引入并沿相反方向扩展。渐近变形场的结构将在平面应变条件下测量，以研究某种类型的应变不连续，称为扭结剪切不连续，这是由理论预测并在某些材料中在某些条件下观察到的。扭结剪切不连续的存在主要取决于非常小长度尺度上的塑性本构关系。下一组实验将测量在单调和循环载荷下断裂的方向依赖性，以记录沿晶界不同方向的裂纹扩展程度。最后一组实验将测量靠近裂纹尖端的晶体晶格曲率，以确定几何上必要的位错密度，这些位错在应变梯度塑性中起重要作用。所有的实验将与其他研究人员合作，用离散位错塑性技术进行模拟。教育部分是与哥伦比亚大学附近的中学，特别是哈莱姆区的中学联系，开发一个适合高中最后两年学生的科学模块，目的是激励他们继续学业。该模块将通过讨论衍射现象来证明材料是由离散原子组成的。为了做到这一点，学生们将首先通过识别和匹配衍射光栅中的对称性以及用标准激光笔创建的相关衍射图案来直观地了解衍射现象。然后介绍面心立方金属的晶体学方面和立方体的对称性。最后，学生将被要求在不同的劳厄背向反射x射线衍射图中识别两重、三重和四重旋转对称性，并将这些模式与表现出相同对称性的晶体学方向联系起来。因此，学生将识别晶体固有的对称性，而不必了解衍射过程的任何细节。

AbstractThe research and educational program consists of developing a multi-scaleexperimental program to study the mechanics of fracture in elastic-plasticmaterials. The research is intended to complement and guide multi-scalesimulations of fracture in elastic-plastic materials. The experiments willfocus on understanding the behavior of cracks that exist along the grainboundary of symmetric tilt bicrystals of either pure aluminum or purecopper. In such a specimen there is a well known, but poorly understood,phenomenon known as directional dependence of fracture. If a crack isintroduced along the grain boundary, the amount it grows macroscopicallydepends upon the direction within the grain boundary that it propagates. Ajudicious choice of crystallographic orientation and loading techniqueswill ensure that the mechanical properties at the macroscopic length scaleare identical for both cracks, yet the amount of macroscopic growth willbe different. Thus the explanation for the directional dependence mustdepend upon deformation mechanisms at the smaller length scales as well asthe interaction of the deformation mechanisms across length scales.In the experiments, cracks will be introduced and propagated in oppositedirections within the grain boundary of symmetric tilt bicrystals. Thestructure of the asymptotic deformation fields will be measured underplane strain conditions to investigate a certain type of straindiscontinuity, known as kink shear discontinuity, that is predicted bytheory and observed in some materials under certain conditions. Theexistence of kink shear discontinuities depends critically upon plasticconstitutive relations at very small length scales. The next set ofexperiments will be to measure the directional dependence of fractureunder both a monotonic and cyclic loading to document the degree of crackgrowth in different directions along a grain boundary. The final set ofexperiments will measure the lattice curvature of the crystal close to thecrack tip to ascertain the density of geometrically necessary dislocationswhich play an important role in strain gradient plasticity. All theexperiments will be simulated with the discrete dislocation plasticitytechnique in collaboration with other researchers.The educational component is to reach out to secondary schools in theneighborhoods around Columbia University, particularly in Harlem, todevelop a science module that is suitable for students in their final twoyears of high school with the goal of inspiring them to continue theireducations. The module will demonstrate that materials are made ofdiscrete atoms by discussing the phenomenon of diffraction. To do so, thestudents will first gain intuition into the diffraction phenomenon byidentifying and matching symmetries in diffraction gratings and therelated diffraction patterns that are created with a standard laserpointer. Then the crystallographic aspects of face-centered cubic metalsand the symmetries of a cube will be introduced. Finally the students willbe asked to identify the two-fold, three-fold, and four-fold rotationsymmetries in separate Laue back reflection x-ray diffraction patterns andcorrelate the patterns with the crystallographic orientations that exhibitthe same sets of symmetries. Thus the students will identify thesymmetries inherent in crystals without having to understand any of thedetails of the diffraction process.