ACOUSTIC 5.
FATIGUE
OF
POLYMER
MATERIALS.
F I L L E D RUBBER S. L . S k a l o z u b , K. a n d R . P° A p i n i s
G.
Kirilov,
UDC 678.7:539.43
Methods a r e proposed f o r e x p e r i m e n t a l l y e s t i m a t i n g the t e m p e r a t u r e - t i m e aging of a fiIled r u b b e r and the d e g r e e of damage accumulation in h i g h - f r e q u e n c y fatigue t e s t s . A p r o c e dure f o r e x p e r i m e n t a l l y d e t e r m i n i n g the e n e r g y dissipation function of a m a t e r i a l f r o m the s p e c i m e n t e m p e r a t u r e kinetics is d e s c r i b e d . The r e s u l t s of an investigation of the fatigue p r o p e r t i e s of two s e r i e s of filled r u b b e r s at a vibration frequency of 20 kHz are presented. It is shown that the fatigue failure of the m a t e r i a l s tested is thermal in c h a r a c t e r . No accumulation of mechanical damage in the m a t e r i a l in the c o u r s e of intense vibration could be detected.
Soft p o l y m e r m a t e r i a l s , including heavily filled rubbers, a r e extensively used to combat noise and vibration as well as for v a r i o u s s t r u c t u r a l p u r p o s e s . Vibrational loads e m b r a c i n g the frequency range f r o m s e v e r a l cycles p e r second to 50 kHz and more a r e being i n c r e a s i n g l y encountered in the a e r o s p a c e and shipbuilding industries [1, 2]. In many c a s e s these vibrational loads a r e so intense that they cause fatigue failure [3]. At the same time, to judge f r o m the available data [1] the fatigue of p o l y m e r m a t e r i a l s and especially r u b b e r s has not been investigated at frequencies above 100 Hz. This p a p e r p r e s e n t s the r e s u l t s of an experimental study of the acoustic fatigue of a filled r u b b e r at a vibration frequency of 20 kHz together with c e r t a i n new developments in the t e s t i n g p r o c e d u r e [4]. The investigation employed specially designed a c o u s t o e l e c t r o n i e equipment [5, 6] and was based on the data of e x p l o r a t o r y e x p e r i m e n t s [7]. P r e v i o u s investigations of the fatigue of p o l y m e r m a t e r i a l s [4, 5] have shown that intense vibrational loading causes a continuous r i s e in t e m p e r a t u r e as a result of vibroheating and that failure may take one of two f o r m s - t h e r m a l o r mechanical, T h e r m a l failure o c c u r s at a critical t e m p e r a t u r e c o r r e s p o n d i n g to the onset of one of the following p r o c e s s e s : a) t h e r m a l degradation; b) a phase t r a n s i t i o n accompanied by a sharp i n c r e a s e in the damping p r o p e r t i e s of the m a t e r i a l and hence a substantial i n c r e a s e in the liberation of heat, In the l a t t e r case the intense t e m p e r a t u r e r i s e leads either to t h e r m a l degradation or to mechanical failure as a r e s u l t of loss of strength at elevated t e m p e r a t u r e s . The mechanical mode of failure r e s u l t s f r o m loss of strength due to the accumulation of damage [8]. The mode of fatigue failure can be e x p e r i m e n t a l l y determined by c o m p a r i n g the t e m p e r a t u r e d e pendences of the dynamic c h a r a c t e r i s t i c s of the specimen r e c o r d e d in the p r e s e n c e of intense and weak (without vibroheating) vibration, ff the regions of sharply changing dynamic p r o p e r t i e s coincide and c o r respond to the critical t e m p e r a t u r e of t h e r m a l degradation (phase transition), then t h e r m a l failure wilt o c c u r . Mechanical failure o c c u r s at b e l o w - c r i t i c a l t e m p e r a t u r e s . Institute of P o l y m e r Mechanics, A c a d e m y of Sciences of the Latvian SSR, Riga. T r a n s l a t e d f r o m Mekhanika P o l i m e r o v , No. 4, pp. 662-668, July-August, 1969. Original a r t i c l e submitted F e b r u a r y 14, 1969.
© 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West ]7th Street, New York, N. Y. ]0011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without permission of the publisher. A copy of this article is available from the publisher for $15.00.
577
Ir
i 1
ii
,
Fig. 1. Specimen t e m p e r a t u r e k i n e t i c s in the p r e s e n c e of intense v i b r a t i o n p e r i o d i cally discontinued.
The s a m e p r o c e d u r e can be used to e s t i m a t e the accumulation of d a m a g e (or hardening) by c o m p a r i n g the t i m e dependences of the dynamic c h a r a c t e r i s t i c s in the p r e s e n c e of s t r o n g and weak v i b r a t i o n when the t h e r m a l r e g i m e of the s p e c i m e n r e m a i n s the s a m e . However, it is difficult to e m p l o y this method to investigate the m a t e r i a l s t e s t e d in the p r e s e n c e of h i g h - f r e q u e n c y v i b r a t i o n s in view of the nonuniform distribution of v i b r o h e a t i n g t e m p e r a t u r e o v e r the volume of the s p e c i m e n . T h e r e f o r e in o r d e r to e s t i m a t e the a c c u m u l a t i o n of d a m a g e ( h a r dening) in a m a t e r i a l subjected to the l o n g - t i m e action of a cyclic load we s e l e c t e d the constant v i b r o h e a t i n g t e m p e r a t u r e r e g i m e . It is difficult to r e p r o d u c e this r e g i m e at constant dynamic load by r e g u l a t i n g the heat t r a n s f e r p r o c e s s e s owing to the low t h e r m a l conductivity of the m a t e r i a l s t e s t e d and the c o r r e s p o n d i n g need to e m p l o y v e r y s m a l l s p e c i m e n s . However, c o n s t a n c y of the v i b r o h e a t i n g t e m p e r a t u r e can be achieved by suitably r e g u l a t i n g the dynamic exciting load, a step which does not lead to any f u r t h e r c o m p l i c a t i o n of the a p p a r a t u s and can be r e a d i l y automated.
M o r e o v e r , in o r d e r to take aging effects into account, the t i m e dependences of the dynamic c h a r a c t e r istics of the m a t e r i a l should be r e c o r d e d in the p r e s e n c e of weak v i b r a t i o n at a constant s p e c i m e n t e m p e r a t u r e equal to the m e a n v i b r o h e a t i n g t e m p e r a t u r e obtained for intense v i b r a t i o n . To a c o n s i d e r a b l e extent the r e l i a b i l i t y of fatigue t e s t data depends on a c o r r e c t choice of the f a i l u r e c r i t e r i o n . This c r i t e r i o n should be e s t i m a t e d f r o m the e x p e r i m e n t a l l y r e c o r d e d s p e c i m e n c h a r a c t e r i s t i c m o s t s e n s i t i v e to s t r u c t u r a l changes in the m a t e r i a l . F o r the p r e v i o u s l y investigated m a t e r i a l [4] this c h a r a c t e r i s t i c was the d e g r e e of attenuation of sound in the s p e c i m e n . F o r rigid p o l y m e r m a t e r i a l s [8-10] the dynamic modulus of e l a s t i c i t y (functionally r e l a t e d with the speed of sound) and the v i b r o h e a t i n g t e m p e r a t u r e proved to be s e n s i t i v e to failure° As the f a i l u r e c r i t e r i o n it is also possible to employ the r e l a t i v e i n c r e a s e in volume or c h a r a c t e r istic length of the s p e c i m e n , if failure is a c c o m p a n i e d by a change of volume that can be a c c u r a t e l y r e corded by the m e a s u r i n g a p p a r a t u s e m p l o y e d . By c o m p a r i n g the t i m e dependences of the a b o v e - m e n t i o n e d four c h a r a c t e r i s t i c s s i m u l t a n e o u s l y d e t e r m i n e d in the c o u r s e of a single t e s t it is p o s s i b l e to s e l e c t the c h a r a c t e r i s t i c m o s t s e n s i t i v e to s t r u c tural changes and f r o m its b e h a v i o r d e t e r m i n e the onset of f a i l u r e . Determination of the Acoustic Loading
Energy
Dissipation
Function
of the
Material
Under
Intense
In the p r e s e n c e of v i b r a t i o n a l heating the e n e r g y balance is e x p r e s s e d by the equation [11-13] dT
1
dt
2
I"
1
t
(o(~o2-7-" + ' - 7 - - d i v [:~* grad T] + - ~ - - IV, up c9 up
(1)
where "I" is the l o s s compliance ; p is the density, C the specific heat, and k* the t h e r m a l conductivity of the m a t e r i a l ; W is the distribution function of the additional e n e r g y s o u r c e s (or sinks) a s s o c i a t e d with r a d i a t i v e and convective heat t r a n s f e r . If we a s s u m e that the expenditure (replenishment) of p a r t of the e n e r g y as a r e s u l t of m e c h a n i c a l l y activated c h e m i c a l r e a c t i o n s and s t r u c t u r a l changes in the m a t e r i a l can be taken into account by m e a n s of the c o r r e c t i o n coefficient "/*(T, t, ~0), then we can r e w r i t e Eq° (1) in the f o r m 1
~
¥* (T, t, ¢Jo)
yo)ao- C(T, t),o(V, t)
F'(T,t, ~)
dT dt
dT_ dt
(2)
H e r e , dT_/dt is the r a t e of change of t e m p e r a t u r e a s s o c i a t e d with the o v e r a l l heat losses* dT_ _ dt
1 W1 div[).* grad T]+~-~-O Cp
(3)
*We a s s u m e that in the p r e s e n c e of r a d i a t i v e and convective heat t r a n s f e r the d r a i n a g e of e n e r g y is e x c l u s i v e l y involved. 578
vm/! 7 °
r~
^
$%~Npl
I. °m 500 80
•~
lo.gl~
e
~.~
o,sF
~7}~'5 7e~ 3N
°':f
'I¢0-o,
200 ] 2Q
to 6o~
o,3
a2{ -
-
-
' ~ 'o';0 ~
-
. e
.
~
-
~
6 8to 7
~ 2
...... q
6 8 ~,0a
czsl
~
Ncv~i~
N~,. . . . 2
q
6 8109"-
Fig. 2
2
fsec 20
#3
60
80
230 250 270 290
MO
tO
20
30
~0
g~.
~
70
Fig. 3 Fig. 2. Dependence of the e x p e r i m e n t a l l y d e t e r m i n e d quantit i e s on the n u m b e r of v i b r a t i o n c y c l e s (material of s e r i e s 2, n o n i s o t h e r m a l loading r e g i m e ) . Fig. 3. Kinetics of the v i b r o h e a t i n g t e m p e r a t u r e s of the i n t e r i o r and s u r f a c e of s p e c i m e n s of the m a t e r i a l of s e r i e s 1: a) internal and b) e x t e r n a l t e m p e r a t u r e ; input v i b r a t i o n amplitude: 1) 10o0; 2) 8 . 0 ; 3) 7 . 0 ; 4) 5 . 8 ; 5) 5 . 3 p ° E x p r e s s i o n (2) is noteworthy in that it can be used f o r the e x p e r i m e n t a l d e t e r m i n a t i o n of the r e s u l t a n t d i s s i p a t i v e function of the m a t e r i a l
Fo(T, t, ~o) =
y*(T, t, ~o) I " (T, t, (~o) C(T, t)p(T, t)
(4)
since the quantities w and cr0 a r e d e t e r m i n e d in the c o u r s e of the test, while the t i m e d e r i v a t i v e s of the t e m p e r a t u r e can also be obtained if a m i n i a t u r e t h e r m o c o u p l e is introduced into the s p e c i m e n and the v i b r a t i o n b r i e f l y discontinued (a0 = 0). In this c a s e the d e r i v a t i v e s dT+/dt and d T / d t a r e found by graphical d i f f e r e n tiation of the heating and cooling c u r v e s with and without vibration, r e s p e c t i v e l y (Fig. 1), i . e . , dT+/dt A T + / A t + , d T - / d t ~ A T _ / A t + and
AT+ Fo(T, t, (Yo) =
AT 1
~ - 0)002
(5)
579
....
-V-
Ya deg.crn4/kgf z ]4-o I
!
I
--
f~___~
[
,
tO00
2000
[
;
~
:
'
j
=
I
i
!
[
J903
I
r~c
;tmi, ~'000
Fig. 4
3D
35
~'5
55
6-.'
Fig. 5
Fig. 4. T i m e dependence of the acoustic c h a r a c t e r i s t i c s of m a t e r i a l of s e r i e s 2 in the p r e s e n c e of s t r o n g and weak v i b r a t i o n ( i s o t h e r m a l loading r e g i m e , T =+ 65°C). m) v, Crm= 0 ; ©) v, 2 . 5 9 k g f / c m 2; A) v, 2 . 8 3 k g f / c m 2; E])fi, crm=0; e) fi, 2 . 5 9 k g f / c m 2; A) fi, 2.83 k g f / e m 2. Fig. 5. 2).
T e m p e r a t u r e dependence of the r e s u l t a n t d i s s i p a t i v e function {material of s e r i e s
In principle, if the boundary conditions a r e known the s t r e s s - t e m p e r a t u r e - t i m e c u r v e s of the function FS, found by the method d e s c r i b e d above, can be used to calculate the kinetics of the t e m p e r a t u r e field in the s p e c i m e n or component in the intense a c o u s t i c loading r e g i m e . Fatigue
Properties
of Filled
Rubber
The acoustic fatigue of soft p o l y m e r m a t e r i a l s was investigated on s p e c i m e n s p r e p a r e d f r o m filled r u b b e r of the butyl type. The p r i n c i p a l object of the e x p e r i m e n t s was not only to investigate the fatigue p r o p e r t i e s of the r u b b e r but a l s o to check the e x p e r i m e n t a l technique and a p p a r a t u s . Accordingly, we s e l e c t e d filled r u b b e r s of two s e r i e s with r e l a t i v e l y quite different m e c h a n i c a l and t h e r m o p h y s i c a l c h a r a c t e r i s t i c s and a s h a r p l y e x p r e s s e d t e m p e r a t u r e - t i m e dependence of the m e c h a n i c a l p r o p e r t i e s . The s p e c i m e n s took the f o r m of cylindrical r o d s 10 m m in d i a m e t e r and 6-12 m m tall. They w e r e cut with a device that e n s u r e d fiat end f a c e s p e r p e n d i c u l a r to the g e n e r a t o r of the cylinder and bonded to the a d a p t e r head and the s u p p l e m e n t a r y load m a s s (or m e t a l foil) with an epoxy a d h e s i v e in special c e n t e r i n g clamps. In o r d e r to s e l e c t the acoustic failure c r i t e r i o n we employed a s p e c i m e n with one f r e e end in the i n t e n s e vibration r e g i m e . During the e x p e r i m e n t we r e c o r d e d the t i m e dependences of the acoustic c h a r a c t e r i s t i c s , the r e l a t i v e elongation of the s p e c i m e n , and the v i b r o h e a t i n g t e m p e r a t u r e s . F o r the m a t e r i a l of s e r i e s 1 the attenuation v e c t o r [4] and f o r the m a t e r i a l of s e r i e s 2 the r e l a t i v e elongation of the s p e c i m e n p r o v e d to be m o s t sensitive to failure (Fig. 2). In all the e x p e r i m e n t s with s p e c i m e n s of m a t e r i a l of s e r i e s 2 at constant v i b r a t i o n amplitude at the s p e c i m e n "input" we obtained two q u a s i - s t a t i o n a r y t e m p e r a t u r e r e g i m e s (see Fig. 2) s e p a r a t e d by a region of instability (on the i n t e r v a l 40-60°C) a c c o m p a n i e d by an intense change in all the c h a r a c t e r i s t i c s of the s p e c i m e n (apart f r o m the r e l a t i v e elongation) and the s t r e s s and s t r a i n a m p l i t u d e s . This b e h a v i o r was t h e o r e t i c a l l y p r e d i c t e d in [11, 12, 14] and is caused by the kinetics of the v i b r o h e a t i n g t e m p e r a t u r e , which depends on the d y n a m i c s t r e s s level, the t e m p e r a t u r e dependence of the dynamic and t h e r m o p h y s i c a l c h a r a c t e r i s t i c s of the m a t e r i a l , the heat t r a n s f e r conditions, the s p e c i m e n g e o m e t r y , and other f a c t o r s . E s t i m a t i o n of the Mode of Fatigue F a i l u r e . F o r the p u r p o s e s of a quantitative e s t i m a t i o n of the mode of fatigue f a i l u r e (thermal o r mechanical) we conducted fatigue t e s t s in which we m e a s u r e d the t e m p e r a t u r e s of the loading s u r f a c e and the r e g i o n s of m a x i m u m v i b r o h e a t i n g in the i n t e r i o r of the s p e c i m e n . The m a x i m u m values of the t e m p e r a t u r e s c o r r e s p o n d i n g to the m o m e n t of f a i l u r e w e r e subsequently c o m p a r e d
580
with the t h e r m a l d e g r a d a t i o n t e m p e r a t u r e , which is equal to 250°C for the m a t e r i a l of s e r i e s i and 75°C f o r the m a t e r i a l of s e r i e s 2. In all t h e s e e x p e r i m e n t s the t e m p e r a t u r e of the a m b i e n t m e d i u m was 20°C. The v i b r o h e a t i n g t e m p e r a t u r e s w e r e m e a s u r e d by m e a n s of m i n i a t u r e c o p p e r - e o n s t a n t a n t h e r m o c o u p l e s with w i r e s 0.05 m m in diameter. The kinetics of the v i b r o h e a t i n g t e m p e r a t u r e s of s p e c i m e n s of the m a t e r i a l of s e r i e s 1 a r e p r e s e n t e d in Fig. 3 f o r v a r i o u s acoustic p r e s s u r e l e v e l s . The "input" vibration amplitudes v a r i e d between 5~ 3 and 10.0 in the different e x p e r i m e n t s , which c o r r e s p o n d e d to N= (650 - 7 ) • 104 c y c l e s to f a i l u r e . The t i m e dependences of the internal t e m p e r a t u r e s (see Fig. 3a) have m a x i m a that coincide in t i m e with a s h a r p i n c r e a s e in the attenuation coefficient, which indicates the a p p e a r a n c e of a f r a c t u r e c e n t e r in the s p e c i m e n . The p r e s e n c e of an internal t e m p e r a t u r e m a x i m u m can be attributed to the fact that at the m o m e n t of f a i l u r e t h e r e is a r e d i s t r i b u t i o n of the intensity of the acoustic field within the s p e c i m e n . In the interior of the s p e c i m e n in the r e g i o n of a m a c r o d e f e c t damping of the v i b r a t i o n s i n c r e a s e s to such a point that it leads to a d e c r e a s e in the dynamic s t r e s s e s and r e d u c e d heat generation. In all the e x p e r i m e n t s the s u r f a c e t e m p e r a t u r e of the s p e c i m e n i n c r e a s e d monotonically before and a f t e r the o n s e t of f a i l u r e (see Fig. 3b). F r o m a c o m p a r i s o n of Figs. 3a and 3b it follows that t h e r e is a v e r y l a r g e r a d i a l t e m p e r a t u r e gradient that attains a value of 100-150°C. A s t a t i s t i c a l a n a l y s i s of the c r i t i c a l values of the internal and e x t e r n a l t e m p e r a t u r e s , obtained f o r different s t r e s s l e v e l s and c o r r e s p o n d i n g to the m o m e n t of failure, gave the following r e s u l t s : T c r int = 234°C~: 11%; T c r ext--96°C±10%° The s c a t t e r of the m e a s u r e d t e m p e r a t u r e s is chiefly d e t e r m i n e d by the i n a c c u r a t e p l a c e m e n t of the hot junctions in the s p e c i m e n . Thus, within the l i m i t s of a c c u r a c y of the m e a s u r e m e n t s it m a y be a s s u m e d that the c r i t i c a l internal and e x t e r n a l t e m p e r a t u r e s of a s p e c i m e n of m a t e r i a l of s e r i e s 1 do not depend on the acoustic loading level. The m e a n c r i t i c a l internal t e m p e r a t u r e (234°C) is close to the t h e r m a l d e g r a d a t i o n t e m p e r a t u r e (250°C), which c o n f i r m s the t h e r m a l mode of failure of the m a t e r i a l of s e r i e s 1 when exposed to intense acoustic radiation. S i m i l a r e x p e r i m e n t s w e r e p e r f o r m e d on s p e c i m e n s of the m a t e r i a l of s e r i e s 2. The m e a n c r i t i c a l internal v i b r o h e a t i n g t e m p e r a t u r e , obtained on the b a s i s of 15 e x p e r i m e n t s , was equal to 74°C± 10%, i . e . , lay within the t e m p e r a t u r e r a n g e c o r r e s p o n d i n g to t h e r m a l degradation of the m a t e r i a l . Consequently, within the l i m i t s of a c c u r a c y of the e x p e r i m e n t a l technique e m p l o y e d it m a y be a s s u m e d that for this m a t e r i a l a l s o the t h e r m a l mode of failure plays the leading role in a c o u s t i c loading. E x p e r i m e n t a l Investigation of the P r i n c i p a l F a c t o r s Responsible for the Change in Mechanical P r o p e r t i e s of the Material in the P r e s e n c e of Intense Vibration. In the p r e s e n c e of intense vibrational loading the d y n a m i c p r o p e r t i e s of p o l y m e r m a t e r i a l s v a r y continuously with t i m e . T h e m a r e t h r e e p r i n cipal c a u s e s of this v a r i a t i o n : 1) an i n c r e a s e in s p e c i m e n t e m p e r a t u r e as a r e s u l t of v i b r o h e a t i n g ; 2) t e m p e r a t u r e - t i m e a g i n g of the m a t e r i a l ; 3) i r r e v e r s i b l e s t r u c t u r a l changes due to the a c c u m u l a t i o n of d a m a g e (or hardening) in the p r e s e n c e of intense a l t e r n a t i n g loads. The t e m p e r a t u r e - t i m e aging of the m a t e r i a l was e x p e r i m e n t a l l y investigated on s p e c i m e n s of m a t e r ial of s e r i e s 2 at a t e m p e r a t u r e of 65°C {without vibroheating) o The t i m e dependence of the acoustic c h a r a c t e r i s t i c s of the s p e c i m e n (attenuation coefficient and acoustic phase velocity v) is shown in Fig. 4 (cr= 0). The sound velocity v i n c r e a s e s with t i m e , w h e r e a s the attenuation coefficient fl fails. Within 67 h of the beginning of the e x p e r i m e n t the attenuation coefficients had fallen by a f a c t o r of five, while the sound v e l o city had a p p r o x i m a t e l y doubled as c o m p a r e d with the s t a r t i n g value. After the end of the e x p e r i m e n t the s p e c i m e n was cooled to + 20°C, and at this t e m p e r a t u r e the quantities fl, v, and 5 l / l w e r e m e a s u r e d in the weak v i b r a t i o n r e g i m e . Similar m e a s u r e m e n t s at + 20°C w e r e a l s o made at the beginning of the e x p e r i m e n t . A c o m p a r i s o n of the c o r r e s p o n d i n g c h a r a c t e r i s t i c s showed that the o b s e r v e d changes a r e i r r e v e r s i b l e in c h a r a c t e r . Thus, the e x p e r i m e n t indicates that the m a t e r i a l of s e r i e s 2 p o s s e s s e s v e r y intense t e m p e r a t u r e time aging p r o p e r t i e s . In o r d e r to experimentally investigate the a c c u m u l a t i o n of d a m a g e (hardening) under dynamic loads we employed the l o n g - t i m e acoustic loading r e g i m e at a constant s p e c i m e n v i b r o h e a t i n g t e m p e r a t u r e of +65°C. The t i m e dependences of the acoustic c h a r a c t e r i s t i c s thus obtained w e r e c o m p a r e d with the c u r v e s d e s c r i b e d above {see Fig. 4) r e c o r d e d at the s a m e t e m p e r a t u r e , but in the weak v i b r a t i o n r e g i m e .
581
The s t a n d a r d deviations of the values of ~ and v, m e a s u r e d in the p r e s e n c e of weak and s t r o n g v i b r a tions at a p p r o x i m a t e l y the s a m e m o m e n t of t i m e , do not exceed 5-10%, i . e . , lie within the l i m i t s of r e producibility of the e x p e r i m e n t a l r e s u l t s obtained for different s p e c i m e n s . This m e a n s that on the i n t e r v a l of a c o u s t i c p r e s s u r e s (to 3 k g f / c m ~) and t e s t durations {to 50-60 h) investigated m e c h a n i c a l d a m a g e (hardening) effects do not develop in the m a t e r i a l of s e r i e s 2. TemPerature-Time Material
DePendence
of the
Resultant
Dissipative
Function
of the
In o r d e r to e x p e r i m e n t a l l y d e t e r m i n e the r e s u l t a n t d i s s i p a t i v e function F~ of the m a t e r i a l of s e r i e s 2 in a c c o r d a n c e with the method d e s c r i b e d above we p e r f o r m e d a s e r i e s of e x p e r i m e n t s in the intense v i b r a tion r e g i m e at constant s p e c i m e n v i b r o h e a t i n g t e m p e r a t u r e s of +35°C, +45°C, +55°C and +65°Co The hot junction of the t h e r m o c o u p l e used to m e a s u r e the stabilized t e m p e r a t u r e was located in the c e n t e r of the s p e c i m e n 1 m m f r o m the upper face° E x p e r i m e n t s w e r e p e r f o r m e d on s e v e r a l s p e c i m e n s at each of the above t e m p e r a t u r e s . At a p p r o x i m a t e l y the s a m e m o m e n t of t i m e five e x p e r i m e n t a l points w e r e r e c o r d e d f o r each s p e c i m e n . In the c o u r s e of the e x p e r i m e n t (lasting about 10 h) 30 s e t s of m e a s u r e m e n t s w e r e made. A s t a t i s t i c a l a n a l y s i s of the r e s u l t s showed that within the l i m i t s of e r r o r a p r o b a b i l i t y of 95% the r e s u l t a n t d i s s i p a t i v e function m a y be a s s u m e d invariant t i m e and depends only on t e m p e r a t u r e . The c o r r e s p o n d i n g c u r v e , b a s e d on the F~, is shown in Fig° 5. It is c l e a r f r o m the figure that the function F~ =f(T) is c r e a s e s s h a r p l y at t e m p e r a t u r e s above 55°C.
of the d e t e r m i n a t i o n with with r e s p e c t to loading t i m e - a v e r a g e d values of distinctly nonlinear and in-
SUMMARY 1. Methods a r e p r o p o s e d for the e x p e r i m e n t a l e s t i m a t i o n of the t e m p e r a t u r e - t i m e aging of a m a t e r ial and the d e g r e e of d a m a g e a c c u m u l a t i o n in acoustic fatigue t e s t s on p o l y m e r m a t e r i a l s . A method of e x p e r i m e n t a l l y d e t e r m i n i n g the e n e r g y d i s s i p a t i o n function in the p r o c e s s of intense v i b r a t i o n of the s p e c i m e n is also d e s c r i b e d . 2. It is e s t a b l i s h e d that on the r a n g e of t e m p e r a t u r e s and acoustic p r e s s u r e s investigated the fatigue f a i l u r e of the m a t e r i a l s t e s t e d is t h e r m a l in c h a r a c t e r ° 3. It is shown e x p e r i m e n t a l l y that the m a t e r i a l of s e r i e s 2 is c h a r a c t e r i z e d by s h a r p l y e x p r e s s e d t e m p e r a t u r e - t i m e aging and the a b s e n c e of p e r c e p t i b l e m e c h a n i c a l d a m a g e . 4. The t e m p e r a t u r e - t i m e dependence of the r e s u l t a n t d i s s i p a t i v e function of the m a t e r i a l of s e r i e s 2 has been r e c o r d e d and is shown to be invariant with r e s p e c t to loading t i m e .
LITERATURE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
582
CITED
A.V. Kantor, Measuring Equipment and Procedure Used in Rocket Testing [in Bussian], Moscow (1963)o Yu. S. U r z h u m t s e v and S. L. Skalozub, Mekhan. P o l i m . , No. 1, 108 (1969). V . V . Bolotin, in: P r o b l e m s of Mechanical Fatigue [in Russian], Moscow (1964), p. 167. S . L . Skalozub and Yu. S. U r z h u m t s e v , Mekhan. P o l i m . , No. 1, 73 (1967). Yu. S. Urzhuratsev and S. L. Skalozub, Mekhan. P o l i m . , No. 6, 911 (1966). S . L . Skalozub, A u t h o r ' s c e r t i f i c a t e NOo 228564. Byull. Izobro, No. 31 (1968). Yu. S. U r z h u m t s e v , Mekhan. P o l i m . , No. 3, 467 (1967)o P . P . Oldyrev, Mekhan. P o l i m . , No. 1, 111 (1967); No. 3, 483 (1967); P. P. Oldyrev and V. P. T a m u z h , Mekhan. P o l i m . , No. 5, 864 (1967). V . I . Korobov, Heating of Cyclically D e f o r m e d P o l y m e r s and Its Role in Fatigue F a i l u r e , a u t h o r ' s a b s t r a c t of c a n d i d a t e ' s d i s s e r t a t i o n , Moscow (1966). Y. F r a n k and W. M~iller, I E L - M i t t . , 4, No. 8, 300 (1965)o R . A . Schapery, Raketn. Tekhn. i K o s m o n a v t . , No. 5, 55 (1964). R . A . Schapery, J . Appl. M e c h . , No. 3, 150 (1965). N . A . Y a r y s h e v , T h e o r e t i c a l B a s i s of Nonstationary T e m p e r a t u r e M e a s u r e m e n t [in Russian], Moscow (1967). G . I . B a r e n b l a t t , Yu. I. K o z y r e v , N. I. Malinin, D. Ya. Pavlov, and S. A. Shesterikov, Zh. P r i k l . Mekhan. i Tekh. F i z . , No. 5, 68 (1965).