Phase field theory for pressure-dependent strength in brittle solids with dissipative kinetics

A phase field theory of fracture mechanics is formulated to address dependence of material strength on stress state, noting that brittle solids are usually more fracture resistant when mean stress is compressive. Fracture is addressed via a dissipative kinetic law which instills rate dependence and viscous resistance to propagation. A dependence of kinetic viscosity on triaxiality for locally compressive stress states is proposed. Solutions are derived to one-dimensional problems for an isotropic material, linear or nonlinear elastic, under different loading protocols: uniaxial stress extension, uniaxial stress compression, and uniaxial strain compression. Analytical results enable determination of parameters and verification of finite element predictions. Three-dimensional simulations of polycrystalline microstructures are enacted under similar loading protocols. Results provide insight into effects of crystalline microstructure and anisotropy for different stress states. With increasing confinement, the ratio of macroscopic pressure to shear stress increases, and influences of microstructure and anisotropy on average stress and ductility are reduced.

Automated summary

A phase field theory is used to study fracture mechanics, considering the influence of stress state on material strength. It is found that brittle solids are more resistant to fracture when mean stress is compressive. The theory incorporates a dissipative kinetic law that introduces rate dependence and viscous resistance to propagation. Analytical solutions are derived for one-dimensional problems of isotropic materials under various loading conditions, and three-dimensional simulations are conducted for polycrystalline microstructures. Results reveal the effects of microstructure and anisotropy on different stress states, with increasing confinement reducing the influence of these factors on average stress and ductility.