Thermodynamically-consistent derivation and computation of twinning and fracture in brittle materials by means of phase-field approaches in the finite element method [article]

Benhour Amirian, Hossein Jafarzadeh, Bilen Emek Abali, Alessandro Reali, James David Hogan
2022 arXiv   pre-print
A computational method is proposed for simulating and informing on controlling failure pattern development in anisotropic brittle solids experiencing extreme mechanical loading. Constitutive equations are derived by using thermodynamics in order to establish a fully coupled and transient fracture mechanics model. A phase-field approach is developed for modeling twinning, fracture, and fracture-induced twinning in single crystals at nanometer length-scale. At the nanoscale, this continuum
more » ... cs based formulation is implemented in a monolithic computational scheme ensuring necessary accuracy for the following problems: (i) twin evolution in 2D single crystal magnesium and boron carbide under simple shear deformation; (ii) crack-induced twinning for single crystal magnesium under pure mode I and mode II loading; and (iii) study of fracture in homogeneous single crystal boron carbide under biaxial compressive loading. The results are verified by steady-state phase-field approach and validated by available experimental data in the literature. The success of this computational method relies on using two separate phase-field (order) parameters related to fracture and twinning. A finite element method-based code is developed within the Python-based open-source platform FEniCS. We make the code publicly available and the developed algorithm may be extended for the study of phase transformations under dynamic loading or thermally-activated mechanisms, where the competition between various deformation mechanisms is accounted for within the current comprehensive model approach.
arXiv:2202.13781v1 fatcat:ea2fene2rbcp7nv35ypilmwuhq