Crack Propagation Resistance of Random Fiber Composites

29 Crack Propagation Resistance of Random Fiber Composites

Downloaded by UNIV OF PITTSBURGH on May 3, 2015 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/ba-1976-0154.ch029

S. K. GAGGAR and L. J. BROUTMAN Department of Metallurgical and Materials Engineering Illinois Institute of Technology, Chicago, Ill. 60616

The random arrangement of glass fibers in resin matrices produces composite materials which have planar isotropy and are of great importance to many structural and engineering applications. Random fiber composites offer a good combination of mechanical properties and are extensively used in various industries. This study deals with the characterization of strength and fracture behavior of random glass fiber reinforced polyester composites. The concepts of linear elastic fracture mechanics (LEFM) have been applied to these composites to obtain meaningful toughness parameters. Substantial slow crack growth occurs prior to unstable fracture and the total fracture behavior of the material should be studied by applying the concepts of crack growth resistance curves (R-curves).

The incorporation of brittle glass fibers into brittle resins results in composite materials stronger and tougher than its constituent materials. The random arrangement of glass fibers in resin matrices produces composite materials which have planar isotropy and are very important to many structural and engineering applications. Random fiber composites offer a good combination of mechanical properties and are used extensively in industry. The properties of aligned discontinuous fiber composites have been studied to some extent but only a limited amount of information exists on the fundamental properties of random fiber composites. After the work of Wu (I), a number of papers have been published in recent years dealing with the application of linear elastic fracture mechanics ( L E F M ) to predict fracture properties of composites. Wu considered the case of a unidirectional glass reinforced 355 In Toughness and Brittleness of Plastics; Deanin, R., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1976.

356

TOUGHNESS A N D BRITTLENESS O F PLASTICS

epoxy resin with a crack parallel to the direction of the fibers and reported that the critical stress intensity factor, K , did not vary significantly with the crack length. Konish et al. (2) studied a wide variety of composites and concluded that the failure mechanism of the specimens tested was crack dominated in most cases and the procedures of linear elastic fracture mechanics ( L E F M ) could be applied even where the overt failure mechanism was not so obviously dominated by the starter crack. Recently, Owen and Bishop (3) have carried out fracture toughness tests on a polyester resin containing various forms of glass reinforcement. The K values in most cases were not independent of crack size, but a method similar to the plastic zone correction in metals can be used to obtain K values independent of the crack length. Ellis and Harris (4) studied the effect of specimen size and other test variables on the fracture properties of some fiber reinforced epoxy resins. The work of fracture values depended on the dimensions of the test specimen, crack length, and type of fracture test. Beaumont and Phillips (5) investigated random glass fiber polyester composites with respect to application of L E F M and the effect of strain rate, crack length, and test method on fracture properties. The stress intensity factor did not vary significantly with the crack length when the specimens were fractured in a three-point bending mode. More recently, Mandell et al. (6) have shown that the candidate stress intensity factor (K ) is almost completely insensitive to the thickness of the specimen for the roving mat type of composites. In the present study, the principles of L E F M and the concept of crack growth resistance (Rcurves) have been applied to a random fiber polyester composite to characterize the fracture behavior. c

c


c

Q

Experimental A polyester resin P-43 (Rohm and Haas) was selected as a matrix material. The glass fiber reinforcement was in the form of a chopped strand mat ( M 700) weighing IV2 oz/sq ft bonded together with a high solubility polyester resin. The chopped fibers were about 2 in. long and the fiber diameter was about 0.0004 in. In order to produce test specimens, 10 in. X 5 in. composite plates were first molded. The volume fraction of fibers was varied by varying the number of glass fiber mat layers or by varying the thickness of the final composite plate. Benzoyl peroxide (1.5 wt % ) was used as a curing agent. The curing agent was dissolved in styrene (10 wt %) and the resulting solution was added to polyester resin (100 wt %). The cast mixture thus prepared was poured over the fiber mat layers which were placed in a mold. The mold was then placed in a vacuum chamber for about 1 hr to drive off the air bubbles entrapped in the material during the mixing and pouring process. The resin impregnated mat layers were then transferred to a larger mold (10 in. X 10 in.) which was placed on

In Toughness and Brittleness of Plastics; Deanin, R., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1976.

29.

GAGGAR A N D B R O U T M A N

Crack Propagation Resistance

357

GRIPPING • AREA


L

Figure 1.

SEN test specimen

a hot plate ( 1 5 0 ° F ) . Burlap strips were placed around the mat layers and the resin was slowly squeezed out using a flat knife. The squeezing process was continued until there were no visible air bubbles in the resin which was removed. The mold was transferred to a compression press and a top plate was placed on the mold. The curing cycle required 2 hr at 220°F. The composite plates thus prepared were quite clear and transparent at low volume fractions (t; < 25%). At higher fiber volume fractions the plates became translucent because of the close packing offibersand larger interface surface area. Flexure and tension tests were conducted on an Instron testing machine at a crosshead speed of 0.05 in./min. Single edge notch (SEN) fracture tests were conducted at a crosshead speed of 0.1 in./min. Figure 1 shows the SEN specimen configuration. The width and thickness of the specimen are 1 in. and 0.090 in., respectively. The notches were machined on a milling machine using a jewelers saw (6 mil) which produced a square notch as shown in Figure 1. Two small strips (%-in. square pieces cut from a unidirectional glass fiber composite plate) were bonded to the specimen using Eastman 910 adhesive on both sides of the crack as shown in Figure 1. These strips were bonded to the specimen to accommodate a strain gage extensometer to monitor the crack mouth opening displacement during the fracture test. An Instron transverse strain sensor ( G 57-12) was used to monitor the crack mouth displacement. The strain sensor is quite sensitive and displacement values up to 1 X 10' in. could easily be measured from the chart recorder. The load displacement records were analyzed in accordance with the procedure recommended in Method ASTM E 399-71 (7). The candidate stress intensity factor K was calculated using the following K-equation (8). f

4

Q


358

TOUGHNESS A N D BRITTLENESS OF PLASTICS

Q

(i)

tw

where t is the thickness of test specimen Y is a calibration factor P Q is the load as obtained from load displacement records a is the initial crack length w is the width of the specimen.


Results The flexural and tensile properties of polyester composites at various fiber volume fractions are listed in Table I. Strength values increase up to afibervolume fraction of about 40% but then decrease with increased fiber volume fraction. This is caused by the poor wetting and extensive fiber damage which occurs at higher volume fractions because of compaction and close packing of the fibers. The ultimate flexural strain shows a similar trend. The modulus values increase almost linearly with fiber volume fraction. Table I.

Tensile and Fexural Properties of Polyster Composite (9) Flexural

0 20 30 40 50

Properties

Strength, psi

Modulus, X 10 psi

13,000 30,000 38,000 50,000 40,000

0.6 1.5 1.95 2.40 2.85

G

Figure 2.

Tensile

Strain, %

Strength, psi

2.4 2.75 2.85 2.60 1.75

6,000 14,500 19,000 27,000 24,000

X

Properties Modulus, 10 psi 6

0.6 1.33 1.75 2.06 2.4

Tensile specimen before and after failure


Strain,

%

0.9 1.75 1.90 1.84 1.96

29.

GAGGAR A N D B R O U T M A N

359


12.5

9^ = 0.2 w

0.3


0.4

J

I I

i

I 2

i

I 3

i

I 4

DISPLACEMENT,

Figure 3.

LA I 5 -2 10 IN.

i

l \ 6

i\

I 7

Load displacement curves at various crack lengths

Massive debonding of the fibers occurred prior to catastrophic failure of the test specimen. Figure 2 shows a tensile specimen before and after failure. The initially transparent specimen becomes translucent when loaded in tension. Some transverse cracks begin to appear on the surface of the specimen at about 30-40% of the failure load values. The density of these cracks increased as the load on the specimen was increased. Owen and Duke (JO) reported that the debonding in polyester composites started as early as 30% of maximum load. Thus, the debonding in these materials starts occurring along the transverse fibers and then spreads to fibers which are at progressively smaller angles to the load direction. The onset of debonding can thus be considered to be the crack initiation mode in these materials. Fracture Results. The polyester resin specimen (SEN) fails in a brittle manner. The average value of candidate stress intensity factor for polyester resin as calculated from Equation 1 is 1.97 ksi-inA The load displacement records for the composite (v « 0.29) at various crack lengths are shown in Figure 3 and the K values as a function of crack length are shown in Figure 4. A minimum of four specimens were tested at each crack length. The results indicate that the K values increase as the initial crack is increased. The method of determination of load P from the load displacement record is recommended for crack length to width ratios greater than 0.45, and thus the load P obtained at smaller crack lengths may be somewhat erroneous. In other words, the value of t

Q

Q

Q

Q



360


cn 6

Figure 4.

Variation of K g with crack size

0.3

CRACK

SIZE a/

w

P obtained at smaller crack lengths may not correspond to the same crack growth stage as for large crack lengths. At smaller crack lengths, the constraint at the crack tip is more severe and thus the material undergoes less deformation or less debonding takes place at the crack tip. This results in smaller values of material resistance to crack propagation. Table II lists the K values, K values based on maximum load and initial crack length, and K values based on maximum load and instantaneous crack length at that load. K values are much higher than K and K values. This indicates that the crack growth resistance of the material increases as the crack extension occurs in the material. The instantaneous crack lengths were obtained using the following procedure. A compliance crack detection curve as shown in Figure 5 was first constructed using the load displacement records obtained from the fracture tests. This compliance is based on the crack mouth opening displacement and is thus not to be confused with the compliance of the Q

t

Q

R

R

Q

{

Table II.

Various Stress Intensity Factors for Polyester Composite

a/w

Average K , ksi-in.

Average K*, ksi-in.

Average K , ksi-in.v*

0.2 0.3 0.4

10.3 11.3 12.2

11.80 13.05 14.05

16.85 16.70

Q

1/z

1/2

R


GAGGAR AND BROUTMAN


29.

I

i


I 0.1

i

I 0.2

i

I 0.3

CRACK SIZE a Figure 5.

i

I— 0.4

/w

Compliance vs. crack size

DISPLACEMENT Figuer 6.

Compliance determination at various stages of fracture process


361


362


specimen. Initial straight line portions of the load displacement record at various initial notch lengths were used to calculate the compliance and these compliance values at various notch lengths were plotted to get the crack detection curve shown in Figure 5. If, during a crack propagation test, the compliance at any load value is measured, then the crack length corresponding to that load can be determined from Figure 5. From the results presented in Table II, the resistance of the material increases as crack growth occurs in the material. It is thus necessary to calculate the material resistance values as a function of crack length if the fracture behavior of the material is to be fully characterized. This type of approach known as the R-curve approach has been used to study the fracture behavior of many metallic materials. The R-curve concept has been completely reviewed (11). A load displacement record obtained from the fracture test can be used to develop the R-curve for the material. The procedure used for establishing the R-curve for the material is described below. (1) A straight line is drawn from the origin to a point on the load displacement record as shown in Figure 6. The compliance is the reciprocal of the slope of this line. 24-

f 20 o: o z < UJ

16

12

I en o

• - — a=0.3

Crack Propagation Resistance of Random Fiber Composites

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