A finite-deformation isotropic non-associative viscoplasticity/damage coupled thermodynamic model for ductile fracture of thick adhesive composite joint

Abstract

This paper develops a finite-deformation isotropic non-associative viscoplasticity/damage coupled model to predict ductilefracture behaviors of thick adhesive composite joint within the framework of irreversible thermodynamics. First, a damage variable is introduced into the elastic constitutive model, along with the Drucker-Prager’s type yielding function and plastic potential function which take into account the variable hydrostatic pressure and non-associative plasticity. An exponential damage potential function is developed to derive the damage evolution law relating to the thermodynamic force. Second, both kinematic hardening and isotropic hardening are considered that are represented by the back stress, hardening stress and their conjugate relationships with the corresponding internal variables, derived by the Helmholtz free energy. Third, an extended version of the Perzyna’s type model is developed by incorporating an over-stress function to derive the consistency plasticity factor for the viscoplasticity/damage coupled model. Fourth, the strain, stress, back stress, thermodynamic force, damage variable and tangent modulus are updated within the corotated configuration in the integration procedure. To simplify numerical computation, the stress and strain at time n + 1 are initially updated using the frozen damage variable and the back stress at time n, and the latter two values are independently updated at time n + 1. Finally, the developed model and numerical algorithm by implicit FEA are employed to predict the strain, stress, back stress, damage and fracture behaviors of the dog-bone MMA specimens under tensile loads and the thick MMA ductile adhesive specimens under shear loads.