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Factors Affecting Thermal Stress Resistance of Ceramic Materials

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Factors Affecting Thermal Stress Resistance of Ceramic Materials Factors Affecting Thermal Stress Resistance of Ceramic Materials by W. D. KINGERY Ceramics Division, Department of Metallurgy, Massachusetts lnstihrte of Technology, Cambridge, Massachusetts The sources and calculation of thermal stresses II. Nomenclature are considered, together with the factors in- The nomenclature and letter symbols employed in the volved in thermal stress resistance factors. consideration of thermal stresses have varied considerably. Properties affecting thermal stress resistance of In this paper the following definitions will be employed: ceramics are reviewed, and testing methods are considered. Thermal stress: A stress arising from a temperature gradient. Thermal stress resistance: Resistance to weakening or to frac- ture from thermal stresses. 1. Introduction Spalling: The breaking away of pieces of a shape or struc- HE susceptibility of ceram$ materids to thermal stresses ture. has been recognized for a long time. More than one Thermal spalling: Spalling caused by thermal stresses. Thundred years ago equations for the thermal stresses aris- Thermal fracture: Fracture caused by thermal stresses. ing from temperature gradients in a cylinder were derived by Thermal endurance: Resistance to weakening or fracture Duhamel (1838).‘ Since that time, about thirty papers have when subjected to conditions causing thermal stresses. appeared which mainly consider the calculation of thermal Thermal shock: A sudden transient temperature change. stresses in an infinite cylinder subjected to temperature gra- Thermal shock resistance: Resistance to weakening or frac- dients. It is apparent that thermal stresses are not a new ture when subjected to thermal shock. or uninvestigated phenomenon. The first quantitative treatment of thermal stress fracture 111. Origin and Calculation of Thermal Stresses in ceramic materials was prepared by Winkelrnann and Schott The origin of thermal stresses is the difference in thermal (1894).2 Hovestadt and Everhart (1902)3 gave a correct expansion of various parts of a body under conditions such solution for the case of infinitely rapid cooling. A number of that free expansion of each small unit of volume cannot take investigators considered testing methods for glasses and for place.5 This condition can arise in a number of ways. refractories and their correlation with service results. Norton Stresses Arising at Uniform Temperature ( 1926)4 studied the problem and first suggested that shear (I) stresses must be considered as well as tensile stresses. More If a ceramic body is changed from an initial temperature, recently, several investigators, particularly those interested to, to a new uniform temperature, t’, no stresses arise providing in special refractory applications, have considered the prob- that the body is homogeneous, isotropic, and unrestrained lem of thermal stresses from both theoretical and experimental (free to expand). Under these conditions, the linear expan- points of view. New attempts have been made to define and sion of each volume element is a(t’ - to) and the shape of the to measure a material property which can be called “resistance body is unchanged. to thermal stresses.” Although these attempts have not been If the body is not homogeneous and isotropic, as in a poly- completely successful in a quantitative way, they have led to crystalline material with anisotropic crystals or in a mixture a much improved understanding of the factors that con- of two materials (such as a glass-mullite porcelain), stresses tribute to thermal stress resistance. It is the purpose of the will arise due to the difference in expansion between crystals present paper to consider these factors and their effect on or phases. The magnitude of the stresses will depend on the thermal stress resistance. elastic properties and expansion coefficients of the compo- nents. These “microstresses” or “tessellated stresses” have been thoroughly investigated in connection with magnetic and fatigue properties.6 In extreme cases they may lead to serious weakening or fracture.’ A similar effect on a larger scale is Presented at the Symposium on Thermal Fracture sponsored the stresses caused by differences of expansion between a by the New England Section, The American Ceramic Society, at Massachusetts Institute of Technology, Cambridge, Massa- chusetts, on September 16, 1953. Received April 20, 1954. 6 S. Timoshenko, Theory of Elasticity, McGraw-Hill Book Co., The author is assistant professor of ceramics, Ceramics Divi- Inc., New York. 1934. 415 pp. sion, Department of Metallurgy, Massachusetts Institute of ’ 8 (a) F. LBszlb, “Tessellated Stresses,” J. Iron Steel Inst. Technologv. (London). 148 111 173-99 (1943). J. M. C. Duhamel, “Memoire sur le calcul des actions molec- . (b) F.’P.Bowden, “Experiments of Boas and Honeycombe on ulaires developpers par les changements de temperature dans les Internal Stresses Due to Anisotropic Thermal Expansion of Pure corps solides,” Memoirs . de Z’institute de France. V,440 (1838). Metals and Alloys.” J. Inst. Metals, Symposium on Internal a A. Winkelmannand 0.Schott, “Uebet thermische Widerstands- Stresses in Metals and Alloys, Preprint No. 1100, 6 pp. (1947). coefficienten vershiedener Glaser in ihrer Abhangigkeit von der (c) J. P. Nielsen and W. R. Hibbard, Jr., “X-ray Study of chemischen Zusammensetzung,” Ann. Physik. Chem., 51, 730 Thermally Induced Stresses in Microconstituents of Aluminum- f 1894). Silicon Alloys,” J. Appl. Phys., 21, 853-54 (1950). \----I H. Hovestadt and J. D. Everhart, Jena Glass, Macmillan Co., 7 (a)N. N. Ault and H. F. G. Ueltz, “Sonic Analysis for Solid New York, 1902, p. 228. Bodies,” J. Am. Ceram. Soc., 36, 161 199-203 (1953). 4 F. H. Norton, “Mechanism of Spalling,” J. Am. Ceram. Soc., 9 (b) W. R. Buessem, N. R. Thielke, and R. V. Sarakauskas, [7] 446-61 (1926); “A General Theory of Spalling,” ibid., 8 111 “Thermal Expansion Hysteresis of Aluminum Titanate,” Ceram. 29-39 (1925). Age, 60 [5] 38-40 (1952). 3 4 Journal of The American Ceramic Society-Kingery Vol. 38, No. 1 COMPRESSION TENSION t -I- 14 T)4 n T) +a t S ~ Fig. 1. Stresses in glaze on infinite slab. Fig. 3. Temperature and sfmu distribution for lo) cooling and lb) heating a slab. uli = E(to - t')(a,i - ab)(l -j)(l - 3j + 6j2) (1) = E(fo - f')(m- a,i)(j)(l - 3j + 6j') (2) I I where j = &l/db. Fig. 2. Restraint of expansion by Axed supporb. Similarly, if a bar of material is completely restrained from expanding by application of restraining forces due to the design of a part, stresses arise as for Fig. 2, where glaze or enamel and the underlying ceramic or metal. If stress-free at to, the stresses will depend on the new tem- perature, t', the elastic properties, and the coefficients on on Stresses such as these, although not due to a temperature of expansion. For a thin glaze an infinite slab, the stresses on gradient and therefore not classified thermal stresses the will be as shown in Fig. 1. The stresses* are given in equa- as as term has defined here, will be additive with any thermal tions (I) and (2) for the simplest case where the elastic proper- been ties of glaze and body are the same. stresses developed and must be considered in any practical applications of thermal stress resistance. (2) Stresses Arising from Tempemrum Gmdientss A temperature gradient does not necessarily give rise to * (a)J. x. Goodier, "On the Integration of Thermo-elastic thermal stresses. F~~instance, in an infinite slab with a linear Equations," Phil. Mag., 23, 1017 (1937). (b) W. M. Hampton, "Study of Stresses in Flashed Glasses," J. temperature gradient, the body can expand without incorn- SOC.Glass Technol., 20,273 (1936) patible strains and no stresses arise. In general, however, the temperature is not a linear function of dimen- sion and free expansion of each volume element Table 1. Surface and Center Stresses in Various Shapes would lead to separation of the elements so that __ they could not be fitted together. Since they are Shape Surface Center - -~ ---___ - -.__- constrained in the same body, stresses arise Infinite u1 = 0 UI = 0 which can be exactly calculated for a number slab a, = uz = (* En- .)(la - 1.1 U" = Uz = (I EL%- p)('" - 1,) of purely elastic bodies from the theory of elas- ticity. Without going into these calculations in Thin plate uy = uz = 0 u,, = uz = 0 detail, it can be shown that for symmetrical uz = aE(1. - 1,) uI = aE(f. 1,) - temperature distributions, the stresses resulting Thin disk u, = 0 Or = (1 AEE"(1"- I,) for simple shapes are those given in Table I. The 2(1 - 2/41 stress at any point is determined by the tem- Ue = 1") - (1 - a)Ea (1 - r)Ea (1, - 03 - TT--2,5(1"- 1,) (1 - 2/41 perature distribution, by the shape of the body, Long solid ur = 0 Eff and by the physical constants E, a, and p, cylinder ur = ~ (t. - 1,) which are taken independent of temperature. 2(1 - /4) as Ea Ea If these factors are known, the stress can be 00 = u* = (, --fi)(fa - 1.) 00 = u* = - - ----(la - I,) 2(1 - P) calculated at any point for sufficiently simple Long u, = 0 u, = 0 shapes. hollow Ea Ea The temperature and stress distribution for = 01 = (, x-~(fo- 1.) Ue = UI = ( - 1,) cflinder --+(la heating and cooling the surface of an infinite Solid u, = 0 slab at a constant rate is shown in Fig. 3. On sphere cooling, the maximum stress is the tensile stress ct = WT)('"Ea - t.) 0, = ut = ___2Ea (to - t,) 3(1 - P) on the surface and the center is in cornpewion. Hollow u, = 0 01 = 0 aE On heating, the maximum stress is the compres- sphere ~- L%E g,= ( - lo(t" - t,) g, = - p)(t" - Ic) sive stress on the surface, and the center is in -~ ___ - ________ -~ tension. There also are shear stresses equal to January 1955 Thermal Stress Resistance of Ceramic Materials 5 half the difference between the principal stresses.
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