Temperature dependence of the back-stress in shear for glassy polycarbonate

Back-stress is the equilibrium stress and represents conditions under which relaxation events in the material stop and the material can carry an applied load indefinitely without a change in strain. In most models for glassy polymers, back-stress plays a central role since relaxation in materials is closely related to the distance of the current conditions from equilibrium. A number of these models that are commonly used for modeling glassy polymers use a modeling structure similar to large deformation plasticity. The flow rule for the plastic strain in these models are directly connected to the "over-stress," a properly invariant difference between the stress and the back-stress. The importance of correctly evaluating the back-stress to use in these models is clear. For this class of models, the authors have recently developed a method for directly calculating the back-stress under shear deformations. This method is based on evaluating the slope of the stress-strain response under conditions of similar elastic and plastic strain, but different strain rates. Since plastic flow goes to zero at equilibrium, the back-stress can be found by locating points of zero plastic strain rate. Using the proposed method, the back-stress in glassy polycarbonate has been evaluated under shear in isothermal tests going from room temperature to 120 °C, just below the glass transition temperature for polycarbonate. The proposed method provided a full map of the back-stress for polycarbonate over a large range of shear strain and temperature.