EFFECT

OF

S. I.

SURFACE-ACTIVE

MEDIA

ON P O L Y M E R

STRENGTH

Mikitishin

UDC 678:539.4.019+541.013.5

Previous investigations [1-3] have shown that, depending on the size of the stress concentrators (fissure type), the strength of polymers in surface-active media either increases or decreases in comparison with that in air. The technical strength of solid bodies is largely governed by their number of defects. Thus the theory of fissures readily explains both the increase in the strength of inorganic glass attained by removing the defective surface layer (the Ioffe effect), and its decrease in active media as a result of the reduced surface energy of the solid (Rebinder effect) [4]. I have attempted to explain the change in polymer strength in surface-active media from the viewpoint of the theory of fissures. Figure 1 plots the strength of polymethylmethacrylat e (PMMA) specimens* in active media vs the length of the outer fissure. It will be seen that the breaking stresses of specimens without artificial fissures or short fissures are less in water, alcohol and kerosene than in air, and that for specimens with large fissures the stresses are far greater in these media. Following [4], to explain the change in strength of PMMA specimens with outer fissures we shall use the model shown in Fig. 2. Assuming that the depth 5 of penetration of the medium into the material at a given stress and temperature in a specific period is the same in all directions, the length of the fissure l and the radius of curvature of its apex p may be represented as t=10~ 6, R=~0+~. * C r o s s section 1 •

(1)

mm, rate of elongation 5 mm/min, test t e m p e r a t u r e 20~

2

Fig. 1

l. rain Fig. 2

Fig. i. Strength of PMMA specimens, plotted vs length of outer fissure: 1) air; 2) water; 3) alcohol; 4) kerosene. Fig. 2. Diagram of the increase in defect size under the effect of surface-active media. P h y s i c o m e c h a n i c a l Institute, A c a d e m y of Sciences of the Ukraine, L'vov. T r a n s l a t e d f r o m FizikoKhimicheskaya Mekhanika Materialov, Vol. 8, No. 3, pp. 113-114, May-June, 1972. Original article submitted F e b r u a r y 12, 1970. 9 1074 Consultants Bureau, a division of Plenum Publishin~ Corporation, 227 ff'est 17th ('~treet, New York, N. Y. 70011. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in uny .form or by any means, electronic~ mechanical, photocopying~ microfilming, recordin~ or otherwise, without written permission of the publisher. .1 copy of this article is available from the publisher for $75.00.

375

The plasticized surface layer of thickness 6 may be regarded as nonload-bearing, because under the effect of the medium its s t r e s s e s relax more rapidly than in the r e m a i n d e r of the specimen [6] and failure o c c u r s below this layer. T h e r e f o r e we must also take into account the d e c r e a s e in the s p e c i m e n ' s c r o s s section due to formation of a l a y e r of thickness 6 :

S=So--Lb.

(2)

where SO is the initial c r o s s section and L is its p e r i m e t e r . To verify Eq. (2), we tested PMMA specimens of various thicknesses (0.25-3 mm) without artificial f i s s u r e s , retained beforehand (~ 10 min) in water, kerosene, alcohol, and acetone. The 6 values obtained from m e a s u r e m e n t s of PMMA strength in each of these media for specimens with different ratios of the c r o s s - s e c t i o n a l a r e a to the p e r i m e t e r are similar: ~ 0.4, ~ 0.09, ~ 0.12, and 0.3 mm for water, kerosene, alcohol, and acetone, respectively. The calculated 5 values are s i m i l a r to those observed by penetration of a colored medium. However, the d e c r e a s e in the c r o s s - s e c t i o n a l a r e a due t o the swollen l a y e r cannot c h a r a c t e r i z e the PMMA strength in media because the free surface energy of the material and the factor of s t r e s s concentration still d e c r e a s e . According to Inglis [5], the s t r e s s at the apex of a fissure, as follows:

ef, is related to the applied s t r e s s , ~,

p--

(3) where l is the depth of the ellipsoidal fissure, and p is its radius of curvature at the apex. F o r a m a t e r i a l deformed in s u r f a c e - a c t i v e media the p a r a m e t e r s in the right-hand part of Eqo (3)willbe different from those obtained in air. Thus under the effect of s u r f a c e - a c t i v e substances the free surface energy of a solid dec r e a s e s , which is equivalent to a d e c r e a s e of a f in Eq. (3). F u r t h e r m o r e , according to Eq. (2), the factor of s t r e s s concentration "]l/p will v a r y with the ratio of the p a r a m e t e r s l, p, and 5. Assuming that the radius of curvature of the apex of short and long f i s s u r e s is the same, it will be seen from Eq. (3) that when l is commensurable with p and 5 (in the case of specimens with no f i s s u r e s or only short fissures), the factor of s t r e s s concentration will v a r y little or remain constant. Hence owing to the d e c r e a s e of the surface energy of the p o l y m e r and its c r o s s - s e c t i o n a l area, the strength of specimens in s u r f a c e - a c t i v e media must decrease. When l >> 5 and p ~ 5 (specimens with large fissures) the dec r e a s e in the s t r e s s concentration becomes predominant [6], and the strength of the specimens in s u r f a c e active media i n c r e a s e s . A s i m i l a r dependence of PMMA strength in s u r f a c e - a c t i v e m e d i a on the radius of curvature of a V-shaped s t r e s s concentrator was noted by Soshko et al. [3]. It may thus be i n f e r r e d that the overall effect of the change in p o l y m e r strength in s u r f a c e - a c t i v e media depends not only on the d e c r e a s e in the p o l y m e r ' s surface e n e r g y and the d e c r e a s e in the l o a d - c a r r y ing c r o s s section owing to swelling and solution of the m a t e r i a l ' s surface, but also greatly on the change in the factor of s t r e s s concentration in the material under the effect of the medium. We are v e r y grateful to P r o f e s s o r E. D. Shchukin for discussing the results. LITERATURE

1. 2. 3. 4. 5. 6.

376

CITED

A . I . Soshko, A. N. Tynnyi, and M. M~ Gudimov, Fiz.-Khim. Mekh. Mat., No. 5 (1965). S. L Mikitishin and N. D. Shcherba, Fiz.-Khim. Mekh. Mat., No. 6 (1966). A . I . Soshko, V. F. Koval', and A. N. Tynnyi, Fiz.-Khim. Mekh. Mat., No. 6 (1967). Symposium: Glass Strength [Russian translation], Izd. Mir (1969). C . E . Inglis, T r a n s . Inst. Nay. Archit., 55, 219 (1913). N . D . Shcherba, S. I. Mikitishin, et al., Fiz.-Khim. Mekh. Mat., No. 4 (1969).