Due to the assumption made ~ith respect to the existence of small values of 6ik in comparison with 1, the approach presented is sufficiently accurate for the diagnosis of the elastic characteristics cll, c22, cl2, and c~6 and consequently of Ell, Ez2, El2, and G66 but allows only an approximate assessment to be made of the other elastic characteristics of the composite. Thus, e.g., the e r r o r in the determination 6ik of 10% for a composite with organic or carbon fibers leads to an e r r o r in the determination of Ell, E2z, v~, and G66 of less than 1%. Thus, the pulse method is useful for measurement of the velocity of UO in composites with selected reinforcement schemes and stable properties of the components to determine the elastic characteristics of the material En, Ez2, vl,, and G66, the reinforcement coefficient ~r, the content by volume of different layers in the composite h I and h2, and the density p. The pDrosity of the material #p must be known. LITERATURE 1. 2. 3. 4. 5. 6. 7. 8.

CITED

I . A . Zudov and I. M. Zudova, "Determination of the rigidity characteristics of orthotropic materials with imperfect elasticity by the use of ultrasonic methods," Mekh. Polim., No. 2, 195-206 (1973}. M.V. Gershberg, S. V. II'yushin, and V. I. Smirnov, Nondestructive Testing Methods for Fiberglass Plastics in Shipbuilding [in Russian], Leningrad (1970}. A . I . Potapov and F. P. Pekker, Nondestructive Testing of Constructions Made of Composite Materials [in Russian], Leningrad (1977). A . K . Mahneister, V. P. Tamuzh, and G. A. Teters, The Strength of Rigid Polymeric Materials [in Russian], 2rid Edition, Riga (1972). T.D. Shermergor, Theory of Elasticity of Microinhomogeneous Media [in Russian], Moscow (1977). S.S. Abramchuk, "Propagation of elastic waves in some composite materials," Mekh., Polim., No. 3, 531-536 (1978}. A . L . Rabinovich, Introduction to the Mechanics of Reinforced Polymers [in Russian], Moscow (1970). Ya. A. Skhouten, Tensor Analysis for Physicists [in Russian], Moscow (1965).

TENSILE

TESTING

UNIDIRECTIONAL I.

G.

Zhigun

OF H I G H - S T R E N G T H COMPOSITES a n d V. V. M i k h a i l o v

UDC 620.17:678.067.5:539.4

The development of high-strength reinforcing fibers and their use in the fabrication of unidirectional polymer composites have led to considerable difficulties in obtaining stable values of the tensile strength of these materials. The analysis of numerous test data and the mode of specimen fracture indicate that the principal factors responsible for the difficulty of obtaining stable and reproducible tensile strength characteristics are slippage of the specimen in the grips of the testing machine, longitudinal debonding of the specimen at high loads, and the difficulty of obtaining specimen fracture in the required cross section. The f i r s t factor is especially characteristic of high-modulus composites reinforced with carbon, boron, and synthetic fibers. As a rule, slippage of the specimen in ordinary wedge-type grips begins at high stresses. As a result of slippage the surfaces of the specimen may be scratched, pitted, and spalled. Repeat loading of the specimen after slippage is often unsuccessful and merely aggravates the defects, causing the specimen to fail in the damaged area. To prevent slippage various auxiliary devices are used. These considerably complicate the test without completely solving the problem. A brief review of these techniques is given in [1, 2]. Slippage is one of the factors responsible for longitudinal debonding of the specimen, which usually begins in the grips as a r e s u l t of damage to the polymer matrix and spreads along the entire length of the specimen. Longitudinal debonding is a consequence of the low compressive strength of the composites at right angles to the plane of the laminations. It is characteristic of all unidirectional polymer composites with a strictly parallel arrangement of the laminations and the fibers, especially when the number of laminations is small and any random relative displacement is excluded. Debonding begins when the contact pressure on the bearing surfaces reaches values exceeding the transverse compressive strength of the composite. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. All-Union ScientificResearch Institute of Aviation Materials, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 717-723, July-August, 1978. Original article submitted May 24, 1977.

586

0032-390X/78/1404-0586507.50

©1979 Plenum Publishing Corporation

O1 OO

95 86--I05 125 117--131 106 100--109 115 108--121 102 90--I10

65 52--80 102 94--1t0

dumbbellshaped R-- 80 mm

I. . . . . .

108 lO0--1h4

82 60--95 115 109--123

88 80--95 118 tt0--128 105 IO0--1tO

g [ ~ ] p~e~sboard R~ ±z~ mrr]

with

cylindrical]

84 66--96 110 106--120

Duralumin D-16 80 68--92 I10 103--121

glass laminate

TenSile strenith of end reinforcement _

Plastics

I

•

1t8 1t2----t25

6O

I 10

90

i

1

60

~

I31 I27--t32

115

specimen base length, mm

,20

II7 I12--I21

50

w

t

119 118--I22

12o

of Different Shapes

glass-laminate end reinforcement of length, mm

Obtained Using Specimens

I24 i19--126

" 'specimen, kgf/mm 2

of the Tensile Strength Values for Carbon-Reinforced

........................................

Comparison

bar-shaped

1.

Remark: For each point we tested not less than t0 specimens. T h e s p e c i m e n s of d i f f e r e n t s h a p e ( d a t a g i v e n i n t h e c o l u m n s o f t h e t a b l e ) w e r e o b t a i n e d f r o m t h e s a m e s h e e t ; t h e s a m e m a t e r i a l s w e r e a l s o u s e d f o r v a r y i n g t h e l e n g t h of t h e e n d r e i n f o r c e m e n t and the specimen b a s e l e n g t h ° T h e g a u g e w i d t h o f t h e s p e c i m e n s w a s 10 r a m .

1,9

1,4

1,25

1,2

mm

ness~

thick-

Specimen

TABLE

Fig. 1. Mode of tensile f a i l u r e of s p e c i m e n s of unidirectional c a r b o n r e i n f o r c e d p l a s t i c s : a) longitudinal debonding of bar s p e c i m e n s in the g r i p s ; b, c) the s a m e for a s p e c i m e n with a t r a n s v e r s e c y l i n d r i c a l groove, r a d i u s 80 m m , and a d u m b b e l l - s h a p e d s p e c i m e n , r e s p e c t i v e l y ; d) d a m a g e to a bar s p e c i m e n in the g r i p s due to slippage; e) the s a m e for a dumbbell specimen. Fig. 2. Mode of tensile failure of s p e c i m e n s of unidirectional c a r b o n r e i n f o r c e d p l a s t i c s with r e i n f o r c e d ends: a, b) g l a s s - r e i n f o r c e d p l a s t i c r e i n f o r c e m e n t 120 and 60 m m in length, r e s p e c t i v e l y ; c, d) wood p r e s s board r e i n f o r c e m e n t 110 and 60 m m in length, r e s p e c t i v e l y ; e) D u r a l u m i n r e i n f o r c e m e n t 110 m m in length.

~A

Fig. 3. Loading of s p e c i m e n in self-tightening t a p e r e d g r i p s : 1) body of g r i p s ; 2) r o l l e r b e a r ings; 3) m o v i n g jaws; 4) s p e c i m e n . T h e s e two f a c t o r s m a k e it difficult to obtain the n e c e s s a r y mode of s p e c i m e n f r a c t u r e in the c r o s s section taken for calculation p u r p o s e s . A f u r t h e r c o m p l i c a t i o n is the f a c t that owing to the low s h e a r strength of unid i r e c t i o n a l c o m p o s i t e s it is not p o s s i b l e to use d u m b b e l l - s h a p e d s p e c i m e n s with e s t a b l i s h e d g e o m e t r i c p a r a m e t e r s [2]. Typical m o d e s of s p e c i m e n f a i l u r e p r o v o k e d by slippage, low s h e a r s t r e n g t h and low t r a n s v e r s e c o m p r e s s i v e s t r e n g t h a r e i l l u s t r a t e d in Fig. 1. The o c c u r r e n c e of these m o d e s of' f a i l u r e can be avoided in v a r i o u s ways [2, 3]. The best method is to r e i n f o r c e the ends of the s p e c i m e n [4]. However, as t r i a l s have shown, even this method cannot always e n s u r e failure of the s p e c i m e n in the r e q u i r e d section. As will be shown below, tensile testing of high-modulus c a r b o n and b o r o n - r e i n f o r c e d p l a s t i c s gives positive r e s u l t s only when the end r e i n f o r c e m e n t m a t e r i a l is c o r r e c t l y m a t c h e d with the specimen. Neglecting these f a c t o r s leads to f a i l u r e of the s p e c i m e n at the points of application of the load or n e a r the end r e i n f o r c e m e n t , with a c o n sequent i n c r e a s e in the s c a t t e r of the s t r e n g t h values. A graphic confirmation of this is provided by photog r a p h s of the f r a c t u r e of s p e c i m e n s of the s a m e c a r b o n - r e i n f o r c e d p l a s t i c (Fig. 2) tested a f t e r r e i n f o r c i n g the ends with different m a t e r i a l s .

588

4.

#

~ lg32

$

2

4

+'

5

~'

l t?

f3

O( ° --

2

,+_

_

Fig. 4

O- ~

°

9

L

_

13

~7

Fig. 5

Fig. 4. P a r a m e t e r s fif as a function of the t a p e r ~ of the grip jaws and the coefficient of f r i c t i o n f at ~=2°: f = 0 . 6 (I); 0.5 (2); 0.4 (3); 0.3 (4);

o.a (5); 0.15 (6). Fig. 5. Values of the parameter q~=l~; 2) ~=2°; 3) q~=3 °.

fi as a function of the angle ~:

I) at

When the reinforcement consisted of anisotropic material with stiffness in the principal directions less than or similar to that of the tested material, the specimen failed in the required cross section. The use of isotropie materials led to failure of the specimen near or beneath the end reinforcement (see Fig. 2). Establishing the conditions for obtaining stable values of the tensile strength of high-streng~1 unidirectional composites with allowance for the above-mentioned factors was the aim of our research. The specimen

can be considered reliably secured in the grips when the following condition is satisfied:

where P is the load applied to the specimen; specimen within the grips.

F is the force of friction on one of the lateral surfaces of the

For seLf-tightening tapered grips (Fig. 3) the expression for determining

the force of friction takes the

form

F=

p ~ 2 t~(~+q,)

P f~, 2

(2)

where f, the coefficient of friction of the composite with respect to the surface of the grips, depends on the type of reinforcement and its arrangement in the composite; ,~ is the reduced angle of rolling friction on the inclined surface of the grips; fi is a coefficient characterizing the transmission of normal pressure from the grips to the specimen. Using (2), we can write condition (i) in the form I~/'~ t.

(3)

Graphs of fif as a function of the angle ~ and the coefficient of friction f are presented in Fig+ 4. They clearly show the ranges of variation of the angle ~ and the coefficient of friction f that satisfy condition (3). The mean values of the coefficient of friction in the direction of reinforcement against the steel surface of jaw's grooved at an angle of~ 45 ° with a 1 ram interval are 0.26, 0.32, and 0.32 for carbon, boron, and glassreinforced plastics, respectively. For a well-machined steel surface these values were 0.17 for carbon and boron-reinforced plastics. As experiments have shown, increasing the velocity and pressure by an order has practically no effect on the values of the coefficients of friction of these materials. Knowing one of these parameters, we can ensure that the specimen is reliably clamped by making a correct choice of the values of the other. The coefficient of friction f can be improved by reinforcing the ends of the specimen with cover plates of wood pressboard or some other material with a better coefficient of friction than the composite being tested. The coefficient fi is determined by the taper of the jaws and the reduced angle of rolling friction 9~. The dependence of the values of fl on these parameters is indicated in Fig. 5 for the loading scheme in question.

589

In s e l e c t i n g the angle ~ it i s n e c e s s a r y to take into account not only the s a t i s f a c t i o n of condition (3) but a l s o the t r a n s v e r s e w e a k n e s s of unidirectional c o m p o s i t e s in c o m p r e s s i o n . A s m a l l angle ~ leads to the d e v e l o p m e n t of high v a l u e s of the n o r m a l p r e s s u r e , and consequent longitudinal debonding of the m a t e r i a l . To a v o i d longitudinal debonding it is n e c e s s a r y that q < R z - or t3R~+s < R ~ ,

(4)

Sl

w h e r e R z - , Rx + a r e the t r a n s v e r s e c o m p r e s s i v e s t r e n g t h and the tensile s t r e n g t h in the direction of r e i n f o r c e m e n t of the s p e c i m e n , r e s p e c t i v e l y ; s is the a r e a of the s p e c i m e n in the t e s t c r o s s section; s 1 is the a r e a of one of the l a t e r a l s u r f a c e s of the s p e c i m e n s u b j e c t e d to n o r m a l p r e s s u r e in the grips. F r o m condition (4) we h a v e si~p s

R~+ ,G-

(5)

or

_ Rx+ _~b t I';"I~RT- b, "

(6)

H e r e b and b i a r e the width of the s p e c i m e n in the t e s t c r o s s section and at the point of application of the load; l 1 is the length of the loading zone. Knowing the s t r e n g t h r a t i o and the v a l u e s of fl d e t e r m i n e d f r o m condition (3), we can e s t a b l i s h the n e c e s s a r y s p e c i m e n a r e a r a t i o s s l / s that exclude longitudinal debonding and slippage in the g r i p s . F o r m o d e r n h i g h - m o d u l u s c o m p o s i t e s the r a t i o R + ~ z - is 6-40. Satisfaction of condition (5) f o r the upper l i m i t of this p a r a m e t e r r e q u i r e s high v a l u e s of the r a t i o s s l / s . In its turn, e n s u r i n g the latter in the c a s e of s p e c i m e n s of n o r m a l length i m p o s e s c e r t a i n c o n s t r a i n t s on the d i m e n s i o n s of the gauge c r o s s section. This is p a r t i c u l a r l y evident f r o m an a n a l y s i s of (6). F o r a bar s p e c i m e n of unit t h i c k n e s s a change in the length of the loading zone l 1 c o r r e s p o n d s to a change in Sl/S. It is e a s y to s e e that even in the c a s e of s t r i p s of m i l l i m e t e r t h i c k n e s s at the upper v a l u e s of the p a r a m e t e r s entering into (6) the length of the loading zone (2l 1) is c l o s e to the t o t a l length of the s p e c i m e n s c u r r e n t l y used for d e t e r m i n i n g the s t r e n g t h of r e i n f o r c e d c o m p o s i t e s [2]. As the t h i c k n e s s of the s p e c i m e n i n c r e a s e s , t h e r e is a p r o p o r t i o n a l i n c r e a s e in l 1, which l i m i t s the p o s s i b i l i t y of testing r e l a t i v e l y thick s p e c i m e n s . Thus, e.g., for t e s t i n g a s t r i p 3 m m thick at m e d i u m v a l u e s of the s t r e n g t h r a t i o R x + / R z = 2 5 the length of the loading zones m u s t be about 500 ram. A c e r t a i n d e c r e a s e in l l can be a c h i e v e d by r e d u c i n g the r a t i o bl/b; this leads to the bar s p e c i m e n becoming d u m b b e l l - s h a p e d . Owing to the low s h e a r s t r e n g t h such s p e c i m e n s can be s u c c e s s f u l l y used for d e t e r m i n i n g the s t r e n g t h of m o d e r n c o m p o s i t e s only if the f o r c e of friction on the f r e e l a t e r a l s u r f a c e s (F 1) does not exceed the s h e a r r e s i s t a n c e of the e d g e s of the s p e c i m e n , i,e., F 1 -< Rxzt/1 or

(b~-b)F <.R,,:d

(7)

S1

F r o m (7),using (I),we obtain ( b ~ - - b ) ~ 2 lG~ - - - - - s, , Rx s

(8)

w h e r e Rxz is the s h e a r strength; for u n i d i r e c t i o n a l c o m p o s i t e s it is 3 - 7 k g f / m m z. F r o m an a n a l y s i s of (8) it follows that the extent to which the width of the s p e c i m e n at the point of a p p l i cation of the load e x c e e d s the width in the t e s t c r o s s section is d e t e r m i n e d both by the s t r e n g t h r a t i o of the c o m p o s i t e and the a r e a r a t i o s l / s . As shown by the a n a l y s i s of (8), in the c a s e of c o m p o s i t e s of m i l l i m e t e r t h i c k n e s s the m a x i m u m of bl - b is quite s m a l l . H o w e v e r , even at s m a l l v a l u e s of the difference (b 1 - b = 1-3) l l is significantly reduced. As the t h i c k n e s s i n c r e a s e s , t h e r e i s a p r o p o r t i o n a l i n c r e a s e in the width difference and the length of the loading zone d e c r e a s e s . The value of l l can a l s o be r e d u c e d by r e d u c i n g the t h i c k n e s s of the s p e c i m e n in the t e s t c r o s s section or s i m u l t a n e o u s l y r e d u c i n g i t s t h i c k n e s s and width. We note that w h e r e dumbbell s p e c i m e n s a r e used e n s u r i n g the n e c e s s a r y a r e a r a t i o does not solve the p r o b l e m c o m p l e t e l y . In o r d e r to obtain f a i l u r e in the t e s t c r o s s section it is n e c e s s a r y to m a k e a c o r r e c t

590

choice of the fillet radius. Experiments have shown that using dumbbell-shaped specimens for testing highmodulus carbon and boron-reinforced plastics gives positive results only at large fillet radii (R -> 125 ram) and when there is a smooth transition from the fillets to the gauge zone and the surfaces are well machined. The technology- for obtaining such specimens is very laborious, especially in the case of boron-reinforced plastics, which of course restricts their practical use, However, the difficulty of obtaining specimens is not the decisive factor in selecting a reliable determination of the strength properties of composites. Special attention should be given to ensuring a homogeneous state of stress, failure in the test cross section, and high stable and reproducible strength characteristics. In order to discover such a method, we have compared the strength values obtained for the same high-modulus composites by different techniques (Table I). The test data on the bar specimens were obtained with allowance for the above recommendations coneerning the choice of the lengih of the loading zone and the jaw taper. The table also contains data on the effect of the stiffness of the end reinforcement, its length and the gauge dimensions of the specimen on the values of the characteristic determined. An analysis of the experimental data shows that using bar specimens i0 mm wide with a layer of emery paper between the jaws and the specimen gives the highest values of the strength of the unidirectional composites. In this case the specimen usually fails in the test cross section. The use of dumbbell-shaped specimens with a fillet radius R - 80 mm gives strength values lower than those obtained with bar specimens, failure usually occurring near the fillets (see Fig. i). Increasing the fillet radius results in an increase in strength values. Tests show that using specimens with a fillet radius R - 125 mm makes it possible to obtain Rx + values almost the same as those for bar specimens. These data have not been given in Table i, since the comparison was made for other high-modulus composites whose mean tensile strength was 120 kgf/mm 2. Good results are obtained by testing bar specimens with pressboard end reinforcement. The use of similar glass-laminate and D-16 Duralumin reinforcement leads to a decrease in strength values° As the tests show (see Table i), in this case the values of the characteristic determined also depend significantly on the length of the end reinforcement and the base length of the specimen. The best results are obtained for a short base length and long end reinforcement; in this case the specimen also has good failure characteristics. In most cases, if the end reinforcement is short, the specimen fails as a result of longitudinal debonding or at the grips (under the end reinforcement). The thickness of the end reinforcement does not have much effect either on the values of Rx + or on the mode of failure of the specimens. Testing specimens with edge or transverse cyLindricaL grooves of radius R -> 125 mm gives strength values close to those obtained with specimens having pressboard end reinforcement (see Table I}, and the specimens usually fail in the test cross section. CONCLUSIONS !. In order to obtain stable values of the tensile strength of high-strength unidirectional composites is necessary to use bar specimens with pressboard end reinforcement 90-110 mm in length.

it

2. In determining the strength on specimens without end reinforcement it is necessary to select their size and shape with allowance for the transverse compressive strength, the shear strength and the taper of the grip jaws. LITERATURE I.

2.

3.

4.

CITED

E. M. Lenoe, M. Knight, and C. S. Schoene, 'Preliminary evaluation of test standards for boron epoxy laminates," in: Composite Materials: Testing and Design. ASTM STP No.460,Philadelphia~Pa. (1969), pp. 122-139. Yu. M. Tarnopol'skii and T. Ya. Kintsis, Static Testing Methods for Reinforced Plastics [in Russian], Moscow (1975). I. K. Park, "Tensile and compressive test methods for high-modulus graphite-fiber-reinforced composites," Intern. Conf. on Carbon Fibers, Their Composites and Applications, London, 1971. Paper No. 23, p. 5. E. M. Lenoe, "Testing and design of advanced composite materials," J. Eng. Mech. Div. Prec. Am. Soc. Civ. Eng., 809-823, December 1970.

591