1、U.S. DEPARTMENT OF COMMERCENational Technical Information ServiceNACA TR 1170BEHAVIOR OF MATERIALS UNDER CONDITIONS OFTHERMAL STRESSNational Advisory Committee for AeronauticsWashington, DC1954./Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TR
2、 1170 iNATIONAL ADVISORY COMMITTEEFOR AERONAUTICSREPORT 1170BEHAVIOR OF MATERIALS UNDER CONDITIONSOF THERMAL STRESSBy S. S. MANSON/._1954- _ . REPRODUCEDBYj_ NATIONAL TECHNICAL iINFORMATION SERVICE i _, U.S. DEPARIMENTOF COMMERCESPRtNGIEL_D.yA. 22161_ ,. = .Provided by IHSNot for ResaleNo reproducti
3、on or networking permitted without license from IHS-,-,-REPORT 1170BEHAVIOR OF MATERIALS UNDER CONDITIONSOF THERMAL STRESSBy S. S. MANSONLewis Flight Propulsion LaboratoryCleveland, OhioiProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-National Adviso
4、ry Committee for AeronauticsHeadquarters, 1512 H Street N_:, Washington 25, D. U.Created by act of Congress approved 5larch 3, 1915, for the supervision and direction of the scientific studyof the problems of flight (U. S. Code, title 50, sec. 151). Its membership was increased from 12 to 15 by acta
5、pproved March 2, 1929, and to 17 by act approved May 25, 1948. The members are appointed by the President,and serve as such without compensation.JEROME C. HUNSAKER, Sc. D., Massachusetts Institute of Technology, ChairmanDETLEV W. BRONK, PH.D., President, Rockefeller Institute for Medical Research, V
6、ice ChairmanJOSEPH P. ADAMS, LL.D., member, Civil Aeronautics Board. RALPH A. OFSTIE, Vice Admiral, United States Navy, DeputyALLEN V. ASTIN, PtL D., Director, National Bureau of Standards. Chief of Naval Operations (Air).PRESTON R. BASSETT, M. A., President, Sperry Gyroscope Co DONALD L. PUTT, Lieu
7、tenant General, United States Air Force.Inc. Deputy Chief of Staff (Development)LEONARD CARMICHAEL, PIt. D., Secretary, Smithsonian Insti- DONALD A. QUARLES, D. Eng., Assistant Secretary of Defenestution. (Research and Development).RALPH S. DAMON, D. Eng., President, Traus World Airlines, Inc. ARTHU
8、R E. RAY,_IOND, Sc. D., Vice President-Engineering,JAMES H. DOOLITTLE, Sc. D., Vice President, Shell Oil Co. Douglas Aircraft Co., Inc.LLOYD HARRISON, Rear Admiral, United States Navy, Deputy FRANCIS W. _EICHEI.DERFER, SC. D., Chief, United Statseand Assistant Chief of the Bureau of Aeronautics. Wea
9、ther Bureau.RONALD M. HAZEN, B. S., Director of Engineering, Allison OSWALD RYAN, LL.D., member, Civil Aeronautics Board.Division, General Motors Corp. NAT_Ar F. TWINING, General, United States Air Force, Chiefof Staff.-VUGH L. DRYDEN, PH.D., Director JoHN F. VICTORY, LL. D., Executive SecretaryJOHN
10、 W. CROWLEY, JR., B. S., Associate Director for Research EDWARD H. CHAMBERLIN, Executive O_cerHENRY d. E. REID, D. Eng., Director, Langley Aeronautical Laboratory, Langley Field, Va.SMITH J. DEFRANCE, D. Eng., Director, Ames Aeronautical Laboratory, Moffett Field, Calif.EDWARD R. SHARP, SC. D., Dire
11、ctor, Lewis Flight Propulsion Laboratory, Cleveland Airport, Cleveland, OhioLANGLEY AERONAUTICAL LABORATORY AMES AERONAUTICAL LABORATORY LEWIS FLIGHT PROPULSION LABORATORYLangley Field, Va. Moffett Field, Calif. Cleveland Airport, Cleveland, OhioConduct, under unified control , _r“ all agencies, of
12、scientific research on the fundamental problems of flightII Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-_: :/ :i:/ i : :,1REPORT 1170BEHAVIOR OF MATERIALS UNDER CONDITIONS OF THERMAL STRESS 1By S. S. MANSONSUMMARY these superimposed strains witho
13、ut inducing enough stressA review is presented ofa_ailable i nJormation on the behavior to cause rupture; ductile materials, on the other hand,of brittle and ductile materials under conditions of thermal can usually withstand these additional strains, but maystress and thermal shock. For brittle mat
14、erials, a Simple formula ultimately fail if subjected to a number of cycles of imposedrelating physical properties to thermal-shock resistance ,is temperature.derived and used to determine the relative significance of two The problem of thermal stress is of great importance inindices currently in us
15、e Jot rating materials. The importance current tfigh-power engines. The present trend toward in-of _imulating operating conditions in thermal-_hock testing is creasing temperatures has necessitated the use of refractorydeduced from the formula and is experimentally illustrated by materials capable o
16、f withstanding much higher tempera-showing that BoO could be either inferior or superior to Alp03 tures than normal engineering materials. One salient prop-in thermal shock, depending on the testing conditions. For erty of these materials is lack of ductility. For this reason,ductile materials, ther
17、mal-shock resistance depends upon the thermal stress is one of the most important design criteriacomplex interrelation among several metallurgical variables in the applicatio n of these materials. Thermal stress iswhich seriously affect strength and ductility. These variable, also currently receivin
18、g considerable attention in connectionare briefly “discussed and illustrated from literature sources, with ductile materials since there is considerable evidenceThe importance of simulating operating conditions in tests for that failure of many ductile engine components can be at-rating ductile mate
19、rials is especially to be emphasized because tributed to thermal cycling. The problem of high-speedof the importance of testing conditions in “metallurgy. A hum- flight, with attendant increases of temperature and temper-bet of practical methods that have been used to minimize the ature gradients in
20、 aircraft bodies, has further generateddeleterious effects of thermal stress and thermal shock are concern over the significance of thermal stress in ductileoutlined, materials.INTRODUCTION Thermal stress and thermal shock may be distinguishedWhen a material is subjected to a temperature gradient by
21、 the fact that in thermal shock the thermal stresses areor when a composite material consisting of two or more produced by transient temperature gradients, usually suddenmaterials having different coefficients of expansion is heated ones. For example, if a body originally at one uniform tera-either
22、uniformly or nonuniformly, the various fibers tend to perature is suddenly immersed in a medium of differentexpand different amounts in accord with their individual temperature, a condition of thermal shock is introduced.temperatures and temperature coefficients of expansion. .At any instant the str
23、esses are determined by the tempera-To enable the body to remain continuous, rather than allow- ture distribution and are no different flom what they woulding each fiber to expand individually, a system of thermal be if this temperature distribution couhl be obtained in thestrain and associate5 ._t_
24、esses may be introduced depending steady-state condition. But the temperature gradients thatupon the shape of the body and the temperature distribution, can be established in the transient state are generally muchIf the material cannot withstand the stresses and strains, higher than those that occur
25、 in the steady state, and hencerupture may occur, thermal shock is important relative to ordinary thermalBrittle and ductile materials react in considerably different stress because of the higher stress that can be induced.manners to thermal stress. Brittle materials can endure Another distinction b
26、etween thermal stress and thermalonly a very small amount of strain before rupture; ductile shock is that in thermal shock the rate of application of:_ materials can undergo appreciable strain without rupture, stress is very rapid, and many materials are affected by theSince thermal stress behavior
27、depends essentially on the rate at which load is applied. Some materials are em-:! ability of the material to absorb the induced strains necessary brittled by rapid application of stress and therefore may not:i to maintain a continuous body upon the application of a be able to withstand a thermal sh
28、ock stress which if appliedi thermal gradient, brittle materials cannot readily withstand slowly could readily be absorbed.i Suporsedes HAPA TN 2933, “Behavior of Materials Under Conditions of Thermal Stress“ by S, S. Manson, 1953. Based on lecture presented at Symposium on Heat Transfer, Unicef,! s
29、ity of Michigan, June 27-28, 1952.i.tProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,- . (, . j 2 REPORT l l70-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS.7 Nond_mensionol flat plate initially at uniform temperature and suddenly im-p heattransfer, mer
30、sed in a medium of lower temperature. This case is_/3=_-_- treated because the temperature problem of the flat plate.6 ao.o is well known, and because most of the recent publications/-_ on tile thermal stress problem also consider this case (for_ example, refs. 1 and 2). There is, therefore, a consi
31、derable,o.o background of information from which to draw results and_ with which to make comparisons. Furthermore, most of/ “-“_ the one-dimensional problems can be treated in essentially5.0 the same way as the flat plate problem treated herein, andtherefore any important conclusions that pertain to
32、 the fiat_ 4 plate are probably also shapes, providedvalid for other/ _- _ 3.0 that the necessary changes are made in the constants. Note“b _ .t“ _-. also that in this case the temperature problem is one-dimen-“ / -_ a.o sional; that is, in the fiat plate, temperature variations willL“U-r-*-“-“ _ ,.
33、5 be considered only in the ttiickness direction. The problemis treated in this way because there are relatively few two-“_ / _ _“_-“_ I.o dimensional problems solved in the literature and also be-/“ cause the qualitative conclusions reached in the fiat plate.5 problem are believed to apply to more
34、complicated cases.The first problem in connection with the flat plate is to1 I/ determine the temperature distribution at a timet after thel ._ .I surrounding temperature has been changed. Once thistemperature has been determined, the stresses can readilyo ._ .2 .3 .4 .5 ._8= ,f be determined in acc
35、ordance with very simple formulaspaz-_ derived from the theory of elasticity. Assuming that theFIGURe.1.-Nondimensional stress versus nondimensional time for properties of the material do not vary with temperature andsurface of fiat plate, that the material is elastic, the following equation can hew
36、ritten for the stress at any point in the thickness of the plate:It is also necessary to distinguish between a single cycle Too-Tof thermal stress and thermal fatigue. When failure is a*- (1)caused by the application of several similar thermal stress Tocycles, rather than a single cycle, the process
37、 is referred to Physically, a* can be considered as the ratio of tlie stressas thermal fatigue. The processes that take place in a body actually developed to the stress that would be developed ifin successive cycles of stress application are extremely com- thermal expansion were completely constrain
38、ed. The for-plex; the mechanism leading to cyclic failure is as yet in-mula for a* iscompletely understood. In most of the basic work, there- _, _(1-_)fore, attention is directed at the conditions under which = E_-To (2)failure will occur in one cycle merely because this case lendsitself to analysis
39、. The problem of thermal fatigue is, of wherecourse, a most important one in engineering application. _ actual stressThe objectives of this presentation are: First, some of jL Poissons ratiothe information contained in recent publications on the E elastic modulhsmathematics of thermal shock will be
40、outlined, and a simple a coefficient of expansionformula will be derived for correlation of thermal shock be- T_, average temperature across thickness of platehavior with material properties. Second, the variables in T temperature at point where stress is consideredthe simplified relation will be ex
41、amined and from it methods To initial uniform temperature of plate above ambientfor minimizing thermal stress will be deduced. For brit- temperature (ambient temperature assumed to betie materials the single-cycle criterion of failure will be zero for simplicity)considered; for ductile materials the
42、 discussion will be Stress at surfaoe.-In order to obtain the surface stress,directed at available information on the problem of thermal it is therefore necessary first to determine the average tem-fatigue, perature and the surface temperature. The temperatureproblem has been thoroughly treated in t
43、he literature and theTHERMAL SHOCK OF BRITTLE MATERIALS AS DEDUCED result is usually given in the form of an infinite series. InFROM STUDY OF FLATPLATE figure 1 are shown the results of some computations that haveGe_eraI equation for stress._In order to make the dis- beenmade by substituting the exa
44、ct series solution forcussion specific, the case considered is that of a homogeneous temperature into the stress equations.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-:BEHAVIOR OF MATERIALS UNDER CONDITIONS OF THERMAL STRESS 3In the exact solutio
45、n there are three important variables. PQ, PQ, etc. These curves must fit two boundary condi-First is the reduced stress, already mentioned, and second, tions: (1) At the center they must have a horizontal tangent_h because the center of thc plate is a line of symmetry, andthe value 8 which is equal
46、 to (where a is the half thickness no heat is transfcired across the center line; (2) at theof the plate, h is the heat-transfer coefficient, and k is the surface tile slope must be in accord with tile smface heat-conductivity of the material). The heat-transfer coefficient transfer coefficient, whi
47、ch is equivalent to the condition thatis defined as the amount of heat transferred from a unit the tangent to the curves at the surface pass through thearea of the surface of the plate per unit temperature differ- fixed point 0 representing the ambient temperature whichonce between the surface and t
48、he smrounding medium. The has been taken equal to zero. These temperature distribu-variables a, h, and k always occur as a group as a result of the tions must also satisfy the differential equations of heatmanner in which they appear in the differential equation; transfer, which is achieved by adjus
49、ting certain constants sotherefore, in the generalized treatment of the problem it is that the final result will be consistent with the curve ofnot the individual value of a, h, or k that is of importance figure 2, which of course does satisfy the differential equation.but their value as grouped together to form tlie term 8. The It is as
