Study on the effect of stress state and crystal orientation on micro-crack tip propagation behavior in phase field crystal method

Abstract

A nanometer scale mechanism for micro crack propagation under uniaxial tension in single crystals is investigated using phase field crystal (PFC) simulation. The uniaxial tensile loading is strain controlled. And three initial typical stresses of pre-existing center crack in (111) crystal plane of face centered cubic structure are chosen to study the effects of initial stress state on micro-crack propagation. Moreover, the influences of different crystal orientations, when the crystal suffers from uniaxial tension, are also investigated. Due to the influence of time scale and length scale in the PFC method, the motion of dislocations, vacancies, shear band and twinning structure should be observed and described during the propagation process of micro cracks. In addition, the free energy curves of different processes are drawn and discussed in order to explain the different behaviors of the crystal in the propagation of cracks. Simulation results show that the propagation behavior of micro cracks can be closely associated with the initial stress state. It is found that the propagation behavior mainly occurs in the 11>(111) slip system. Besides, the crystal orientation has a significant effect on the mechanism of activation and evolution. In the pre-stretching system, slip dislocation is induced near the micro-crack tip, and then its slide in [011] direction will cause the cleavage of a certain crystal plane, and promote the micro cracks to extend. However, to a certain level, the propagating direction of the micro-crack tip will turn to another slip direction [101]. As a result, zigzag edge appears. By contrast, in the pre-shear system, the tip of the micro crack propagates in a cleavage mode, and results in the appearance of slip dislocation [101] near the micro-crack tip. Afterwards, the motion of slip dislocation promotes the production of vacancies. And owing to the aggregation and combination of vacancies, secondary cracks form and propagate in the process that follows. At the same time, in a pre-deviatoric system, the micro crack propagates forward with direct cleavage of [101] slip direction near the micro-crack tip until the single crystal sample fractures. Furthermore, no slip dislocation appears during the whole process. The mechanism of micro-crack tip propagating behavior varies with crystal orientation. When the crystal orientation angle is lower, the micro-crack tip prefers to produce slip dislocation around it, and the following dislocation slide will induce vacancies, then a secondary crack also forms because of the aggregation and combination of vacancies. On the other hand, when the aggregation degree is higher, the micro-crack tip is inclined to directly propagate in a cleavage mode, and its propagating direction is nearly perpendicular to the stretching direction.