Numerical Analysis of the Anisotropic Damage Evolution due to a Growing Mixed-Mode Crack
Damage of materials is a progressive physical process through which the macroscopic properties of the material changes and it might end with the final failure of a part and in some cases can be disastrous. The main mechanism of brittle damage is the nucleation and growth of microcracks. A way to model the anisotropic damage is to consider its influence on the compliance/stiffness of the material at the meso-level. A numerical study of a growing mixed-mode internal crack in a unit cell was undertaken with the help of a finite element simulation. The model enables us to measure the components of the elastic compliance tensor modified by damage as the crack grows, showing the evolution of the anisotropic damage and the evolution of the type of material symmetries. The evolution of the elasticity tensor shows that the damage associated with a growing elliptical crack changes the virgin isotropic properties into orthotropic ones and by crack growth the axes of orthotropic symmetry, initially aligned with the local coordinates of the crack, rotate towards the principle loading axes. The matrix material of the unit cell is considered to be isotropic linear elastic, homogenous and the response is perfectly brittle. The characteristic crack size is small compared to the unit cell, so that the non-interacting crack assumption for the damage models is fulfilled. Crack propagation is simulated using the stepwise method, which consists of the succession of straight segments and crack growth is governed by the principle of maximum driving force which is a direct consequence of the variational principle of a cracked body in equilibrium and considers the effect of all three stress intensity factors. Without any ad hoc assumption, the crack growth rate is calculated using its thermodynamic duality with the local maximum driving force.
J. Alfaiate, M.H. Aliabadi, M. Guagliano and L. Susmel
K. Molla-Abbasi and H. Schütte, "Numerical Analysis of the Anisotropic Damage Evolution due to a Growing Mixed-Mode Crack", Key Engineering Materials, Vols. 348-349, pp. 401-404, 2007