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Considerations in development and implementation of elasto-viscoplastic constitutive model for high temperature applications

The prediction of inelastic behavior of metallic materials at elevated temperatures has increased in importance in recent years. The operating conditions within the hot section of a rocket motor or a modern gas turbine engine present an extremely harsh thermomechanical environment. Large thermal transients are induced each time the engine is started or shut down. Additional thermal transients from an elevated ambient occur whenever the engine power level is adjusted to meet flight requirements. The structural elements employed in such hot sections, as well as any engine components located therein, must be capable of withstanding such extreme conditions. Failure of a component would, due to the critical nature of the hot section, lead to an immediate and catastrophic loss in power. Consequently, assuring satisfactory long term performance for such components is a major concern. Nonisothermal loading of structures often causes excursion of stress well into the inelastic range. Moreover, the influence of geometry changes on the response is also significant in most cases. Therefore, both material and geometric nonlinear effects are considered.

Riff, Richard↗

Structural analysis

Hot section components of aircraft gas turbine engines are subjected to severe thermal-structural loading conditions, especially during the start-up and take-off portions of the engine cycle. The most severe and damaging stresses and strains are those induced by the steep thermal gradients induced during the start-up transient. These transient stresses and strains are also the most difficult to predict, in part because the temperature gradients and distributions are not well known or predictable, and also because the cyclic elasto-viscoplastic behavior of the materials at these extremes of temperature and strain are not well known or predictable. One element of the structures program will develop improved time-varying thermal-mechanical load models for the entire engine mission cycle from start-up to shutdown. The thermal model refinements will be consistent with those required by the structural code including considerations of mesh-point density, strain concentrations, and thermal gradients. Models will be developed for the burner liner, turbine vane and turbine blade.

Johns, R. H.↗

Thermo-elasto-viscoplastic analysis of problems in extension and shear

The problems of extension and shear behavior of structural elements made of carbon steel and subjected to large thermomechanical loads are investigated. The analysis is based on nonlinear geometric and constitutive relations, and is expressed in a rate form. The material constitutive equations are capable of reproducing all nonisothermal, elasto-viscoplastic characteristics. The results of the test problems show that: (1) the formulation can accommodate very large strains and rotations; (2) the model incorporates the simplification associated with rate-insensitive elastic response without losing the ability to model a rate-temperature dependent yield strength and plasticity; and (3) the formulation does not display oscillatory behavior in the stresses for the simple shear problem.

Riff, R.↗

The dynamic aspects of thermo-elasto-viscoplastic snap-through and creep buckling phenomena

Use of a mathematical model and solution methodology, to examine dynamic buckling and dynamic postbuckling behavior of shallow arches and spherical caps made of a realistic material and undergoing non-isothermal, elasto-viscoplastic deformation was examined. Thus, geometric as well as material type nonlinearities of higher order are included in this analysis. The dynamic stability problem is studied under impulsive loading and suddenly applied loading with loads of constant magnitude and infinite duration. A finite element model was derived directly from the incrementally formulated nonlinear shell equations, by using a tensor-oriented procedure. As an example of the results, the time history of the midspan displacement of a damped shallow circular arch is presented.

Riff, R.↗

Non-isothermal elastoviscoplastic snap-through and creep buckling of shallow arches

The problem of buckling of shallow arches under transient thermomechanical loads is investigated. The analysis is based on nonlinear geometric and constitutive relations, and is expressed in a rate form. The material constitutive equations are capable of reproducing all non-isothermal, elasto-viscoplastic characteristics. The solution scheme is capable of predicting response which includes pre and postbuckling with creep and plastic effects. The solution procedure is demonstrated through several examples which include both creep and snap-through behavior.

Simitses, G. J.↗

Thermo-elasto-viscoplastic analysis of problems in extension and shear

The problems of extension and shear behavior of structural elements made of carbon steel and subjected to large thermomechanical loads are investigated. The analysis is based on nonlinear geometric and constitutive relations, and is expressed in a rate form. The material constitutive equations are capable of reproducing all nonisothermal, elasto-viscoplastic characteristics. The results of the test problems show that: (1) the formulation can accommodate very large strains and rotations; (2) the model incorporates the simplification associated with rate-insensitive elastic response without losing the ability to model a rate-temperature dependent yield strength and plasticity; and (3) the formulation does not display oscillatory behavior in the stresses for the simple shear problem.

Riff, R.↗

Non-isothermal buckling behavior of viscoplastic shell structures

Described are the mathematical model and solution methodologies for analyzing the structural response of thin, metallic elasto-viscoplastic shell structures under large thermomechanical loads and their non-isothermal buckling behavior. Among the system responses associated with these loads and conditions are snap-through, buckling, thermal buckling, and creep buckling. This geometric and material nonlinearities (of high order) can be anticipated and are considered in the model and the numerical treatment.

Riff, Richard↗

Adaptive Finite Element Methods for Continuum Damage Modeling

The paper presents an application of adaptive finite element methods to the modeling of low-cycle continuum damage and life prediction of high-temperature components. The major objective is to provide automated and accurate modeling of damaged zones through adaptive mesh refinement and adaptive time-stepping methods. The damage modeling methodology is implemented in an usual way by embedding damage evolution in the transient nonlinear solution of elasto-viscoplastic deformation problems. This nonlinear boundary-value problem is discretized by adaptive finite element methods. The automated h-adaptive mesh refinements are driven by error indicators, based on selected principal variables in the problem (stresses, non-elastic strains, damage, etc.). In the time domain, adaptive time-stepping is used, combined with a predictor-corrector time marching algorithm. The time selection is controlled by required time accuracy. In order to take into account strong temperature dependency of material parameters, the nonlinear structural solution a coupled with thermal analyses (one-way coupling). Several test examples illustrate the importance and benefits of adaptive mesh refinements in accurate prediction of damage levels and failure time.

Min, J. B.↗