Mechanical Properties of Discontinuous Fiber Reinforced Thermoplastics.

II. Random-in-Plane Fiber Orientation BRUCE F. BLUMENTRITTO

BAN T. VU** and STUART L. COOPER Department of Chemical Engineering

and Materials Science Center

The Univereity of Wisconsin Madison, Wisconsin

The mechanical properties are presented for a series of dis- continuous fiber-reinforced thermoplastic composites made with random-in-plane fiber orientation. The matrix and fiber materials were chosen to provide a wide range of strength, modulus, ductility and adhesive properties. In many cases strong, rigid, yet tough composites were fabricated. Strength levels of over 20,000 psi and modulus values over 1,000,000 psi were reached in several systems reinforced with short Kevlar-49 and graphite fibers. A strong dependence of com- posite strength and modulus on fiber strength and modulus was noted indicating good transfer of load from matrix to reinforce- ment. Fiber efficiency factors for modulus and strength were calculated for the experimental composite systems and aver- aged 0.19 and 0.11 respectively. Data were analyzed using basic composite theory. Properties of the experimental com- posites could not be predicted from constituent properties.

INTRODUCTION omposites in which the fibrous reinforcement is c discontinuous and controlled in orientation have

good mechanical properties and can be fabricated into complex shapes. In a previous paper ( l ) , the authors presented data on a range of thermoplastic matrix composites reinforced with short fibers which were unidirectionally oriented. These composites are highly anisotropic with strengths parallel to the fiber axis which may be an order of magnitude greater than strengths perpendicular to the axis of fiber ori- entation. Under certain conditions, highly oriented composites of this type can be produced in a flow molding process (2).

A composite in which the fibers are dispersed ran- domly in two dimensions will be referred to as a random-in-plane composite. Mechanical properties measured at any angle within the plane of the rein- forcement should be uniform while mechanical prop- erties measured perpendicular to the plane will be much lower. Sheet molding compounds and lami- nates approximate such random-in-plane structures.

This project was a study of a variety of short fiber reinforced thermoplastics made with random-in- plane fiber orientation. Mechanical properties of the

0 Present address: IBM Corporation, Rochester, Minnesota. O O Present address: Rohm and Haas Corporation, Bristol, Pennsyl- vania.

materials are reported and the data are analyzed us- ing basic composite theory.

EXPERIMENTAL Six reinforcements were used in this study, four

organic fibers and two inorganic fibers, In order of increasing stiffness, the fibers used were duPont type 702 nylon 6/6, duPont type 73 poly ( ethylene tereph- thalate ) , Kuralon poly ( vinyl alcohol), Owens- Coriiings type 801 E-glass, duPont Kevlar-49, and Union Carbide Thornel@ 300 graphite. Prop- erties of the fibers are given in Table 1 . The poly- (vinyl alcohol) fibers were supplied in 5 mm lengths and the glass fibers in 1/4 in. lengths. The other fibers were obtained in continuous yarn form and were cut to uniform 3/s in, lengths.

Five thermoplastics were used as matrix materials. In order of increasing stiffness, these were du Pont Surlyns 1558 type 30 ionomer, duPont Alathonm 7140 high-density polyethylene, Huels grade L-1901 nylon 12, General Electric Lexanm 105-111 polycar- bonate, and duPont Lucitem 47 poly( methyl meth- acrylate) (PMMA). The first three resins are all ductile semicrystalline polymers while polycarbonate and PMMA are representative of ductile and brittle glassy polymers respectively. Thus thermoplastics were selected to represent a range of mechanical properties and also a range in adhesive properties

POLYMER ENGINEERING AND SCIENCE, JUNE, 1975, Vol. J5, No. 6

Mechnicd Properties of Discontinuow Fiber Reinforced Thermoplastics. I I . Randomin-Plane Fiber Orientation

Table 1. Properties of Reinforcing Fibers

Fiber

Ultimate tensile Tensile Ultimate Fiber Specific strength, modulus, elongation, diameter, gravity psi psi percent in.

Nylon 616 1.14 129,000 950,000 16.5 0.0011 Polyester 1.38 166,000 2,000,000 12 0.0010 Poly(viny1 alcohol) 1.26 142,000 3,000,000 9 0.0010 Glass 2.53 200,000" 10,500,000 1 0.0004

Graphite 1.70 325,000 34,000,000 1 0.0003 Kevla r-49 1.45 400,000 19,ooo,oO0 2 0.00046

*Approximate strength of glass fibers in the composites.

when used as composite matrix materials. Properties of the matrix materhls are given in Table 2.

Composites were made by blending powdered resin with chopped jibers in a V-shaped blender with an intensifier bar. The components were mixed until the fiber bundles were well-opened and the resin was uniformly distributed. In the organic fiber com- posites, the mixing process caused no reduction in fiber length. In the glass and graphite fiber materials, there was some fiber damage but it did not result in a significant reduction in average fiber length.

The random-in-plane specimens were made by a hand lay-up process. Star-shaped bits of the fiber and matrix blend were placed into a 3 in. by 5 in. fully positive compression mold to form layers of the raw material. Siiccessive layers were added un- til the desired quantity of raw materials had been placed into the mold. The mold was closed and placed into a hot platen press. Contact pressure was applied and the mold was heated to the desired molding temperature. The pressure was then in- creased to the molding pressure desired and held for about one minu.te. The mold was cooled under pressure and the composite panels were ejected at room temperature. The molded panels were about 0.040 in. thick. This procedure produced panels with good random-in-plane fiber orientation and good fiber dispersiori.

Each panel was machined into four tensile test specimens. The specimen configuration is shown in Fig. 1. Tensile tests were conducted at approxi- mately 23°C using an elongation rate of 0.2 in. per minute for all tests. Fracture energies of the composites were determined by measuring the areas under tensile stress- strain curves with a planimeter. The tensile results reported are an average of data on three to four specimens at each fiber loading. Specimens with obvious defects were discarded. Tests in which data varied from the mean by more than 10 percent were repeated with another set of specimens. Because of the relatively large number of materials included in this study, the number of speci- mens used for each test was limited and measures of variability in the properties were not applied. The results should be considered typical properties of the materials when they are fabricated and tested as described above.

RESULTS AND DISCUSSION Values for tensile properties of the experimental

composites are given in Table 2. Specific gravities were calculated from the specific gravities of the component materials and are included in the table for comparison of these composites with other struc- tural materials. Fracture energy is given in terms of the area under the tensile stress-strain curve to the yield point or to fracture, whichever occurs first. All values are based upon specimen dimensions before testing rather than instantaneous dimensions.

The data show that, within the range of 10 to 50 volume percent reinforcement, tensile strength and modulus generally increase with increasing fiber con- centration. Ultimate elongation tends to decrease with increasing fiber content and toughness, which depends upon strength and elongation, does not vary predictably with fiber concentration.

In most of the composites, reinforcement of strength and modulus was obtained. Composites made with Kevlar-49 fibers had very good mechanical properties. Low strength composites were the result of poor fiber to matrix adhesion, as in the case of polyethylene reinforced with poly (vinyl alcohol) fi- bers, or were due to brittle fracture of the matrix before the fibers were fully loaded, as in the case of PMMA reinforced with nylon 6/6 fibers. Organic fi- ber reinforced composites were significantly tougher than corresponding inorganic fiber composites, pri- marily due to the high values of elongation to frac- ture for these materials.

Figures 2 and 3 show series of typical stress-strain curves for the experimental composites, Ductile com- posites generally have stress-strain curves like those shown for polyethylene reinforced with polyester fibers and brittle composites have stress-strain curves like those for PMMA reinforced with Kevlar-49 fibers. In ductile composites, the slopes of the curves de- crease significantly at elongations greater than 2 to 4 percent. This decrease in secant modulus is at- tributed to fiber ends breaking loose from the matrix while the remainder of the composite maintains its integrity. Near the fiber ends, the matrix is free to deform plastically and, therefore, the stress-strain curve of the composite resembles the stress-strain curve of the pure matrix material.

Figures 4-8 show the dependence of composite tensile properties on the properties of the constituent

429 POLYMER ENGINEERING AND SCIENCE, JUNE, 197S, Vol. 15, No. 6

Bruce F . Blumentritt, Ban T . Vu, and Stuart L. Cooper

Table 2. Tensile Properties of Random-in-Plane Composite Materials

Matrix

Fiber per- Tensile Tensile Ultimate cent, Specific strength, Modulus, elongation, Curve area

Reinforcement by vol. gravity psi psi percent in.4blin.3

lonorner

Polyethylene

Nylon 12

None Nylon 6/6

Polyester

Poly(viny1 alcohol)

Glass

Kevlar-49

Graphite

None Nylon 6/6

Polyester

Poly(viny1 alcohol)

Glass

Kevlar-49

Graphite

None Nylon 6/6

Polyester

Poly(viny1 alcohol)

- 20 40 10 20 30 40 50 20 40 10 20 30 40 20 40 50 10 20 30 40 50

20 40 50 10 20 30 40 50

10 20 30 40 50

10 20 30 40

20 40 50

10 20 30 40 50

20 40 50

20 40 50

20 40 50

-

-

0.95 0.99 1.03 0.99 1.04 1.08 1.12 1.17 1.01 1.07 1.11 1.27 1.42 1.58 1.05 1.15 1.20 1.02 1.10 1.17 1.25 1.32 0.95 0.99 1.03 1.05 0.99 1.04 1.08 1.12 1.17

0.98 1.01 1.04 1.07 1.12

1.11 1.27 1.42 1.58

1.05 1.15 1.20

1.02 1.10 1.17 1.25 1.32

1.01 1.04 1.06 1.08

1.08 1.16 1.20

1.06 1.10 1.14

1,810 (yield) 3,100 4,360 2,400 5,430 6,310 6,490 7,780 5,600 6,080 4,250 6,940 8,500

11,600 17,300 23,100 25,100

5,500 11,600 12,300 12,700 8,150 3,250 (yield) 3,380 3,930 4,280 3,140 3,920 6,580 7,220 9,890

2,740 2,950 2,950 3,160 3,040

6,640 6,110

11,700 13,200

10,700 20,200 24,300

5,590 8,500 8,800 5,840 5,500

6,190 (yield) 6,640 9,680

10,700

8,450 13,000 15,000

8,400 9,550

11,900

23,500 61,900 97,700 51,200

116,000 140,000 191,000 234,000 212,000 337,000 242,000 422,000 665,000 729,000 730,000 985,000

1,100,000 600,000

1,020,000 1,180,000 1,370,000 1,450,000

155,000 147,000 196,000 2 11,000 176,000 191,000 216,000 237,000 278,000

196,000 241,000 253,000 288,000 307,000

332,000 495,000 728,000 956,000

749,000 1,040,000 1,120,000

670,000 966,000

1,220,000 1,350,000 1,050,000

181,000 167,000 236,000 258,000

223,000 3 54,000 404,000

313,000 470,000 594,000

17 (yield) 22 21 40 25 22 14 12 7.7 4.8 1.9 1.7 1.6 1.9 2.9 3.5 3.0 0.98 1.3 1.2 1.1 0.87

13 (yield) 14 11 9.5

20 17 16 13 9.0

4.9 3.4 2.9 3.2 3.3

3.1 1.9 1.9 1.7

2.3 3.4 3.5

1.0 1.0 0.80 0.57 0.63

12 (yield) 18 17 14

19 9.8 7.8

7.7 6.2 4.9

229 (yield) 447 549 730 901 911 626 655 276 178 42 53 77

118 289 474 405 32 78 80 65 36

301 (yield) 349 266 258 475 502 751 612 554

97 81 62 89 89

95 62

126 138

154 426 505

31 41 39 17 19

594 (yield) 832

1090 936

1100 805 67 1

424 391 366

430 POLYMlFR ENGINEERING AND SCIENCE, JUNE, 1975, Vol. IS, No. 6

Mechanical Propsrties of Discontinuous Fiber Reinforced Thermoplastics. ZI. Random-in-Plane Fiber Orientation

Table 2. Tensile Properties of Random-in-Plane Composite Materials (cont’d.) ~~

Fiber per- Tensile Tensile Ultimate cent, Specific Modulus, strength, elongation, Curve area

Matrix Reinforcement by vol. gravity psi psi percent in.4blin.3

Po I ycarbona te

PRD-49

None Glass

PRD-49

Graphite

Polymethyl methacrylate None Nylon 6/6

Polyester

Poly(viny1 alcohol)

Glass

Kevlar-49

Graphite

10 1.05 20 1.10 30 1.14 40 1.19 50 1.23

- 1.20 10 1.33 20 1.47 30 1.60 40 1.73

20 1.25 40 1.30 50 1.33

10 1.25 20 1.30 30 1.35 40 1.40

- 1.19 20 1.18 30 1.18 50 1.17

20 1.23 40 1.27 50 1.29

20 1.20 40 1.22

10 1.32 20 1.46 30 1.59 40 1.73

10 1.22 20 1.24 30 1.27 40 1.29 50 1.32

10 1.24 20 1.29 30 1.34 40 1.39 50 1.44

11,400 15,500 21,000 28,200 37,900

8,920 (yield) 7,000 8,900

13,500 13,000

16,800 34,500 36,300

9,300 10,000 11,300 11,400

10,600 3,410 4,690 8,640

6,000 9,210 9,860

6,840 7,490

7,860 4,890 6,500 7,300

16,900 26,400 35,500 37,700 45,400

11,800 13,600 14,400 11,100 12,000

447,000 605,000 779,000 911,000

1,230,000

280,000 470,000 572,000 977,000

1,180,000

734,000 1,260,000 1,440,000

1,060,000 1,240,000 1,600,000 1,540,000

381,000 328,000 361,000 293,000*

385,000 382,000 395,000

571,000 738,000

603,000 653,000 871,000 973,000

718,000 1,130,000 1,370,000

1,630,000

1,030,000 1,390,000 1,550,000 1,750,000 1,830,000

1,440,000

3.3 5.9 4.7 5.6 5.4

2 18 498 541 914

1110

6.2 (yield) 1.9 2.0 1.7 1.5

3.0 4.0 3.5

1.1 0.84 0.64 0.83

4.6 1.2 2.2

15*

2.0 11 9.1

1.5 2.2

1.6 0.90 1.0 0.80

2.7 3.0 3.0 3.9 3.6

1.2 1.0 0.83 0.65 0.75

339 (yield) 75 96 76 60

282 761 79 1

60 48 35 45

301 20 52

884

68 739 609

73 123

83

58 45

242 436 554 813 871

72 70 68 37 47

-

Thermal degradation of fibers.

materials. The lines drawn in these and subsequent figures are fit to the data points using the method of least squares. Because there are intervening variables such as fiber-to-matrix adhesion and processing vari- ations, the correlations between composite properties and constituent propei%es are not precise. However, the figures do show trends in the data. As shown in Figs. 4 and 5, composite tensile strength and mod- ulus are clearly dependent upon fiber strength and modulus, as would be expected when the fibers are the primary load bearing element. Composite ulti- mate elongation has ii strong dependence on fiber ultimate elongation in ductile matrix composites as shown in Fig. 6. In brittle matrix composites, the

dependence of composite ultimate elongation on fi- ber elongation is small, According to Fig. 7, the yield strength of the matrix material has little in- fluence upon composite tensile strength, probably because matrix properties other than strength, such as surface properties, are greater factors in the strength of composites. Data in Fig. 8 show that, in composites reinforced with lower modulus fibers, the matrix modulus is an important contribution to the composite modulus. However, in composites re- inforced with high modulus fibers, the influence of the matrix modulus on composite modulus is much reduced, since the matrix modulus becomes rela- tively small compared to the fiber modulus.

POLYMER ENGINEERING AND SCIENCE, JUNE, 1975, Vol. 15, No. 6 431

Bruce F . Blumentritt, Ban T . Vu, and Stuart L. Cooper

I I- 0

a I- In

5 20-

15-

In z W

w In 0

0 0

10-

c-

:

A method which allows different composite mate- rials to be compared in relative efficiency of utiliza- tion of fiber strength and modulus properties is the calculation of fiber efficiency factors from the rule of mixtures expressions

uuc = KuuufVf + urn'( 1 - Vf)

Ec = KEEfVf + Em(1- vf) (1)

( 2 ) where uUc is the ultimate strength of the composite; K , is the fiber efficiency factor for strength; a,, is the ultimate strength of the reinforcing fiber; Vf is the fiber volume fraction; urn' is the matrix stress at the fracture strain of the composite; E , is the Young's modulus of the composite in the plane of the fibers; K E is the fiber efficiency factor for modu- lus; E, is the modulus of the reinforcing fiber; and Em is the matrix modulus.

5 -

3/4" RADIUS

0 ,;

NOMINAL 2"GAGE SECTION OF ll(WIDTH

Fig. 1 . Diagram of random-in-plane composite tensile speci- men.

1 I I I

OPOLYETHYLENE MATRIX COMPOSITES

I I I I I 1 I

o f I I I I I I I 0 4 8 12 16 20 24 28 3

TENSILE STRAIN, %

Fig. 2. Tensile stress-strain curves of polyethylene/polyester fiber composites. Random-in-plane fiber orientation.

432

Fig . 3. Tensile stress-strain curves of PMMA/Kevlar-49 fiber composites. Random-in-plane fiber orientation.

0 POLYETHYLENE MATRIX COMPOSITES

U P M M A MATRIX COMPOSITES p 25

01 I I I 2

I I 3 4

FIBER TENSILE STRENGTH, 1osPsi

Fig. 4. Composite tensile strength us fiber tensile strength, 20 v/o fiber composites.

-. 3 0 PMMA MATRIX COMPOSITES

I-

a 0 g o 24 32 u

FIBER TENSILE MODULUS, d p s i

Fig. 5. Composite tensile modulus us fiber tensile modulus, 20 o/o fiber composites.

POLYMER ENGINEERING AND SCIENCE, JON€, 1975, Yo/. 15,' No. 6

Mechanical Properties of Dhcontinwus Fiber Reinforced Thermoplastics. II. Random-in-Plane Fiber Orientation

w u) 0

c

In random-in-plane composites, the values for the fiber efficiency factors are relatively small since most fibers lie at some angle to the applied. stress and do not contribute significantly to the reinforcement of mechanical properties. In real composites, a variety of defects act to further reduce the fiber efficiency. Since Young's modulus is determined from the

2ow I I 1 1 *. 0 POLYETHYLENE MATRIX COMWSITES

-

-

u I I I

4 8 12 16

ULTIMATE FIBER ELONGATION, %

Fig. 6. Composite ultimate elongation vs fiber ultimate elonga- tion, 20 v/o fiber Composites.

I I I

0 POLYESTER FIBER COMPOSITES OPRD-49 FIRER COMPOSITES

20 a I- 4

0

0 0 1

0 2 4 6 8 10

MATRIX YIELD STRENGTH, I O ~ ~ ~ ~

Fig. 7. Composite tensile strength vs matrix yield strength, 20 v/o fiber composites.

MATRIX TENSILE MODULUS, 10'psi

Fig. 8. Composite tensile modulus vs matrix tensile modulus, 20 v/o fiber composites.

POLYMER ENGINEERING AND SCIENCE, JUNE, 1975, Vol. 15, No.

initial portion of the stress-strain curve, K E is re- duced by defects such as imperfect fiber orientation, packing defects, and damage to fibers during proc- essing. KU is reduced by these defects and also by poor fiber-to-matrix adhesion, voids and other matrix flaws, and thermal stresses in the composite resulting from differences in coefficients of thermal expansion of matrix and fiber.

K E and KU values for the experimental compos- ites were calculated from the data in Tables 1 and 2. Results are given in Table 3. Fiber efficiency factors for modulus ranged from 0.06 to 0.44 and for strength from 0.00 to 0.25. Instances where KU is greater than KE may be due to 'the fact that, since fiber properties were measured using relatively long fibers, the actual strengths of the short fibers in the composites may have been somewhat higher than the reported values for fiber strength.

Low fiber efficiency factors for strength may have been due to poor fiber-to-matrix adhesion, as in some of the polyethylene matrix composites, or to fracture of a brittle matrix before more ductile reinforcing fibers were carrying much of the applied load, as in PMMA matrix composites reinforced with the lower modulus fibers. Packing defects led to low fiber ef- ficiency factors in composites with the higher volume fractions of reinforcement.

The average value of K E for the random-in-plane composites was 0.19 and the average value of Ko for these materials was 0.11. This compares with average values for K E and KU of 0.43 and 0.25, respectively, for similar composites but with unidirectional fiber orientation ( 1). Thus, to a crude approximation, the fiber efficiency in an unidirectional fiber composite was twice the fiber efficiency in a random-in-plane composite, holding other factors constant.

The question arises as to whether the properties of the experimental random-in-plane composites can be calculated from the properties of the constituent materials. Young's moduli Ell and Ezz for a unidirec- tional short-fiber composite can be calculated from the Halpin-Tsai equation (3 )

where

i = 2 ( z ) L ( 5 )

EZ2 is calculated using the same equation with 5 = 2. Approximations for the in-plane modulus of a random-in-plane composite have been proposed by

1 3

cox (41,

E = - E Z i (6 )

by Loewenstein ( 5 ) ,

6 433

Bruce F . Blumentritt, Ban T . Vu, and Stuart L. Cooper

Table 3. Fiber Efficiency Factors for Experimental Composites ~~

Polymethyl lonomer Polyethylene Nylon 12 Polycarbonate methacry late

Reinforcement Vf KE Ka KE KLT KE KLT KE KI7 KE K,

Nylon 6/6

Polyester

Poly(viny1 alcohol)

Glass

Kevlar-49

Graphite

20 30 40 50

10 20 30 40 50

10 20 30 40 50

10 20 30 40

10 20 30 40 50 10 20 30 40 50

0.23

0.22

0.15 0.24 0.21 0.22 0.22

0.32

0.27

0.21 0.19 0.21 0.17

0.19

0.13 0.12

0.17 0.15 0.11 0.10 0.07

- -

- -

-

- -

0.06

0.06

0.05 0.12 0.11 0.08 0.08

0.16

0.10

0.19 0.17 0.14 0.14

0.21

0.14 0.12

0.16 0.17 0.12 0.10 0.05

- -

-

- -

- -

0.12

0.27 0.28

0.18 0.17 0.18 0.18 0.20

0.19 0.20 0.16 0.16 0.15

0.18 0.18 0.20 0.21

0.16

0.13 0.11

0.16 0.12 0.11 0.09 0.06

-

- -

0.03

0.04 0.04

0.02 0.04 0.09 0.08 0.10

0.02 0.04 0.04 0.03 0.03

0.23 0.12 0.17 0.15

0.11

0.12 0.11

0.14 0.12 0.08 0.04 0.03

-

- -

0.12

0.34 0.35

0.20

0.31 0.31

0.28

0.30 0.34

-

- -

- -

- - - -

0.15 0.12 0.12 0.11 0.12 - - - - -

0.08

0.12 0.12

0.12

0.14 0.15

0.13

0.12 0.13

-

- -

- -

- - - -

0.18 0.14 0.14 0.16 0.17 - - - - -

- - - - - - - - - - - - - -

0.21 0.17 0.25 0.26

0.13

0.14 0.14

0.24 0.15 0.14 0.10

- -

-

- - - - - - - - - - - - - -

0.14 0.13 0.18 0.13

0.14

0.19 0.16

0.21 0.12 0.10 0.08

- -

-

0.12 0.33

0.22

0.20

0.19 0.20

0.44

0.43

0.25 0.17 0.19 0.18

0.20 0.30 0.19 0.16 0.15

0.20 0.16 0.13 0.11 0.10

-

- -

-

-

-

0.00 0.00

0.05

0.03

0.04 0.06

0.09

0.06

0.15 0.06 0.06 0.07

0.25 0.25 0.24 0.20 0.20

0.24 0.16 0.13 0.07 0.07

-

- -

- - -

3 E = - E I ,

8

and by Tsai and Pagano ( 6 )

( 7 )

When properties of the fibers and matrices used in this study were inserted into Eq 3-5, the cal- culated values for Ell were only slightly less than modulus values predicted by the rule of mixtures. Calculated values for the in-plane modulus of the random-in-plane composites were significantly higher than the measured modulus values, even when the Cox approximation was used. Apparently, because of the defects present in the experimental materials, composite modulus values cannot be cal- culated from the properties of the constituents unless some empirical relation is used. Since composite strength properties are more difficult to predict than modulus properties, composite strengths also cannot be predicted from the properties of the constituents.

It remains to be determined whether the prop- erties of random-in-plane composites can be calcu- lated from experimental data on corresponding uni- directional fiber composites. Data on unidirectional short-fiber composites presented in ( 1 ) were used

434

with E q 8 to calculate moduli of corresponding ran- dom-in-plane composites. Results are shown in Fig. 9. Agreement between calculated and experimental values was good at the lower fiber concentrations but the calculated moduli were higher than the experi- mental values in composites with high fiber concen- trations. This deviation may be explained by the rapid increase in the concentration of packing de- fects in the experimental composites with the higher fiber concentrations.

Lees ( 7 ) and Chen (8) have suggested expres- sions which can be used to calculate the strength of random-in-plane composites from data on the corre- sponding unidirectional fiber composites. These au- thors noted that, in composites with unidirectional fiber orientation, different fracture mechanisms be- come operative as the angle between the applied stress and the fiber axis is varied from 0 to 90 deg. The strength of a random-in-plane composite was assumed to be equal to the strength of a correspond- ing unidirectional composite integrated over the fi- ber orientation angles from 0 to 90 deg. The Lees equation is

7r -+In- u22um' P 1 (9 )

and the Chen equation is:

POLYMER ENGlNEERlNG AND SCIENCE, JUNE, 1975, Vol. 15, No. 6

Mechanical Properties of Discontinuous Fiber Reinfmced Thermoplastics. 1Z. Random-in-Phw Fiber Orientdim

E

A. NYLON 12/PRD-49 FIBER COMPOSITES I I

CALCULATED

E XPERlMfNTAL

5 O L - 0 lo 20 30 40 50

VOWME Yo FIBERS

B. PMMA/PRD-49 FIBER COMPOSITES 2 0 0 .-

CALCULATfD

EXPERIMENTAL

Fig. 9. Calculated and experimental tensile moduli of ran- dom-in-plane composites.

where T is the shear strength of the unidirectional fiber composite, uz2 is the transverse strength of the unidirectional composite, and t is a strength d- ciency factor which relates the strength of a discon- tinuous fiber composite to the strength of a corre- sponding continuous fiber composite.

Measured properties of unidirectional fiber com- posites (1, 9) were used with these equations to ca€- culate values for the strength of Kevlar-49 fiber rein- forced random-in-plane composites. In these calcu- lations, the efficiency factor < in E q 10 was approxi- mated by the rule of mixtures efficiency factor KO from E q 1. The calculated and experimental tensile strength values are shown in Fig. 10. Eqs 9 and 10 predict results much lower than the actual strengths. A similar result was reported by Lavengood (10) for epoxy matrix composites.

In general, the prediction of the mechanical prop- erties of discontinuous fiber composites is difficult because of the large number of variables which in- fluence the properties of these materials. Although much is known about the behavior of random-in- plane com sites, work remains to be done both on theory a n r o n process technology before the me- chanical properties of these materials can be ac- curately predicted.

POLYMER ENGINEERINC AND SCIENCE, JUNE, 1975, Vol. 15, No. 6

A. NYLON 12/PRD-49 FIBER COMPOSITFS '% I I

W

z I I I I 10 20 30 40 50

VOLUME Yo FIBERS

B. FWMA/PRD-49 FIBER COMPOSITES m g 40 E XPERlMfNTAL

a I- v)

W 16

n 2 n

n LEES 0 ,

I - I 01 I I I I I 0 10 20 30 40 50

VOLUME O h FIBERS

Fig. 10. Calculated and experimental tensile strengths of random-in-plane composites.

CONCLUSIONS Random-in-plane short fiber reinforced thermo-

plastics can be made which have very good strength, stiffness, and toughness. Tensile strengths over 20,- 000 psi and Youngs moduli over 1,000,000 psi were obtained in a number of the composites. Strength and modulus of the experimental composites in- creased with increasing fiber concentration in the range of 0.10 to 0.50 fiber volume fraction in nearly all cases. Fiber efficiency factors for modulus aver- aged 0.19 and for strength 0.11.

Mechanical properties of the composites generally showed a strong dependence on fiber properties and a lesser dependence on matrix mechanical proper- ties, indicating that the fibers acted as the primary load bearing element. Organic fiber reinforced ther- moplastics tended to have much greater fracture toughness than corresponding inorganic fiber rein- forced thermoplastics due to their greater ultimate elongations.

Existing models for composite mechanical be- havior could not be used to calculate composite properties from the properties of the constituents. Moduli of random-in-plane composites can be cal- culated from the moduli of corresponding unidirec- tional fiber composites. However, experimental strength values for random-in-plane composites are generally much higher than strengths calculated from

435

Bruce F. Blumentritt, Ban T . Vu, and Stuart L. Cooper

unidirectional composite properties using the Lees or Chen models.

ACKNOWLEDGMENT Support of the graduate study of Bruce F. Blumen-

tritt by the IBM Corporation is gratefully acknowl- edged. Materials for this work were supplied by E. I. duPont de Nemours and Co., General Electric Co., Chemische Werk Huels, Kuraray Co., Owens- Corning Fiberglas Co., and Union Carbide Corp.

REFERENCES 1. B. F. Blumentritt, B. T. Vu, and S. L. Cooper, Polym.

2. J. P. Bell, I . Comp. Mat., 3,244 ( 1969). Eng. Sci., 14, 633 (1974).

3. J. E. Ashton, J. C. Halpin, and P. H. Petit, “Primer on Composite Materials: Analysis,” Technomic, Stamford, Conn. ( 1969).

4. J. L. Cox, Brit. J. AppZ. Phys., 3, 72 (1952). 5. K. L. Loewenstein, in “Composite Materials,” Holliday

and Elsevier, eds., New York ( 1966). 6. S. W. Tsai and N. J. Pagano, in “Composite Materials

Workshop,” Tsai, Halpin, and Pagano, eds., Technomic, Stamford, Conn. ( 1968).

7. J. K. Lees, Polym. Eng. Sci., 8, 195 (1968). 8. P. E. Chen, Polyrn. Eng. Sci., 11, 51 (1971). 9. B. F. Blumentritt, B. T. Vu, and S. L. Cooper, unpub-

lished data. 10. R. E. Lavengood, Polym. Eng. Sci., 12,48 (1972).

436 POLYMER ENGINEERING AND SCIENCE, JUNE, 1975, Vol. 15, No. 6