An improved phase-field model incorporating the critical energy release rate for simulating damage evolution in cracked Brazilian disks under non-uniform compressive loading

Abstract

Fracture is one of engineering materials’ most critical failure modes, directly threatening structural safety and stability. Accurate prediction of crack propagation behaviour is crucial for the reliable design and extended service life of engineering structures. To address the limitations of traditional numerical approaches in capturing complex crack topologies, this study develops an improved phase-field model that incorporates the critical energy release rate (CERR) derived from the weight function method for Brazilian disk specimens under non-uniform compressive loading. A staggered scheme decouples elastic deformation from fracture evolution, ensuring stability and efficiency. The model is validated by strong agreement between simulated and experimental load–displacement responses and strain energy evolution. System simulations investigated the effects of loading angle on strain energy evolution, crack initiation angle, crack propagation trajectory, and damage accumulation. Results reveal that loading angle critically influences crack morphology and structural capacity, with larger angles enhancing shear contributions and promoting mixed-mode fracture. These findings advance the theoretical understanding of fracture in brittle materials and establish a reliable predictive framework for evaluating and optimizing fracture resistance in engineering applications.