A thermo-mechanical phase field fracture model considering solid–liquid transition

Temperature variations may cause solid–liquid phase transition and damage evolution, which requires more refined modelling. In this study, a solid–liquid thermo-mechanical phase field model based on thermodynamically approach is established. A novel predictive equation of temperature-dependent critical strain energy density is firstly derived by combining force-heat equivalent principle and effective heat capacity method. The critical strain energy density of typical brittle materials with narrow phase transition interval (e.g., ice and Al 2 O 3 ) can be successfully captured by the proposed formulation. A simple but effective degradation function associated with phase transition variable is embedded in the phase field model to describe the mechanical degradation within phase transition and avoids the undesirable damage that occurs in liquid-state domain. The established multi-physical framework is implemented through finite element method. In numerical simulations, the phase transition part is verified through the two-phase Stefan’s melting issue preliminarily. Then, the thermo-mechanical module is studied through the shrinkage cracking of a 1D bar. The insensitivity of length scale and fracture toughness degradation under the assumption of small transition interval is proved. The proposed model is subsequently applied to thermal cracking in additive manufacturing and electrothermal de-icing, with its effectiveness and accuracy demonstrated by comparing with experimental results and empirical criterion