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RESEARCH PAPERS: Gas Turbines: Vehicular

A Viscoplastic Constitutive Theory for Monolithic Ceramics—I

[+] Author and Article Information
L. A. Janosik

NASA Lewis Research Center, Cleveland, OH 44135

S. F. Duffy

Cleveland State University, Cleveland, OH 44115

J. Eng. Gas Turbines Power 120(1), 155-161 (Jan 01, 1998) (7 pages) doi:10.1115/1.2818069 History: Received February 01, 1996; Online November 19, 2007

Abstract

This paper, which is the first of two in a series, provides an overview of a viscoplastic constitutive model that accounts for time-dependent material deformation (e.g., creep, stress relaxation, etc.) in monolithic ceramics. Using continuum principles of engineering mechanics, the complete theory is derived from a scalar dissipative potential function first proposed by Robinson (1978), and later utilized by Duffy (1988). Derivations based on a flow potential function provide an assurance that the inelastic boundary value problem is well posed, and solutions obtained are unique. The specific formulation used here for the threshold function (a component of the flow potential function) was originally proposed by Willam and Warnke (1975) in order to formulate constitutive equations for time-independent classical plasticity behavior observed in cement and unreinforced concrete. Here constitutive equations formulated for the flow law (strain rate) and evolutionary law employ stress invariants to define the functional dependence on the Cauchy stress and a tensorial state variable. This particular formulation of the viscoplastic model exhibits a sensitivity to hydrostatic stress, and allows different behavior in tension and compression.

Copyright © 1998 by The American Society of Mechanical Engineers
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