Extension of the viscoplasticity theory based on overstress (VBO) to capture non-standard rate dependence in solids

The viscoplasticity theory based on overstress (VBO) can model unusual loading rate effects. Included are rate-insensitivity and positive and negative rate sensitivity. An augmentation function is required that operates on the dynamic recovery term of the growth law for the equilibrium stress, which is a state variable in VBO. The augmentation function does not affect the initial, quasi-elastic region. Its full effect appears when the long-time, asymptotic solution, which corresponds to the flow stress region is reached in an experiment. The flow stress of the VBO model consists of monotonic, rate-independent hardening affected by the kinematic stress, the viscous, rate-dependent hardening through the overstress and the rate-independent hardening represented by the isotropic stress. With the augmentation function it is possible to have only rate-dependent contributions to the flow stress. Through a proper choice of the augmentation function the rate-dependent and the rate-independent contributions can be apportioned to yield positive, zero and negative rate dependence in a consistent manner. As a demonstration, the stress-strain curves of Copper, a fcc metal, are reproduced. In fcc metals the positive rate dependence increases with deformation. The rate-dependent stress-strain curves of polymethylmethacrylate (PMMA) exhibiting a distinct yield point are also reproduced. Numerical creep tests performed at the same stress level before and after the yield point lead to unlimited creep strain and primary creep, respectively. The modeling of these very different types of material behavior requires only different material constants and augmentation functions within the same general constitutive equation.