A phase-field model for thermo-mechanical fracture

Abstract

In this article, we propose a thermodynamically consistent phase-field model for thermo-mechanical fracture and provide an open-source implementation of the proposed model using a recently developed finite element toolbox, Gridap in Julia. Here, we have derived the balance equations for the thermo-mechanical fracture by invoking the virtual power principle and determined the constitutive relations for the thermodynamic fluxes based on the satisfaction of the thermodynamic laws. Our proposed formulation provides an equation of temperature evolution that can easily accommodate dissipative effects such as viscous damping. We provide very compact and user-friendly open-source codes for implementing the proposed model using Gridap in Julia that requires very low memory usage and gives a high degree of flexibility to the users in defining weak forms of the governing partial differential equations (PDEs). We have validated the proposed model and its implementation against such standard results available in the literature as crack propagation in the cruciform shape material, single edge notched plate, bi-material beam, and a quenching test.

New Frameworks of PFM for Thermal Fracturing in The Linear Thermoelasticity Solids Based on a Microforce Balance Approach

“…Meanwhile, the crack path tends to the right side for pure thermal load. Qualitatively, our result matches well with the previous study [20,36,43,45]. At this point, we can draw a strong conclusion that the thermal effect very clearly influences the deviation of the crack path.…”

“…We have given a new perspective of PFM for thermal fracturing in linear thermoelasticity solids which is different from that of the previous PFM studies [15,22,35,36,43]. Also, different from other studies [1,38,40,49] which consider the mechanical dissipation, we did not consider the mechanical dissipation because our study applies the linear thermoelasticity solid material.…”

“…The approach gives more advantages, for instance; allowing one to derive the governing equation of PFM for more complex crack problems [21] and the developed model is automatically thermodynamically consistent. Especially for thermal fracturing, as far as the author is aware, some studies have proposed PFM for thermal fracturing based on the microforce balance approach [43,44]. However, their studies do not consider the deformation evolution and the dissipation energy of PFM in the thermal evolution equation.…”

A phase-field model for electro-mechanical fracture with an open-source implementation of it using Gridap in Julia

“…Despite this, the phase-field model has gained a lot of popularity because it can easily be implemented in any commercially available finite element (FE) software [49][50][51][52][53][54]. Recently, there are also attempts toward developing open-source codes for the implementation of the phase-field models for fracture under mechanical loading [55][56][57] and thermo-mechanical loading [58,59], to make the models available to a wider class of researchers and practitioners. But to the best of the authors' knowledge, there is no open-source implementation of a phase-field model for electro-mechanical fracture.…”