This project intends to expand the understanding of the role of temperature in controlling the dynamic failure behavior of advanced materials subject to combined thermo-mechanical loading. This objective will be achieved by improving the continuum-based modeling of the fracture properties of materials in conjunction with the formulation and development of a corresponding numerical approach for the solution of the resulting governing equations.
The goal of the proposed modeling effort is the inclusion of temperature dependence in the description of the fracture behavior of the material. In addition to modeling the bulk material as a fully coupled linear thermo-elastic solid, this goal will be achieved by using rate and temperature dependent cohesive zone (CZ) models to account for the highly localized, nonlinear, and softening behavior of the material ahead of the propagating crack. In this project, the cohesive stresses will be assumed to be physically-based constitutive functions of the opening displacement, opening displacement rate and temperature. Finally, the CZ will be assumed to fail in two basic ways: (i) by achieving a critical crack opening displacement; and/or (ii) by experiencing a critical value of cohesive stress. Both the critical crack opening displacement and the critical cohesive stress will be assumed to be functions of temperature.
The primary objective of the proposed numerical development is the formulation of a high accuracy and unconditionally stable solution scheme for the combined parabolic/hyperbolic problem describing dynamic fracture in a linear thermo-elastic solid. Adaptivity will be a primary feature of the proposed numerical scheme as it will be is crucial for the accurate quantification of the microscopic features that are nucleated during propagation as these features are a means of comparison between theory and experiments. Said numerical approach will be based on the discontinuous Galerkin finite element method (DG FEM). The DG FEM has been shown to be extremely effective in the solution of both parabolic and hyperbolic problems in the presence of moving discontinuities.
To provide an alternative strategy for the assessment of the fracture properties resulting from a given choice of the CZ constitutive law, and to provide a tool to test the efficacy of the proposed DG FEM development, the proposed research also includes the use of a different numerical technique previously developed by the proposer and a collaborator. This technique, based on the notions of Neumann-to-Dirichlet map and product integration, is highly accurate but only applicable to problems with idealized geometry (e.g., dynamic propagation of a semi-infinite crack along a planar bi-material interface). The aforementioned technique will be expanded and refined for the purpose of creating an effective benchmarking tool for the proposed DG FEM.
You can view some results concerning this work here: a presentation I have given in December 2005 at the Mathematics Department of the University of California--Berkeley. This presentation has three movies which you can download here: Displacement Response; Stress Response; Temperature Response.
A couple of more recent movies concerning the stress and temperature response of a linear thermo-elastic plate subjected to tension can be seen here: Stress Response; Temperature Response.