Phase-field viscoelastic fracture modeling of polymer composites using strain tensor spectral decomposition

Abstract

The mechanical behaviors of polymer composites exhibit strong time-dependent nonlinearities, and the tensile and compressive strengths can be vastly different. Such a strength differential effect poses a great challenge in fracture modeling using existing phase-field models. To address this problem, this study develops a new viscoelastic fracture phase-field model, in which the strain tensor spectral decomposition is proposed to decompose the elastic energy of the equilibrium and non-equilibrium branches into tensile and compressive components. The non-negativity of elastic energy and the thermodynamic consistency are theoretically verified. Various case studies, spanning from material uniaxial tension–compression and compression under isostatic pressure to fracture processes of realistic structural components, are used to validate the proposed method. Results of the proposed method are compared with those of existing methods and the actual testing data of polymer composites to demonstrate the effectiveness of the method. It is shown that the proposed method can accurately model not only the strong strength differential effect but also the isostatic pressure dependence of viscoelastic materials. Furthermore, the proposed method offers a more precise prediction of the fracture path and can deal with the loading rate effect.