Mathematical modeling of material behaviors in the fracture process zone

This Ph.D. research focuses on employing the cohesive crack models to investigate the fracture process zone behavior. The main contributions are summarized as the following: (1) A generalized mixed mode Dugdale model is developed. Research shows that the crack interaction will result in highly nonsymmetrical fracture process zone behavior. The nonsymmetrical fracture process zone behavior may be important in evaluation of effective properties of cracked materials if the local unsymmetrical loading induced by its neighbor crack interactions cannot be ignored. (2) A closed form solution of the stress history effect on the mixed mode Dugdale crack is obtained. Then a numerical procedure is proposed for studying the residual stress behavior of the loading and unloading path dependent Dugdale crack. (3) A general weight function method is developed for simulating the fracture process zone behavior. With this method the fracture process zone behavior can be easily simulated with singular solutions. (4) A numerical procedure is developed to investigate the strain-hardening or strain-softening effect on the Dugdale crack. Numerical examples show that, for a given J_c, the far-field failure stress of strain-hardening or strain-softening materials are very close to the Dugdale solution and this implies that the fracture failure criteria used in elastic-plastic material can be extended to the strain-hardening or strain-softening materials in the static loading situation. Stress distributions in the process zone have been calculated for several strain-hardening and strain-softening materials. An empirical equation of power-law type is proposed to represent the stress distribution as a function of the position in the process zone. It is shown that the power-law index varies linearly with the size of the fracture process zone. For static loading, J_c is the controlling parameter and the fracture process zone behavior is a secondary issue.