Phase-field fracture modeling for large structures

The phase-field modeling framework for linear elastic fracture mechanics problems is modified for the purpose of analyzing crack growth in large structures. The phase-field approach to fracture replaces sharp crack surfaces with a diffuse fracture zone that represent the traction-free crack faces. The diffuse fracture zone is characterized by a length scale that appears prominently in the governing partial differential equation that governs the evolution of the phase-field variable. Within numerical calculations the diffuse fracture zone must be resolved with a sufficient number of degrees of freedom in order to obtain accurate solutions. Additionally, all material fracture problems possess a physical process zone length scale that scales with the ratio of the fracture energy to the square of the material strength. For the vast majority of problems governed by linear elastic fracture mechanics, this physical process zone length scale is small, for example it is on the order of microns for aluminum alloys. If the material strength is to be captured, then the most commonly used formulation of the phase-field approach to fracture ties the diffuse phase-field crack length scale to the physical process zone length scale. This presents a challenge for extending such models to large structures that may be on the order of meters in size due to the prohibitive meshing requirements for the phase-field crack length scale. This is especially the case for three-dimensional problems. To address this problem a new form of the phase-field degradation function is introduced that allows for a decoupling of the phase-field length scale from the physical process zone length scale. The behavior and limitations of this new formulation are discussed and illustrated with a series of numerical test cases.