Phase-Field Crack Simulation for Thermomechanically Coupled Problems

Abstract

In the past several decades, the community of computational solid mechanics has devoted a lot of efforts to develop robust and accurate numerical methods to model fracture initiation and propagation. Some of the prominent methods include the cohesive zone model, the embedded discontinuity approach, and the extended finite element method approach. However, these earlier methods either suffer from pathological mesh-dependence or rely on heuristic fracture tracking algorithm to track crack propagation. These tracking algorithms cannot robustly handle complex crack geometries such as merging and branching even in 2D problems, not to mention complex 3D crack surfaces. Recently, the phase- field method (PFM) has drawn more and more attentions for simulations of crack propagation in solids due to its capability of naturally handling complex crack patterns such as merging and branching. In the view of energy functional, the PFM converts the sharp crack problem into a constrained optimization problem possessing a variational structure. The PFM constructs a nonlinearly coupled problem between the displacement eld and the phase-field, which can be solved by either the staggered approach or the monolithic approach. In this thesis, algorithms for both approaches are adopted, which respectively rely on the alternate minimization (AM) and the limited-memory BFGS (L-BFGS) scheme. These two algorithms can both overcome the convergence issues caused by the non-convex nature of the energy functional in fracture mechanics. The PFM algorithms are further combined with heat conduction problems to model the crack propagation under thermomechanically coupled loads. Several numerical examples, including crack simulations in the quenching problem and the thermal barrier coating problem, are provided to demonstrate the capabilities of the developed method. The limitation of current model and possible solutions in future research are discussed.