Isotropic and Anisotropic Thermal-Conductivity Degradation Across Cracks in Coupled Thermo-Mechanical Systems Modeled by the Phase-Field Fracture Method

Dynamic loads applied to metals may lead to brittle or ductile fracture depending on the imposed strain rates, material properties, and specimen geometry.  With an increase in the applied velocity, brittle to ductile failure mode transition may also be observed. Furthermore, at high strain rates, ductile fracture may be preceded by shear bands, which are narrow bands of intense plastic deformation, typically accompanied by a significant rise in temperature.

Reliable models are needed to predict the response of metals subject to dynamic loads. In particular, capturing the interplay between heat conduction and crack propagation using the phase-field fracture method is still an open research field. To capture the heat transfer across crack surfaces, damage models degrading thermal-conductivity are necessary. While isotropic thermal-conductivity degradation models were proposed, they may lead to errors as they are indifferent to crack directionality.

In our current work, first we present an isotropic degradation of the thermal conductivity is proposed, which couples the thermal diffusion process with the extent of damage across a crack. The closed form solution is derived analytically based on a micro-mechanics void extension model of Laplace's equation. We investigate the behavior of the aforementioned technique on two benchmark problems and show the necessity of such physics-based degradation function in dynamic fracture problems.

Second, a new anisotropic approach will be presented in which thermal-conductivity, which depends on the phase-field gradient, is degraded solely across the crack. It is shown that this approach improves the near-field approximation of temperature and heat flux compared with isotropic degradation, when taking the discontinuous crack solutions as reference. Additionally, the anisotropic degradation approach is implemented in a unified dynamic fracture model and a couple of examples demonstrate the viability of this approach.

References:

[1]  C. McAuliffe, and H. Waisman, A unified model for metal failure capturing shear banding and fracture, International Journal of Plasticity, 65:131--151, 2015.

[2] C. McAuliffe, and H. Waisman, A coupled phase field shear band model for ductile–brittle transition in notched plate impacts, Computer Methods in Applied Mechanics and Engineering, 305:173--195, 2016.

[3] L. Svolos, C. Bronkhorst and H. Waisman, Thermal-conductivity degradation across cracks in coupled thermo-mechanical systems modeled by the phase-field fracture method, Journal of the Mechanics and Physics of Solids, Volume 137, April 2020, 103861

[4] L. Svolos, Hashem M. Mourad, C. Bronkhorst and H. Waisman, Anisotropic thermal-conductivity degradation in the phase-field method accounting for crack directionality, under review 2020.