MICROMECHANICS-BASED CRITERION FOR MICRO-FRACTURE PROPAGATION IN VISCOELASTIC MATERIALS

Resumo

Most of engineering materials exhibit natural or load-induced fractures, which strongly
affect both the instantaneous and delayed mechanical behaviors at macroscopic level. Unlike cracks,
fractures are mechanically regarded as interfaces able to transfer normal and tangential efforts. The
aim of this paper is to formulate the conditions for fracture propagation in randomly-micro-fractured
viscoelastic materials. The homogenized viscoelastic relaxation tensor was formulated by applying the
correspondence principle upon the already-known homogenized elastic stiffness tensor. Extending the
Griffith-like thermodynamic framework to the macroscopic viscoelastic context, the propagation
criterion is first formulated, once again comparing the energy release rate to the critical energy.
Mathematical evidences shows the energy release rate is written as the derivative of the macroscopic
elastic energy, written to the viscoelasticity, with respect to the parameter which represents the
damage in the macroscopic scale. Under certain conditions, the elastic energy derivative can be
simplified, being reduced only to an instantaneous term, leading to a simplified propagation criterion.
It was notably found that for constant strain loadings, the fracture propagation is exactly driven by
elastic components. Analyses performed for constant strain rates on specimen made of Burger solid
matrix show that the energy release rate increases from zero to a constant asymptotic value. This
asymptotic energy release rate is used in a time-independent propagation criterion, evidencing an
interval to initial damage parameter where the propagation is possible. The main contribution of
asymptotic energy release rate, however, refers to the estimative of final damage parameter after the
end of propagation.