8. B .P . Gumenyuk and V. G. Karnaukhov, ,Thermal instability in related dynamic problems of thermo- viscoelasticity," Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 7, 609-613 (1978).

9. T . L . Cost and J. M. Hurd, "Finite-element computation of related thermoviscoelastic effects in designs subject to prolonged periodic vibration,, Rocket Eng. Space Travel, 1_66, No. 8, 35-40 (1978).

10. S. Mukherjee, ,Variational principles in dynamic thermovisooelasticity,n Int. J. Solids Struct., 9, No. 10, 1301-1316 (1973).

11. E .C . Ting, "Dissipation function of viscoelastic material with temperature dependent propert ies , , J. Appl. Phys., 4~4, No. 11, 4956-4960 (1973).

12. R. Christensen, Introduction to Viscoelasticity Theory [Russian translation], MAr, Moscow (1974). 13. O. Zenkevich, The Finite-Element Method in Engineering [Russian translation], Mtr, Moscow (1975). 14. ft. (9den, Finite Elements in Nonlinear Confinuum Mechanics [Russian translation], Mir, Moscow (1976), 15. A. A, Samarskii, Introduction to the Theory of Resonant Systems [in Russian], Nauka, Moscow (1971). 16. H.C. Martin and G. F. Carey, Introduction to Finite Element Analysis, McGraw-Hill, New York (1973). 17. L. 8egerlind, Application of the Finite-Element Method [Russian translation], Moscow (1979), 18. J . C . Bruch, Jr . and G. Zuvaloski, "Transient two-dimensional heat-conduction problems solved by the

finite-element method,, Int. ft. Numer. Methods Eng., No. 8, 481-494 (1974).

E S T I M A T I N G THE E F F E C T OF THE T E M P E R A T U R E F A C T O R

ON THE B E A R I N G C A P A C I T Y OF A R E E L OF M A G N E T I C T A P E

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

UDC 539.315 : 678

When estimating the integrity of a reel of magnetic tape and choosing conditions of winding, one must take into account the effect of the temperature changes encountered under actual operating conditions.

The field of residual s t resses in a reel wound on a core of dissimilar material can change substantially with the system temperature. As experiments show, the radial compressive s t ress between turns is consider- ably decreased at certain temperatures; as a result, the tape is broken.

In connection with this, it is of interest to theoretically and experimentally estimate the effect of change in temperature on the distribution of s t resses in the reel.

Fields of residual s t resses , depending on the conditions of winding of the magnetic tape, were deter- mined in [1]. On the assumption of an absolutely rigid core, without allowance for the rheological properties of the tape, the following expressions were derived for radial displacements and radial and tangential s t resses* :

U*~ "H~ ~- - (n+ l ) [ r 1~

r~+ 11~-- ~O, (n+ 1)1. +(~5+lXe)(ftn~k)r-f~b~+l + a ~ (n-t-l)~--~ 2 ['

a ' = -o 1 { [(~)~-, ~_)~+,] . .~+, 1} --~.-.T(n+l),_~ ~ ~2,~ [ + ( n + l ) i k (-~-1 --p" ; (2)

H, ~ {*Qn .~_ B-l+. - - ( n + l ) kn(~) ~+1

where

[ k~+~+~ (~ + .e,) - ~e,1 (n+ 1) + 1~' f i n = k~+~(~+~6,)+~ ~-~(l~-~e,) ' (4)

p=r/a is the relative radius of winding; r, instantaneous radius of winding; a , core radius; b, outer radius of the wound reel; k=b/a; H0, tension in the tape at r= a; n, exponent in the expression for change of tension in

* In [1] the expressions for the radial and tangential s t resses contain e r rors .

Kiev Polytechnic Institute. Translated from Problemy Prochnosti, No. 8, pp. 62-65, August, 1981. Original article submitted March 24, 1980.

0039-2316/81/1308-1011 $07.50 �9 1982 Plenum Publishing Corporation 101t

O Fig. 1. Geometr i - cal parameters of r e e l - core system.

~ z kg .-~-. 1O, mm---~-- deg

I

, \ -, o \

~2 Io9 1,5 t8 /~ , \ 2 ~

o

o \ \ "\' 7

kg

Fig. 2. Distribution of relative thermal s t resses in 1-4406-6 mag- netic tape reel: 1, 3) winding on aluminum core; 2, 4) winding on steel core,

k . '

&TO 1205

0 a

0.~0

&t5 ~

C ~0 1,~ t~ tO

b t~ e

T_._e r d e____g Mo

8~77{78 ~ ?

r~

= "-;2 200

IO0 ~ 0 1.0 1,4 1,8 /7

Fig. 3 Fig. 4

Fig. 3. Change in radial s t resses in reel of 1-4406-6 magnetic tape, wound on aluminum (a) and steel {b) cores at various temperature drops: 1) AT=0; 2) AT=-10*C; 3) AT =-20~ 4) AT = .-30"C.

Fig. 4. Curves of cri t ical temperature drop of ree l of 1-4406-6 magnetic tape versus relative radius (at k=2): 1, 3) aluminum core with ree l wound respectively with constant tension and constan~ torque; 2~ 4) steel core with reel wound respectively with constant tension and constant ~orque~

the tape in the process of winding H(r) =H0(r/a)n; 6, tape thickness and h tape width; /32 =E| E| and Er, moduli of elast ici ty of the reel in the tangential and radial directions; POt, Posson 's coefficient characterizing the contraction in the radial direction on stretching in the tangential direction; /~r| Poisson's coefficient characterizing the elongation in the tangential direction on compression in the radial direction; E|174 =Er/~Or.

'Une field of initial s t r e s ses and displacements is denoted by an as ter isk .

Now we shall consider thermal s t r e s ses appearing in the r e e l - c o r e sys tem (Fig. 1).

As before [t], we assume that the wound reel of magnetic tape is a homogeneous, cylindrically ortho- trop~.c disk~ whereas the core is an absolutely rigid body with is| thermophysical constants.

1012

Below we shal l cons ider the case of an a x i s y m m e t r i c , s t a t ionary t e m p e r a t u r e field i n t h e r e e l - c o r e sys t em, which is rea l ized exper imen ta l ly and is usual ly encountered when tapes a re s tored and played.

We introduce the following symbols : ~ ' , change in s y s t e m t e m p e r a t u r e ; O~rC~| coefficients of l inear t h e r m a l expansion of the r ee l in the rad ia l and tangent ia l d i rec t ions; and st, coefficient of l inear t h e r m a l ex- pansion of the core.

The stat ic , geomet r ic , and physica l equations of the a x i s y m m e t r i c p rob l em of t he rmoe la s t i c i t y for the body being invest igated give the reso lvent for radia l d isplacement :

d~U T 1 dU r ~ ur ---- • (1 - - ~[3 2) + 37 ' (5) dr ~ +-7"" dr --P"=7"=

where the following notation is used for brevi ty:

= ar + ~ + . % ; ~ = (% + ~+,ar)/(~, .+t%'%).

Under the boundary conditions: 1) no radia l s t r e s s e s T = 0 on the f ree su r face of the r ee l at r = b; 2) per . fect contact (at the expense of ini t ial s t r e s s field) at the boundary of r e e l and core at r =a, so that Uree l = Ucore , and at constant t e m p e r a t u r e drop, solving the equation gave the following expres s ions for the rad ia l and tangent ia l s t r e s s e s and the rad ia l d isplacement :

~ 1 - ~ - ~ j + . . + " -

Eo.T 1(I + ~gro)'A ~0 T = 1 -- $1rO. ttor ( B p~--I

@-- ~s).o [(l--;~fi~) 0 +~+) ]} B p-B-1 _.~ X[ 1 - - [ ~ - - - I ;

~ ' T ' a [ ' B - P + - F + 1--~2 '

where the constants have the f o r m

A = [ a x (2 --z~)

B ~- [(~ - - ~ o ) k - ~ - L + (~ + IXor) k~- l ] ;

') _ , } .

(6)

(7)

(s)

(9)

(i0)

(11)

As a c r i t e r ion for es t imat ing the c r i t i ca l t e m p e r a t u r e drop, at which the danger of layer ing of the r e e l appears , one may set the total radia l s t r e s s equal to ze ro at any radius :

F r o m this we find

a; -{- (%r _ 0. (12)

'Fcr H 0 (1 -- p Or" ~er)' B

(13) ~ n I ( p ) ~ - l : I ~ ) [ 3 + l ] + ( n + l ) kn(k)f~+t:p n]

X

Equation (13) enables one to e s t ima te the c r i t i ca l value of un i fo rm t e m p e r a t u r e drop with r e spec t to the con- ditions of winding of the r ee l and its physica l and geome t r i ca l p a r a m e t e r s .

The t h e r m a l - s t r e s s fields were calculated for type 1-4406-6 magnet ic tape ree l s on a polyethylene t e r eph - thalate (Lavsan) base , which is widely used in prac t ice .

Since determinat ion of the mechanica l c h a r a c t e r i s t i c s of a ree l (E| Er,/z @r, PrO ) entai ls cer ta in e x p e r i m e n - ta l diff icult ies, the moduli of e las t ic i ty of the r ee l in the tangent ia l d i rec t ion O were de te rmined dynamica l ly by s t re tch ing the tape, f r o m which the r ee l was wound, by the method descr ibed in [2]. The rad ia l modulus E r and the Poisson coefficients # | and Pr| were e s t ima ted approx ima te ly by c o m p r e s s i n g packets , ga thered f r o m the tape, in a spec ia l ly constructed device.

1013

The coefficient of linear thermal expansion o~O, corresponding to longitudinal stretching of the tape, was found by the method and with the experimental apparatus described in [3].

Certain difficulties appear when determining the coefficient of thermal expansion of the reel in the radial direction d r. This quantity was estimated by cooling a packet, gathered from samples of magnetic tape, by the well-known method of measuring thermal deformation in a dilatometer. Thus, the following parameters were obtained for a reel of type 1-4406-6 magnetic tape:

E~ ~ 600 kg/mm 2, E r = 110 kg/mml"lxrs~0.056;

~er-~.0.302; r -~ deg'l;

ar~___5.0.10 -s deg -1.

(Tape thickness 5 =0.037~ reel thickness h =6.25 mm).

Curves of distribution of the thermal s t resses #r T and or| T for a reel of 1-4406-6 magnetic tape wound on an aluminum core (c~ =Io3.10 - sdeg -i) and a steel one (~ =1.3.10 -5 deg'l), plotted according to Eqs. (6) and (7), are shown in Fig. 2.

As shown above, the main danger to the integrity of the formed reel consists in cooling of the latter to some temperature, at which the level of radial elastic s t resses at a point on the radius, caused by winding, is decreased to zero by thermal s t resses of opposite sign.

The character of change of the field of initial radial compressive s t resses for cooled reels, wound on aluminum and steel cores, is shown inFig. 3, where curves 1 correspond to the field of initial radial s t resses of the reel of I~4406-6 magnetic tape, wound at constant tension. The points in Fig. 3 correspond to data ob- tained by the method of determining radial s t resses , based on introduction of thin steel plates into the body of the winding [1]. in accordance with this method, the reels were wound at 20, 30, 40, and 50~ then the formed reels were cooled to normal temperature and the radial s t resses measured.

Comparison of experimental data with the results of analytical calculation shows that the given theoretical relations describe the redistribution of radial s t resses in the ree l with changing temperature with sufficient accuracy for practical purposes.

The appreciable shortfall of the experimental results relative to theoretical values, especially in regions near p=l~ may be explained by rheological effects which become active at elevated temperatures and were not taken into account in the theoretical formulas.

As is evident from Fig. 3, cooling of the reels even by 20-30~C decreases the residual radial stress sub- stantially in a considerable region adjacent to the outer edge of the reel, which causes layering.

Curves of Tcr versus the relative radius of winding, derived by using Eq. (13), are shown in Fig. 4, The solid lines correspond to winding of a reel with constant tension on the tape (the exponent of the curve of change of force n=0), and the dashed lines, to winding of the reel with constant torque on the winding-motor shaft (n--- l ) .

As is evident, one should expect layering caused by cooling to begin near the outer edge of the reel, since the temperature drop required is smallest there; this is confirmed by experiment.

tt is also evident f rom Fig. 4 that, all other conditions being equal, f rom the viewpoint of providing integ- rity of the reel on cooling after winding, it is more expedient to produce a field of residual s t resses by intro- ducing winding with constant tension along the entire radius of winding. We note that decreasing the coefficient of linear thermal expansion of the core material will increase the permissible temperature drop of the r e e l - core system.

Thus~ by using the derived formulas, one can quite simply estimate the disruption of continuity of a reel of specified dimensions and properties on cooling below the temperature of formation of the reel.

2~

LITERATURE CITED

E o S. Umanskii, V. V~ Kryuchkov, and V. A. Rakovskii, "Determination of the stressed state of magnetic tape would on a reel, ~ Problo Prochn., No. 3, 98-100 (1978). Eo S, Umanskii, V. V. Kryuchkov, N. S. Shidlovskii, et al., "Dynamic characteristics of magnetic tapes and their bases, subjected to longitudinal vibrations, . Tekh. Sredstv Svyazi. Ser. Obshchetekh., No. 2(6), 74-s0 (1977).

I014

3. E. S. Umansidi, V. V. Krynchkov, N. S. Shidlovskii, et al., "Thermal shrinkage of magnetic tapes," Tekh. Bredstv Svyazi. Set. Obshehetekh., No. 2(6), 81-89 (1977).

STI~ENGTHENING MECHANISM OF ADHESIVE BONDED JOINTS

IN METALS MADE WITH THE SPRUT-5M ADHESIVE

B. Ao L y a s h e n k o , M. A. G e n n i n a , E o A. Z h e z h e n k o , Yu. F. Z a b a s h t a , T. P. T a n t s y u r a , a n d A. Ya. F r i d m a n

UDC 678.4.063.01 ; 539.4

As a result of successes in the synthesis of polymer adhesives, these substances are extensively used in various areas of national economy. Modern synthetic adhesives bond all materials, form high-strength joints with long durability, and can operate in a wide range of temperatures and in any climatic conditions.

One of the most widely used types of adhesive-bonded joints is opposite materials in which parts of the parent material (substrate) are joined by an interlayer of adhesive. In most cases, the joined substrate sur- faces have the simplest form (flat) and, consequently, in the examination of the mechanical properties of com- posite materials with inserts of complicated form, the adhesive-bonded joints can be regarded as model mate- rials~

In this work, it was attempted to clarify the mechanism of strengthening of adheslve-bonded joints in metals under the effect of static loading.

The investigations into adhesive-bonded joints in metals made with the Sprut-5M adhesive developed at the Institute of the Chemistry of High-Moleoular Compounds of the Academy of Sciences of the Ukrainian SSR [1] showed that these joints strengthen under the effect of constant loading over a specific period of time.

Specimens for the determination of pull strength (GOST 14760-69) were loaded for 25, 50, and 100 h with a load equal to 25 and 50% of the fracture load. Subsequently, the residual strength of the adhesive-bonded joint was determined.

The dependence of shor t - term strength on the duration and level of prior loading is shown in Fig. 1. It may be seen that the adhesive-bonded joint begins to strengthen after loading for 24 h.

~q. kgf/cm 2

20 ~0 60 ~0 t h

Fig, 1

g 8 t, min

Fig. 2

Fig. 1. Dependence of short- term strength on the duration and level of prior loading: 1, 2) prior load corresponding to, respectively, 25 and 50% of fracture load.

Fig. 2. Dependence of double refraction on the time elapsed from the removal of load: 1-3) holding under load for, respectively, 3 days, 1 day, and 6 h.

Institute of Strength Problems, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prob- lemy Prochnosti, No. 8, pp. 65-68, August, 1981. Original article submitted January 1, 1980.

0039-2316/81/1308-1015507.50 @ 1982 Plenum Publishing Corporation 1015