Phase – Field Modeling of Brittle and Ductile Fracture Under Complex Loading Conditions - Nidhi Sahu (International Journal of Fracture Mechanics and Damage Science, 2025)
Phase-field modeling has emerged as a powerful computational framework for predicting fracture behavior in engineering materials, offering a unified description of crack initiation, propagation, branching, and coalescence without the need for explicit crack tracking. This study presents an in-depth examination of phase-field modeling applied to both brittle and ductile fracture under complex loading conditions, including multiaxial stress states, cyclic loading, thermal gradients, and dynamic impact. The phase-field approach regularizes the sharp crack topology through an auxiliary scalar field, enabling smooth numerical representation of damage evolution while naturally capturing discontinuities in displacement. For brittle materials, the method accurately reproduces crack paths driven by tensile stresses and energy minimization, while for ductile materials the framework is extended by incorporating plastic deformation, strain-hardening behavior, and rate-dependent dissipation mechanisms. The study highlights the significance of selecting appropriate degradation functions, length-scale parameters, and constitutive laws to ensure physically meaningful predictions across different material classes. Coupled thermo-mechanical and elasto-plastic phase-field formulations are discussed to demonstrate the adaptability of the approach to real-world scenarios such as thermal shock, fatigue crack growth, and fracture in heterogeneous microstructures. Numerical simulations validate the model’s capability to capture transitions between brittle and ductile fracture modes and to predict mixed-mode crack propagation under complex boundary conditions. The findings confirm that phase-field modeling provides a versatile, robust, and computationally efficient tool for fracture mechanics, offering improved predictive accuracy for design, safety assessment, and failure analysis in structural, aerospace, automotive, and energy applications.
Keywords: Phase-field modeling; brittle fracture; complex loading conditions; crack initiation and propagation; ductile fracture; fracture mechanics; mixed-mode fracture