Chapters authored
A Fractal Model of the Stress Field Around a Rough Crack
This chapter presents a model of a stress and displacement fields around a rough crack tip in brittle and ductile materials using a pre-fractal model. This approach allows for a more realistic fractal scaling, of a real fracture. A special stress vector for rugged surfaces was defined, and it was also shown that the pre-fractal consideration also results in different asymptotic limits for the singularity degree of the stress field at the crack tip for brittle materials. The asymptotic limit obtained here differs from the singularity degrees presented by other authors. Therefore, other consequences such as fracture instability are also included in the mathematical model presented here. A generalization of the stress fields for brittle and ductile materials is proposed. Changes in geometric shapes of the stress field are due to the roughness at the crack tip as shown by the mapping of simulated stress fields around a crack tip. The fractal stress field functions were mapped at different singularity power degrees indicating that the qualitative aspects of these fields alone, do not sufficient to determine which model presents the best fit to experimental results. Therefore, the model need a validation based on quantitative experimental measurements.
Part of the book: Fracture Mechanics