FRACTURE PULSATING Z.

I.

OF

BRITTLE

MATERIALS

UNDER

LOAD Polyakov

and

A.

V.

Vshivtsov

UDC 539.4

In s o m e types of m a c h i n i n g of b r i t t l e m a t e r i a l s , e.g., d u r i n g u l t r a s o n i c m a c h i n i n g , the p a r t is e x p o s e d to the i m p a c t of a b r a s i v e g r a i n s [1, 2]. This p r o d u c e s pits on the s u r f a c e of the m a t e r i a l being w o r k e d . The a m p l i t u d e of an i m p a c t p u l s e c a u s e d by a b r a s i v e g r a i n s is not l a r g e (a few tens of kg) while the d u r a t i o n of a pulse is m e a s u r e d in t e r m s of tens of m i c r o s e c o n d s . It is i n t e r e s t i n g to c o n s i d e r the s t r e n g t h of b r i t t l e m a t e r i a l s , such as g l a s s , under p u l s e loading of this type. In this p a p e r we give s o m e e x p e r i m e n t a l d a t a on the f a i l u r e of g l a s s d u r i n g d y n a m i c l o a d i n g by a c e r m e t i n d e n t e r . The i n v e s t i g a t i o n was c o n c e r n e d with the shape of the c r a t e r and involved the d e t e r m i n a tion of the r e l a t i o n s h i p between its d i m e n s i o n s , tip r a d i u s , and i m p a c t p u l s e a m p l i t u d e . A c o m p a r i s o n of the r e s u l t s obtained under s t a t i c and d y n a m i c loads is given. The t e s t s w e r e c a r r i e d out on a s p e c i a l l y made a p p a r a t u s shown in Fig. 1. S p r i n g m e c h a n i s m 1 a c c e l e r a t e s s t r i k e r 2 whose i m p a c t on wave c o n d u c t o r 3 e x c i t e s in it a s t r e s s p u l s e . S p e c i m e n 4 is p l a c e d between wave c o n d u c t o r 3 and a s e c t i o n a l m e a s u r i n g rod 5. A c e r m e t indenter with a s p h e r i c a l tip was s o l d e r e d to the b o t t o m p o r t i o n of rod 5. The r o d c a r r i e d a p i e z o t r a n s d u c e r 6 r e c o r d i n g the s i z e of the i m p a c t pulse. The c r o s s - s e c t i o n a l a r e a s of all e l e m e n t s of the m e a s u r i n g r o d 5 w e r e s e l e c t e d in such a m a n n e r that they s a t i s f i e d the condition of e q u a l i t y of t h e i r a c o u s t i c r e s i s t a n c e s . The l e n g t h of the wave c o n d u c t o r and the m e a s u r i n g rod. as well as the point at which the s e n s o r was mounted w e r e s e l e c t e d so as to avoid s e c o n d a r y i m p a c t s of the i n d e n t e r on the s p e c i m e n and that the wave r e f l e c t e d from the f r e e end of the m e a s u r i n g rod had no t i m e to s u p e r i m p o s e its v i b r a t i o n s on the waves r e c e i v e d by s e n s o r 6. The s e n s o r s i g n a l was a p p l i e d to an OK-17M o s c i l l o s c o p e with a s i n g l e s l a v e sweep. P i e z o t r a n s d u c e r 6 was c a l i b r a t e d on a v e r t i c a l i m p a c t t e s t i n g machine by the conventional method [3]. The d e s c r i b e d a p p a r a t u s p r o d u c e s i m p a c t p u l s e s with a d u r a t i o n of 1 5 - 2 5 p s e c and an a m p l i t u d e f r o m 0.5 to 200 kg. P u l s e d u r a t i o n was v a r i e d by the use of s t r i k e r s of d i f f e r e n t l e n g t h s . It is kaaown f r o m [4] that if a s p h e r e is s t a t i s t i c a l l y p r e s s e d into a b r i t t l e m a t e r i a l , the f a i l u r e b e gins by f o r m i n g a c i r c u l a r c r a c k along the i m p r e s s i o n contour which r e a c h e s deep into the m a t e r i a l as a d i v e r g i n g cone. Under d y n a m i c load the f r a c t u r e a p p a r e n t l y a l s o begins by f o r m i n g a s i m i l a r c r a c k . F i g u r e 2a shows a g l a s s s p e c i m e n s u b j e c t e d to a s m a l l - a m p l i t u d e i m p a c t . The r i n g f o r m e d by the c i r c u l a r c r a c k can be seen on the d i a g r a m . I n s i d e this r i n g the m a t e r i a l is not d i s p e r s e d s i n c e a c r a t e r was not f o r m e d . With i n c r e a s i n g i m p a c t a m p l i t u d e the m a t e r i a l is f r a c t u r e d i n s i d e the p r e s s u r e contour (Fig. 2b). The longitudinal s e c t i o n through the c r a t e r obtained d u r i n g d y n a m i c f r a c t u r e is. shown d i a g r a m m a t i c a l l y in Fig. 3. The d i s p e r s e d b r o k e n m a t e r i a l s t i l l inside the c r a t e r has a d i f f e r e n t a p p e a r a n c e . The inside of the c r a t e r with an angle a . is f i l l e d with tiny g l a s s p a r t i c l e s of v a r i o u s s h a p e s . T h e y a r e tightly p a c k e d into a c l e a r l y v i s i b l e opaque m a s s (Fig. 2b). The c o m p r e s s e d m a s s of p a r t i c l e s extends f r o m the i n t e r i o r of the cone (Fig. 3). The s u r f a c e of this m a s s has a s p h e r i c a l p i t with a r a d i u s p c o r r e s p o n d i n g to the r a d i u s of the i n d e n t e r s p h e r e . The p e r i p h e r y of the upper p a r t of the c r a t e r with angle/~ contains f r a c t u r e d m a t e r i a l c o n s i s t i n g of thin l a m i n a s with t r a n s p a r e n t edges r e s t i n g on the c r a t e r s u r f a c e . T h e s e l a m i n a s a r e much g r e a t e r than the c o m p r e s s e d p a r t i c l e s . Like other s t a t i c f r a c t u r e s [5], the c r a t e r has a total depth H, inner cone depth h, and d i a m e t e r s D on the s u r f a c e and d at the l e v e l w h e r e the c r a t e r angle changes. S. O r d z h o n i k i d z e C h e l y a b i n s k M a c h i n e - T o o l P l a n t . T r a n s l a t e d f r o m P r o b l e m y P r o c h n o s t i , No. 12, pp. 60-62, D e c e m b e r , 1974. O r i g i n a l a r t i c l e s u b m i t t e d M a r c h 27, 1973.

9 1975 Plenum Publishing Corporation, 227 West 17th Street, New Yurk, N. Y. 10011. No part o f this publication may be reproduced, stored in a retrieval system, or transmitted, in any fi~t'm or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission o f the publisher. ,4 copy o f this article is available from the publisher for $15.00.

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6 4

J Z

j!

Fig. 1

Fig. 2

Fig. 1. Schematic d i a g r a m of experimental apparatus. Fig. 2. Type of f r a c t u r e of g l a s s under dynamic contact load: a) formation of c r a c k along the i m p r e s s ion contour; b) f r a c t u r e of material inside the p r e s s u r e contour. The investigation included the experimental determination of the dependence of c r a t e r size on impact amplitude and indenter radius. The specimens were made from the same batch of 2.5 mm thick window glass. F i g u r e 4 shows the relationship between c r a t e r depth H and impact pulse amplitude obtained for a s p h e r e radius of 60 pm and a pulse duration of 20/~sec. The c r a t e r depth was m e a s u r e d under a MBI-3 binocular m i c r o s c o p e with the AU-12 binocular head using a fine-focusing m i c r o m e c h a n i s m [6]. Because of the dispersion of the s t r e n ~ h p r o p e r t i e s of glass a wide s c a t t e r of experimental points was observed. The s t a t i s t i c a l p r o c e s s i n g of experimental data produced an e x p r e s s i o n linking c r a t e r depth H with impact pulse amplitude P m : H = A1 (P,~ -- B).

(1)

The analytical relationships were found for eight indenter radii within the range 10-120 /~m. In all c a s e s the type of relationship between depth H and impact amplitude P m r e m a i n e d unchanged. It was found that coefficient A 1 r e m a i n e d constant for the tested material (A1 = 0.0017 m m / k g ) while the B value was found to depend on indenter radius p. hi c o n t r a s t to the r e s u l t s obtained in [7] for static loading, the d e pendence of ]3 on indenter radius is d e s c r i b e d by the p a r a b o l a B = Co 2. The C value r e m a i n e d constant for the investigated m a t e r i a l (C = 1724 k g / m m 2 ) . The r e l a t i o n s h i p between other c r a t e r d i m e n s i o n s , impact pulse amplitude, and indenter radius were of the s a m e nature and can be d e s c r i b e d by the following exp r e s s ions: h = 0 , 0 0 0 7 3 (Pro - - 1724,o"-);

D -- 0 , 0 2 2 d = 0.0072

(P,.,, - - 1724p=); ( P , , , - - ]724p2).

(2)

A change in pulse duration within the range 15-25 psec has no m a r k e d effect on the above r e l a t i o n s h i p s . E x p r e s s i o n s (1} and (2) provide the m i n i m u m impact pulse amplitude P m m i n , c h a r a c t e r i z i n g the f o r mation of the c r a t e r P m m i n = Cp 2. F i g u r e 5 shows the r e s u l t s of e x p e r i m e n t a l determination of m i n i m u m

1484

/

-

H ,um

~

80

~0

f

nin, Rg lO

z...

p:60gm

/

o

Fig. 3

25

50

75

Pm,kg

0

~ 25

Fig. 4

o

5O

75

p, ~m

Fig. 5

Fig. 3. Longitudinal section of c r a t e r obtained by dynamic contact loading of g l a s s . Fig. 4. C r a t e r depth H as a fraction of impact pulse amplitude PmFig. 5. Minimum b r e a k i n g force as a function of indenter radius for dynamic (1, 2) and static (3) loading.

impact pulse amplitude Pmmin. The experimental points thus obtained satisfy the expression Pmmin = 1784 pi.96 (curve 1). Curve 2 corresponds to the earlier determined relationship Pmmin = 1724 02. These curves satisfactorily agree with one another. In the work being described the last strength characteristics obtained in dynamic and static contact loading were compared. The static load was applied using a spring dynamometer; the loading time was 5-20 sec. Figure 5, curve 3 represents the relationship between the minimum static breaking force P and the indenter tip radius. During dynamic contact loading of glass the minimum impact pulse amplitude was ~7 times larger than the minimum breaking force in static loading. The phenomenon of increase in glass strength when changing from static to dynamic loading conditions at a pulse length of 20 usec is also observed when comparing Eqs. (1) and (2) with similar relations for static loading. The static force producing a crater of the same size as a certain impact pulse, is only a seventh of the amplitude of this impact pulse. LITERATURE CITED 1.

2. 3. 4. 5. 6. 7.

L. D. Rozenberg and V. F. Kazantsev, "On the physics of ultrasonic machining of materials," Dold. A-lind. Nauk SSSR, 124, No. 1 (1959). A. I. Markov, Ultrasonic Cutting of Hard Materials [in Russian], Mashinostroenie, Moscow (1968). G. S. Batuev, Yu. V. Golubev, et al., Engineering Methods of Investigation of Impact Processes [in Russian], Mashinostroenie, Moscow (1969). N. N. Kachalov, Foundations of Glass Grinding and Polishing Processes [in Russian], Izd. AN SSSR, Moscow (1949). L. L. Shreiner, Hardness of Brittle Bodies [in Russian], Tzd. AN SSSR, Moscow-Leningrad (1946). T. ]3. Lavrov and T. V. Ermakova, Volume Measurements under Microscope. Abrasive and Diamonds. Scientific-Technical Reference ]3ook [in Russian], No. 1, Izd. NIImash, Moscow (1965). V. F. Kazantsev,"Ultrasonic cutting," in: Physics and Technology of Strong Ultrasonic Vibrations [in Russian], Nauka, Moscow (1970).

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