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

Columbia University, New York NY

Investigators

Abstract

Abstract The research and educational program consists of developing a multi-scale experimental program to study the mechanics of fracture in elastic-plastic materials. The research is intended to complement and guide multi-scale simulations of fracture in elastic-plastic materials. The experiments will focus on understanding the behavior of cracks that exist along the grain boundary of symmetric tilt bicrystals of either pure aluminum or pure copper. In such a specimen there is a well known, but poorly understood, phenomenon known as directional dependence of fracture. If a crack is introduced along the grain boundary, the amount it grows macroscopically depends upon the direction within the grain boundary that it propagates. A judicious choice of crystallographic orientation and loading techniques will ensure that the mechanical properties at the macroscopic length scale are identical for both cracks, yet the amount of macroscopic growth will be different. Thus the explanation for the directional dependence must depend upon deformation mechanisms at the smaller length scales as well as the interaction of the deformation mechanisms across length scales. In the experiments, cracks will be introduced and propagated in opposite directions within the grain boundary of symmetric tilt bicrystals. The structure of the asymptotic deformation fields will be measured under plane strain conditions to investigate a certain type of strain discontinuity, known as kink shear discontinuity, that is predicted by theory and observed in some materials under certain conditions. The existence of kink shear discontinuities depends critically upon plastic constitutive relations at very small length scales. The next set of experiments will be to measure the directional dependence of fracture under both a monotonic and cyclic loading to document the degree of crack growth in different directions along a grain boundary. The final set of experiments will measure the lattice curvature of the crystal close to the crack tip to ascertain the density of geometrically necessary dislocations which play an important role in strain gradient plasticity. All the experiments will be simulated with the discrete dislocation plasticity technique in collaboration with other researchers. The educational component is to reach out to secondary schools in the neighborhoods around Columbia University, particularly in Harlem, to develop a science module that is suitable for students in their final two years of high school with the goal of inspiring them to continue their educations. The module will demonstrate that materials are made of discrete atoms by discussing the phenomenon of diffraction. To do so, the students will first gain intuition into the diffraction phenomenon by identifying and matching symmetries in diffraction gratings and the related diffraction patterns that are created with a standard laser pointer. Then the crystallographic aspects of face-centered cubic metals and the symmetries of a cube will be introduced. Finally the students will be asked to identify the two-fold, three-fold, and four-fold rotation symmetries in separate Laue back reflection x-ray diffraction patterns and correlate the patterns with the crystallographic orientations that exhibit the same sets of symmetries. Thus the students will identify the symmetries inherent in crystals without having to understand any of the details of the diffraction process.