Multiscale ceramic matrix composite thermomechanical damage model with fracture mechanics and internal state variables

This work presents a multiscale damage model that accounts for ceramic matrix composite (CMC) length scale dependent behavior, including scale-specific brittle matrix damage initiation and propagation. Internal state variable theory is implemented to obtain the stress–strain constitutive relationship for damaged ceramic matrix material using damage variables which capture the effects of matrix cracking and nucleation and growth of matrix porosity. Matrix cracking is modeled using a damage variable determined using fracture mechanics and the self-consistent scheme. This methodology provides an effective way to model the effects of matrix cracks which initiate when stress intensity factors exceed the fracture toughness of the material, and whose growth is governed by crack growth kinetics. An additional source of material nonlinearity, matrix porosity, occurs as a result of material diffusion around grain boundaries and is related to the material entropy dissipation. These effects are captured using a porosity state variable that is explicitly related to the volumetric strain. The nonlinear predictive capabilities of the material model are demonstrated for monolithic silicon carbide, unidirectional (UD) carbon fiber/silicon carbide matrix (C/SiC) CMC, and five-harness satin (5HS) woven C/SiC CMC. The model predictions are in excellent agreement with experimental observations for 2D woven C/SiC CMCs from literature.