#### Date of Completion

12-14-2014

#### Embargo Period

12-11-2014

#### Advisors

Eric Jordan, Alexander Staroselsky

#### Field of Study

Mechanical Engineering

#### Degree

Master of Science

#### Open Access

Open Access

#### Abstract

Numerically predicting crack growth is difficult due to the infinite stresses at the crack tip as well as the extreme change in material properties which will introduce numerical instabilities. This project encompasses the development of a Finite Element Code that implements the phase field physics theory developed in order to analyze crack propagation. Under this theory a new state variable is introduced which describes the phase as failed or virgin material. The phase is modeled as diffusion through the material and is driven by specified equations, and is especially useful in the prediction of high temperature creep rupture.

To test the code, a number of test cases were modeled. Two key tests included an eight element block undergoing a shear and a tension load. The first test case included a static stress analysis under the application of tensional load. This test case allowed the model to be stretched along the axis of applied force and measurements of maximum displacements were recorded. The results of the first case agree with the commercial FE results as expected. The second test case involves the same eight element block being applied a shear load on the top plane for stress analysis. This test case allowed the model to be stretched along the normal axis of applied force and measurements of maximum displacements were recorded and compared for the top plane. The results of the second case agree with the commercial FE results as expected. To test the addition of time dependence in the code, a number of verification test cases were modeled. Two key verification tests involve a four element stack undergoing transient phase diffusion. The first test case included a transient phase diffusion analysis without the application of any forcing function. This test case allowed the model to be readily duplicated using commercial FE codes simulating single direction thermal diffusion through conduction. The results of the first case agree with the commercial FE results, as well as with an analytical expression developed. The second test case involves the same four element stack undergoing a transient phase diffusion analysis with the application of a second order forcing function for the phase. This test case could not be readily modeled using commercial software, but an analytical solution was developed. The results of the second case agree the analytical expression developed with minimal error. All the cases agree with the analytical solutions developed to model each case.

From these results presented, and other tests, it is clear that the particular phase field physics theory can be appropriately applied to cracks using the developed FEA code. This project has successfully proven that this FEA code is ready for practical fracture analysis using finite elements.

#### Recommended Citation

Mathioudakis, Alexandros N., "Finite Element Formulation of Phase Field Fracture" (2014). *Master's Theses*. 699.

https://digitalcommons.lib.uconn.edu/gs_theses/699

#### MajorÂ Advisor

Brice Cassenti