# Accession Number:

## ADA303067

# Title:

## A Theory of Viscoplasticity Based on Infinitesimal Total Strain,

# Descriptive Note:

# Corporate Author:

## RENSSELAER POLYTECHNIC INST TROY NY DEPT OF MECHANICAL ENGINEERING AERONAUTIC AL ENGINEERING AND MECHANICS

# Personal Author(s):

# Report Date:

## 1978-05-01

# Pagination or Media Count:

## 49.0

# Abstract:

A viscoplasticity theory based upon a nonlinear viscoelastic solid, linear in the rates of the strain and stress tensors but nonlinear in the stress tensor and the infinitesimal strain tensor, is being investigated for isothermal, homogeneous motions. A general anisotropic form and a specific isotropic formulation are proposed. A yield condition is not part of the theory and the transition from linear elastic to nonlinear inelastic behavior is continuous. Only total strains are used and the constant volume hypothesis is not employed. In this paper Poisson1s ratio is assumed to be constant. The pro posed equation can represent initial linear elastic behavior initial elastic response in torsion tension after arbitrary prestrain prestress in tension torsion linear elastic behavior for pure hydrostatic loading initial elastic slope upon large instantaneous changes in strain rate stress strain-rate sensitivity creep and relaxation defined behavior in the limit of very slow and very fast loading. Stress-strain curves obtained at different loading rate C will ultimately have the same slope and their spacing is nonlinearly related to the loading rate. The above properties of the equation are obtained by qualitative arguments based on the characteristics of the solutions of the resulting nonlinear first- order differential equations. In some instances numerical examples are given. For metals and isotropy we propose a simple equation whose coefficient functions can be determined from a tensile test. Specializations suitable for materials other than metals are possible. The paper shows that this nonlinear viscoelastic model can represent essential features of metal deformation behavior and reaffirms our previous assertion that metal deformation is basically rate-dependent and can be represented by piecewise nonlinear viscoelasticity. MM

# Descriptors:

# Subject Categories:

- Properties of Metals and Alloys
- Mechanics