1.

2,

3.

4,

5.

6.

L I T E R A T U R E C I T E D

G. N. Tret'yachenko, A. P. Voloshchenko, V. A. Konev, et al., "Studies on the effect of seawater salts on the thermal stability of materials and structural elements of gas-turbine engines," Probl. Prochn., No. 12, 40-43 (1972). G. N. Tret'yachenko, A. P. Voloshchenko, V. A. Konev, et al., "The effect of seawater salts in a gas flow on the thermal stability of turbine blades, " Probl. Prochn., No. 12, 40-43 (I 972). G. N. Tret'yachenko, L. V. Kravchuk, and I~. P. Kosygin, "A study of the effect of sulfur compounds in fuel combustion products on the weakening of materials and structural elements, " Fiz. -Khim, Mekh. Mater., No. 5, 95-98 (1973). G. N. Tret'yachenko, L. V. Kravchuk, and I~. P. Kosygin, "A study of the effect of non-steady-state operating conditions on the efficiency of gas-turbine blades," Probl. Prochn., No. i0, 15-20 (1974). G. N. Tret'yachenko, L. V. Kravchuk, and I~. P. Kosygin, "The effect of sulfur compounds in fuel combustion products on the efficiency of ship gas-turbine blades during cyclic thermal stresses," Probl. Prochn., No. 7, 9-13 (1974). G. N. Tret'yachenko, L. V. Kravchuk, and 1~. P. Kosygin, "The kinetics of fracture of gas-turbine blades for thermal cycling stress in a gas flow containing sulfur compounds, " Probl. Prochn., No. 6, 28-31 (1975).

EFFECT OF RADIATION HEATING ON THE

CREEP OF POLYMERIC MATERIALS

B. I. Verkin, Yu. S. Stroilov, K. Sh. Bocharov, and V. F. Udovenko

UDC 678.01:620.17:551.52

According to the kinetic theory of s t rength, the total c r eepde fo rma t ion of a polymeric specimen can be written as the sum of two t e rms [1]:

where e~Y is the elastic (highly elastic) deformation rapidly reaching saturat ion, which determines the initial relaxation section of creep, and e a is the fract ion of deformation growing l inearly with t ime , determined by the elementary acts of f r ac tu re (the thermal fluctuation rupture of chemical bonds), which charac te r izes the creep at the s teady-s ta te stage.

At present it is usual to consider that in a radiation field the ra te of the displacement p rocesses of the molecules relat ive to each other s ca rce ly var ies at all , and the effect of radiation on the relaxation component may be neglected [2, 3]. The action of radiation on loaded polymers leads p r imar i ly to an additional rupture of the chemical bonds of the chain molecules and to an inc rease in the ra te of the disintegration p rocesses . On this basis the rate of creep of polymers in a radiation field (after the relaxation processes have taken place) is charac te r ized by the sum of the independent t e rms in the f i rs t approximation [1, 4]:

~ = ~ ((r, T) q- ej(g, T, I), (2)

where ~a is the force relat ionship known f rom the kinetic theory of strength; ~,, radiation component of the J

ra te of c reep determined for a given mater ia l by the magnitude of the applied s t r ess ~, the t empera tu re T, and the dose ra te I.

To examine the analytical fo rm of the ~j(cr, T, I) relat ionship, experimental data on the variat ion in the length of a specimen immediately af ter svitching on the radiation and after switching it off are widely used.

It must be noted that no account is taken in Eq. (2) of the increase in the t empera tu re of the specimen due to radiation heating by a quantity AT and the appearance of an additional deformation e T ~ aLxT. For polymers under load the value of AT, the magnitude and the sign of the thermoelas t ic coefficient a depend on the integral absorbed dose, the thermophysica l proper t ies and initial s t ruc tu re of the specimen, the a tmosphere , etc.

Low-Tempera tu re Engineering Physics Institute, Academy of Sciences of the Ukrainian SSR, Kharkov. Transla ted f rom Problemy Prochnost i , No. 3, pp. 35-37, March, 1979. Original ar t ic le submitted July 11, 1978.

262 0039-2316/79/1103- 0262 $07.50 �9 1979 Plenum Publishing Corporat ion

Fig. 1 Fig. 1. Diagram of apparatus .

~g2 g l

0 z ~ 6 6 train a

-a~ O Z ~ 6 8 L min

b

Fig. 2

Fig. 2. Effect of VUV radiation on the creep of poly- ethylene (a) and of vulcanized rubber (i0): t 1) moment of switching on; t2) moment of switching off.

Taking the radiation heating into account, the deformation of loaded polymeric mater ia ls in a radiation field may be put in the form

= % ((~, T + AT) + ~j (~, T -t- AT, 1) -f- ~ (~z, ,~V). (3)

For a sufficiently smal l s t r e s s the contribution f rom the f i rs t t e r m in Eq. (3) can be neglected. In this case the deformation of the specimen will be determined by the inc rease in length due to the rupture of chemi- cal bonds under i r radiat ion ej and the variat ion in length with t empera tu re e T.

Since the number of bonds ruptured would seem to be determined only by the acting s t r e s s and the rad ia - tion intensity, over the course of a sufficiently prolonged period the ra te of radiation creep ej remains constant. The variation in the length of the specimen due to the increase in t empera tu re reaches a final value over ~he period At (the t ime to establish the equilibrium tempera tu re T + AT), the quantity e T varying f rom the maxi- mum value to zero. Depending on ~ and AT the increase in length a T may reach an appreciable value and ~lso determine virtually completely the total deformation e and the ra te of its variat ion e just af ter switching the radiation on and switching it off.

This can be shown most c lear ly for the example of the action of radiation on polymers whose the rmo- elastic coefficient differs not only in absolute magnitude but a lso in sign. In this case radiation heating should lead to substantial ly different creep relat ionships just af ter switching on the radiation and switching it off.

By way of confirmation, we present experimental data for the creep of thin layers of polyethylene and vulcanized rubber (dimensions of specimens 0.04 x 9 x 30 mm and 0.07 x 9 x 30 ram, respect ively) . Accord - ing to the resul ts f rom the i so thermal heating of loaded specimens , the coefficient ~ for polyethylene is posi- t ive, v i z . , +300.10 -6 deg -1 and for vulcanized rubber it is negative, v i z . , --200.10 -6 deg -1 (the accuracy of determinat ion was not worse than 20%.

All the investigations were conducted in a specially designed unit {Fig, 1), consisting of a high-vacuum chamber 1 and a source of VUV radiation 2 hermet ical ly joined with it. The working vacuum of 10-6-10 -7 mm Hg is achieved by means of the c ryogenic-sorp t ion pumping sys tem 3. We used a gas ; j e t light source (GLS) [5], the principal intensity of which occurs in the wavelength region f rom 1500 to 500 A (the vacuum ultraviolet region). The absence of a longwave region of radiation and the radiat ive nature of the heating a re caused by no effect of radiation on the c reep of the polymers being observed on placing a f i l ter having a lower t r a n s m i s - sion limit of 3500 A between the GLS and the specimen.

According to the measurements made, the radiation heating was ~ I~ Specimens secured in the upper and lower clamps by the "press ing" method [6] were placed in the high-vacuum chamber. Deformation mea- sured by means of the inductive sensor 4 was recorded automatically on the chart tape of an t~PP-09 through an IM-131 mult ipl ier (the accuracy of measurement was not worse than 2-3% of the quantity being measured). The s t r e s se s applied (0.4 and 0.045 kgf /mm 2) were chosen such that af ter complete passage of the relaxation p rocesses the dependence of deformation on t ime had the fo rm of a horizontal line over the measurement range concerned, and at this stage the VUV radiation was switched on.

It is seen f rom Fig. 2 that the nature of the e - - t cu rves for polyethylene and the rubber differ great ly . Just a f t e r switching on the radiation the length of the polyethylene specimen inc reases , the rate of increase

263

in deformation with t ime dec reases , and af ter 5-7 min becomes constant, i . e . , the appearance of a s teady- s ta te s tage of c reep is observed in the radiation field. The ra te of creep at this stage is charac ter ized by the quantity tan 0. The length of the rubber specimen f i rs t decreases and only on reaching a certain minimum value does it inc rease and gradual ly reach a s teady-s ta te stage of creep. After switching off the radiation the length of the f i r s t specimen decreases but the second increases (in both cases with the formation of a res idual deformation eres) .

The effects indicated a re associa ted neither with a change in the s t ruc ture of the polymers as a resul t of radiat ion-ini t ia ted degradat ion and s t ruc tur ing processes nor with an additional rupture of chemical bonds under i r radiat ion. The experimental relationships obtained can be explained only if account is taken of the possibil i ty of a change in the length of the specimens having thermoelas t ic coefficients of different sign due to radiation heating.

We may note that the revers ib le lengthening of a specimen for smal l loadings is connected with an in- c rease in the volume of polymers in a radiation field as a resul t of the formation of radiolytic products [7]. The observed dec rease in length of the rubber specimen just af ter switching on the irradiat ion contradicts the conclusions in [7]; the well-known evolution of gas eous products during the action of radiation on vulcanized and unvulcanized rubber [8] should also have led to an increase in the length of the vulcanized specimen in the VUV radiation field.

Since in our supposition on the smal lness of e a (experimentally achieved by selecting the appropriate value of a) the deformation of the specimens is determined by the sum of ej and e T, and e T = 0 over the period At, then ej = tan 0 charac te r i zes the t rue ra te of radiation creep (like the ra te of increase in length due to the rupture of chemical bonds under irradiat ion). Here the res idual deformation eve s =" ~j(t 2 - tl) and the revers ib le thermal elongation e T = s A T .

Thus, when discussing problems of the creep of polymeric mater ia ls in a radiation field, it is neces - sa ry to take into account the possibility of an increase in the t empera tu re of a specimen due to radiation heating.

The reve r s ib le change in the length of the specimen by a quantity e T is caused by a change in the highly elastic proper t ies of the polymer with a change in t empera tu re and in this sense the quantity e T is analogous to the deformation eaY over the initial section of creep. The quantity eT would also appear to be a quantitative measure of the change in relaxation proper t ies of polymeric mater ia ls under the action of radiation.

To determine the analytical fo rm of the ej (a, T, I) relationship, experimental data on the rate of s teady- state c reep in the radiation field or on the residual deformation after switching on the radiation should be used. In the general case it is a lso necessa ry to take account of the dependence of e a on AT.

Of course , the effect of radiation heating on mechanical proper t ies Is especially marked in the absence of efficient heat removal f rom the specimens -- a phenomenon observed in vacuum. Data on the c reep ra te of polymeric mater ia ls obtained under these conditions just af ter switching on the radiation and switching it off, without taking account of radiation heating, may not provide the co r rec t charac ter i s t ic of the rate of radiation creep.

1.

2.

3.

4.

5.

6.

L I T E R A T U R E C I T E D

V. R. Regel ' , A. I. Slutsker, and IS. E. Tomashevski i , "Rheological models with elements of f r ac tu r e , " in: Kinetic Nature of the Strength of Solids [in Russian], Nauka, Moscow (1974), pp. 521-528. V. R. Regel ' , N. N. Chernyi, V. G. Kryzhanovskii , and T. B. Boboev, "The effect of ultraviolet rad ia- tion on the ra te of creep of p o l y m e r s , " Mekh. Po l im. , No. 3, 404-408 (1967). V. F. Stepanov, S. l~. Vaisberg , and V. L. Karpov, "Some special features of the radiation c reep and durability of po lymers , " F iz . -Kh im. Mekh. Mate r . , No. 1, 65-68 (1971). V. R. Regel ' , T. B. Boboev, A. M. Leskovskii , and L. G. Orlov, "The effect of UV radiation on the growth kinetics of main cracks in p o l y m e r s , " Fiz. Tverd. Tela, 3, No. 2, 635-637 (1971). B. I. Verkin, t~. T. Verkhovtseva, and Ya. M. Fogel ' , "A gas - je t source of vacuum ultraviolet rad ia - t ion ," in: The Physics of Vacuum Ultraviolet Radiation [in Russian], Naukova Dumka, Kiev (1974), pp. 38-58. K. Sh. Bocharov, Yu. S. Stroilov, V. F. Udovenko, et a l . , "Multiposition tens i le - tes t unit MRV-1M for testing polymeric mater ia ls in vacuum and in gaseous media, ' Probl. Prochn. ,No. 11, 108-110 (1976).

264

7.

8.

I. P. Bell , A. S. Michaels , A. S. Hofman, and A. E. Mason, "Trans ien t acce le ra t ion of c r eep r a t e s of po lymer s during high-intensi ty i r r a d i a t i o n , " in: I r rad ia t ion of P o l y m e r s , Washington (1967), pp. 79- 112. The Radiat ion Stabili ty of P o l y m e r s (Handbook) [in Russian] , Atomizdat , Moscow (1973).

D E T E R M I N I N G E L A S T I C A N D S T R E N G T H P R O P E R T I E S

OF C O M P O S I T E S W I T H H O L L O W S P H E R I C A L I N C L U S I O N S

P . G . K r z h e c h k o v s k i i UDC539.3

Fo r s o m e t i m e pas t compos i te m a t e r i a l s based on m i c r o - or m a c r o s p h e r e s have been widely used in industry; they a r e heterogeneous s y s t e m s consis t ing of hollow spher i ca l inclusions (the f i l ler) d is t r ibuted in a ma t r ix of po lymer binder [1, 2]. The mechanica l s t r u c t u r e of such m a t e r i a l s cons is t s of an e las t ic body con- taining sphe r i ca l cavi t ies which a r e suppor ted by thin sphe r i ca l she l l s .

One of the p rob l ems a r i s ing in designing s t rength p rope r t i e s for a given compos i te is r e la t ing the mech an - ical p r o p e r t i e s of the components to the mechanica l p rope r t i e s of the whole composi te . The mos t na tura l model for the evaluation of the elast ic constants of the type composi te under study is the concen t r i c - sphe r i ca l model [2]. However , the use of ava i lab le evaluations obtained for the given model and applied to the m a t e r i a l s being considered resu l t s in values which a r e too low for the p a r a m e t e r s of the composi te even if the i r upper l imi ts a r e taken as the va lues . One of the reasons for this d i sc repancy lies in the neglect of the effect on an isola ted inclusion of the r e s t of the s p h e r e s , w h i c h i n the case when the r igidity of the ma t r i x is g r e a t e r by fa r than the r ig id i ty of the inclusions r e su l t s in the des i red elast ic p roper t i e s being too low.

In accordance with [3] we shal l introduce t h r ee desc r ip t ive levels for composi te m a t e r i a l s . The sca l e of the lower level h will be equal to the d i am e te r of the hollow spher ica l inclusion; the level with sca le H is. that at which the quanti tat ive and volume content of the phases in the r ep re sen t a t i ve volume precipi ta ted inside the compos i t e and in the compos i te i t se l f is t h e s a m e , i . e . , it is poss ib le to rep lace inhomogeneous ma te r i a l locally with homogeneous equivalent ma te r i a l . The level A is equal to the cha rac t e r i s t i c s ize of the a r t i c l e . Moreove r , let us a s s u m e that h <<H <<A.

In the p re sen t work in finding the elast ic p rope r t i e s the or iginal s t r e s s s ta te of the inclusions at level h is de te rmined by the a v e r a g e s t r e s s e s calculated at the desc r ip t ive level A, i . e . , wholly dependent on the values being sought. The p rope r t i e s obtained in this manner for the s e p a r a t e phases by the averag ing method a r e used for de termining the upper and lower values of the mechanica l p rope r t i e s for the compos i te as a whole. On the basis of the resu l t s of the calculat ion, the l imit ing values can be obtained for one of the mechanica l p rope r t i e s of the compos i t e , the hydros ta t ic s t rength .

Let a dis c re te quanti tat ive distr ibution of inclusions for a prec ip i ta ted volume of composi te be given by the sca l e H or exper imenta l ly de te rmined with r e spec t to the p a r a m e t e r X = R / 6 , where R, 5 a r e the outer radius and the tMckness of the thin hollow sphe res :

N(~ = (Ni, N 2 . . . . . N~_1), (1)

i. e . , we cons ider the m a t e r i a l being studied as an n -phase heterogeneous s y s t e m . Knowing the quanti tat ive dis tr ibut ion of inclusions with r e spec t to the phases , we can compute the volume content in the composi te :

vs =(~1)vT) ' v~3) . . . . . v~n_l)). (2)

Consequently, n - - I n - - I

= ' + ) = ( a )

i : I i ~ l

where v s and v m a r e the volume contents of the f i l le r and the mat r ix ; 3's (i) ~ 3,Y2/Xi ' apparent density of the inclusion of the i - th phase; "gk' 3'm, and ~/2, densi t ies of the compos i te , ma t r ix , and the m a t e r i a l of the sphe re s , r e spec t ive ly .

Nikolaev Shipbuilding Insti tute. Trans la ted f r o m Prob lemy Prochnost i , No.3 , pp .37-40 , March, 1979. Original a r t i c l e submit ted March 10, 1977.

0039-2316/79/1103-0265507.50 �9 Plenum Publishing Corpora t ion 265