Supporting capacity of roll polymer films

21. N.N. Morgunova, B. A. Klypin, V. A. Boyarshinov, et al., Alloys of Molybdenum [in Russian] , Metal- hirgiya, Moscow (1975).

22. Constructional and Heat-Resistant Materials for New Technology [in Russian], Nauka, Moscow (1978). 23. E.M. Savitskii and G. S. Burkhanov, The Metallurgy of Alloys of Refractory and Rare Metals [in Rus-

sian], Nauka, Moscow (1971).

24. S.A. Golovin, V. K. Kharchenko, Yu. I. Davydov, and Yu. P. Babkin, "An investigation of the mechanical properties of molybdenum alloyed with hafnium," Probl. Proehn., No. 4, 57-59 (1975).

25. S.I. Yudkovskii, V. K. Kharchenko, V. A. Borisenko, et al., "The influence of heat treatment on the structure and mechanical properties of 4605 molybdenum alloy," Probl. Prochn., No. 3, 63-66 (1980).

26. V.S. Gnuchev, E. E. Zasimchuk, K. N. Kas'yan, et al., "The mechanical properties and structural inhomogeneity of cermet tungsten," Probl. Prochn., No. 2, 100-104 (1978).

27. V.S. Kravchenko, I. V. Sheina, V. S. Gnuchev, et al., "The temperature relationship of yield strength of tungsten with different microstructures," Probl. Prochn., No. 2, 54-57 (1979).

28. D.M. Karpinos, A. A. Kravchenko, Yu. L. Pilipovskii, et al., "Investigation of the mechanical characteristics of hot pressed tungsten-copper pseudoalloys," Probl. Prochn., No. 12, 64-68 (1970).

29. V.K. Kharchenko, "The influence of temperature on the strength of cermet materials in the 20-2800~ range," in: Questions of High-Temperature Strength in Machine Building [in Russian], Kiev (1963), pp. 16 -22.

30. G.V. Samsonov, V. K. Kharchenko, and L. I. Struk, "Rules of the change in static strength of refractory compounds at high temperatures," Poroshk. Metall., No. 3, 59-63 (1968).

31. E.M. Savitskii, The Influence of Temperature on the Mechanical Properties of Metals and Alloys [in Russian], Izd. Akad. Nauk SSSR, Moscow (1957).

32. R.A. Andrievskii, A. G. Lanin, and G. A. Rymashevskii, The Strength of Refractory Compounds [in Russian], Metallurgiya, Moscow (1974).

33. I.V. Gridneva et al., "The influence of temperature on the strength characteristics of zirconium car- bide," Poroshk. Metall., No. 8, 73-81 (1976).

34. A. Kh. Bychkov, V. S. Neshpor, and S. S. Ordan'yan, "The influence of plastic deformation on certain properties of niobium monocarhide in the area of homogeneity," Poroshk. Metall., No. 7, 51-57 (1974).

SUPPORTING CAPACITY OF ROLL POLYMER FILMS

E. S. Umanskii, V. V. Kryuchkov, and N. S. Shidlovskii

UDC 539.315:678

1. At p resen t there is broad industr ia l product ion of rol l po lymer f i lms having quite high phys icomechan- ical p rope r t i e s . Mate r ia l s of this c lass a r e used in var ious branches of technology but p r i m a r i l y (up to 60%) a r e used as a h igh-s t reng th base for the production of magnet ic tape. The la t t e r is used for the record ing , s t o r age , and reproduct ion of in format ion both in t radi t ional and in new a r e a s of modern technology, such as in compu te r s , spacec ra f t , etc.

During production, s t o r age , and use a po lymer f i lm, including magnet ic tape, is wound in a rol l under var ious conditions of deformat ion. In view of the speci f ics of these ma te r i a l s (very thin, f r o m 0.007 to 0.055 m m , with a quite high s t reng th , 10 to 20 kgf /mm2; s ignif icant m a x i m u m deformat ions , up to 200%) there a r i s e definite difficulties in the use of s t andard equipment and methods for invest igat ing their s t rength and v i sco- e las t ic p r o p e r t i e s , and for invest igat ing the support ing capaci ty of rol ls of po lymer f i lms appropr ia te methods and appara tus and s tandard equipment a r e comple te ly lacking.

This r e p o r t s u m m a r i z e s the resu l t s of ce r t a in invest igat ions made in the Po lymer Mechanics Labora to ry of the Depar tment of Res i s t ance of Mater ia l s of Kiev Polytechnic Insti tute during the course of s eve ra l yea r s on f i lm po lymer type m a t e r i a l s .

In the course of this work , a s e r i e s of or iginal methods and equipment was c rea ted for studying the basic rules of deformation of polymer films wound in rolls, taking into consideration the factors of time, temperature,

Kiev Polytechnic Inst i tute. T rans l a t ed f r o m P rob l emy Prochnos t i , No. 10, pp. 104-113, October , 1980. Original ar.ticle submit ted Apri l 12, 1980.

1294 0039-2316/80/1210-1294 $07.50 �9 1981 Plenum Publishing Corpora t ion

1 I '8

Fig. 1 Fig. 2

Fig. I. Electromechanical plan of the unit for investigating" the short-term strength and deformability of film materials: I) sample; 2, 3) clamps; 4) intermediate element; 5) dynamometer with semiconductor resistance strain gauges; 6) holder; 7) knife-edge; 8) controlled temperature chamber; 9) nut; i0) dc electric motor; ii) V-belt transmission; 12, 13) gears; 14) gear clutch; 15) rotation sensor; 16, 17) rectifiers; 18) voltmeter; 19) lever; 20) bearing; 21) selsyn transducer; 22) gear transmission; 23) shaft; 24) selsyn receiver; 25) voltage divider; 26) compartment for holding the sample under the conditions of the experiment; 27) heating elements; 28) fan; 29) contact thermometer; 30) automatic temperature regulation block; 31) resistance strain gauge sensor - l a rge deformation transducer; ICh-50) interchangeable dial indicator; N-700) oscillograph; KSP-4) electronic potentiometer; R-32) resistance bridge; BSP-24) stabilized voltage source.

Fig. 2. Electromechanical plan of one of the sections of the 12 point stand: 1) ring dynamometer; 2) rod; 3) stationary clamp; 4) resistance thermometer; 5) sample; 6) heating elements; 7) screen; 8) guide rods; 9) movable clamp; 10) controlled temperature chamber; 11) controlled temperature chamber casing; 12) cable; 13) slide-wire sensor; 14) block; 15) double interchangeable blocks; 16) cover; 17) fans; 18) inspection window; 19) cathetometer; 20) resistance strain gauge sensors-large deformation transducers; 21) equalizer; 22) indicator holders; 23) weights; 24) movable stage; 25) four-entry screw; 26) stand; 27) adjusting rod; 28) micrometer screw; 29) voltage divider; 30) channel switch; ]~MP-109IM3) electronic bridge with a thyristor automatic temperature regulator; N-700) oscillograph; BSP-24/1) stabilized voltage source; t~PP-09M3) electronic potentiometer; R-32) resistance bridge.

dimensions of samples and rolls, and the character of effective stresses under conditions close to service. The results obtained on experimental and theoretical investigations have been introduced into industry and are being widely used in the development of effective systems for recording and reproducing information.

In the general combination of mechanical properties, short-term strength and deformability of polymer films are two of the most important indices of mechanical behavior of the investigated class of materials. For experimental study of the short-term strength and deformability, a unit (Fig. i) has been created, a distin- guishing feature of which in comparison with existing ones is the use of a multichannel system of measurement and recording of forces and deformations. As a result of such a system, it is possible to obtain the full deformation curve and its initial portion individually, which has important practical value under service conditions of operation of films, with the required degree of accuracy. Recording of the forces and deform ations in this and in other units developed is done with elastic elements with semiconductor sensors -force transducers

1295

p repa red in co l labora t ion with the Depar tmen t of Die lec t r ics and Semiconductors of Kiev Polytechnic Insti tute [1].

The high coeff icient of s t r a i n sens i t iv i ty of the s e n s o r s makes it poss ib le to m e a s u r e a force on the o rder of s e v e r a l g r a m s with a high degree of accuracy .

In this unit the normal ly occurr ing difficult ies re la ted to providing fastening of very thin f i lms have been ove rcome with the use of spec ia l ly designed c lamps made in the f o r m of s emicy l ind r i ca l a s y m m e t r i c a l l y located c r i m p s held together with chamois .

The unit a l so makes it poss ib le to study h y s t e r e s i s and re laxa t ion phenomena and to make tes ts taking into cons idera t ion the sca le fac tor in the range of r a t e of de format ion f r o m 10 to 103 m m / m i n with t e m p e r a - tu res f r o m 400 t o - 1 8 0 ~

The conditions of p repa ra t ion and s e r v i c e of po lymer f i lms a r e cha r ac t e r i z ed by force loads over a wide t ime and t e m p e r a t u r e range , which may lead to s ignif icant deformat ions . In connection with this , quest ions of expe r imen ta l s tudy of the c reep and l o n g - t e r m s t rength of these ma te r i a l s a r e espec ia l ly press ing . For this purpose methods of studying the rheologica l p rope r t i e s have been developed and spec ia l stands built.

The stand designed for invest igat ions at inc reased t e m p e r a t u r e s consis ts of 12 identical ve r t i ca l ly located sect ions (Fig. 2), which a r e located in the c o m m o n control led t e m p e r a t u r e chambe r of the mechanical s y s t e m , which provides smooth loading and r e m o v a l of the load, a s y s t e m for regulat ing and maintaining the speci f ied t e m p e r a t u r e , and a mult ichannel s y s t e m for m e a s u r e m e n t s and record ing of deformat ions [12].

It should be noted that the des ign of the stand makes it poss ible to r e co rd both smal l and large de fo r - mat ions and forces with high accu racy and re l iabi l i ty . The initial por t ion of the c reep curve (7 = 0.1-30 sec) and r e c o v e r y a f te r r e m o v a l of the load w e r e r eco rded on the N-700 loop osci l lograph.

To obtain the full c r eep and r e c o v e r y curve with la rge deformat ions , s l i de -wi re s enso r s we re used. Visual m e a s u r e m e n t s of de format ion w e r e made with mechanica l d i sp lacement s enso r s ( interchangeable dial indica tors with r anges of 1-50 ram). The deformat ions of the sample w e r e a lso measu red with a ca the tomete r f r o m the change in dis tances between the r e f e r e n c e points on the sample .

The chamber pe rmi t s t es t s on l a rge samples (up to 300 m m long and 50 m m wide).

The c reep and r e c o v e r y of magnet ic tapes a f t e r r e m o v a l of the load in the - 8 0 to + 80~ t e m p e r a t u r e range , including in impulse and cyclic loading, were also studied on a spec ia l ly built unit [3], a fea ture of which is the use of semiconduc tor t h e r m o e l e c t r i c ba t t e r i es for cooling the working volume of the chamber . The plan for r ecord ing fo rces and deformat ions is quite un iversa l s ince it pe rmi t s de te rmina t ion of the e las t ic , hype r - e las t ic , p las t ic , and full deformat ions not only for a cycle but a l so for a definite number of cycles . Impulse loading is accompl i shed as a r e s u l t of the act ion of a plunger e l ec t romagne t , liquid buffers , and load impulse genera to r .

The p r o g r a m of impulse loading is se t up so that tes ts a r e as close as possible to the actual operat ing conditions of magnet ic tape and the conditions of s t a r t ing and stopping of the equipment.

The operat ing conditions of all types of r eco rd ing equipment include the use of magnetic tape under s ignif icant dynamic act ions . For the solut ion of a number of technological p rob lems (vibrat ions, t r ans ien t p r o c e s s e s in s t a r t ing and stopping of the equipment) it is n e c e s s a r y to have avai lable values of the moduli of e las t ic i ty of po lymer f i lms obtained by dynamic methods in t r a n s v e r s e and longitudinal osci l la t ions of s amples and a l so the c h a r a c t e r i s t i c s of deformat ion. In connection with th is , a method has been developed and equipment built for de te rmin ing the dynamic modulus of e las t ic i ty and the dec remen t of osci l la t ions in longitudinal osci l la t ions of s amp l e s in the cycl ica l ly un i fo rm l inear s t r e s s e d condition [4].

The bas is of the unit is an or iginal method of r ecord ing induced, including resonan t and damping, o s - c i l la t ions or iginat ing in the in te rac t ion of the a l te rna t ing magnet ic field of a solenoid with the field of a p e r - manent magnet mounted a t the end load.

Record ing of osci l la t ions is done with an additional solenoid, the s ignal f r o m which is fed through a spec ia l ampl i f i e r to an S I -19B osc i l lograph. Int roduct ion into the c i rcu i t of the load of diodes, the r e s i s t a n c e of which d e c r e a s e s with an inc rease in the ampli tude of the e l ec t r i ca l s ignal according to an exponential law, makes it poss ib le to obtain on the osc i l lograph s c r e e n a logar i thmic v i b r o g r a m of the damping osci l la t ions.

For invest igat ion of d iss ipa t ion of energy by the method of the dynamic h y s t e r e s i s loop, there is a r igid dynamomete r with semiconduc tor s t r a i n gauges.

1296

The described unit permits making tests at resonant frequencies of oscillations from 20 to 70 Hz and amplitudes of stresses up to 1 kgf/mm 2.

A significant portion of film polymer materials is used and stored in the form of rolls wound on a spool of the same material. The life of a roll and its strength properties depend not so much on the material of the film as on the winding conditions.

To study the strength and deformation characteristics of rolls, an experimental unit was built making it possible to wind in the -80 to +80~ temperature range.

The system of regulation used in the described unit includes a tension strain gauge sensor, a KSP-4M recording instrument, and a controllable voltage source making possible the use of various programs for winding the tape.

The rolls are wound with forces of tension of the tape from 0 to 0.2 kgfandwith fixed rates of movement of the tape of 9.53, 19.05.~ and 38.1 em/sec.

An important and very difficult element in setting up investigations on determining the stressed condition of a formed coil is measurement of the interturn pressure. The dimensions of appropriate pressure sensors lead to a substantial change in the field of residual stresses. In connection with this, to record interturn pres- sures it was desirable to use a principle, the basis of which is measurement of the stretching force of very thin steel plates placed in the roll during winding. Preliminary experiments established that the disturbance introduced by these plates is negligibly small.

The stretching forces were measured with the use of a ring strain gauge dynamometer on a special stand.

2. The rules of strength and viscoelastic properties of polymer films and also of magnetic tape in the -80 to +80~ range were studied on the described equipment.

Typical deformation curves at various temperatures are shown in Fig. 3.

Despite the high initial orientation of the investigated materials, in tension there is additional orientation of the macromolecules and strengthening during deformation. Specially set-up experiments showed that a significant share of the total deformation (50-60%) is elastic deformation, which decreases with an increase in temperature.

The deformation curves of the studied films, with the exception of the initial Hooke portion, may be approximated by an exponential relationship with the form

--~ Ja s with ~>0, (i)

where ~ : In (i + e) is the logarithmic deformation, andfor 1-4406 magnetic tape the constants in the relationship given are for T = 20~ logA = -4.0117 and s = 2.9062.

The temperature relationships of strength of magnetic tapes are given in Fig. 4. As may be seen, with a change in temperature from + 80 to-80~ the tensile strength ~t and the proportional limit ~pr of the investigated materials decrease to an average of half, and ffpr is about 30% of o" t. The relative elongation at rup-

ture ema x and the residual elongation after rupture ere s decrease by up to 50% with a reduction in temperature.

In this temperature range there is a practically linear relationship of the strength indices to temperature [1, 5].

The var ie ty of information record ing equipment existing at present is the resu l t of the use of magnetic tape of various s izes with different ra tes of its deformation. In connection with this, an investigation was made of the influence of sample dimensions and rate of deformation on mechanical propert ies in s h o r t - t e r m tests over a wide tempera ture range.

It was established that in logar i thmic coordinates the relat ionship between s t rength and sample length is l inear:

lg a t (T) : lg AL (T) - - BL (T) lg L, (2)

where AL(T) = l o g % . J, BL(T) = 1 / r e ( T ) , L is sample length, and ~0, J, and re(T) a re pa ramete r s of the Weibull distribution, the values of which a re given in Table 1 for 1-4406 magnetic tape.

The relat ionship of the charac te r i s t i c s of s t rength and deformabil i ty to the rate of tension at increased tempera tures is descr ibed quite well by the exponential equation

1297

r ~ o, kg f/r~

~ 5 ] o t,kgf/mm a

' ~ / . - ' 2 1 ~ , _ % ~ o , .

O' 20 40 GO 55 S,% -80 -gO 0 z~O T~

Edy n, kgf/mm 2 ~000~ - -

~176 l -80 -~a 0 )a r.0c

Fig. 3 Fig. 4 Fig. 5

Fig. 3. Tensi le curves of polyethylene te rephtha la te base magnet ic tape at var ious t e m p e r a t u r e s .

Fig. 4. T e m p e r a t u r e re la t ionships of the rupture s t reng th of ce r t a in types of magnet ic tape: 1) R E - 41; 2) RE-31; 3) Pyra l ; 4) V-1.

Fig. 5. Relat ionship of the dynamic modulus of e las t ic i ty of 1-4406 n~gnet ic tape (curve 1) and its base (curve 2) to t empera tu re .

% =A~ W'; ema~ = K~'V% (3)

where V is the ra te of de format ion and Av, Kv, nl, and r~ a r e constants .

I t should be noted that the exponents in Eq. (3) a r e p rac t ica l ly independent of the type of invest igated magnet ic tapes wi th polyethylene te rephtha la te bases (n I = 0.0385 and n 2 = 0.045).

In view of the spec i f ics of the inves t igated m a t e r i a l s , al l of the cons idered c h a r a c t e r i s t i c s have a s ta t ic c h a r a c t e r . In connection with this , an invest igat ion was made of a quite la rge quantity of samples and the r e - sults w e r e s ta t i s t i ca l ly t r ea ted on the basis of the normal and Weibull dis t r ibut ions.

In calculat ions of the var ious p r o c e s s e s r e l a t ed to the behavior of magnet ic tape in magnet ic r ecord ing equipment, it is n e c e s s a r y to have avai lable not only the s t rength but a lso the e las t ic p rope r t i e s of tapes. The values of the moduli of e las t ic i ty de te rmined d i rec t ly f r o m deformat ion curves a r e on the low side in the m a j o r - ity of cases as a r e s u l t of hypere la s t i c deformat ion developing a t low ra tes of deformat ion. There fo re , the values of the moduli of e las t ic i ty used in fur ther calculat ions w e r e de te rmined by dynamic methods with longitudinal and t r a n s v e r s e osci l la t ions of the s amples [4, 6].

F igure 5 shows the re la t ionship of the dynamic modulus of e las t ic i ty to t e m p e r a t u r e for 1-4406 magnet ic tape and its base . As may be seen , the value of the dynamic modulus of e las t ic i ty approx imate ly doubles with a drop in t e m p e r a t u r e f r o m +80 to -80~ The modulus of e las t ic i ty of the base is higher than for the magnet ic tape as a whole, which may be explained by the g r e a t e r r igidi ty of the base in c o m p a r i s o n w i t h the f e r r o m a g - netic l aye r .

The major i ty of po lymer f i lms obtained by biaxial s t re tch ing posses s an iso t ropy of mechanica l p r o p e r - t ies. It has been exper imenta l ly es tabl i shed that the d i rec t ion of the main axes of e las t ic s y m m e t r y , as a ru l e , does not coincide wi th the longitudinal axis of the tape, which in uniaxial tension leads to shifts in the t r a n s v e r s e sect ions .

F igure 6 shows theore t ica l and exper imen ta l re la t ionships of the modulus of e las t ic i ty of magnet ic tapes to the d i rec t ion of cutting s ample s . In E vs ~ coord ina tes , where

(4) Z c~ cp -1- 2 B cos 2 cp . s in ~ ~ 2 t- s i n ~ cp '

the relationship of the modulus of elasticity to the direction of cutting the samples corresponds quite well to known relationships [7], andthe value of a varies from 1 to • with a change in the angle of the cut from 0 to 90 ~

Therefore, the relationships given may be recommended for calculating the elastic properties of a broad class of anisotropic polymer films in which the main axes of elastic symmetry coincide with the longitudinal and transverse axes of the samples.

To investigate the stressed condition of a roll it is necessary to know the viscoelastic properties in the radial direction of the wound body. Experimental determination of these properties directly on a formed roll, where there is a field of residual stresses, is very difficult. Therefore, the elastic properties were determined in compression of a packet made up of individual samples of magnetic tape. The value of the radial

1298

TABLE 1. Values in Eq. (2) fo r 1-4406 M a g - net ic Tape

T, ~

20 40 60 80

lg A L

1,464 1,446 1,434 1,412

BL

0,0867 0,106 0,128 0,143

8,17 7,55 6,8 6,5

TABLE 2. Values of the Parameters of Eq. (12) for 1-4406 Magnetic Tape at Vari- ous Temperatures

T emp . , ~

Parameter 1oo

e s ~ --0,068 Y. 10 ~ 0,96

e 1,17

modulus of e l a s t i c i ty E r for 1-4406 magne t i c tape was about 110 k g f / m m 2.

60 80

--0,165 1,13 1,08

--0,550 1,35 0,93

As noted above, in determining the dynamic conditions of information recording and reproducing sys- terns, there may be important value in the damping characteristics of the materials used. Dissipation of energy in various polymer materials, as experiments indicate, has a strongly expressed frequency and also amplitude character [8]. For magnetic tapes and their polyethylene terephthalate bases, as our investigations showed, this character of dissipation of energy is maintained in the material. The application of a magnetic layer to the base of the tape significantly increases its damping capacity. At the same time, technological fea- tures of application of a naagnetic field have a substantial influence on the decrement of oscillations.

It should be noted that the increase in damping capacity may be increased by heat treatment of the magnetic tape. For example, baking at 100~ for i0 h increases the decrement of oscillations by 1.2-1.3 times in comparison with the decrement of oscillations of the same tapes in the original condition.

The temperature relationship of the decrement of oscillations of magnetic tape may be judged from Fig. 7. At low temperatures the decrement of oscillations of tape and its base remains practically constant and its minimum value is at 70~ which corresponds to the glass transition temperature of the polyethylene terephthalate base.

Resonant curves of longitudinal oscillations for magnetic tapes and their polyethylene terephthalate bases are described very satisfactorily with the use of the amplitude-frequency relationship [8]

(_~ . ) ~Al(~a) 1 2= 1 + -. ~a =F ~ [e2B~ (~amax) - - e2B~ (~)]~, (5)

w h e r e p is the na tu ra l f r equency of osc i l l a t ions of the s y s t e m ; ~a, ampl i tude of de fo rmat ion ; e, a s m a l l p a r a - m e t e r ;

and

A~ (~)]= y . sO ~ , cos ~d~; 0

2~ --~

0

The funct ion ~ , wh ich takes into c o n s i d e r a t i o n d i s s ipa t ion of e n e r g y in the m a t e r i a l , may be chosen on the bas i s of g e n e r a l i z e d equat ions of the con tour of the h y s t e r e s i s loop p roposed by P i s a r e n k o [9].

F igu re 8 shows the r e s o n a n t cu rve ca lcu la ted a c c o r d i n g to Eq. (5) fo r 1-4406 magne t i c tape. The points c o r r e s p o n d to expe r i m e n t a l data obtained in the osc i l l a t ions of a s amp le wi th an end load of 0.75 kgL

The expe r imen t a l l y e s t ab l i shed r e l a t i onsh ip be tween the h y p e r e l a s t i c de fo rma t ions developing with t ime and s t r e s s makes it poss ib le to use as the bas i c r e l a t ionsh ip the l i nea r in t eg ra l full equat ion which in the un i - d imens iona l ca se wi th cr = cons t fo r i s o t h e r m a l tes t condi t ions may be r e p r e s e n t e d on the bas i s of the a p p r o x i - ma t ion of M. I. Rozovsk i i of the f r ac t iona l exponent ia l funct ions of Rabo tnov in the fol lowing manne r [10]:

o [ %T ] 8 (t, T) -- ~ 1 -p - - ~ - (1 - - e -c~ (:@(T).t~(r)) , (6)

where E (T) = 341.1-1.515T k g f / m m 2.

The solution of Eq. (6) and determination of the rheologieal parameters entering into it from experimental creep and recovery curves (Fig. 9) were made on the computer.

!299

5 / ' f \'o..._/( 0..9 ~ t.3 t ,7 a 20 40 oo L~

,% lO ~

0.9,5 a98 /.00 1.02 w/p

Fig . 6 F ig . 7 F ig . 8

Fig. 6. Theoretical (solid lines) and experimental (points) relationships of the dynamic modulus of elasticity to the direetion of cutting samples: i) RE-31; 2) 1-4406; 3) 1-4404.

Fig. 7. Temperature relationships of the decrement of oscillations of 1-4406 magnetic tape (solid line) and its base (broken line).

Fig. 8. Resonant curve of longitudinal oscillations of polyethylene terephthalate base magnetic tape.

The r e l a t i o n s h i p of the r h e o l o g i c a l p a r a m e t e r k to t e m p e r a t u r e fo r t he se m a t e r i a l s and t e s t cond i t ions w a s found to be l i n e a r :

~, (T) = AT -[- BT " T, (7)

and the t e m p e r a t u r e r e l a t i o n s h i p of the p a r a m e t e r s ~,~oo and 0J0, w h i c h c h a r a c t e r i z e the p r o p e r t i e s of the m a - t e r i a l , m a y be a p p r o x i m a t e d by a c u r v e of the s e c o n d o r d e r :

o~,~ = a tT 2 - b~T + C6 (8)

~ 1 7 6 = azTZ - - bzT + C2" (9)

F o r 1-4406 m a g n e t i c t ape t h e s e c o n s t a n t s have the fo l lowing v a l u e s : A T = 0.15; BT = 2.5 �9 10-3; a 1 = 1.713 �9 10-5; b 1 = 1.708 �9 10-3; C 1 = 55.3 �9 10-3; a 2 = 2.5 �9 10-5; t92 - 1.475 �9 10 -3, C 2 - 79.5 �9 10 -3 ( ca l cu l a t i ons w e r e m a d e t ak ing into c o n s i d e r a t i o n the f ac t tha t T i s g iven in ~ and E and ~ in k g f / m m 2 ) .

A s a n e x a m p l e , F ig . 10 shows the r e l a t i o n s h i p of l o n g - t e r m s t r e n g t h of 1-4406 m a g n e t i c t ape to the l e v e l of c o n s t a n t s t r e s s . I t w a s e s t a b l i s h e d tha t w i t h t = 1000-2000 h the l o n g - t e r m s t r e n g t h i s 0 .75-0 .85 of the c o r - r e s p o n d i n g v a l u e s of s t r e n g t h u n d e r the 5 - s e e a c t i o n of c o n s t a n t l o a d s .

S i m u l a t i n g a s a m p l e of m a g n e t i c t ape by a s y s t e m of n o n i n t e r a c t i n g p a r a l l e l m o l e c u l a r cha ins p o s s e s s i n g d i f f e r e n t v a l u e s of r e s i s t a n c e to r u p t u r e and c o n s i d e r i n g the k i n e t i c s of i t s f a i l u r e u n d e r c o n s t a n t l oad , we ob - t a i n e d the fo l lowing equa t ion for r a t i n g l o n g - t e r m s t r e n g t h :

1 ~t = ~ .0--% (10)

w h e r e L i s s a m p l e l eng th and a and m a r e p a r a m e t e r s d e t e r m i n e d f r o m the t e n s i l e and l o n g - t e r m s t r e n g t h c u r v e s .

T h u s , the t h e o r e t i c a l v a l u e s of l o n g - t e r m s t r e n g t h of s a m p l e s of 1-4406 and R E - 3 1 m a g n e t i c t a p e s a t n o r m a l t e m p e r a t u r e m a y be d e t e r m i n e d by the e x p r e s s i o n

lgx t = 26.85 - - 25,48%.

The k i n e t i c s of d e f o r m a t i o n of th is m o d e l c o n s i d e r e d in t e n s i o n w i t h a c o n s t a n t r a t e of m o v e m e n t of the c l a m p m a d e i t p o s s i b l e to d e t e r m i n e the s t r e n g t h of the i n v e s t i g a t e d m a t e r i a l s in r e l a t i o n to the r a t e of d e - f o r m a t i o n and s a m p l e d i m e n s i o n s by the e x p r e s s i o n

1

w h e r e C is a c o e f f i c i e n t d e p e n d e n t upon the p a r a m e t e r s of the m a t e r i a l .

F o r R E - 3 1 m a g n e t i c t ape w i t h T = 20~ the r e l a t i o n s h i p of s t r e n g t h to the above f a c t o r s is d e t e r m i n e d by the equa t ion

1300

E.% I l = 8 ~ ~ - [ /

-- ZO ZO

o 12 2# 35 48 50 72 8~ t, h

'R

-3 7 9 I9~ r kg f./mm '2

Fig. 9 Fig. I0 Fig. Ii

-~2 80

F %'*" ......,. ---.-- /oo -O5

0 lO0 200 500 ~+00 500 t, rain

Fig. 9. Curves of creep and r ecove ry af ter removal of a load of ~ = 0.4 k g f / m m 2 for 1-4406 magnetic tape at different t empera tures .

Fig. 10. Relationship of the average life of 1-4406 magnetic tape to the level of constant s t r e ss at normal and increased tempera tures .

Fig. 11. Thermal shrinkage curves of 1-4406 magnetic tape.

Ig (~t = 1,361 + 0.03771gV-- 0.0751g L.

Therefore , the possibili ty has been shown of predicting the average strength of various polymer films taking into considerat ion the rate of deformation and sample dimensions both in s h o r t - t e r m and in long- t e rm tests .

It is known that in polyethylene terephthalate base magnetic tapes with an increase in tempera ture together with thermal expansion there is a lso thermal shrinkage. Figure 11 shows charac te r i s t i c thermal shr ink- age curves of 1-4406 magnetic tape. As the experiments showed, the rate of shrinkage of this magnetic tape af ter holding for 8 h at 100~ is pract ical ly zero.

Many experiments have confirmed that the process of thermal shrinkage both under i so thermal conditions and with a cyclic change in tempera ture is descr ibed sa t i s fac tor i ly by the relationship [11]

e s (t) = es~o [1 - - exp (--7.te)], (12)

where esoo, T, and e a re constants obtained direct ly f rom experiments . The values of these constants de te r - mined by the l ea s t - squa res method f rom experimental data for 1-4406 magnetic tape are shown in Table 2.

3. As a l ready noted, in the investigations made there is very important value in a study of the suppor t - ing capaci ty of rol ls taking into considerat ion the various serv ice fac tors , since failure of rolls during s e r - vice or s torage leads to complete or part ial loss of the recorded information.

The existence of a rol l as such is provided by the presence of res idual radial compress ive s t r e s s e s , the amount of which is determined by the conditions of winding and also by the mechanical and geometr ic pa ra - meters of the tape being wound. The level of these s t r e s se s has a subtantial influence on the s t rength of the rol l under the action of t empera ture , vibration, and other factors .

Taking into considerat ion the thinness of a turn of magnetic tape in compar ison with the outer radius of the roll and assuming the wound body to be a regular continuous medium possess ing cyl indrical anisotropy, in winding on a r igid spool the following expressions for displacements and radial and c i rcumferent ia l res idual s t r e s s e s were obtained [12]:

e~(O)=-- 6h ( ~ + 1 ) - ~ : +~ p / j + ( n + l ) k" )~+~+p~'. p I' (14)

Ho O0(P)-- ~'(Iz~-l)2--~2{Qn[(~)#--l'Ju(~)fl+l]--(n-~])[ kn/kl~+l~--~'] -~ Pn (rt-]- I' ]} ' p 0-5)

where

[k# +~+" ({3 + ~er) -- ~o~] (n § 1) + (3~ (16)

1301

I~.I. kgf/mm a [?.20 . ~

~o~

ROt - -

r=Oh I

~.2 1.4 ~,o 1,8 p

I~rl, 888

0.02

0 LO

f/ram 2

\

K \

Fig. 12 Fig. 13

Fig. 12. T h e o r e t i c a l d i s t r ibu t ion c u r v e s of r ad i a l s t r e s s e s in a ro l l of 1-4411 magne t i c tape i m m e d i a t e l y a f te r winding and a f t e r holding the ro l l a t T = 20~ for 100 h.

Fig. 13. D i s t r ibu t ion of r ad i a l s t r e s s e s in ro l l s of A-4409 magne t ic tape t r e a t e d a c c o r d i n g to a p r o g r a m of: wind rol l a t T = 20~ hea t to Th, hold ro l l fo r 2 h, cool to T = 20~ and d e t e r m i n e s t r e s s e s at T = 20~

0 = r / a is the r e l a t ive rad ius of winding; r , c u r r e n t rad ius of winding; a, r ad ius of the spool; b, ou ter rad ius of the wound rol l ; k = b / a ; H0, t ens ion of the tape wi th r = a; n, exponent in the e x p r e s s i o n for the change in the f o r c e of t ens ion of the tape dur ing winding; H(r) = H0( r / a )n ; 5, tape th ickness ; h, tape width; f12 = E 0 ] E r ; E 0 and E r , modul i of e l a s t i c i ty in the c i r c u m f e r e n t i a l and r ad ia l d i r ec t ions ; and P0r and PrO, P o i s s o n ' s ra t io .

In the ac tua l tape m o v e m e n t m e c h a n i s m s two condi t ions of winding occu r m o s t f requen t ly , winding wi th a cons tan t m o m e n t on the shaf t of the winding m o t o r (M = cons t , n = - 1 ) and winding wi th a cons tan t fo rce of t ens ion of the tape (H = cons t , n = 0).

As a s e r i e s of e x p e r i m e n t s showed, under these condi t ions of winding Eqs. (14) and (15) de sc r ibe the field of r e s idua l s t r e s s e s wi th a su f f i c ien t deg ree of a c c u r a c y .

Roi ls of magne t i c tape , as for D a c r o n tape, p o s s e s s rheo log ica l p r o p e r t i e s revea led , in pa r t i cu l a r , in r e l axa t ion of rad ia l r e s i d u a l s t r e s s e s . With long s t o r a g e and s e r v i c e of ro i l s the re is the danger of s e p a r a - t ion of turns as a r e s u l t of a d e c r e a s e in r ad ia l s t r e s s e s . T h e r e f o r e , the neces s i t y a r i s e s of inves t iga t ing the p r o c e s s of r e d i s t r i b u t i o n of r ad i a l r e s idua l s t r e s s e s a f t e r winding for the purpose of mainta in ing the in t ac t - ness of the ro i l s .

Cons ide r ing a ro l l of tape as a body p o s s e s s i n g e i a s t o h e r e d i t a r y rheo log ica [ p rope r t i e s and mainta in ing the above hypo theses , the p r o b i e m of de t e rm i n ing the r ad ia l and c i r c u m f e r e n t i a l s t r e s s e s inside the ro l l taking into c o n s i d e r a t i o n the t ime f ac to r was solved. Rep lac ing in the e las t ic so lu t ion of Eqs . (14) and (15) of the p r o b l e m , a c c o r d i n g to the V o l t e r r a p r inc ip le [13], the e las t i c cons tan t s by the c o r r e s p o n d i n g rheo log ica l o p e r - a t o r s and app rox ima t ing the l a t t e r by the f r ac t iona l exponent ia l funct ions of Rabotnov , wi th M = cons t we ob- ta in the following ope ra t iona l e x p r e s s i o n s [13]:

1 [ . . ] % (t) = ar (co) -~- p+~. F (-- a) "~r + 0 (g.-- ~r) a, (co); (17)

and

, [ . ~ 1 a o ( t ) = ( , o ( c o ) + tl+~.r(~ ) ~ +o(.-~-o--7~o) ao(~); (18)

(~r(~) and ~0(~) may be found f r o m Eqs . (14)-(16) by r ep lac ing the coeff ic ient /~ by its l imi t ing value:

(go -- Xo ) G ]K % = ~~ ( ~ - ~ ) E J " (191

F i g u r e 12 shows c u r v e s of the change in r ad ia l s t r e s s e s for type 1-4411 magnet ic tape ca lcu la ted us ing Eqs . (14)-(19). The fol lowing values of the cons tan t s in these equat ions w e r e chosen: M = 0.675 kgf . c m ; 6 = 0.032 ram; h = 6.25 ram; a = 45 ram; a = - 0 . 4 0 ; gr = - 0 . 5 3 2 ; go = - 0 . 9 9 5 ; Xr = 0.24; • = 0.096; fl0 = 4; ~0r = 0.18; t = 100 h. The points in Fig. 12 des igna te e x p e r i m e n t a l l y obtained data on the change in rad ia l s t r e s s e s

1302

aef, m/see e IO [tOO

618~ #o 4

/

O.OI a02 0.03 aO# ~05 H, kgf

mril 2 3 1 1 I

O.OJ~

0.0!2

~0t0 2

z2oo8 ~ ~ " - " " / i

OOg5 T -~" 0004 ~- "-- aoo2

o �9 2 I00 200 JO0 y, rad/sec

Fig. 14 Fig. 15

Fig. 14. Relationship of the failure acceleration in transverse

oscillations of rolls of 1-4406 magnetic tape to the force of tension in winding.

Fig. 15. Relationships of the minimum allowable radial resid-

ual stresses in a roll of 1-4406 magnetic tape to angular acceleration: I) co = 105 rad/sec; 2) ,2 = 147 rad/sec; 3) ,2 = 209 rad/sec.

after a 100-h hold of the roll at normal temperature.

The use of magnetic tape at temperatures other than normal (range of operating temperatures -60 to

+60~ increases the probability of failure of rolls as a result of activation of theological processes and the

occurrence of additional temperature stresses. To rate the strength of roils under the action of the tempera-

ture factor, the change in fields of residual stresses in rolls held at various temperatures and cooled to normal was determined.

Figure 13 shows experimental distribution curves of radial stresses obtained after the 2-h action of various temperatures on rolls of magnetic tape.

In cooling a roll there is that temperature differential Tcr at which, depending upon the properties of the roll and the parameters of winding of it, the radial compressive stresses on the corresponding portion become equal to zero, which is equivalent to loss of intactness of the roll. The value of the critical temper-

ature differential may be determined from an equation from the above-mentioned hypotheses on continuity and cylindrical orthotropicity of the wound body:

H o (1 --~J.rO~l, Or).~ ~"~n [(lolk)'B--1 - - (k/P)[3+l -~" (n-{- 1)1 [kn.(k/p) f~+l - - p n] (20)

ATcr = 5h [(n + 1)~-- ~2].E r - - [(13 + ~or)-A~.p 13-I - - ({3 -- l~0,).Dc~.p -1]-~] + xB~ [(i--- ,XI32) (1 + ~0r) (1 - - ~2)-1 __ I] '

where

& , = [ ~ - z (I - x82) (1 - - 82)] ( I S - - ~o , ) k - ~ - ' - - x [(1 - - ~82) (1 + ~0 , ) (1 - - 8~) - 1 _ l j;

O~ ----- [o~ - - X (1 - - o~82 ) (1 - - 8u) -1 (8 4 - ~o~) k~-' + Z [(1 - - &82) (1 4- ~0~) (I - - 82) - I - - 11;

X = c~ r + Fo~ + co0 ;

w h e r e a r and ~0 a r e the c o e f f i c i e n t s of l i n e a r t h e r m a l e x p a n s i o n in the r a d i a l and c i r c u m f e r e n t i a l d i r e c t i o n s and a is the c o e f f i c i e n t of l i n e a r t h e r m a l e x p a n s i o n o f the s p o o l .

Under service conditions, many types of tape movement mechanisms may experience significant vibra-

tion actions. Rolls of tape, absorbing these dynamic loads, are subjected to the danger of failure.

An experimental determination of the dynamic characteristics of the roll-spool system was made with

transverse oscillations of rolls with a constant tape tension of 0.020-0.125 kgf. The rolls were subjected on a

1303

special e lectrodynamic stand to the s h o r t - t e r m action of vibrat ion loads at a fixed frequency of t r ansverse oscillations. At the same t ime, the amount of acce le ra t ion was changed gradually f rom zero to a value c o r r e - sponding to failure of the roll.

It was established that the breakdown in intactness of the roll (separation) occurs close to the spool with a relat ive radius of winding of p = 1.00-1.15, i .e. , in the a rea where the grea tes t tangential s t r e s se s occur in t r ansve r se oscillations.

Figure 14 shows the relat ionship of failure acce lera t ion to the force of tension in winding. It may be noted that the amount of this acce lera t ion is pract ical ly independent of the frequency of oscil lations and is determined pr imar i ly by the residual s t r e s se s in the wound body.

Under the act ion on the roll of c i rcumferen t ia l loads ( " s t a r t - s t o p " conditions, acce lera ted rewinding in serv ice of recording equipment) the layers of magnetic tape may slip relat ive to one another, forming i r - revers ib le defects.

On the basis of the above-accepted premises on the continuity and cyl indrical or thotropy of the wound body, the following express ion was obtained determining the amount of the minimum allowable in ter turn p re s - sures under the action of the above loads:

0o ~ 7-b ~" (1--~l 4) _{_ O~r, (21) r 4g.~t 2./fr

where j is the angular acceleration of the roll; ~, specific gravity of the tape material; b, outer radius of the roll; ~?, ratio of the radius of the spool to the outer radius of the roll; ffr, coefficient of friction between the turns; a~, additional stress occurring as a result of the action of centrifugal acceleration,

o, [ - ,or + (3 + ,or) + k3- . (3 + ] ~7 g-~ - ~ ) (I3 + ~o~) ~ _ ~o~ + ~2~. (~ + ~o~) "p~-' - - (l~ - - ~o~) ~ + ~o~ + k-2~'(~ - ~o~) P - - (3 + ~o,)" P~ ;

(22)

and ~ is the maximum angular ra te of rotat ion of the roll.

Figure 15 shows relat ionships of the radial residual s t r e s se s at which the danger of separat ion of the rol l occurs to angular acce le ra t ion in braking drawn with the use of Eq. (21) for rol ls of 1-4406 magnetic tape. Exper iments made on a stand imitating " s t a r t - s t o p " se rv ice conditions showed that Eq. (21) determines the necessa ry winding s t r e s s e s with a sufficient degree of accuracy .

1.

2.

3.

4.

5.

6.

7.

8.

LITERATURE CITED

F.. S. Umanskii, I. E. Debrivnyi, and V. V. Kryuchkov, "An investigation of the strength and deformability of magnetic-carrier-type thin composite materials. Report I. Strength and deformability at increased temperatures," Probl. Prochn., No. 5, 40-45 (1972). E. S. Umanskii, V. V. Kryuchkov, I. E. Debrivnyi, et al., "A stand for investigating the creep and long-term strength of magnetic-carrier-type composite films at increased temperatures," Probl. Prochn., No. 5, 103-107 (1973). E. S. Umanskii, V. V. Kryuchkov, I. E. Debrivnyi, etal., "Aunitforinvestigatingthecreepandlong-terrn sflrength of film materials at increased temperatures," Probl. Prochn., No. 9, 107-111 (1973). E. S. Umanskii, V. V. Kryuehkov, N. S. Shidlovskii, et al., "An investigation of the dynamic characteristics of magnetic tapes and their bases in longitudinal oscillations," Tekh. Sredstv Svyazi, Set. OT,

No. 2(6), 74-80 (1977). E. S. Umanskii, I. E. Debrivnyi, and V. V. Kryuchkov, "An investigation of the strength and deformability of magnetic-carrier-type thincornposite materials. Report 2. Strength and deformability at low ~mperatures," Probl. Prochn., No. 12, 50-54 (1972). E. S. Umanskii, I. E. Debrivnyi, V. V. Kryuchkov, and I. E. ll'yushek, "An investigation of the elastic characteristics of magnetic carriers by the dynamic method," Vopr. Radioelektron., Ser. OT, No. 9,

60-67 (1972). A. L. Rabinovich, An Introduction to the Mechanics of Reinforced Polymers [in Russian], Nauka, Mos- cow (1970). G. S. Pisarenko, A. P. Yakovlev, and V. V. Matveev, The Vibration Absorbing Properties of Con- s t ruct ional Materials [in Russian] , Naukova Dumka, Kiev (1971).

1304

9. G.S. Pisarenko, "A new approach to describing a mechanical hysteresis loop in the theory of mechani-

cal oscillations," Probl. Prochn., No. 6, 21-22 (1971). i0. E.S. Umanskii, V. V. Kryuchkov, and S. S. Veremchuk, "Creep and recovery of composite films at

increased temperatures," Probl. Prochn., No. 7, 111-115 (1973). ii. E.S. Umanskii, V. V. Kryuchkov, N. S. Shidlovskii, et al., "Temperature shrinkage of magnetic tape;'

Tekh. Sredstv Svyazi, Ser. OT, No. 2(6), 81-89 (1977). 12. E.S. Umanskii, V. V. Kryuchkov, and V. A. Rakovskii, "The question of determining the stressed

condition of magnetic tape wound in a roll," Probl. Prochn., No. 3, 83-85 (1978). 13. E.S. Umanskii, V. V. Kryuchkov, V. A. Rakovskii, et al., "An investigation of relaxation of stresses

in magnetic tape wound in a roll," Vestn. Kiev. Politekh. Inst., IViashinostr., No. 17, 3-7 (1980).

CRITERIA OF ADHESIVE- COHESIVE EQUALITY OF STRENGTH

AND THE HEAT RESISTANCE OF PROTECTIVE COATINGS

B. A. Lyashenko UDC 620.191.355;536.495;686.4

Recommendations or quantitative criteria on the optimum ratio of adhesive and cohesive strength of coatings are lacking in the literature sources known to us. In [i] it was noted that an increase in cohesion does not always lead to an increase in adhesion and the reverse. In [2] it is called the optimum case when the adhesive, cohesive, and autohesive forces of a heterogeneous system are equal. At the same time, it is em- phasized that excessive strengthening of one link occasionally leads to weakening of the system as a single

chain.

An analysis of failure of coatings and adhesive bonds in strength tests of them is an indication of the very broad range of ratios of adhesive and cohesive strength. In tests of coatings by the method of pressing out of a depression, the ratio of adhesion and cohesion across the depth of the depression at which peeling or cracking of the coating occurred was determined. The ratio of the adhesive strength to the cohesive lies in the 0.25 to 2.87 range, i.e., within the limits of a whole order of magnitude.

In [4] the qualitative ratio A > ~t < ~T was proposed as the basic condition of cracking or peeling of a coating, where A is adhesion, fit is the residual stresses in the coating, and fiT is the cohesive strength of the coating. Attempts [5] have been made to optimize the ratio of adhesive and cohesive strength for composite materials reinforced with fibers. For full realization of the cohesive strength fff of a fiber reinforcement with a diameter of d and a length of I the minimum adhesive strength in shear Tad must satisfy the ratio Tad ->

~f(d/2 l).

In determining the rat io of the necessa ry adhesive and cohesive strengths of a coating such ext remes are encountered as the hyperbolized role of cohesion with total neglect of adhesion. It is assumed that insuf- ficient adhesive s t rength is the resu l t of unsat isfactory preparat ion of the surface, and the quality of coatings is determined only by the cohesive strength.

For a soundly based choice of coating mater ia l and its thickness and elast ic proper t ies and also for op- t imum production conditions in application of the coating it is necessa ry to have a c r i t e r ion of a d h e s i v e - c o - hesive equality of s t rength of a coating. For this purpose let us use relat ionships between the s t r e s sed condition of the coating, the base, and the plane of adhesive contact [7], using the designations in [7].

Cohesive failure occurs under the act ion of s t r e s s e s in the coating ~c caused by cr i t ica l deformation of the base ecr when these s t r e s ses are equal to the tensile s t rength of the coating (~c = ~Tc). Upon reaching the base cr i t ical deformation ecr adhesive peeling in the zone of the c rack formed must occur simultaneously with cohesive failure of the coating. Only under such conditions will the propert ies of the coating mater ia l and of adhesive contact be used in full measure . The optimum adhesive s t rength Tad will be at equality with the value of tangential s t r e s se s Tma x in the plane of adhesive contact [7]:

Cmax = ear& .Ech .th (kl), (1)

Institute of Strength P rob lems , Academy of Sciences of the Ukrainian SSR, Kiev. Translated f rom Prob - lemy Proehnost i , No. 10, pp. 114-116, 126, October, 1980. Original ar t ic le submitted April 21, 1980.

0039-2316/80/1210-1305507.50 �9 1981 Plenum Publishing Corporat ion 1305

Documents

Supporting capacity of roll polymer films