Strength of Materials, Vol. 26, No. 1, 1994

STRESS RELAXATION IN ZIRCONIUM CARBIDE. REPORT 1.

TEST METHOD AND STRESS RELAXATION CURVES

P. V. Zubarev, A. B. Kuraev, A. S. Maskaev, E. V. Astakhova, and A. A. Bessarabov UDC 620.174

A method of stress relaxation tests with use of four-point bending is described. Experimental data is given on pure stress relaxation in ZrC1.oo with different grain sizes (d = 6-35/Jm) in the area of the ductile-to-brittle temperature (1600-2200 ~

Stress relaxation may have a significant influence on the processes of crack formation and fracture of materials in

operation of them in the area of the ductile-to-brittle transition temperature. Refractory compounds, among them transition

metal carbides and solid solutions based on them, are very promising materials for high-temperature technology. Since

known literature data on stress relaxation for these materials is extremely limited [1, 2], investigations of stress relaxation

of ZrCI.00 in the area of the ductile-to-brittle transition temperature (1600-2200~ were conducted.

Stress Relaxation Test Method, The tests were made in a He atmosphere (APex = 0.02 MPa) in a furnace with a graphite heater using a four-point bend method.

Use of bending made it possible to: a) reduce by more than an order of magnitude the requirement for sensitivity of the servosystem in comparison with tension and especially compression, which made it possible to use standard test

equipment for the tests, particularly the 1246R-2/2300 machine [3]; b) measure directly from the specimen by a differential method, thereby reducing to a minimum the requirements for rigidity of the clamp, hardness of the supports, and tempera-

ture constancy and providing maximum measurement accuracy, maintenance of constancy of deformation, and a short hold time before the start of a test; c) use specimens of simple form, which is especially significant for carbide-base materials.

Among the disadvantages of bending are the necessity of additional processing of the primary relaxation curves, which reflect the change in the stress curve in the cross section and are the moment relaxation curves.

To construct stress relaxation curves: from moment relaxation curves as'the result of limitedness of concepts of the mechanism of this process it is desirable to use methods not using any preliminary concepts relative to the form of the

curve in the specimen in bending. Two such methods [4, 5] based only on the hypothesis of plane sections and the premise

of the close to linear stress distribution in a section of a specimen being bent in the elastic condition are known.. These

original assumptions are fulfilled in pure bending. Therefore in this work four-point bending in which the investigated portion of the specimen located between the outer supports is in this condition was selected as the loading method,

The stress relaxation investigations were made on 2.75 x 2.75 x 60 rnm specimens prepared by die extrusion.

The specimen loading method is shown in Fig. la. To points 1-3 by rods is connected a strain gauge located in the

cold zone. Constancy of deflection (strain) was provided by maintaining of constancy of displacement of point 2 relative to points 1 and 3 to which were connected the rods of the differential strain measurement system. Forces caused only by the

weight of the rods themselves act at the points of contacts of the rods. This method is used on a specially developed clamp.

Both hard materials (ZrC, (Zr0.sNb0.5)C) and a comparatively soft (with a low coefficient of friction in a pair with carbides) material, MPG-6 graphite, were used as the material of the support rods. No changes in the test results were observed in switching to graphite.

In the tests the specimen (ZrCI,0o, d = 6 gin) was loaded to a specified initial stress (Fig. lb), after which the servosystem of the 1246R-2/2300 machine, receiving a signal from one of the two bridges of the 1814 DPT-2 strain gauge

for measurements of displacements, automatically maintained constant the deflection corresponding to this level, decreasing during the tests the moment of the force acting on the specimen. Simultaneously the signal from the second bridge was

received by the KST4 recorder (i div. = 2 /zm) from the readings of which were measured the work of the automatic system of maintaining of constancy of deflection and, if necessary, a correction was made.

Ray Scientific and Production Union Scientific-Research Institute, Podol'sk. Translated from Problemy Prochnosti, No. 1, pp. 76-83, January, 1994. Original article submitted April 12, 1991.

0039-2316/94/2601-0063512.50 �9 Plenum Publishing Corporation 63

I Yt2

50 ~ ~'-- I 1 I_ t

~, MPa Yr,/~m

8 p ~ s e = ~OO Mna

~7 2_g ~ '-r 50 ~ t, rnin

Fig. 1. Loading method of the specimen in stress relaxation tests (a) and a typical stress relaxation curve (b}: 1-3) points of connection of the specimen deflection measuring system rods; 4} cylindrical supports; 5) specimen; a k) calculated as the elastic approxi- mation according to Eq. (6); Yx) vertical deflection of point 1 relative to points 2 and 3.

Let us determine the contributions of the portions with pure and transverse bending to the amount of total deflec-

tion for the method with the given dimensions. For the amounts of displacement in pure bending along the Y-axis in

portions I and II we may obtain the equations

Yz=2E_JL4 6 + T (a+v) 4 [2 + a , _ ~ - (1)

l < . l wire ~.-,~_~ x ST;

Pa < l YII = ~ [ x 2 - v21 with 0 < x _ ~ - - a, (2)

where z, = l /2 - a.

Then for a = 15 mm and L = 50 mm we obtain

Y/tMra l = (PIE.I) 3000 MMS; (3)

YII [MM ] = (P/E.J) 375 MM 3, (4)

where P is the tensile stress of the loading chain, E is Young's modulus, and J is the moment of inertia of the section. The strain in the extreme fiber of the portion with pure bending will be

," = h Y H f ( O , S L - a), (5)

where h is specimen thickness.

Since the total deflection is directly proportional to the moment, the reliability of the method developed may be evaluated from the presence of agreement of the values of the relaxing moment (AM/Mo) obtained from the moment

relaxation curve, from the readings of the measuring system strain gauge (fresStr/f0-str), and from the results of measure-

ments of the initial and residual deflection with a KM-6 cathetometer and a profilometer (fresPrOf/f0-cat). The results shown in Table 1 indicate good agreement between the evaluations made by independent methods.

64

TABLE 1. Values of the Relaxing Moment Determined by Independent Methods

ttes t �9 o C O.o, 7test, AM/Mo, tr Y, g l K 2,, MPa rain % /~m//zrn %

1800 100 SO 31 24/80 30 1800 150 80 32 45/135 33 1800 200 80 30 54] 160 34 t800 250 80 35 82J 235 35

#prof/r eat ,try. S /10

~,'m/um % 29/87 33

47/146 32 56/155 36 92/230 40

Explanat ion. fo -str and f0 -cat are the average amounts of deflection during the test t ime from measurement data of the strain gauge and the cathetometer and fres str and fres pr~ are the amounts of residual deflection from measurement data of the strain gauge and the profi lometer.

E-~-. 3 MPa

t~TO

350

2F~

Fig. 2. Temperature relationship of Young's modulus for ZrCl.oo determined from Fig. 3 (E = a/e) (1) and for ZrCo.96 from [6} {2}.

The values of Young's modulus obtained with Eqs. (2) and (4) from the results of loadings in stress relaxation tests

when the initial stress did not exceed the elastic limit were close (Fig. 2) to the dynamic moduluses taken from [6]. This

also confirms the reliability of the readings of the strain measurement system.

The method of calculation of the stress relaxation curves from the moment relaxation curves. In the majority of

cases the stress curve in the section of a specimen being bent is nonlinear in relaxation, which is the result of the nonlinear

relationship of relaxation rate to stress. This fact makes calculation as an elastic approximation incorrect. As already

mentioned, in the case of pure bending there are methods of construction of stress relaxation curves from moment relax-

ation curves not based on any preliminary assumptions relative to the form of the relationship of relaxation rate to stress.

It is known that if a specimen is in the condition of pure bending there are no tangential stresses in the planes

perpendicular to its axis and each fiber deforms independently of the other fibers and is in the uniaxially stressed condition.

Then, knowing the stress curves in the section for different moments of time, it is possible to construct the stress relaxation

curves for any fiber and they will correspond to the stress relaxation curves obtained in tests in the uniaxial stressed

condition with the corresponding initial stresses.

Despite the fact that the stress ~rk(t) calculated as an elastic approximation is in the case of relaxation in bending

only some conditional characteristic, the relationship of it to time has a definite physical sense,

First, it is related to the bending moment by the relationship

~( t ) = M(t)/W, (6)

where W is the moment o f resistance of the section of the specimen.

65

TABLE 2. Chemical Analyses of ZrC~ .oo Specimens

Lot Chemical analysis, wt. % Zr Cto t C free 0 N W

l]-I 85,9 11.7 0,3 0,08 0,01 0,9 11-2 87,2 11,9 0,07 0,06 0,03 0,4 I"1-3 87,5 11,5 0,5 0,05 0.07 0.5

e~, MPa

~'~0 i I~/~ oC

a

I t ~0 4O

b

ZO 60

~, MPa

~ J - . .

o

200

tOO

L p, % r ,~m

5 6 5 14 3 16

I ~DO"C ?,~tO ~ " ~O0"C

29 4~ 2 ~, & 8 tO Iz',min

a, nm

0,4695 0,4607

I I

20 40 r, mm A

t ~ ~

i o �9

" * o t . o ~* . I . o ~

a b I I I _ I

t i , , t g ~ ',

20 40 zo 6q~

2800 ~

C J I

~g ~o

h I I

I x 40

Z2~"r

20 .~ 'r,.mm

Fig. 3. Stress relaxation curves for ZrCI.oo of lots P-1 (A) and P-2 and P-3 (B). A: a-d) d = 6pro, P- l ; e-f) d = 14" /Jm, P-l ; B: a-e) d = 14 /~m, P-2; f-g) d = 30*/ . tm, P-2; h-i) d = 16pm, P-3 (* - after annealing at 2700oc for 1 h); 1) a 0 = 100 MPa, 2) a o = 150 MPa; 3) cr o = 200 MPa; 4) ~r 0 = 250 MPa, 5) a 0 = 5 MPa. Points) crk(t) = M(t)/W; solid line) ~t calculated using Eq. (8}.)

66

o, MPa

~ 0

150

~ 0

m n

5 0

0

~ mOO~

*~

a ~- I I

ZO 4O

fgO0~

b I I,

Z~O~

k .% d, .-.]

~. mm A

M P a

3

~1 . - . 2 ~ " . 3

5 - " . " ' 2 . f

a

4O

o' .~

~Tbr t.O

d ~ 1 7 6

i C

I , "r m l r l

Fig. 4. True stress re laxat ion curves for ZrCI .oo of d i f ferent lots w i t h close (A) and d i f ferent (B) grain sizes. A: solid line) P-3, d = 16 pm; broken) P-2, d = 14 /Jm; dot ted) P - l , d = 1 4 * g m ; B : a-c: solid lines) P - l , d = 6 p m ; d o t t e d ) P - l , d = 1 4 * / J m ; d - e : s o l i d lines) P-2, d = 1 4 g i n ; dot ted) P-2, d = 3 0 * ,urn (* - af ter anneal ing at 2 7 0 0 ~ for 1 h); 1) ~0 = 100 MPa; 2) cr o = 150 MPa; 3) c~ o = 200 MPa, 4) ao = 250 MPa.

Second, it is the maximum stress in the triangular diagram equimoment to the true, that is,

Y

f ~(x)-x.dx = i/3-c#(y).y 2. (7) 0

Based on Eqs. (6) and (7) in [4] for the first loading there was obtained the equation

a(c~o) = 2/3-o~(co) + 1/3-co. (do~ld,o), (8)

on the basis of which the present calculations were made. From Eq. (8) it may be seen that for determination of the stresses acting in the fibers of the specimen at the

moment of time of interest it is necessary to know the relationship of crk to cr 0. Therefore after conducting a series of Z

tests with different initial stresses including the maximum o'0max of the representative range, for the selected moments of

time (the smaller the range, the more accurate will be the true relaxation curves constructed) Z values of stresses ok(t) are

found, the ek--e 0 relationships are constructed, and after determination of the derivatives dok/dcr 0 from Eq. (8) the stresses

in the fibers of the bent specimen are calculated and the diagrams of true stresses are constructed. The diagrams of stresses

at a series of moments of time of interest obtained in this manner make it possible to construct the relaxation curves of true

stresses for any initial stress e 0 < o'0max. Results of Experimental Investigations. Three lots of ZrC1.00 with different original grain sizes (6-16/zm) were

investigated (Table 2). For the purpose of determination of the influence on stress relaxation of this very important technical parameter

specimens of lots P-1 and P-2, which for grain growth were additionally high-temperature annealed at 2700~ for 1 h,

were also tested. The stress relaxation curves obtained from the results of bend tests after calculation as an elastic approximation and

according to Eq. (8) are shown in Fig. 3. The relaxation curves agree with the data obtained in uniaxial tension [2] for ZrC with a close grain size, which

confirms the correctness of the test and conversion methods.

67

a b

0 L x, L I I Y l I I l I 1 ( V I I f t f F r ~ t ~

&O ~ 4q7 %; mm

0 c J l r ~ ~ ~ [ l 1 v r l I I I I .I I

ZO 40 20 ~ "~, rain

Fig. 5. Stress resource curves for ZrCl .oo: a) P - l , d = 6 /Jm, P = 5 % ; b) P - l , d = 1 4 " p m , P = 3 % ; c) P-2, d = l C p m , P = 5 % ; d) P-2, d = 3 0 * /Jm, P = 3 % ; e) P-3, d = 1 6 / J m , P = 3 % (* - af ter anneal ing at 2 7 0 0 ~ for 1 h); 1) a 0 = 100 MPa; 2) <70 =

150 MPa; 3) cr o = 200 MPa; 4) G o = 250 MPa; 5) cr o = 3 0 0 MPa. R = [at(t) /Go] �9 1 0 0 % , whe re at(t) is the t rue stress ob ta ined f rom Eq. (8) and a 0 is the init ial

s t ress ob ta ined f rom Eq (6).

The spread in relaxation curves obtained in testing specimens of different lots with a close grain size (Fig. 4A) is

insignificant. Doubling of the grain size (from 6 to 14 ~m) as the result of annealing led to an =200~ increase in

relaxation resistance in the whole investigated 1600-2200~ temperature and 100-200 MPa stress ranges (Fig 4B, a-c). At

the same time it was established that a similar increase in grain size from 14 to 25-30 gm at 2000~ increases the relax-

ation resistance only in the case of a low initial stress (a -- 100 MPa) but at 2200~ decreases it in the whole investigated

stress range (Fig. 4B, d-e). The curves of the resource [7] of true stresses

R = ( t (O/c~0). t00%, (9)

where at(t), the true stress calculated according to Eq. (8), and % the initial stress calculated according to Eq. (6), are

shown in Fig. 5. It may be seen that the difference in the calculation results and also the spread in standardized relaxation

curves increase with an increase in initial stress, temperature, and grain size. This is the result of the increase in curvature

of the curve in a specimen being bent caused by the increase in the cross section of the share of fibers in which relaxation

occurs according to mechanisms with a stronger relationship of the rate of this process to stress.

68

LITERATURE CITED

1.

2.

3.

4.

5.

6.

7.

V. M. Sura and D. L. Kohlstedt, "Inelastic deformation of (Ti, V)C alloys," J. Mater. Sci., 21, 2356-2360

(1986). "A method of stress relaxation tests of refractory materials under conditions of uniaxial tension," Authors' Abstract of Candidate of Technical Sciences Thesis [in Russian], Moscow (1971). V. V. Klyuchev (ed.), Testing Technology (A Handbook), in Two Volumes [in Russian], Vol. 1, Mashinostroenie,

Moscow (1982). E. A. Khein, "Calculation of relaxing stresses in a circular specimen," Zavod. Lab.,. No. 9, 1114-1118 (1966). G. F. Lepin and Yu. D. Bondarenko, "Construction of relaxation curves in tension from the results of tests of

circular specimens," Probl. Prochn., No. 5, 81-84 (1971). V. M. Baron, V. I. Knyazev, and O. S. Korostin, "Temperature relationships of the elastic constants of non-

stoichiometric zirconium carbides," ibid., No. 9, 45-47 (1973). I. A. Oding and F. I. Aleshin, "The influence of temperature and the stress relaxation criterion in metals," Izv.

Akad. Nauk SSSR, Met. Gorn. Delo, No. 5, 98-112 (1963).

69