A Thermo-Mechanical Localizing Gradient Damage Model With Modified Mazars Strain

Abstract

This work establishes a thermo-mechanical coupling model for thermally induced cracks in quasi-brittle materials within the framework of localizing gradient damage theory. The constitutive relation considering the thermal expansion effect, and the heat conduction equation integrating the volumetric strain and damage evolution, are formulated based on the Clausius–Duhem inequality to ensure thermodynamic consistency. In particular, to accommodate the tension-compression strength asymmetry across different quasi-brittle materials, a modified Mazars strain is proposed as the driving force for the micro equivalent strain, where the first invariant of strain tensor and an adjustable ratio of compressive strength to tensile strength ($k$) are introduced. The numerical implementation employs the generalized-α method for time domain discretization and the staggered scheme for decoupling. Numerical simulations demonstrate a nice feasibility of the modified Mazars strain in capturing both tensile and mixed-mode failures, and the proposed model proves capable of characterizing complex crack behaviors under thermal loading in both quasi-static and dynamic scenarios. The quenching test simulations of ceramic plates highlight the bidirectional coupling effects on crack patterns. Unidirectional coupling models that ignore the influence of volumetric strain and damage evolution on the temperature field would underestimate the temperature gradient, resulting in larger crack spacing and fewer cracks. In the thermal shock tests of cylindrical specimens, the transition in crack patterns from spiral shear bands to an annular damage zone with increasing compression-tension strength ratio ($k$) is precisely captured, demonstrating the generality of the proposed model for various quasi-brittle materials with tension-compression strength asymmetry.