Abstract
The phase-field formulation for fracture based on the framework of representative crack elements is extended to transient thermo-mechanics. The finite element formulation is derived starting from the variational principle of total virtual power. The intention of this manuscript is to demonstrate the potential of the framework for multi-physical fracture models and complex processes inside the crack. The present model at hand allows to predict realistic deformation kinematics and heat fluxes at cracks. At the application of fully coupled, transient thermo-elasticity to a pre-cracked plate, the opened crack yields thermal isolation between both parts of the plate. Inhomogeneous thermal strains result in a curved crack surface, inhomogeneous recontact and finally heat flow through the crack regions in contact. The novel phase-field framework further allows to study processes inside the crack, which is demonstrated by heat radiation between opened crack surfaces. Finally, numerically calculated crack paths at a disc subjected to thermal shock load are compared to experimental results from literature and a curved crack in a three-dimensional application are presented.
Highlights
A crack contact criterion and the decomposition into degraded and transferred forces through the crack are approximated by splits of the deformation energy potential in phase-field models for fracture
The principle of total virtual power δPtot = δPint − δPext = 0 balances the virtual power, which is associated with a thermodynamic system and the virtual power transferred to the system from the exterior for all admissible generalised virtual velocities ∀δv ∈ Varv and their generalised local strain rate actions D(δv)
The solution of the mechanical and thermal Representative Crack Elements (RCE) depends on the crack contact state, which is identified by 1
Summary
A crack contact criterion and the decomposition into degraded and transferred forces through the crack are approximated by splits of the deformation energy potential in phase-field models for fracture. Unphysical predictions of deformations at cracks are reported for common splits like the volumetric-deviatoric, the spectral and similar splits. The crack driving force of the phase-field variable is significantly controlled by the split approach and, may result in unreliable predictions for the fracture process. Artificial splits are replaced by Representative Crack Elements (RCE) in [1], which allows to overcome the kinematical deficiencies. After first application to anisotropic elasticity [1], the framework is successfully applied to phasefield fracture for visco-elastic materials [2], for inelastic materials, crack surface friction, finite deformations [3] and
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