Indian Journal of Engineering & Material s Sciences Vol. 9, August 2002, pp. 269-274

Evaluation of intralaminar fracture toughness of angle ply laminate

R Ramesh Kumar" , S Joseh & G Venkateswara Rao"*

"Structural Design and Anal ysis Division. Structural Engineering Group, Vikram Sarabhai Space Centre, Thiruvananthapuram 695 022, India

bDepartment of Mechanical Engineering. T.K.M. Co llege of Engineering, Koll am 691 005, India

Received 9 October 2001; accepted 28 May 2002

Intralaminar fracture toughness values of [0°130' 145°130 and [90°130 carbon/epoxy laminates are theoreticall y eva luated based on the well-known MCCI method corresponding to the fracture loads obtained by testing C(T) specimens. Compari ­son of fracture toughness of angle ply laminate, which is assoc iated with both mode I and mode II , show a very good agreement with the theoreti cal prediction. A new empiri cal relationship is developed to obtain the intralaminar fracture toughness of an angle ply laminate from the corresponding value of the 0° laminate. The new formul a is used to compare fracture toughness of ang le ply laminates ava ilable in literature for glass epoxy Scotch ply 1002 laminate and a reasonabl y good agreement is observed between the test data and the predictions. As a percentage of total fracture toughnes value. toughness due to mode II is max imum of 15.5% when fibre orientation is 45°.

Fibre reinforced composites are generally sensitive to crack propagation on the planes parallel to the fibre direction . For an unidirectional fibre-reinforced lami­nate, the crack propagating in the thickness direction without fibre breakage is called the intralaminar frac­ture, and between the layers it is interlaminar fracture. Various authors have reported the evaluation of intra­and inter-l aminar fracture toughness of laminated composites by experimental and theoretical prediction using the well known modified crack closure integral approach 1-8. Most of the studies reported in literature are confined to the evaluation of interlaminar fracture toughness whose value is much lower (about 2.5 times) than the intralaminar one3

.9

.IO

. However, for the assessment of fracture load of a composite structure with a damage in the form of a through the thickness crack needs the accurate evaluation of intralaminar fracture toughness values.

The theoretical prediction of intralaminar fracture toughness of angle ply fibre-reinforced laminate is quite invol ved as it is associated with both mode I and mode II fracture and requires the knowledge of cracking angle along which the strain energy pos­sesses the minimum value ll

.

Compact tension C(T) specimen was adapted to the special requirements of composite laminates by the studies undertaken by Williams and Cawood l2 and

*For correspondence

other investigators 1.3.9 . Initi ally, the use of C(T) specimen was not common for composite materials due to the difficulties in satisfying the thickness crite­ria specified by ASTM E399 (thickness of the speci­men should be greater than the semi-width )1 3. How­ever, investigations by John 14 on composite fabric laminates using C(T) specimen showed that even though thickness of the specimen was only about 10% of width of the specimen, fracture toughness results obtained compared very well with the theoretical pre­dictions. Similar findings were also reported by Min­netyan and Chamis l s

. C(T)specimen was also used successfully for the evaluation intralaminar fracture toughness of cross ply laminate and its constituent laminates l 6

.

In the present study, an empirical relationship for the prediction of the fracture toughness of angle ply laminate based on its unidirectional value is achieved, which can be used for any other material system from the unidirectional value of that system.

Experimental

Materials

M55JIM I 8 carbon/epoxy laminates are used in the present study . The elastic properties of this material are given in Table 1. As the material is highly brittle, fracture of the specimen may occur without any bending of the ligament (Fig. I) . Hence, a linear elas­tic fracture is expected for this material.

270 IND IAN J. ENG. MATER . SC I. , AUGUST 2002

Table I - Tested mechanical properti es of M55J / M 18 unidi­rec tional carbon/epoxy laminate

Longitud inal Young's modulus, ELI

Transverse Young's modulus, E\"r

Po isson's rati o, V,.'

Shear modu lu s. G.,!,

Longitudinal tensil e sl rength, X,

Longitudinal compressive strength , XC'

Transverse tensile streng th , Y,

Transverse co mpressi ve strength , Yc

Shear strength. S

Specimen preparation

329 GPa

6 GPa

0.346

4.4 GPa

1327 MPa

724 MPa

22 MPa

11 7 MPa

75 MPa

Configurati on of the standard C(T) specimen is available in ASTM standard E399-90 (ASTM, 1993). C(T) specimens with lay up sequences of [0130, [45 ho and [90130 are fab ri cated with W=50 .8 mm and a=25.4 mm for the tests. The M55]/M 18 carbon/epoxy mate­rial is avai lable in the form of pre-preg rolls of 300 mm width and 0.1 mm thi ckness, as manufactured by Hexcel Composites SA, France. Thirty layers of the pre-preg cut to the requi red dimensions are stacked properly and then cured at 175°C for 2 h under vac­uum of 0.8 bar and 5.0 bar pressure.

A two step notching procedure is adopted for the C(T) specimens. First, a st rai ght notch is cut Ll si ng a straight head di sc cutter of 1.5 mm thickness and a razor blade is then used to give a symmetric and rela­tivel y sharp starter notch . In order to measure the crack opening displacement opposite to crack tip (far end) usi ng clip gauge, two attachab le knife edges are adhesively bonded to the specimen edges as shown in Fig. 2. These accurately machined metallic knife edges fixed with a gap of 5 mm between the tips serve as 9i splacement reference points when crack open ing is measured using the clip gauge.

Testi ng procedure The tests are conducted with an Instron 8500 ma­

chine. As fracture load of the laminate is different for di f'ferent fi bre angle (ex), the load i ng rate ranged from 3 kg/min ·to 25 kg/min. For instance, the loading rate for IOho spec imen is 3 kg/min while the same for [90ho is taken as 5 kg/min . Reso lLtli on of the machine is se t to I g whi Ie tes ting the [0130 specimen and for the other spec i mens 109.

The fracture loads (Pc obtai ned fro m tes t are used to determ ine Kc values as a measure of frac ture toughness Llsi ng the data reduction scheme gi ven in ASTM E 399-90 12

.

.2SW±.OOSW 01 2 HOLES

W±.0005W J 1.2SW±.OlOW

(a)

( _ _ 'N ;:; 50 .8 mm -).

(b)

~S: ...,,,,, ..... 0 NO

·+i

S:S: ...,..., 1'-0 NO

• ....j

s: ", 0 0 +i s: ~

it s: ..., C> <=> +i s: ~

B

'\, Gaug~ Blocks

Fi g. I - Configuration of CCT) specimen (a) sta ndard configura­tion; (b) typi cal compact tension spec imen with gauge blocks fix ed

0° I. AMINATE CHACKEU SURFACE f'AHALLEL TO FIRRF. OIRF.CTION

90° LAMINATE

45" ANGL[ PI Y LAMINAT[ CRACKED SUI1FACi= f'AHALLi=L TO FIBRF DIRFCT ION

CRACKED SURrACE PARALL[L TO FltlHE UIHi=CIION

Fig. 2 - Mode of failure of tested C(T) spec imens

-+

+

KUMAR et (II.: EVALUATION OF INTRALAMINAR FRACTURE TOUGHNSS OF ANGLE PLY LAMINATE 271

Kc= PJ(X) I B wtl2 . .. (I)

f(x) is a factor associated with alw and is available in ASTM(1993), and given by :

2 + (a/ w) f(a/w)= 15

[I-(a/ w) ] '

[0.886 + 4.64(a / w) - 13.32(a / w)2 + 14.72(a / w) 3

-S .6(a /w) 4]

Finite element modeling

Tsai-Hill's postulation proposed by Zhang and Tsai is that crack initiates or propagates in a radial direc­tion (cracking direction) along which distortional

h .. I II strain energy possess t e mlillmum va ue . Cracking angle predicted by the extended Tsai-Hill

fracture criterion corresponding to fibre angle a = 0°, IS°, 30°,45°,60°,75° and 90° are 0°, 16°, 29°, 41 °, 51 °, 67u and 84°, respectively . Thus, for an angle ply laminate with fibre orientati on say, 45° to the initial crack direction considered then the cracking direction evaluated is 41 ° which appears to cut the fibre . As it is more difficult for the crack to break the fibre than the matrix , crack may propagate parallel to the fibre direction . Hence, in the theoretical evaluat ion of GI and Gil us ing MCCI approach , branch crack is modeled with its directi on paralle l to the cracking di ­rection 8 =41 ° (Fig. 3) .

For finite element analysis , eight node quadrati c quadrilateral, 2-D plate/shell element ava ilable in MSC/NASTRAN 70.0 is used. The FE model of the C(T) specimen is shown in Fig. 3. A refined element of size alSO is used to represent a branch crack and are used over a length of al6 around the crack tip. For [0] 0 specimens, as the crack growth is in :1 sel f simi­lar manner, no branch crack is introduced . In the FE model branch cracks are introduced both paral lel to

fibre orientat ions and along the cracking direction 0 (Fig. 3) :.. ...

, 1 "HAN( II ( 11 M'"

Fig. 3 - FE lIlode l of C(T) spec imell wit h deta il s of branch crack

Loading and boundary conditions

Fracture load p.I is applied at point A in the C(T) model (Fig. 3). As each specimen dimension differ marginally (by ± 0.5 to ± 1 mm), P, evaluated based on its average value is used in the FE analysis. The point B shown in the Fig. 3 of the C(T) specimen is constrained to all degrees of freedom.

Fracture toughness computation Nodal forces and displacements obtained from FE

analysis with 8 noded elements are used to calculate 17 Th . G, with the help of MCC] Method . e ex press Ion

oiven in literature is valid for unit thickness of the b

cracked model. ]n the present case, it is modified by dividing the thickness of the specimen.

I 1 [ F ] j·2 Gt = -B 2 A F y. j U y.j_ 2 + v. j+ IUy.j _ 1 uQ Crack

... (2)

Forces acting normal to crack extension are F l'j and Fr.J+' acting at nodes j and j+1 respecti vely . Uy,j.j and U ;',j.2 are the crack opening displacements at nods j -I a;ld j-2. A similar expression for Gil can be obtained by replacing F

" by Fx and by Ux '

For the angle ply laminate the loading perpendicu­lar to initial crack can produce both mode I and mode II strain energy release rate. ]n other words, G is the sum of Gt and Gil so as K is the sum of K, and KII . The crit ical value of G con'esponds to the fracture load is Ge. Ke is evaluated based on Ge. FE analysis is carried out for the frac ture load obtained by testing the C(T)specimen . Hence, G is nothing but Ge (= G/c + G llc)' The relationship between G and K is given be­low (K /c and Kilo is thus determined when G,= G ie and Gil = Glle from the analysi s for the failure loads) :

f( - . X - ]Yz 2 G =1 ~ 1-+~~ -VI ' K J

. .. (3) I l En) 2G I~ • ~2EII E~2

Results and Discussion The det3ils of the C(T) specimens tested , al ong

with the test data and results are presented in Table 2. Te:-,t data show that the scatter is minimu m for the l4SJ JO ply laminate and maximum for the [901'0 lam-

272 INDIAN J. ENG. MATER. SC I. . AUGUST 2002

Table 2 - C(T) specimen details with test results

Lay - up Specimen No

W(lllm)

A (mm)

uJlI' f(uJlV) Fracture load. Ps (N) Kic from testing. N. mm-JI2

51.3 25.9

0.504 9.779 74.6 33.93

[Oho 2 3

50.5 5 1. 13 24.0 25.93

0.475 0.507 8.960 9.87 1 82.4 74.7

34.63 34.39

nate. The dev iati on among the fa il ure loads fo r each type laminate wi th respect to its average values are 2.8%, 8.5% and 17% fo r [45ho, [0130 and [90ho lami­nates, respecti vely. The average values of frac ture toughness of [Oho, [90ho and [45ho, lami nates evalu­ated fro m the test are 36.32 N .mm- 312

, 53.65 N.mm-J/2

and 126. 11 N. mm-3/2 respecti vely (Table 3). The fract ure toughness values of these laminates are com­pared with the values evaluated based on MCC I ap­proach corresponding to the average tes t data fo r frac tu re load in Table 3. A good agreement is ob­ta ined between Kc values from test and the es timated Kc fro m the FE analysis.

Table 4 compares the actual crack opening di s­placements measured between the knife edges (the other end of the crack ti p) obtained from tests with the corresponding va lues fro m the linear FE analys is. A compari son of both show a good correlat ion for the [oho and [90)"0 lam inates and a reasonably good agreement with the ang le ply laminate.

III the absence of tes t data fo r fibre orientations other than 00

, 450 and 900, FE method is fo ll owed to

generate Gc corresponding to the failure loads taken from the relationship between the fibre directions and the respective fracture loads. These fracture loads are obtained from curve fitting of tes t data fo r the three types of specimens; Fig. 4. The fracture toughness va lues obtained fro m FEM fo r all models other than a = 00

, with the two different branch cracks orienta­tions are presented in Table 5.

A new empirical relationship is developed to obtain the frac ture toughn ~ss of an angle ply lami nate, Kca, from the corresponding value (Keo) of a 00 laminate, based on the present results (Table 5):

... (4)

Table 6 compares test data fo r the fracture tough­ness of M55 J/M 18 laminates with those of Scotchply 1002 laminates as reported alreadyl8. It can be noticed

[45ho 190bo 4 2 3 2

50.62 50.2 50.7 50.5 50.8 50. 8 25.02 24.5 24.0 24.9 22.9 25. 1 0.494 0.488 0.473 0.493 0 .45 \ 0.494 9.426 9.3 13 8.91 9.45 8.363 9.483 96. 14 127.5 12 1.6 122.6 292.3 33 1.3 42.46 55 .87 50.73 54.35 11 4.35 137.87

Table 3 - Comparison of Kc wit h fin ite elemenl result s (fo r frac ture load)

Lay - up 10ho [45130 190130

Fractu re load (Ps)' N (for a=25 and w=50 mm) 79.97 117 .82 302. 13

Kc based on GJfrom 39.33 54.57 11 8.99 FEM). N.mm-J12

Kc from tesling (average 36.32 53.65 126. 11 va lue) N.lll m-J/2

Table 4 - Compari so n of crack openi ng di sp lacement (at knife edges) from lest and FE results

Lay - up rOJ JO

Fracture load (Ps). N 79.97

Test da ta fo r crack openi ng 0. 125 between kn ife edge. mill

FE analysi s result for crack opening between knife edge. 0. 128 mm

400

350

z 300 -c I ro

250 0 -l

I

I

~ 200 :::J t) ro 150

U:: 100

~r"" ..------

50 o 15 30 45

[45J.lO [90130

123.9 302. 13

0.135 0.368

0. 170 0.399

I

/ 1/

/ ; /'

I I

I I

60 75 90

Fibre Orientation . ex

Fig. 4 - Frac ture load at the onset of frac tu re corresponding to various angle ply laminates

KUMAR e/ a/.: EVALUATION OF INTRALAMIN AR FR ACTURE TOUGHNSS OF ANGLE PLY LAMIN ATE 273

Table 5 - Finite element results on angle ply laminates for frac ture load from Fi g. 4

ex. 8 Frac ture G1c Gll e

load, N J/m2 J/m2

15 15 80 11 4.8 1.37 15 16 80 11 4.3 0.97 30 30 100 150.9 2.79 30 29 100 149. 1 3.39 45 4 1 134.4 196.9 6.3 1 45 45 134.4 199.3 10.0 60 ()O 185 288.9 3.4 60 5 1 185 3 11.1 17. 1 75 75 250 232.3 3. 18 75 67 250 333.34 14.99 90 90 33 1.3 136.9 40.0 90 84 33 1.3 126.9 18.5

Table 6 - Predicted values of k cu> N.mm-3/2 for different materi al systems using the present empirical formul a

Test data on Pred ictions Error (%) Scotch ply using Eq. (4) 1002[ I7J

0 45 .5 45.5

15 47.74 42.29 - 12.87

30 54.89 47 .57 - 15.38

45 69 .52 () 1.33 - 13.35

60 92 .1 4 83.58 - 10.25

75 124.55 11 4.29 -8 .97

90 173.93 153 .5 1 -13.3 1

from Table 6 that the above equati on which is arrived at for M55J/M 18 carbon/epoxy laminate can give ac­curate predi ction of fracture toughness of glass/epoxy angle pl y lam inates fro m a known value of unidirec­tional fracture toughness of the glass/epoxy laminate. This is possible probabl y because for a given geome­try of the C(T) spec imen, the rati o of G, and Gil fo r a given fibre angle must be a constant dependi ng up on its frac ture toughness va lue, say , corres ponding to unidirec tional laminate. Us ing the present empi rica l fo rmul a, one can determine the fracture toughness of an angle pl y lam inate made of any materia l system based on its unidirecti onal laminate toughness value.

Conclusions Intra laminar fracture toughness va lues of M55J/

M 18 carbon/epoxy composite for [OOh o , [45°ho and [90°130 laminates have been theoretically eva luated based on modifi ed crack closure integral method cor­responding to the frac ture loads obtai ned by tes ting C(T) speci mens and compared with test results. A

FE results Ge Kic Kllc Kc

J/m2 N.mm-Jl2 N. mm-3/2 N. mm-3/2

11 6. 17 32 .09 6. 105 38.20 11 5.27 32 .02 5. 137 37.16 153.69 37.50 6.925 44.43 152.49 37 .28 7.082 44.37 203.2 1 46.29 8.286 54.57 209.3 . 46.57 10.43 57.00 292.3 65.38 5.630 7 1.00 328.2 67.83 12.626 80.46

235.48 79.50 5.342 84.84 28 1.03 95 .22 11 .597 106.82 176.9 12 1.23 1.938 123 .17 145.4 11 7.67 1.3 18 11 8.99

good agreement is observed fo r both the fracture toughness values and crack opening (at far end be­tween the knife edges) by the tes t and prediction. A new empirical relationship is developed to obtain the intra laminar fracture toughness of an angle pl y lami­nate, from the corresponding value of the 0° laminate. The new fo rmul a is used to compare fracture tough­ness of angle ply laminates ava ilable in literature for glass epoxy Scotch pl y 1002 laminate and a reasona­bly good agreement is observed between the test data reported in literature and the predictions. Jt is ob­served from the analys is that the opening mode causes about 16% of mode " fracture toughness for the angle ply [45°ho laminate unlike the other two types of laminate.

Acknowledgements Sincere thanks are due to Shri M Ramakrishnan,

Group Head, CMS, REPLACE, Vatt iyoorkavu , for the preparation of tes t spec imens, Shri Chennaiappan , RFF, for the fabrication of the test fixture to use C(T) specimen!> and Shri M Divakar, Fracture Mechani cs Laboratory, MCD, for tes ti ng the specimens.

References I Parhi zgar S. Zachary L W & Sun C T. 1111 J Fran. 20 (1982 )

3. 2 Wil kins 0 J. Eisenm ann J R, Camin R A, Margoli s W S &

Benson R /\ , A57M ST!' 775, ( 1982) 168. 3 Garg A C, Ellg Frau M ech, 29 ( 1988) 557. 4 Reeder J R & Crews J H Jr, AIAA J, 28 (1990) 1270. 5 Lin Ye, COII/pOS Sci Tecl/l/(J/. 43 ( 1992) 49 . 6 Madhukar M S & Lawrence . .I Compos Maler, 26 ( 1992)

936. 7 Arabwa K & Taka hashi K, I IlI J Frac!. 74 (1995) 277. 8 Jose S, Ku mar R R, Rao G V & Sriram P, Ac/v COli/pUS LeI, 9

(2000) 335.

274 INDIAN J. ENG. MATER. SCI. , AUGUST 2002

9 Cowley K D & Beaumont P W R, Compos Sci Tech, 57 ( 1997) 143 3.

10 Crick R A, Leach D C & Moore D R, 11lIerperlation of toughl/ess il/. aromatic polymer composites usil/g a fra cture mechanics approach, Proc. 3 I" 11lIemotiol/ai SAMPE Sym­posium , 1986, 1677.

II Zhang S Y & Tsai L W, lilt J Fract, 40 ( 1989) RIOI -RI04.

12 Williams JG &CawoodMJ , PoiymTest, 9 ( 1990) 15 .

13 ASTM, ASTM E399-90, Standard Test Method for Plane­Strain Fracture Toughness of Metallic Material s, in Anl/ual book of ASTM Standards, Sectiol/ 3.01, Metals test methods

and analytical procedures (A merican Society for Tes ting and Materials, New York) , 1993.

14 John E Masters, NASA COlll raClUr Reporl , NASA-CR-20 1728 ( 1997).

15 Minnetyan L & C ham is C C, Composite lIIaterials: Fmigue al/dfracture (Sixth Volume), ASTM STP 1285 ( 1997) 53 1-550.

16 Kumar R R, Jose S & Rao G Y, Compos Sci Techl/ol, 61 (200 1) 111 5.

17 Raju I S, EI/g Fract Mech , 28 ( 1987) 251 .

18 Lin Ye, EI/ g Fract Mech, 32 ( 1989) 86 1.