A P P A R A T U S F O R S T U D Y I N G D E F O R M A B I L I T Y

M A T E R I A L S U N D E R T W O - W A Y S T R E T C H I N G

E . S. U m a n s k i i a n d S. S. V e r e m c h u k

OF SOFT

UDC 620,171.2

Study of the mechanica l p rope r t i e s of soft re inforced p las t i cs , natural l ea ther and l ea the r - l i ke ma te - r i a l s , f i lms , natural rubber , and vulcanized rubber under two-way s t re tching is of g r e a t p rac t ica l s ignif i - cance, since w a r e s made of these m a t e r i a l s a re subjected to the two-dimensional s t r e s s s ta te during manu- fac ture and use .

The indicated m a t e r i a l s a re apprec iab ly deformed at compara t ive ly sma l l s t r e s s e s , and a study of the i r mechanica l p r o p e r t i e s is the re fo re imposs ib le on equipment and by methods used for invest igat ing meta l s and other " r ig id" m a t e r i a l s .

The mos t widely used method of studying two-dimensional s t r e s s s ta tes in soft m a t e r i a l s is the f o r m a - tion of a spher ica l sur face by applying hydros ta t ic p r e s s u r e to a c i r cu l a r plate with the m a t e r i a l c lamped about the pe r iphery [1-6]. By this method it is poss ible to invest igate s t rength and deformabi l i ty only for the case of quasihomogeneous s t r e s s s ta tes , when the pr incipal s t r e s s e s at and 0" 2 at points over a cons ide r - able pa r t of the bulging plate have the same values .

Study of deformabi l i ty for other re la t ions among the pr incipal s t r e s s e s should be made on c r u c i f o r m samp le s loaded in the plane of deformat ion .

In the appara tus used for invest igat ing the indicated c l a s s of m a t e r i a l s [7, 8], loading in both d i r e c - t ions was effected d i rec t ly by application of weights, and this did not pe rmi t s imple loading to give the de- s i r ed loading ra te and to maintain constant ra te during test ing at any given ra t ios between loads.

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Fig. 1 Fig. 2

Fig. 1. Kinemat ic scheme of the appara tus .

Fig. 2. At tachment of r e s t r a in ing fas tenings to the sample : 1) e las t ic fastening; 2) s a m - ple; 3) s c rew; 4) s c rew c lamp; 5) c lamps .

Kiev Polytechnic Inst i tute. Trans la ted f rom Prob lemy Prochnost i , No. 2, pp. 85-88, August, 1969. Original a r t ic le submit ted December 26, 1968.

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Fig. 3. Deformabi l i ty cu rves of polyvinyl chloride f i lms under uniaxial tension along the ca l - ender ing di rec t ion (1) and a c r o s s it (2): a) 107o SKN-40 rubber ; b) 2070 SKN-40 rubber ; c) 30% SKN-40 rubbe r .

Fig. 4. Deformabi l i ty cu rves of polyvinyl chloride f i lms under two-way s t re tching: a) 10% SKN-40 rubbe r ; b) 20?o SKN-40 rubber ; c) 30% SKN-40 rubber .

Appara tus meet ing these r equ i r emen t s was made by the authors of this paper . It p e rmi t s one to study the deformabi l i ty of soft m a t e r i a l s at any ra t ios between pr incipal s t r e s s e s and over a wide range of loading or deformat ion r a t e s .

The test ing appara tus (Fig. 1) cons i s t s of two identical kinematic networks combined on a single f r a m e . Each network is designed for loading a sample in one direct ion, and in each of them there is a " m e c h a n i s m for loading, a mechan i sm for select ing deformat ion range, and a mechan i sm for recording load and deformat ion .

The sample (1) is loaded and its range of deformat ion se lec ted by means of a f lexible e lement (cord) (2), which is connected at its f r ee ends to f o r m a hinge joint by means of c l amps (3) and through pulleys (4, 5, and 6) to a sl ide b a r (7), which may be displaced ver t ica l ly in guides (8). A sample is loaded in each d i rec t ion by means of a l ever loading mechan i sm. A weight (9) of the given value is d isplaced s imul tane- ously and at constant ra te by f i r s t - c l a s s l eve r s of the s y s t e m (10), which have the same a r m length for each d i rec t ion of loading. Loading on the sample is t r ansmi t t ed through a s l i d e - b a r - p r i s m i l l ) , which is the fu l c rum for shor t a r m s of s econd -c l a s s l e v e r s , the slide b a r (7), and the cord (2). The l eve r s are ba lanced by weights (12). ~he weights a re shifted along the lever a r m s by means of an endless thread (13) connected to the ca tches on the weights and to a nut (14) that produces forward movement as a s c rew (15) is turned. Ro ta ry movemen t is t r ansmi t t ed to the sc rew by an e lec t r ic motor (16) through a two-s tage worm reducing g e a r and a detachable b e v e l - g e a r coupling (17). By appropr ia t e sett ing of this coupling it is possible to change the r a t e of displacing the weights along the lever a r m s and thus the ra te of loading. In acldition, the loading ra t e may be a l t e red by changing the value of the displacing weights (9).

During loading of the sample , constant se lect ion of deformat ion range is made, and, even more signif- icant, the l ever a r m s a re mainta ined constantly in a horizontal posit ion. These effects a re brought about in the following way. With inc rease in deformat ion the f i r s t - c l a s s l eve r s a re deflected downward somewhat,

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closing a contact (18) that switches on the electr ic motor (19), which rotates the screw (21) through the two- stage worm reducing gear and the b e v e l - gear coupling (20). The nut (22), rigidly attached to the slide rod (7), is displaced downward with the rod and the load a rm of the lever again occupies a horizontal position and the c i rcui t o f thee lec t r i c motor (19) is disconnected. Contacts (23) close the same circui t when load is removed.

During loading, the screw (21) may be displaced ver t ical ly relat ively to the b e v e l - g e a r coupling (20), and this makes possible uniform increase of load on the sample. Constant selection of deformation range and maintenance of the levers in a horizontal position permit one to test mate r ia l s undergoing severe de- format ion.

Record of the tension diagram for each direction of loading is made on mi l l imeter paper fastened to drums (24) by means of pencils attached to the levers (25) and displaced with the weights (9) during rotation of the drums, the displacement being proportional to the deformation read f rom the sample. The drums are rotated by threads (26) with weights (27). Deformation of the sample is read by threads (29) attached to screw clamps that are fastened to the active parts of the sample, and the value is amplified by double pul- leys (30) and a sys tem of triple pulleys (28) and drums. The scale of the deformation record thus depends on the relat ions between the d iameters of double pulleys, triple pulleys, and drums, and the scale of the loading record depends on the values of the weights (9).

The apparatus provides for recording changes of load and deformation with time by means of an ordinary s t ra in-gage setup. For this purpose a ring dynamometer (31) is placed between the clamps and the cord of each line of loading, and strain gages in the form of flexible elastic fastenings (Fig. 2) are at- tached to the active par ts of the sampleby means of screw clamps. Resis tance gages are cemented to the dynamometers and the fas teners and are connected to an ordinary bridge c i rcui t . The record of changes in load and deformation with time is made by an ]~PP-09 potenitometer .

The s train proper t ies of polyvinyl chloride fi lms with 10, 20, and 30 par ts per weight of SKN-40 rub- be r per 100 par ts polyvinyl chloride were investigated by means of the apparatus descr ibed above. In addi- tion to rubber, the f i lms contained the 100 parts of polyvinyl chloride, 20 par ts dibutylphthalate p las t ic izer and 30 par ts dioctylphthalate plas t ic izer , 3 par ts calcium stearate s tabi l izer , 4.2 par ts dyes, and 13.8 par ts chalk f i l ler . The test samples were cut so that one direction of loading corresponded to the direction of calendering. The dimensions of the active par ts of the sample are 30 x 30 mm. Deformation was measured at thecen te r of the active part of the sample on a segment measur ing 14 x 14 mm.

In order to assure uniform distribution of loading ac ross the section of the active part of the sample, incisions 15 mm long were made in the segments f rom the c lamps to the active part .

Depending on the relat ions between loads, the rate of loading (along the calendering direction) was made 12-25 kgf /cm 2 per minute.

Changes in loading and deformation with time were recorded by means of a s t ra in-gage setup. In recording loading, the minimal value of a scale division on the potentiometer was 0.05 kg, and for the de- formation record it was 0.02 mm.

Uniaxial s tretching of f i lms was tested on an FM-250 machine. Curves were obtained for the de- pendence of uniaxial deformation on s t r ess conditions at room temperature for uniaxial (Fig. 3) and two- dimensional (Fig. 4) s tretching. To the right of the ordinate axis (Fig. 4), tension curves have been plotted for the calendering direct ion; on the left the curves are for s t retching ac ross the calendering direction. The arabic numera ls on Fig. 4 represent the ratio between s t r e s ses in the longitudinal and t ransverse di- rec t ions . The larges t of the principal s t r e s se s is taken in the calendering direction.

For compar ison with curves of two-dimensional s tretching the initial segments of the d iagrams for uniaxial tension (0, oo) are plotted on Fig. 4. From the cited data it is seen that, with increase in rubber content, under both uniaxial and two-dimensional tension, the strength of the f i lms declines, the deform- ability increases , and the calendering effect is manifested to l e s se r degree. During two-dimensional s t re tch- ing the rigidity of the fi lms is considerably higher than during uniaxial tests, and the rigidity increases with increase in the ratio between the principal s t r e s se s .

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5, 6. 7. 8.

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

G. M. Barten'ev, B. A. Dogadkin, and N. M. Novikova, Zh. Tekh. Fiz., 28, No. 19 (1948). L. Tre loar , Physics of the Elasticity of Rubber [Russian translation], IL (1953}. A. D. Kravchenko, University Bulletin, The Technology of the Light Industry [in Russian], No. 4 (1958). E. S. Umanskii and A. D. Kravchenko, in: Scientific Transactions of the Ukrainian Scientific Research Institute of the Leather and Shoe Industry [in Russian], No. 14, Kiev (1963}. V. V. Lavrent 'ev and O. F. Shlenskii, Kauchuk i Rezina, No. 11 (1966). V. V. Lavrent 'ev and O. F. Shlenskii, Zavod. Lab., No. 5 (1966). A. B. Gubenko et al., Pneumatic Structural Designs [in Russian], Moscow (1963}. L. I. Yarin, Mekhanika Polimerov, No. 1 (1966).

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