THERMO-VISCO PLASTIC ANALYSIS OF HYPERSONICSTRUCTURES SUBJECTED TO SEVERE

AERODYNAMIC HEATING

Earl. A. Thornton, Visiting Scholar*

J. Tinsley Oden, Professor and Director

Texas Institute for Computational MechanicsThe University of Texas at Austin

Austin, Texas 78712-1085Phone: 512-471-5513

Woytek Tworzydlo, Senior Research Engineer

Sung-Kie Youn, Research Engineer./

The Computational Mechanics Co., Inc.Austin, Texas

Abstract of a paper prepared for:

AIANASME/ASCE/AHS/ASC 30th Structures,Structural Dynamics and Materials ConferenceApril 3-5, 1989Mobile, Alabama

*To receive correspondence

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TIIERMO- VISCOPLASTIC ANALYSIS OF HYPERSONIC S1RUCTURES

SUBJECfED TO SEVERE AERODYNAMIC HEATING

The commitment to develop the National Aerospace Plane has generated resurgent interestin the technology required to design structures for hypersonic flight. Such structures will beexposed to aerodynamic heating of unprecedented magnitudes. As the vehicle accelerates ordecelerates at hypersonic speeds in the atmosphere, shocks will sweep across the vehicle andinteract with local shocks and boundary layers. These interactions introduce severe localpressures and heating rates. A recent experimental study (ref. 1) of interacting shock waves on acylindrical leading edge shows heating rates ten times undisturbed levels.

Leading edges of engine structures present a significant design problem because ofintense local heating and pressures. Analysis of the flow, thermal and structural behavior presentserious computational challenges to analysts because of the inherent nonlinearities in all aspectsof the multi-disciplinary problems. Some of the critical computational issues are identified inreference 2. Critical issues include the difficulties involved in (1) analyzing the viscous,compressible flow and predicting the high local aerodynamic heating, (2) modeling and analyzingmulti-mode unsteady heat transfer in a high temperature convectively-cooled structure, and (3)

simulating the transient, nonlinear thermal-structural response for rapid temperature changes.Preliminary structural analysis of an impingement cooled leading edge (ref. 3) showed high localplasticity that seriously degraded the structure's load carrying capacity at elevated temperatures.A recent thermostructural analysis with experimental verification (ref. 4) of cowl lip designsconflrmed that inelastic effects occur and can be signiflcant. In the experimental study, twospecimens failed due to burn-through because of intense local heating or because of loss of

cooling.

The purpose of this paper is to present a thermo-viscoplastic computational method forhypersonic structures subjected to severe local unsteady heating. The analysis employs a unifiedvisco-plastic constitutive model implemented in a finite element approach capable of predictingrate-dependent plasticity effects for temperatures up to about 75% of the melting point.Rate-dependent plasticity effects are known to be important at elevated temperatures. Thebalance of this abstract highlights the unilled viscoplasticity theory, outlines the computationalapproach and presents preliminary results for two thermO-viscoplastic analyses of a convectivelycooled structure.

Unifled visco-plastic constitutive models have evolved over the last twenty years toprovide a means for analytically representing a materials response from the elastic through the

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plastic range including strain-rate dependent plastic flow, creep and stress relaxation. Thetheories are guided by physical considerations including dislocation dynamics and are based onthe principles of continuum mechanics. The flrst multi-dimensional formulations ofelastic-viscoplastic constitutive equations was due to Bodner and Partom. Since then a numberof constitutive models have appeared; many of these theories are summarized in review articlesthat appear in reference 5. A NASA-Lewis sponsored research program (HOST) conducted bythe Southwest Research Institute recently concluded a four year research effort (ref. 6-7) tofurther develop unifled constitutive models for isotropic materials and to demonstrate theirusefulness for analysis of high temperature gas turbine engines. One result of this study ismaterial property data for high temperature nickel-based alloys over a wide temperature range.The unifled models employed were those of Bodner-Partom and Walker.

Unifled visco-plastic theories have been implemented by a number of flnite elementresearchers. Under the NASA HOST program, the Walker model was implemented in the

MARC finite element program (ref. 8) and used to analyze the thermo-viscoplastic response of aturbine blade under simulated flight conditions. In another recent finite element application (ref.9), the Bodner-Partom and Walker theories were compared for a thin circular plate subject to

highly localized, transient heating.In this paper the Bodner·Partom constitutive model is employed, and the flnite element

approach developed in reference 10 for the isothermal case is extended to include thermal effects.The behavior of a thermo-viscoplastic structure subjected to aerodynamic heating is

analyzed assuming that: (1) thermo-mechanical coupling in the conservation of energy equationcan be neglected, (2) the structural response is quasi-static, and (3) deformations areinfinitesimal. With these assumptions, an unsteady thermal analysis may be performed flrst todetermine the temperatures. Then, using these temperatures, the structure's viscoplasticresponse is determined. The solution is thus obtained by separately solving an initial-boundary

value problem for first the thermal and then the structural response.For hypersonic flight, some leading edges and panels require active cooling systems to

keep structural temperatures within acceptable ranges. The internal flow in the coolant passagehas a predominant role in the thermal response of a hypersonic structure subject to externalheating. The paper will describe an engineering heat transfer approach (ref. 11) that is used tomodel heat transfer in a convectively cooled structure.

The viscoplastic initial value problem is formulated in terms of stresses, strains anddisplacements expressed in rate form. The governing equations, boundary and initial conditionsare summarized in Figure 1. The figure shows that strain rates are separated into elastic and

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plastic components. The stress rates are related to the elastic strain components and temperaturerates by Hooke's law. The plastic strain rates are related to stresses and an internal state variableby the unified viscoplastic theory.

The Bodner-Partom constitutive equations are summarized in Figure 2. Note that thestate variable z is given by an evolution equation which must be integrated in time as part of theanalysis.

The finite element formulation for the thermal and structural problem will be presented inthe paper. The finite element solution method is summarized in Figure 3, and steps in thethermo-viscoplastic solution scheme are summarized in Figure 4.

Some preliminary numerical results for a segment of a convectively cooled scramjet

engine strut are presented in Figures 6-11. The figures presented show the thermal andviscoplastic response for a one-D model (Figs. 6-7) and a two D model (Figs. 8-11). Resultsinclude transient temperatures, stresses, deformations and plastic strains. The paper will discuss

the problem in detail and present additional results.The preliminary results show that localized, transient aerodynamic heating caused

significant plasticity in the aerodynamic skin. The structural response was strongly influcnced

by the temperatures and the temperature rates of change. Residual strcsses and permanentdeformations can be predicted without excessive computational expense because the coolant flowcauses a short duration transient. The paper will demonstrate that thermo-viscoplastic analysiscan provide valuable insight into the behavior of hypersonic structures subject to severe

aerodynamic heating.REFERENCES

1. Wieting, A.R. and Holden, M.S.: "Experimental Study of Shock Wave InterferenceHeating on a Cylindrical Leading Edge," AIAA 22nd Thermophysics Conference,Honolulu, Hawaii, June 8-10, 1987, AlAA Paper 87-1511.

2. Dechaumphai, P., Thornton, E.A. and Wieting, A.R. : "Flow-Thermal-Structural Study ofAerodynamically Heated Leading Edges," AIAA/ASME/ASCE/AHS 29th Structures,Structural Dynamics and Materials Conference, Williamsburg, Virginia, April 18-20, 1988,AIAA Paper 88-2245.

3. Dechaumphai, P., Wieting, A.R. and Thornton, E.A.: "Thermal-Structural Performancesof an Actively Cooled Leading Edge Subjected to Type IV Shock Wave InterferenceHeating," Third National Aero-Space Plane Symposium, June 2-4,1987, Paper No. 24.

4. Melis, M.E. and Gladden, H.J.: "Thermostructural Analysis with ExperimentalVerification in a High Heat Flux Facility of a Simulated Cowl Lip,"AIAAIASME/ASCE/AHS 29th Structures, Structural Dynamics and Mateials Conference,Williamsburg, Virginia, April 18-20, 1988, AIAA 88-2222.

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5. Miller, A.K (editor), Unified Constitutive Equations for Creep and Plasticity, ElsevierApplied Science Publishers, 1987.

6. Chan, KS., Lindholm, U.S., Bodner, S.R., Hill, J.T., Weber, R.M. and Meyer, T.G.,"Constitutive Modeling for Isotropic Materials (HOST)," Third Annual Status Report,Southwest Research Institute, San Antonio, Texas, August, 1986, NASA CR 179522.

7. Chan, KS., Lindholm, U.S. and Bodner, S.R., "Constitutive Modeling for IsotropicMaterials (HOST), Final Report, Southwest Research Institute, San Antonio, Texas, June,1988, NASA CR-182132.

8. MARC General Purpose Finite Element Program, MARC Corporation, Palo Alto, CA.

9. Chang, H.T. and Allen, D.H.: "Analysis of Visco plastic Plates Subjected to Rapid ExternalHeating," AIAA/ASME/ASCE/AHS 29th Structures, Structural Dynamics and MaterialsConference, Williamsburg, Virginia, April 18-20, 1988, AIAA Paper 88-2422.

10. Bass, J.M. and Oden, J.T.: "Adaptive Finite Element Methods for a Class of EvolutionProblems in Viscoplasticity," Int. J. Eng. Sci., Vol. 25, No.6, 1987, pp. 623-653.

11. Thornton, E.A. and Wieting, A.R.: "Finite Element Methodology for TransientConductionfForced Convection Thermal Analysis," Progress in Astronautics andAeronautics: Hear Transfer, Thermal Control and Heat Pipes, Vol. 70, Edited by Walter B.Olstad, AIAA, New York, pp. 77-103.

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