Development of accurate three-dimensional (multiaxial) inelastic stress-strain models is critical in utilizing advanced ceramics for challenging 21st century high-temperature structural applications. The current state of the art uses elastic stress fields as a basis for both subcritical crack growth and creep life prediction efforts aimed at predicting the time-dependent reliability response of ceramic components subjected to elevated service temperatures. However, to successfully design components that will meet tomorrow’s challenging requirements, design engineers must recognize that elastic predictions are inaccurate for these materials when subjected to high-temperature service conditions such as those encountered in advanced heat engine components. Analytical life prediction methodologies developed for advanced ceramics and other brittle materials must employ accurate constitutive models that capture the inelastic response exhibited by these materials at elevated service temperatures.
A constitutive model recently developed at the NASA Lewis Research Center helps address this issue by accounting for the time-dependent (inelastic) material deformation phenomena (e.g., creep, rate sensitivity, and stress relaxation) exhibited by monolithic ceramics exposed to high-temperature service conditions. In addition, the proposed formulation is based on a threshold function that is sensitive to hydrostatic stress and allows different behavior in tension and compression, reflecting experimental observations obtained for these material systems.
The objective of this effort was to demonstrate the capabilities and inherent features of the mathematical formulation of the constitutive theory. In this regard, the viscoplastic constitutive equations formulated for the flow law (i.e., the strain rate) and the evolutionary law were incorporated into computer algorithms for predicting the multiaxial inelastic (creep) response of a given homogeneous state of stress. For the solution of a full multiaxial creep problem, 12 coupled differential equations had to be integrated. These represent the constitutive law: that is, six equations from the flow law (i.e., strain rate) and six from the evolutionary law.
Examples have been simulated numerically to illustrate the model’s ability to qualitatively capture the time-dependent phenomena suggested here. For an imposed service (load) history, the computer algorithm can generate creep curves and viscoplastic flow surfaces that demonstrate its ability to capture the inelastic creep deformation response. No attempt was made to assess the accuracy of the model in comparison to the experiment. A quantitative assessment has been reserved for a later date--after the material constants have been suitably characterized for a specific ceramic material. Creep rupture is not considered in the model, although incorporating damage mechanics concepts into the present theory could yield a workable creep rupture model. This task also has been reserved for a future enhancement.
Janosik, L.A.; and Duffy, S.F.: A Viscoplastic Constitutive Theory for Monolithic Ceramics--I. J. Engrg. Gas Turb. Power (ASME Paper 96-GT-368) vol. 120, no. 1, Jan. 1998, pp. 155-161.
Lewis contacts: Lesley A. Janosik, (216) 433-5160,
Authors: Lesley A. Janosik
Headquarters program office: OAT
Programs/Projects: Propulsion Systems R&T, P&PM
Last updated June 8, 1999, by Nancy.L.Obryan@nasa.gov
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