ii. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

24.

G. Z. Lomaev, "The effect of rigidity of universal testing machines on deformation rate of metallic specimens," Zavod. Lab., 31, No. 9, 1130-1133 (1965). B. M. Igolkin, "On the nature of the scale factor," Problo Prochn., Noo 3, 50-52 (1978)o V. P. Zhuravlev, "On the role of yielding capacity of loading device in the failure process," Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 6, 156-158 (1983)~ N. N. Davidenko, Some Problems of the Mechanics of Materials [in Russian], Leningr~ Gaz.-Zh. Knizhn. Izd., Leningrad (1943). Ya. B. Fridman, "On deviations from similarity and on modeling and the scale factor, ~' Zavod. Lab., 26, No. 9, 1104-1106 (1960). A. I. Korshunov, "The scale effect of strength and deformation characteristics of the AMg6 alloy in static tension," Fiz.-Khim. Mekh. Mater., No. 5, 120-122 (1984). G. V. Stepanov, Elastoplastic Deformation of Materials under Pulse Loads [in Russian], Naukova Dumka, Kiev (1979). N. N. Popov, "Mechanical properties of structural materials with static and dynamic loading," Metalloved. Term. Obrab. Met., No. 4, 8-10 (1987). N. N. Popov, Yu. G. Bornin, A. G. Ivanov, etc., "A capacitive deformation meter for specimens with deformation rates of 104 sec-1, '' Zavod. Lab., 49, No. 8, 83-84 (19831). N. N. Popov, A. K. Krinitskii, and Yu. V. Khomutinin, "Automation of the processing of results of high-speed tests," Zavod. Lab., 52, No. i0, 38-40 (1986)~ Ya. B. Fridman, Mechanical Properties of Metals [in Russian], Part 2, Mashinostroenie, Moscow (1974). L. I. Sedov, Similarity and Dimensional Methods in Mechanics [in Russian], Nauka, Moscow (1977). N. N. Popov, A. G. Ivanov, V. P. Strekin, and V. M. Barinov, "Obtaining of complete load-elongation curves of the AMg6 and MA 18 alloys for deformation rates of 10-3-103 Sec-1, '' Probl. Prochn., No. 12, 50-54 (1981). N. N. Popov, "The effect of deformation history on mechanical properties of AMg6 and MA 18 alloys," Tekhn. Legk. Splavov, No. 5, 11-16 (1985).

TOWARD A METHOD OF THERMAL SHOCK TESTING OF STRUCTURAL CERAMICS K. A. Kazakyavichyus

UDC 539o4.016+536~49

Characteristics of the process of development of thermal stresses in a cooled rod with a varying heat transfer coefficient are theoretically studied~ It is established that the dependence of stresses on initial temperature of specimen heating is almost linear with a smooth variation in slope in the range of temperatures corresponding to maximum steepness of the right slope of the temperature dependence of the heat transfer coefficient. The importance of standardizing the water temperature within a narrow range to facilitate reproducibility of the thermal loading rigidity is established. It is recommended that specimens be guarded against cooling during their furnace-towater bath transfer.

In spite of significant recent developments in the field of structural ceramic technology, the thermal shock resistance of these materials is still not sufficiently high. This necessitates constant control over the stability of ceramic components under thermal loading on the part of both structures specialists and production engineers, designers, metallurgists, chemists, etc. Determination of the residual strength after heated rods are cooled in water is the most practical method for specialists in different fields of engineering. In this, it is sufficient only to maintain the specimen size and water temperature to ensure reliabilPhysicotechnical Institute of Power Engineering, Academy of Sciences of the Lithuanian SSR. Translated from Problemy Prochnosti, No. 7, pp. 76-79, July, 1990. Original article submitted January 9, 1989.

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0039-2316/90/2207-1032512.50 9 1991 Plenum Publishing Corporation

!

i

:i

Fig. i. Blot criterion in relation to the dimensionless temperature of specimen surface at water temperatures of 293 K (solid line) and 303 K (dashed line).

l

!

i

9

?5

!

!

:3

i

',5

I---

2.0

e~

ity of results. It is also important to aim for minimum cooling of specimens on their transfer from the furnace to water bath. Complex equipment, measurement of temperature fields, or calculations of stresses are not required in this method. The temperature boundary at which different ceramics begin to soften usually corresponds to the initial heating temperature To = 450-850 K [1-3] and, hence, cooling takes place under boiling conditions. This causes a significant dependence of the heat transfer coefficient h on the cooled surface temperature T R (and, hence, on the time). Since there is a clearly defined peak in the above dependence, with its height and location dependent on water temperature [4], the question arises as to how the T o value reflects the thermal loading rigidity and whether there is need to introduce another argument for this purpose. This article investigates the extent to which the cooling rate, thermal stresses, and failure probability depend monotonically on heating temperature. An estimate is also made of the significant effect of water temperature and heat transfer on thermal stresses during furnace-to-water transfer of the specimen. Since the qualitative features the dependence of the value of h on water, shape and size of specimens, face section to the vertical, water a view to simplify the calculations. as a round rod of radius R.

of the cooling process are of interest at this stage, absolute pressure and presence of impurities in the surface roughness of specimens, angle of examined surbath size, etc., have not been accounted for here with For the very same reason, even the specimen is selected

To raise the generality of the calculations, the heat transfer is defined through the Biot's criterion Bi = hR/X, where X is coefficient of thermal conductivity of specimen material. The temperature in the specimen is expressed by the dimensionless quantity O--

T--T. T~--T.

'

(1)

where T is temperature as a function of time 9 and actual radius r; T, = 293 K is base temperature equal to water temperature in the main investigation; Tm = 538 K is temperature for maximum value of the coefficient of heat transfer at water temperature of 293 K selected on the assumption that, in case anomalies are detected in the cooling process, these will be connected with the position of the peak. Values of the Bi criterion were calculated from the obtained data [4] in relation to the dimensionless temperature of the specimen surface 8R (Fig. i), where R = 0.005 m; ~ = 10 W/mK. The dashed line in Fig. 1 was not used in calculating the dimensionless quantities. Therefore, for purposes of comparison, it was constructed with numerical values of T, and T m as was done for the solid line. The dimensionless temperature 8 as Fourier number (dimensionless time) Fo, method of finite differences [5], where diffusivity of the specimen material; 9 The calculation grid had a spacing Ap = AFo = 4-i0-5.

a function of initial temperature of heating 8o, and dimensionless radius p was determined by the Fo = a~/R2; p = r/R; a is coefficient of thermal is time from start of cooling; r is actual radius. 0.01. Calculations were repeated through intervals

The first of the 102 calculated points was located on the conditional extension of the specimen body at 0.5 Ap distance from the surface, the hundred subsequent points in the 0 < p < 1 interval, and the last at 0.5 Ap distance beyond the specimen center. The dimensionless temperature on the specimen surface 8R was determined as the arithmetic mean of its calculated values at the first and second points. The dimensionless circumferential s z and axial s 2 stresses were found by formulas obtained similarly [6]:

1033

:5 I.o

o,ot Fo

0,ol

Fig. 2

F0 . . . . . .

U.r

"- ....

QO~

T/~

-

g

s./'i

0,8

0.2 0

j ~.~, j

Q2 ~

o

--c 3

J

0,2

o,#

0,6

0.8

F

q5

Fig. 3

1.0

1,5

2,0

oo

Fig. 4

Fig. 2. Variation in time of the dimensionless temperature of specimen surface: i) @ 0 = 2; 2) @ 0 = 1.5; 3) 8 0 = 1. Fig. 3. Distribution of dimensionless circumferential stresses along the radius of specimen for @ o = 1.5: I) Fo = 0.05; 2) Fo = 0.01; 3) Fo = 0.002. Fig. 4. Dependence of maximum calculated sm and reduced s r stresses in a single test as also of the time till their occurrence Fo m and For, respectively, on the initial dimensionless temperature @0 of the given test. s, - - B + C (O) - - O; s2 =

2B

--

(2)

O,

where

0

0

The dimensionless stresses s are connected with the actual stresses o as follows: ~ e (r~ - r , ) 0--~

(3) .... S,

where ~, E, and p are coefficient of linear expansion, modulus of elasticity, ratio of the specimen material, respectively.

and Poisson~s

The temperature fields and stresses in a round rod at water temperature T w = T, and various values of the initial dimensionless temperature 8 o were analyzed using the proposed calculation method. Intensive (at first) cooling is observed for @0 < i. The cooling decreases constantly due to simultaneous decrease in difference in temperatures and Biot's criterion (Fig. 2). The character of cooling is different with higher values of e0: at first, there is a fall in tempo of cooling due to decrease in difference of temperatures, but, with approach toward 8 R = I, it increases again since there is significant increase in the Blot's criterion~ Thereafter, the cooling rate again decreases sharply due to simultaneous decrease in difference of temperatures and Biot's criterion. Higher the initial dimensionless surface temperature, later is the occurrence of repeat increase in cooling tempo.

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TABLE i. Ratio of Maximum Circumferential Stresses in the Cooled Specimen at 293 and 303 K Water Temperature Fixed difference in temperatures AT, K

100 200 3,00 400 500

~

Fixed initial temperature To, K

0,987 1,0,28 i, 169 ],074 1,027

40,3' 50'3 603 703 8,03

~

0,897 0,9'76 1,0,79 1,029 1~024

Initially, thermal stresses increase rapidly and reach a maximum sm when a large portion of the specimen cross section does not even get warmed up (Fig. 3). With inward propagation of the heat, stresses deep in the specimen increase further but begin to fall near the surface. The time from start of cooling till maximum of the stresses Fo m is very significantly dependent on the initial temperature (Fig. 4). It decreases by an order of magnitude in the range of e 0 = 1-1.5. With passage of time, the tensile stresses envelop an increasingly larger volume of the specimen and, that is why, even after reaching Sm, the probability of failure continues to grow. So as not to connect the calculations with the properties of a specific material, we examine, instead of the failure probability, the reduced stress which for the same failure probability as at the indicated instant of cooling would be required in the same rod under a temperature field in the form of the parabola. 0 = A0r(1--p2),

(4)

where Ae r is difference in temperatures selected from the condition that failure probabilities are equal. The reduced stress s r attains a maximum value (and this means even the failure probability) somewhat later than sm (Fig. 4) although even the time for its attainment Fo r varies substantially from test to test in relation to different values of 00. The maximum stresses sm and s r vary monotonically without peaks and steps regardless of such a significant variation in character of cooling with variation in initial temperature. Their dependence on 6o is close to linear with a smooth variation in slope in the i.i < e 0 < 1.3 interval. This range corresponds to the maximum steepness of the right slope of the peak of the dependence Bi (eR). Thus, without looking for other arguments, the initial heating temperature can be taken as the argument for the dependence of the residual strength of specimens on the rigidity of thermal loading but with an indication of the water temperature. Some investigators use the difference in furnace and water temperatures for this purpose [i]. Such a transformation of coordinates does not introduce any errors although, at times, this is taken as testimony of the independence of the loading rigidity from the water temperature if the latter is deducted from the furnace temperature. Thus, the standard [7] which lays down the procedure for determination or thermal stress resistance of inorganic glass, generally does not envisage measurement of the water temperature but suggests that the difference in temperatures be determined by using differentially connected thermal converters. Only a limit of 293 • i0 K is laid on the water bath temperature. The presence of a peak in the temperature dependence of the Biot's criterion (Fig. i) requires a check for the degree to which the water temperature affects the thermal stresses. With this in view, calculated maximum circumferential stresses 0293 at T w = 293 K were compared with stresses 03o 3 at T w = 303 K (upper allowable limit [7]) in case of different values of the initial temperature T01 and difference in temperatures AT = T o -- T w (Table I). At first glance, a strange phenomenon is observed, i.e., if a specimen heated to 603 K is immersed in water at 303 K temperature, then, stresses in it will be 7.9% more than that on cooling in water at 293 K temperature, i.e., in the first case, higher stresses were set

1035

up with smaller difference in temperatures. If, in the second case, the specimen is heated to 593 K and cooled in water at 293 K so that an identical temperature difference is maintained, the difference in stresses is then 16.9%. This phenomenon can be explained as follows. With approach to eR = 1 in the process of cooling, the cooling rate increases sharply and the specimen surface temperature fails very quickly to values corresponding to the left slope of the heat transfer peak (Fig. I), after which, the cooling intensity drops. It is precisely at this time that stresses reach a maximum value. However, at T w = 303 K, film ebullition transforms to bubble ebullition s o m e w h a t later than at T w = 293 K, in view of which, the heat transfer peak is shifted toward the lower temperatures and the specimen surface quickly cools to a lower temperature. This leads to increase in stresses. Consequently, if the difference in temperatures is to be increased by decreasing the water temperature, then, the stresses can either be raised or lowered in relation to the temperature range of the initial heating (Table i). Hence, it is advisable to standardize the water temperature at the 293 K level and precisely such a value is more often than not used in practice. Allowable deviations can be stipulated in the • K range and this does not pose any technical difficulties. However, till such time a standard is adopted, there is no basis for expressing the rigidity of the thermal shock by the difference in temperatures. To this end, it is better to use the initial heating temperature T O with indication of the water temperature. In such a case, we can expect smaller divergence of results obtained by different investigators even if different water temperatures are used. In the standard [7], the time for furnace-to-water bath transfer of specimens is limited to 2 sec. We examine a particular case in which the heating temperature T o = 850 K in order to evaluate the possible effect of this cooling on the experimental data. On cooling this specimen in water at 293 K, the stresses can reach a maximum after 0.43 sec when the surface temperature is lowered to 508 K. The lateral surface of the specimen of I0 cm length releases 3160 J of energy in this time. If up to 30-50 J of energy (~1%) is released during furnace-to-bath transfer of the specimen, then, there will be an insignificant effect of this cooling on the stresses. An approximate estimate of the heat transfer by radiation and convection give s a density of heat flow on the specimen surface during the transfer time of about 20-30 kW/m ~ [8]~ W i t h such a heat transfer, the lateral surface of the specimen will release 30-50 J of energy in 0.3-0.8 sec. Evidently, it will take longer if unprotected specimens are to be taken out manually from the furnace and transferred to the bath, in which case, cooling of the specimen will introduce significant deviations in the values of stresses. Hence, we should use containers or appliances which would guard against cooling of specimens during transfer. Still better would be to mechanize this process. Thus, for instance, not more than 0.2 sec would be required if specimens are allowed to drop from the working zone of a vertical furnace. This will not cause significant cooling before the specimens enter the bath [3]. CONCLUSIONS i. Characteristics of the development of stresses in specimens when cooled in water are theoretically investigated. It is observed that presence of a clearly defined peak in the dependence of heat transfer on specimen surface temperature significantly changes the time till occurrence of critical stresses with variation in initial temperature of specimen~ However, the maximum value of stresses varies monotonically without peaks and steps. Its dependence on the initial temperature of the specimen is close to linear with a smooth variation in the slope in the range of temperature which correspond to the maximum steepness of the right slope of the heat transfer peak. 2. It is established that variation in water temperature has a highly indeterminate effect on stresses in the cooled specimen. In view of this, till such time the water temperature is not limited within a narrow range by a suitable standard, it is suggested that the rigidity of loading be expressed by the heating temperature and not difference in temperatures. 3. The importance of the cooling of specimens during their furnace-to-bath transfer is established. In view of this, it is recommended that specimens be transferred to a protective shell or provisions should be made for free fall of the specimens from thel working zone of the furnace into the water bath. 1036

LITERATURE CITED I. 2. 3.

4. 5. 6. 7. 8.

K. Backhaus, "Bestimmung und Grosse der Temperatur wechselbestandigkeit keramischer Werkstoffe," Electrowarme, No. 3, 62-67 (1959). D. P. H. Hasselmen, "Thermal stress resistance of brittle refractory ceramics," J. Am. Ceram. Soc., 53, No. 9, 490-495 (1970). G. A. Gogotsi, Some Results of Study of the Mechanical Properties of Structural Ceramics as Applied to Engine Components [in Russian], Inst. Probl. Prochn. Akad. Nauk USSR, Preprint, Kiev (1983). A. A. Shmykov, Handbook for Heat Specialists [in Russian], Mashinostroenie, Moscow (1961). A. V. Lykov, Theory of Thermal Conductivity [in Russian], Vysshaya Shkola, Moscow (1967). B. Boli and D. Ueiner, Theory of Thermal Stresses [in Russian], Mir, Moscow (1964). GOST 11103-85, Introduced January i, 1986. V. P. Isachenko, V. A. Osipova, and A. S. Sukomel, Heat Transfer [in Russian], Energiya, Leningrad (1965).

FATIGUE RESISTANCE OF THE HEAT-RESISTANT ALLOY KhN55MVTs Yu. A. Dushin, A. V. Zheldubovskii, E. G. Ivashko, N. A. Medvedev, V. A. Petrov, and A. D. Pogrebnyak

UDC 620.388.1

Fatigue resistance of the nickel alloy KhN55MVTs is investigated in the range of 550-I000~ temperatures and 102-107-cycle durabilities. The alloy is recommended for manufacturing large-size equipment to operate at up to 950~ for prolonged periods. It is shown that, in the initial post-heat treatment state, the alloy displays adequately high resistance to cyclic loads in the short-time range but, in the multicycle range, is inferior in durability to a series of materials used in gas-turbine engineering. To a lesser extent, this difference is observed for specimens of the alloy subjected to prolonged high-temperature holding. Durability of the alloy increases with increase in degree of alloying with zirconium.

Design of equipment meant for operation at high temperatures necessitates a comprehensive study of the properties of materials which are capable of operating under these conditions over a prolonged period and, in some cases, over periods reckoned in hundreds of thousands of hours. The basic requirements for these materials are, high plasticity in processing, structural stability with moderate resistance to hot-working, and structural stability under prolonged (up to 5"104 h) high-temperature (up to 1000~ operating conditions. At present, these requirements are met by the heat-resistant nickel alloy KhN55MVTs which has an undisputable advantage over many nickel alloys in structural stability under the effect of high temperatures [i] and its high plasticity (relative reduction of area in fracture ~ > 60% in the 20-I000~ range). The special features of the alloy become clearly apparent when compared with alloys used in gas-turbine engineering. It is several times superior in plasticity but inferior in equal measure in strength. The effect of a series of production (microadditions of zirconium; prolonged high-temperature isothermal holding), structural (concentration of stresses and welds), and operating (temperature level; anisothermal conditions) factors on its strength properties was investigated simultaneously. In this, characteristics of the mechanisms and kinetics of failure of the alloy were examined under various conditions of loading. Short-time fatigue resistance of the material, investigated under conditions of constant and variable temperatures, was estimated in number of cycles up to failure N. Tests under Institute of Mechanics of the Ukrainian SSR. Translated from Problemy Prochnosti, No. 7, pp. 79-83, July, 1990. Original article submitted July 17, 1987.

0039-2316/90/2207-1037512.50 9 1991 Plenum Publishing Corporation

1037