Modeling Deformation and Fracture of Boron-Based Ceramics with Nonuniform Grain and Phase Boundaries and Thermal-Residual Stress

Abstract

A phase field framework of elasticity, inelasticity, and fracture mechanics is invoked to study the behavior of ceramic materials. Mechanisms addressed by phase field theory include deformation twinning, dislocation slip, amorphization, and anisotropic cleavage fracture. Failure along grain and phase boundaries is resolved explicitly, whereWeibull statistics are used to characterize the surface energies of such boundaries. Residual stress incurred by mismatching coefficients of thermal expansion among phases is included. Polycrystalline materials of interest are the ultra-hard ceramics boron carbide (B4C) and boron carbide-titanium diboride (B4C-TiB2), the latter a dual-phase composite. Recent advancements in processing technology enable the production of these materials via spark-plasma sintering (SPS) at nearly full theoretical density. Numerical simulations invoking biaxial loading (e.g., pure shear) demonstrate how properties and mechanisms at the scale of the microstructure influence overall strength and ductility. In agreement with experimental inferences, simulations show that plasticity is more prevalent in the TiB2 phase of the composite and reduces the tendency for transgranular fracture. The composite demonstrates greater overall strength and ductility than monolithic B4C in both simulations and experiments. Toughening of the more brittle B4C phase from residual stress, in addition to crack mitigation from the stronger and more ductile TiB2 phase are deemed advantageous attributes of the composite.