Geometric micromechanical modeling of structure changes, fracture and grain boundary layers in polycrystals

Abstract

A constitutive framework based on concepts from phase field theory and pseudo-Finsler geometry is exercised in numerical simulations of deformation and fracture of ceramic polycrystals. The material system of interest is boron carbide, a hard but brittle ceramic. Some microstructures are enabled with thin layers of a secondary amorphous phase of boron nitride between grains of boron carbide. The constitutive theory accounts for physical mechanisms of twinning, crystal-to-glass phase transformations, cleavage fracture within grains and separation and cavitation at grain boundaries (GBs). According to the generalized Finsler approach, geometric quantities such as the metric tensor and connection coefficients can depend on one or more director vectors, also called internal state vectors, that enter the energy potential in a manner similar to order parameters of phase field models. A partially linearized version of the theory is invoked in finite element simulations of polycrystals, with and without GB layers, subjected to pure shear loading. Effects of grain size and layer properties — thickness, shear modulus and surface energy — are studied parametrically. Results demonstrate that twinning and amorphization occur prominently in nanocrystals but less so in aggregates with larger grains that tend to fail earlier by fracture. Structural changes occur readily in the latter at smaller applied strains only in conjunction with elastic shear softening in localized degraded or damaged regions. Hall–Petch scaling of peak shear strength with grain size is observed. Strength is increased via addition of amorphous layers that shift the failure mode from transgranular to intergranular and further by cavity expansion in layers that induces local elastic compression and suppresses crack extension. Stiff layers provide the largest peak strength enhancement, while elastically compliant layers may improve toughness and strength in the softening regime.