Fully Associative, Nonisothermal, Potential-Based Unified Viscoplastic Model for Titanium-Based Matrices

To accomplish this, the NASA Lewis Research Center is employing a recently developed, complete, potential-based framework (ref. 1). This framework, which utilizes internal state variables, was put forth for the derivation of reversible and irreversible constitutive equations. The framework, and consequently the resulting constitutive model, is termed complete because the existence of the total (integrated) form of the Gibbs complementary free energy and complementary dissipation potentials are assumed a priori. The specific forms selected here for both the Gibbs and complementary dissipation potentials result in a fully associative, multiaxial, nonisothermal, unified viscoplastic model with nonlinear kinematic hardening. This model (refs. 2 and 3) constitutes one of many models in the Generalized Viscoplasticity with Potential Structure (GVIPS) class of inelastic constitutive equations.

A unique aspect of this GVIPS model is its inclusion of nonlinear hardening through the use of a compliance operator (derived from the Gibb's potential) in the evolution law for the back stress. This nonlinear tensorial operator is significant in that

• It allows both the flow and evolutionary laws to be fully associative (and therefore easily integrated) (ref. 4).

• It greatly influences the multiaxial response under nonproportional loading paths (refs. 1 and 5).

• In the case of nonisothermal histories, it introduces an instantaneous thermal softening mechanism proportional to the rate of change in temperature (ref. 3). In addition to this nonlinear compliance operator, the new consistent, potential preserving, internal unloading criterion (ref. 2) was utilized to prevent abnormalities in the predicted stress-strain curves (which are present with nonlinear hardening formulations) during unloading and reversed loading.

Left: GVIPS correlation with experimental tensile data at 25, 300, 482, 565, and 650 °C, for a total strain rate of 8.33x10^-5. Right: Stress-time response of GVIPS prediction given relaxation tests at two temperatures (300 and 365 °C) and 1.9-percent strain.

References

1. Arnold, S.M.; and Saleeb, A.F.: On the Thermodynamic Framework of Generalized Coupled Thermoelastic-Viscoplastic-Damage Modeling. Int. Jrl. Plasticity, vol. 10, no. 3, 1994, pp. 263-278 (NASA TM-105349, 1991).

2. Arnold, S.M.; Saleeb, A.F.; and Castelli, M.G.: A Fully Associative, Non-Linear Kinematic, Unified Viscoplastic Model for Titanium Based Matrices. NASA TM-106609, 1994.

3. Arnold, S.M.; Saleeb, A.F.; and Castelli, M.G.: A Fully Associative, Non-Linear Kinematic, Unified Viscoplastic Model for Titanium Based Matrices. NASA TM-106609, 1994.

4. Saleeb, A.F.; and Wilt, T.E.: Analysis of the Anisotropic Viscoplastic-Damage Response of Composite Laminates-Continuum Basis and Computational Algorithms. Int. J. Eng. Num. Meth., vol. 36, no. 10, 1993, pp. 1629-1660.

5. Arnold, S.M.; Saleeb, A.F; and Wilt, T.E.: A Modeling Investigation of Thermal and Strain Induced Recovery and Nonlinear Hardening in Potential Based Viscoplasticity. Jrl. Eng. Mater. Technol., vol. 117, 1995, pp. 157-167 (NASA TM-106122, 1993).