APPLICATIONS OF DISLOCATION THEORY TO CRACK GROWTH PROBLEMS

This work contains two new applications of dislocation theory to crack growth problems. The first study considers the growth of crack-like grain boundary voids undergoing a diffusive creep process. The voids are located on grain boundaries that are symmetric with respect to a grain boundary containing a semi-infinite macrocrack which is loaded by remote tension. A stress analysis of the grain boundary voids is performed and an integro-differential equation describing the transient growth of the voids by grain boundary diffusion is derived and solved numerically. All plastic deformations of the material are neglected. The results obtained reveal the nature of the time-dependent stress distribution near the voids and establish trends for the variation of the void extension rates with respect to time. The second study presents a model for the fracture process zone near the tip of a steadily propagating plane strain tensile crack. The material is assumed to be elastic-ideally plastic and completely incompressible. The macroscopic plastic deformation near the advancing crack tip is modeled by a slip element approach in which dislocations are continuously distributed over a planar region. The fracture process zone is modeled by a continuous distribution of dislocations collinear with the advancing crack tip. The results of the study reveal the influence of the fracture process zone on the slip line pattern within the crack tip plastic zone and the elastic-plastic boundary. An application of the fracture process zone model to the critical crack tip opening angle criterion for continued ductile stable crack growth is also presented, and it is shown that the predictions of the model are in good approximate agreement with experimental results.