Theoretical Formulation of Phase Field Fracture

Phase field theory provides a new and different method of modeling crack propagation. This method utilizes a mathematical model to deal with interfaces of multiphase problems. Although it is often used for solidification, in this project it will be used to model fracture dynamics. Which is done by considering a crack and an undamaged material as two separate phases and the crack progress through diffusion. This approach offers a computationally effective approach to model crack propagation, and allows for smooth transition between interfaces. The objective of this project was to test a theoretical phase diffusion model developed by B. N. Cassenti et al.[1] for crack propagation. This was done using a MATLAB code written by Nicholas W. Oren that utilizes finite difference method. A number of tests cases were done to examine the behavior of the governing equations. Test cases consisted of a crack on a plate undergoing tension or shear stress on the boundaries of the plate. Through the test cases the physical dependency of the phase on the random local velocity was studied. In addition the effects of a double-well potential term and an elastic modulus factor on crack growth were also examined. A novel method of tracking the crack front and a test case for crack arrest were presented. The development of a physics based diffusion model will also be discussed