Viscous Behavior

Introduction to the Two-layer Viscoplasticity Model

The two-layer viscoplastic model:

is intended for modeling materials in which significant time-dependent behavior as well as plasticity is observed, which for metals typically occurs at elevated temperatures;
consists of an elastic-plastic network that is in parallel with an elastic-viscous network (in contrast to the coupled creep and plasticity capabilities in which the plastic and the viscous networks are in series);
is based on a von Mises or Hill yield condition in the elastic-plastic network and any of the available creep models in Abaqus/Standard (except the hyperbolic creep law) in the elastic-viscous network;
assumes a deviatoric inelastic response (hence, the pressure-dependent plasticity or creep models cannot be used to define the behavior of the two networks);
is intended for modeling material response under fluctuating loads over a wide range of temperatures; and
has been shown to provide good results for thermomechanical loading.

Material Behavior

The material behavior is broken down into three parts: elastic, plastic, and viscous. Figure 1 shows a one-dimensional idealization of this material model, with the elastic-plastic and the elastic-viscous networks in parallel. The following subsections describe the elastic and the inelastic (plastic and viscous) behavior in detail.

Elastic Behavior

The elastic part of the response for both networks is specified using a linear isotropic elasticity definition. Any one of the available elasticity models in Abaqus/Standard can be used to define the elastic behavior of the networks. Referring to the one-dimensional idealization ( Figure 1), the ratio of the elastic modulus of the elastic-viscous network ( $K_{V}$ ) to the total (instantaneous) modulus ( $K_{P} + K_{V}$ ) is given by

f = \frac{K_{V}}{(K_{P} + K_{V})}

The user-specified ratio $f$ , given as part of the viscous behavior definition as discussed later, apportions the total moduli specified for the elastic behavior among the elastic-viscous and the elastic-plastic networks. As a result, if isotropic elastic properties are defined, the Poisson's ratios are the same in both networks. Otherwise, if anisotropic elasticity is defined, the same type of anisotropy holds for both networks. The properties specified for the elastic behavior are assumed to be the instantaneous properties ( $K_{P} + K_{V}$ ).

Plastic Behavior

A plasticity definition can be used to provide the static hardening data for the material model. All available metal plasticity models, including Hill's plasticity model to define anisotropic yield, can be used.

The elastic-plastic network does not take into account rate-dependent yield. Hence, any specification of strain rate dependence for the plasticity model is not allowed.

Viscous Behavior

You can define the viscous behavior of the material using the Anand, Darveaux, Double-Power, Power Law, or Time Power Law creep laws or by inputting the description with user subroutine CREEP. For more information about the creep laws, see Creep Models. When you define the viscous behavior, you specify the viscosity parameters and choose the specific type of viscous behavior.

If you choose to input the creep law through user subroutine CREEP, you should define deviatoric creep only; more specifically, you should not define volumetric swelling behavior through this user subroutine. In addition, you also specify the fraction, $f$ , that defines the ratio of the elastic modulus of the elastic-viscous network to the total (instantaneous) modulus. You can specify viscous stress ratios under the viscous behavior definition to define anisotropic viscosity.