C R E E P A N D R E C O V E R Y O F C O M P O S I T E

A T E L E V A T E D T E M P E R A T U R E S

E . S . U m a n s k i i , V. V . K r y u c h k o v , a n d S . S . V e r e m c h u k

FILMS

UDC 539,3/5:678

P o l y m e r (Lavsan) f i l m s have a n u m b e r of v a l u a b l e p h y s i c a l and m e c h a n i c a l p r o p e r t i e s : su f f i c i en t m e c h a n i c a l s t r eng th , e l a s t i c i t y , h igh d i e l e c t r i c c h a r a c t e r i s t i c s , r e s i s t a n c e to c o n s i d e r a b l e f luc tua t ions of t e m p e r a t u r e and humid i ty , h igh qua l i t y and h o m o g e n e i t y of the s u r f a c e , and long s e r v i c e l i fe . Th i s p e r -

m i t s u s i n g t hem as the b a s e fo r m a g n e t i c c a r r i e r s u s e d w ide ly in v a r i o u s sound and v ideo r e c o r d i n g dev ices~

r "F--Ps ' " 2 P60<Ci ~, �9 IO:1.Skgl[n~ .- in compu t ing m a c h i n e r y , and in p r o g r a m m e d c o n t r o l

I,~ m 'J

Recovery. aA

~2

s y s t e m s .

During service the magnetic c a r r i e r s a r e s u b j e c t e d

4 zf 20 28 55 4~ J2 50 5# 4 h 0,I sec a

II-2 !~-TZ bgl.mm,2 ~ ,_._,

,J lz~ .t-hn~-, ~o '

o ~ 15 2~" 7f 40 49

b ~7 s~

1,6 - - -

~<! F I

o! 4 IZ 25 28 .]5 44

~l $ 8 c c

F i g . 1. D i a g r a m s of c r e e p and r e c o v e r y of m a g n e t i c c a r r i e r s .

Recovery

55 d4 77 t~ h

ovo,y

•2 69 G g t , h

Kiev P o l y t e c h n i c Ins t i tu t e .

f o r a long t ime to t e n s i l e f o r c e s in a r a t h e r wide t e m - p e r a t u r e r ange , which l e a d s to t h e i r d e f o r m a t i o n and hence to d i s t o r t i o n o r l o s s of the r e c o r d e d i n fo rma t ion . T h e r e f o r e . i t is c o m p l e t e l y u n d e r s t a n d a b l e that the u s e of p o l y m e r - b a s e m a g n e t i c c a r r i e r s for r e c o r d i n g i n f o r - m a t i o n i s un th inkab le wi thout knowledge of the l aws of a c c u m u l a t i o n and r educ t i on of d e f o r m a t i o n s du r ing c e r - t a in h i s t o r i e s of load ing .

R e s u l t s of an e x p e r i m e n t a l s tudy of the s h o r t - t i m e s t r e n g t h and d e f o r m a b i l i t y of d o m e s t i c and fo r e ign m a g - ne t ic c a r r i e r s in the r a n g e of w ork ing t e m p e r a t u r e s f r o m +80 to -80~ w e r e ob ta ined e a r l i e r [1, 2]. As f a r a s we know t h e r e a r e no da ta in the l i t e r a t u r e on the t h e o l o g i - ca l p r o p e r t i e s e i t h e r of m a g n e t i c c a r r i e r s d i r e c t l y o r of L a v s a n f i lm u s e d as t h e i r b a s e .

In connec t ion with th is the p r e s s i n g need a r o s e fo r a c o m p r e h e n s i v e i n v e s t i g a t i o n of c r e e p and r e c o v e r y of the i n d i c a t e d m a t e r i a l s in the o p e r a t i n g r a n g e of l o a d s , t i m e , and t e m p e r a t u r e .

Th i s a r t i c l e p r e s e n t s the r e s u l t s of s tudy ing the t h e o l o g i c a l p r o p e r t i e s of s ix t y p e s of m a g n e t i c e a r m e r s : G - l , V, I -2 , P E - 3 1 , P E - 4 1 , and P y r a i a t t e m p e r a t u r e s 20, 40, 60, and 80~ and o p e r a t i n g l e v e l of s t r e s s e s

f r o m o- = 0 .02a t to o- = 0.16a t.

I s o t h e r m a l c r e e p at each s t r e s s l e v e l was i n v e s t i - ga t ed fo r 48-96 h and r e c o v e r y in the s a m e t i m e and t e m p e r a t u r e r a n g e .

The t e s t s w e r e conduc ted on a 12 s e c t i o n s tand , the d e s i g n o f which and t e s t p r o c e d u r e w e r e d e s c r i b e d in [3].

T r a n s l a t e d f r o m P r o b l e m y P r o c h n o s t i , No. 7, pp . 111-115, Ju ly , 1973o

Original article submitted March 19, 1973.

1 O 1974 Consultants Bureau, a division o f Plenum Publishing Corporation, 227 g'est 17th Street, New York, N. Y. 10011. I No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.

8 8 6

~in, It follows from general concepts of the molecular structure of polymers [4-12] that the theological properties of the investigated mate-

0,~ r ials depend considerably on their s t ructure and physical state. Since the base is the main load-bear ing element of magnetic ca r r i e r s , the p roper t i es of the composite will be determined mainly by the proper t ies

44o of the base.

Aecording to the structure, the base of the investigated magnetic 0,35 carriers represents an oriented, partially crystalline film of polyethyl-

ene terephthalate (Lavsan) whose degree of crystallinity averages 40- 6(P/o. The physical state of the base depends on the temperature; at a

~J2 tempera ture below 90-110 ~ it is in a glassy state.

The resul ts of an investigation of creep and recovery of magnetic 0,26 c a r r i e r s on the basis of the data of an x - r a y s t ruc tura l analysis showed

that s t ructura l changes did not occur in the investigated specimens under the indicated test conditions.

o,24 In connection with the s t ructura l inhomogeneity of the base due

mainly to imperfect ion of the manufacturing p rocess , the mechanical o,2~ 2o ~0 60 T,~ indices of the magnetic c a r r i e r s obtained in tests undergo a consider-

able scat ter . Naturally the rel iabil i ty of the resul ts in such cases de- Fig. 2. Instantaneous (elas- tic) deformation after unload- pends p r imar i ly on the number of specimens tested and method of t rea t -

ing the resul ts . To establish the distribution law of the investigated ing as a function of t empera- quantities, we tested a sufficiently large number of specimens (at least lure of the magnetic c a r r i e r s .

30 at each s t r e s s and tempera ture value).

tt was established that the sca t te r of the mechanical indices is governed by the normal distribution law, according to which the most probable values of deformabil i ty are es t imated by the ar i thmetic mean values and the sca t te r by the standard deviation. The scat ter of the values of elongation and contract ion is comparat ively small (3-5%) and increases with an increase of s t ress and tempera ture .

An analysis of the resul ts obtained showed that the creep and recovery curves for all mater ia ls and test conditions are identical (Fig. 1). In Fig. 1 the c i rc le represen ts the experimental values of creep s t ra ins and recovery (average values of 30 specimens) for different s t r e s ses and tempera tures of mag- netic c a r r i e r s PE-31 and I-2 (Fig. la, b) and also at a s t r e ss equal to 1 k g / m m 2 for all investigated mater r ia ls (Fig. lc) (the calculated values of creep s trains are shown by lines).

As we see f rom Fig. 1, for the given test Conditions p r i m a r y creep, occur r ing at a decreasing rate, and secondary creep, occur r ing at a constant rate, develop in time in addition to instantaneous (elastic) deformation whose rate of propagation is equal to the speed of sound t ransmiss ion in the given mater ia l .

Depending on the s t r e ss and tempera ture values viscoelast ic or viscoelast ic and plast ic components of deformation accumulate in these sections of the creep d iagrams.

We also see f rom the creep and r ecove ry d iagrams that under the same experimental conditions maximum deformations develop in magnetic c a r r i e r s I-2, V, and G-1.

At elevated t empera tu res c a r r i e r s PE-41, PE-31, and Pyra l r e s i s t deformation much better . Thus, at o- = 1 k g / m m 2 and test t empera tu re 80~ creep of c a r r i e r I-2 during 48 h was about 1.5 t imes g rea te r than the total deformation of c a r r i e r s PE-31, PE-41, and Pyra l and 20% grea te r than the defor- mation of c a r r i e r s V and G-1.

Af ter complete unloading instantaneous deformation, which is prac t ica l ly equal in magnitude to that obtained upon loading, d isappears at f i rs t and then viscoelast ic deformation dec reases at a rate decreas ing in t ime, the viscoelas t ic components disappearing most intensely in the initial period after unloading.

We note that during r ecove ry the relaxation p roces se s occur somewhat more intensely than during creep under load.

Thus the creep and r ecove ry curves permi t studying instantaneous, v iscoelas t ic , and residual defor- mations as a function of tempera ture , load, and time.

887

o =l.5~kg/mm 2 ]

//// q0 ~ o.3 ~ x

20 Oo 6a g ~

Fig. 3. Viscoe las t ic and plast ic components of creep strains as a function of temperature of c a r r i e r PE-31.

It was established that for all mater ia l s instantaneous deformation increases l inearly with increase of temperature (Fig. 2), the maximum rate of increase of instantaneous deformation with increase of temperature being observed in c a r r i e r s PE-31 and I-2. In this ease the viscOelastic and plast ic components of deformation increase more intensely with- in- c rease of temperature for the lat ter c a r r i e r than for the others. For the other c a r r i e r s the instantaneous eomponent of total deformation increases with temperature at prac t ica l ly the same rate. The specific magnitude of instantaneous deformation with respect to the total magnitude of c reep de- c reases considerably with increase of temperature . Thus, at 20~ the value of ein is 0.7-0.8 of the value of deformation during 48 h and at 80~ 0.25-0.3. Consequently the proport ion of the viscoelast ic and plast ic com- ponents of deformation (e-ein) increases with increase of tempera ture f rom 0.2-0.3 at 20~ to 0.7-0.75 at 80 ~

The temperature dependence of the indicated components is nonlinear, the viscoelas t ic component accumulating more intensely with increase of the test temperature (Fig. 3).

The maximum value of residual deformation after 48 h recovery for the investigated mater ia l s does not exceed 7%. We should note that it in-

eludes also some portion of revers ib le viscoelast ic deformation which is charac ter ized by a g rea te r re laxa- tion time.

We see f rom the analysis presented that at 20 and 40~ the instantaneous component of deformation predominates and at 60 and 80~ the viscoelast ic component (t = 2 h, o- = i .0 kg /mm 2) for all investigated mater ia ls . The values of the static moduli of elast ici ty were determined on the basis of the value of instan- taneous deformation upon unloading, which lasted about 0.05 sec. A compar ison of these moduli found from the indicated experiments with the dynamic moduli obtained by the resonance method at frequency 20 Hz on the device descr ibed in [13] shows that the dynamic moduli are considerably grea te r than the static (by 1.5- 2 times), the difference between them decreasing with increase of temperature .

Subsequently, in the calculation the dependence of the moduti on temperature in the indicated range can be represented in the form

E(T) = A - - B T . (1)

In selecting the rheotogical model describing the behavior of magnetic c a r r i e r s under real service conditions, it is necessa ry f i rs t and foremost to establish the charac te r of the relation between the acting s t r e s ses and strains.

The indicated relation is l inear in the investigated region. This can be determined f rom the iso- chronous curves ~ - (e -e in ) obtained f rom the creep diagrams for a fixed time.

The l inear relation between s t r e s ses and s trains established experimentally p e r m i t s u s i n g a s the main relationship a l inear integral heredi ta ry equation, which in the one-dimensional ease when ~ = coast for isothermal test conditions can be represented in the following form:

0

The kernel of Eq. (2) is taken in the form of Rabotuov's [141 f ract ional-exponent ia l function:

K(t__. 0 __- Exp,_~ (-- o)=, t - -v) . (3)

Using Rozovski i ' s [15] approximation, we obtain t _ ~ ' 0 .

i 1 ( 1 - - e ). (4)

0

Then with consideration of (4) and the temperature effect the creep equation wilt be

. r ,o o ( r ) . l -+=(T, ~Irrl f<r, )]. e (t, T) = T ~ ) / I + , . ~ ( --e j (5) [ ==,o,

888

TABLE i

Carrier A, kg mm

PE-31 461,4

Pyral 431,3 PE-41 428,5 G-I 364,2 I-2 341,t V 298,5

B,kg ~ram z �9 r

2,31 1,86 1,56 1,43 1,515 0,97

AI BI

0,19 0,0035

0,15 9,00251 0,25 0,0025 I 0,29 0,0015 0,15 0,0025

0,20 10,00251

1,554.10 -5

0 2,78.10 -5 2,5.10 -5 1,7125.10 -5 0,56.10 -5

1,961.10 -3

0 2,8.10 -3 2,62.10 -3 15075.10 -3 0,19.10 -3

0,06889 0,029 0,074 0,0715 0,0553 0,016

1,45.10 -5 1.10 -5 3,25.10 -5 2,7.10 -5 2,5.10 -5 2,1.10 -5

1,53.10 - 3

0 2,31.10 - 3

1,81.10 -3 1,475.10 -3 1,09.10 -3

0,0606

0,043 0,0552 0,046 0,0795 0,042

o,k I 'cm z

O 0,4 0,0 5-ein , %

Fig. 4. Isochronous

curves of creep of carrier

PE-31.

The temperature dependence of the rheological parameter for the indicated materials and test conditions proved to be linear

~,(T) = A a + BIT, (6)

and the t e m p e r a t u r e d e p e n d e n c e of p a r a m e t e r s w ~ and co 0, c h a r a c t e r i z i n g

the p r o p e r t i e s of the m a t e r i a l , c a n be a p p r o x i m a t e d by s e c o n d - o r d e r c u r v e s :

c o = a T2 - - b T -l- c ;

(7) r176 ~ al T2 ~ b t T + c r

T h e v a l u e s of the c o n s t a n t s A, B, A t, B 1, a , b, c , a l , b t , and e 1 a r e g i v e n in T a b l e 1, the c o e f f i c i e n t s b e i n g c a l c u l a t e d wi th c o n s i d e r a t i o n tha t

T i s g i v e n in ~ and E and ~r in k g / m m ~.

T h e c a l c u l a t e d c u r v e s f o r m a g n e t i c c a r r i e r s P E - 3 1 and I - 2 o b t a i n e d

f r o m (5) a r e s h o w n by s o l i d l i n e s and the e x p e r i m e n t a l r e s u l t s by c i r c l e s

( see F i g . ! ) .

We note that the calculated values of creep strains found at the working levels of stresses coincide with the experimental results with an accuracy sufficient for practice. Hence follows that the method of treating the creep curves of the indicated materials described above permits a completely reliable evalua- tion of the magnitude of creep accumulated under the long-time effect of static loads in the operating tem- perature range.

1.

2. 3. 4. 5. 6. 7. 8. 9.

I0. Ii.

12. 13.

14. 15.

LITERATURE CITED

E. S. Umanskii, I. E. Debrivnyi, and V. V. Kryuchkov, Probl. Prochnosti, No. 5 1972). i E. S. Umanskii, I. E. Debrivnyi, and V. V. Kryuchkov, ibid., No. 12 (1972). E. S. Umanskii, V. V. Kryuchkov, et al., ibid., No. 5 (1973). T. Alfrey, Mechanical Properties of High Polymers [Russian translation], IL, Moscow (1952). L. R. G. Treloar, The Physics of Rubber Elasticity, Clarendon Press, Oxford (1951). J. D. Ferry, Viscoelastic Properties of Polymers, John Wiley, New York (1961). B. Rousen (editor), Failure of Solid Polymers [Russian translation], Khimiya, Moscow (1971). Polymer Physics [Russian translation], Mir, Moscow (1969). Encyclopedia of Polymers [in Russian], SE, Moscow (1972). V. E. Gul', Structure and Strength of Polymers [in Russian], Khimiya, Moscow (1971). G. M. Barten'ev and Yu. S. Zuev, Strength and Failure of High-Elasticity Materials [in Russian], Khimiya, Moscow-Leningrad (1964). A. A. Tager, Physical Chemistry of Polymers [in Russian], Khimiya, Moscow (1968). ]~. S. Umanskii, I. E. Debrivnyi, et al., Problems of Electronics - Scientific and Technical Col- lection, Series General Engineering [in Russian], No. 9 (1972). Yu. N. Rabotnov, Creep of Structural Members [in Russian], Nauka, Moscow (1966). M. I. Rozovskii, Izv. Akad. Nauk SSSR, Mekhanika i Mashinostroenie, 2 (1961).

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