Metal Matrix Composites

Metal Matrix Composites

1 Metal Matrix Composites WILLIAM C. HARRIGAN, Jr. DWA Composite Specialties, Inc. Chatsworth, California I. Introduction II. Powder Metallurgy Comp...

789KB Sizes 0 Downloads 20 Views

1

Metal Matrix Composites WILLIAM C. HARRIGAN, Jr. DWA Composite Specialties, Inc. Chatsworth, California

I. Introduction II. Powder Metallurgy Composites A. Whisker Reinforcement B. Particulate Reinforcement C. Particulate versus Whisker D. Mechanical Properties E. Other Reinforcements III. Cast Composites IV. Continuous Fiber Composites A. Large-Diameter Fiber Composites B. Graphite Fiber Composites References

1 2 2 3 5 7 10 11 12 12 13 15

I. Introduction Metal matrix composites as we know them today have evolved over the past 20 years. The primary support for these composites has come from the aerospace industry for airframe and spacecraft structures. More recently, the automotive, electronic, and leisure industries have been seriously working with these composites. At the present time, metal matrix composites can be classified into either continuous fiber composites or discontinuously reinforced composites. These reinforcements have been introduced into aluminum, magnesium, copper, titanium, titanium aluminides, nickel, nickel aluminides, nickel-based superalloys, and various alloys of iron. The aluminum matrix alloy composites are the only ones that have become widely available. The discontinuous reinforced composites have become the most commonly used to date and will be discussed first. The continuous fiber composites are finding limited applications that can take advantage of their unique properties. These composites will be discussed later. 1 Copyright © 1991 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-341832-1

2

W.C. HARRIGAN, JR.

II. Powder Metallurgy Composites Discontinuously reinforced metal matrix composites are a class of materials that exhibit a blending of properties of the reinforcement and the matrix. The reinforcement can be ultra-high strength whiskers, short or chopped fibers, or particles. Each of the reinforcements has property or cost attributes which dictates use in a given situation. The blend of these powders is compacted into a die, the compact is vacuum-hot-pressed to form a billet, and the billet is hot worked into a usable form. At the present time, billets are available from DWA in 15-cm (6-in), 20-cm (8-in), and 35-cm (14-in) diameters. The typical weights for these billets are 9 kg (20 lb), 30 kg (65 lb), and 90 kg (200 lb), respectively. Approximately the same size billets are also available from ACMC. All of these composites have the advantage of being formable by more or less standard metalworking practices. Because of their basis as a powder, these composites must be metal worked to develop the best properties. The composites behave in a manner similar to new high-strength aluminum alloys made by the powder metallurgy technique [/], i.e., the prior particle oxide skins must be broken up by metalworking before the true properties of the matrix metal and, hence, the composite can be achieved. The most common primary breakdown process has been extrusion. Other metalworking processes, such as rolling, forging, shear spinning, and swaging, have been demonstrated. Machining, drilling, or grinding do not cut or break critical fibers and therefore do not degrade mechanical properties. However, the ceramic reinforcements give rise to dulling of the machine tools, which therefore decreases the machinability of these composites. The qualities of low-cost components and use of existing metalworking equipment have contributed to the rapid growth in the use of this form of metal matrix composite. A.

Whisker Reinforcement

Early work in this area was done by Brenner [2, 3] and Sutton [4, 5] with alpha A1203 whiskers. The cost of the whiskers was high, and the strengths achieved were lower than expected, due to bonding difficulties with the alumina whiskers. These difficulties were never overcome, and this composite system never matured. Work by Divecha et al [<5] with beta SiC whiskers in aluminum demonstrated very good strength, modulus, fatigue resistance, and elevated temperature properties. However, high cost for these whiskers limited the continued development of this system. In the late 1970s, researchers at the University of Utah developed a process

1 METAL MATRIX COMPOSITES

3

for making SiC whiskers with rice hulls as the starting ingredient. This made SiC whiskers potentially low cost and prompted renewed research with this form of composite [7, 8, 9, 10]. These SiC whisker are approximately 0.1 micron in diameter and have length-to-diameter ratios as-produced of up to 100 to 1. A high percentage of the original whisker product in 1980 was fine powder rather than whisker. Many improvements have taken place in the processing of the whiskers in subsequent years, and the majority of the present product is high-aspect-ratio (length/diameter) whisker. The most common technique for producing whisker-reinforced aluminum composites in the United States is by powder metallurgy processing. The blending of high-aspect whiskers with metal powders is limited to a volume loading of approximately 25% due to the geometry of the whiskers. The majority of the whisker composite made in the last two years has a whisker content of 15 vol.%. Growth in this area is demonstrated by the emergence of multiple producers of the product. Originally the University of Utah patent was used by Silag Corporation. At the present time that organization has evolved into ACMC division of Tateho Corporation of America. This company has been joined by several other Japanese companies, Tokai Carbon and Tateho Corporation.

B. Particulate Reinforcement In 1978 DWA Composite Specialties, Inc., introduced an alternative form of this composite, with silicon carbide particulates as the reinforcement. Examples of silicon carbide particulates are shown in Fig. 1. These particulates are commercially available in sizes from approximately 0.5 micron to greater than 100 microns. They are available in narrow size ranges, as shown in the AISI size distribution specification in Fig. 2. The particulates more closely match the particle size and size distribution for commercially available aluminum powders. The particulates can therefore be blended more efficiently and at higher volume percents than can the whisker products. Composites containing 40 vol.% particulates are common, and composites with up to 55 vol.% particulates are being developed. Particulates are currently produced in large quantities for the abrasives industry and are currently low priced. The SiC particulates also have a high modulus (380 GPa) and a low density (3.21 g/cc). In 1988, DWA produced 182-kg (400-lb), 45-cm (17.5-in) diameter billets that were pierced by back extrusion to produce a 29-cm (11.5-in) inside

W.C. HARRIGAN, JR.

FIG. 1. Scanning electron micrograph of silicon carbide particles.

diameter tube, and then forward-extruded into 30.5-cm (12-in) OD by 29-cm (11.5-in) ID tubes that were over 10 m (34 ft) long. A photograph of one of these tubes being chem-milled is shown in Fig. 3. This tube, which weighed 148 kg (325 lb) before chem-milling and 132 kg (290 lb) after, is the largest structure made with metal matrix composite to date. This tube was prooftested by securing the ends of the tube and applying up to 5000 kg (11,000 PARTICLE SIZE DISTRIBUTION FOR SILICON CARBIDE

80%·

70%-

Ç

50 % 40%·

30%20%10%·

10.0 PARTICLE SIZE ( microns )

FIG. 2. Size distribution for silicon carbide particles.

1

METAL MATRIX COMPOSITES

FIG. 3. Photograph of 30.5-cm OD by 29-cm ID by 10-meter tube (20 vol.%SiC/6061 Al composite) being chem-milled.

lb) at midspan and measuring the deflection as a function of the load. This test confirmed that the tube responded in an elastic manner with a Young's modulus of 110 GPs (16 million psi) as expected for the 20% SiC/6061 Al composite. This tube was made to replace an aluminum tube in the catamaran Stars and Stripes '88. The tubes were 20% lighter than the aluminum tubes because of the increased modulus in the composite and the stiffness design of the crossbeam. G

Particulate versus Whisker

The majority of the work between 1978 and 1984 involved testing composites that contained either particulates or whiskers. These composites were made by blending atomized powders with the SiC reinforcement. The studies attempted to demonstrate that whisker or particulate reinforcement produced a superior product. All of these studies were flawed because the composites that were compared had reinforcement levels that were different, or else the amount and type of secondary processing were different for each system.

W.C. HARRIGAN, JR.

FIG. 4.

Photograph of SiC/Al composite emerging from extrusion press.

With particulate reinforcement, extrusion of these composites through conical as well as shear face dies is acceptable practice. Photographs of extrusion of the composite taking place are shown in Fig. 4. Typical cross sections of extrusions are shown in Figs. 5 and 6. In order to preserve the whiskers, the extrusion of these composites is restricted to conical or streamline dies [77]. Even with these precautions, substantial whisker breakage is experienced during metalworking. Extrusion of these composites produces alignment of the whiskers and anisotropic mechanical properties. By 1984 the particulate and whisker forms of the composite were characterized to a point where valid comparisons could be made. For a given

FIG. 5. Photograph of plate cross section extrusions.

1

METAL MATRIX COMPOSITES

FIG. 6.

Photograph of tube cross section extrusions.

reinforcement level, a given matrix alloy, comparable metalworking, and heat treatment prior to testing, the whisker composites tend to have higher modulus values in the extrusion (alignment) direction and lower values than the particulate composites in the perpendicular directions. Whisker composites have approximately the same yield strength, a higher ultimate strength, and a lower strain to failure than do particulate reinforced composites in the extrusion direction. Whisker composites have lower properties in the directions perpendicular to the extrusion. In addition, they are limited to a maximum of 25 vol.% due to blending difficulties mentioned earlier. The present cost of whiskers is lower than for earlier products; however, these costs are still substantially higher than the particulates used for reinforcing aluminum alloys, and this is limiting the development of uses for whisker composites.

D.

Mechanical Properties

Silicon carbide particulate-reinforced aluminum composites have transverse tensile properties that are within 5% of the longitudinal properties. In situations requiring multidirectional reinforcement, these composites can outperform fiber-reinforced composites. The shear strength of these composites is greater than the matrix alloy (Table I). This increased shear strength is also reflected in an increase in pin bearing strength (Table II). These bearing strength data are for tests conducted with the center of the pinhole 1.5 and 2 times the pin diameter from the sample edge. These edge distances are more typical of metals than of graphite or glass fiber composites. The SiC/Al composites are thus able to save material and weight by reducing

W.C. HARRIGAN, JR. TABLE I SHEAR STRENGTH OF SIC-PARTICULATEREINFORCED ALUMINUM COMPOSITES

Shear strength (MPa)

Composite 6061 Al (T-6) 25 vol.% SiC/6061 Al 30 vol.% SiC/6061 Al 7075 Al (T-6) 25 vol.% SiC/7091 Al 30 vol.% SiC/7090 Al 2124 Al (T-4 & T-6) 2124 Al (T-81) 25 vol.% SiC/2124 Al

207 277.9 289.6 269 379.2 430.9 283 295 344.8

(T-6) (T-6) (T-6) (T-6)

(T-4)

the excess edge material at joints. These properties were exploited by Lockheed California Co. Electronic racks were made by Lockheed for military aircraft from over 10,000 ft of thin extrusions of 25% SiC/6061 Al composite that was made by DWA Composite Specialties, Inc. These racks were 25% lighter than the aluminum racks that they replaced and were 10% lighter than the graphite/epoxy racks that they also replaced. A photograph of one of these racks is shown in Fig. 7. The expansion of the aluminum is decreased as SiC is added to the composite (Fig. 8). The expansion coefficient is decreased from 13 ppm/°F for aluminum to 6 ppm/°F for 40 vol.% SiC composites. This expansion behavior is isotropic. A design of an advanced-composite optical-system TABLE II PIN BEARING STRENGTH OF SIC-PARTICULATE-REINFORCED ALUMINUM COMPOSITES

Composite 7075 Al (T-73) 20 vol.% SiC/7091 Al (T-6)

2024 Al (T-852) 25 vol.% SiC/2124 Al (T-4)

Edge distance (pin diameters)

Bearing yield strength (MPa)

Bearing ultimate strength (MPa)

1.5 2.0 1.5 2.0 3.0 1.5 2.0 2.0

593 703 690 1000 1000 570 696 827

710 134 724 1310 1448 613 823

1

9

METAL MATRIX COMPOSITES

FIG. 7. Photograph of two-meter-long electronic rack made from extrusions of discontinuous reinforced aluminum composite extrusions.

27

15

& 23

13

S

20

11 UJ

SJ

16

^

Ü ■—

:Γ^ν^

O

LU

O

12

O

0) 2

-J

_

(0

■^-J 3

5

[ U . . .

0

.... 10' ' * '

20

30

40

-i

50

SILICON CARBIDE CONTENT (vol %) FIG. 8.

Expansion coefficient of SiC/Al composite as a function of SiC content.

10

W.C. HARRIGAN, JR.

FIG. 9. Photograph of precision-forced guidance access covers made with low-expansion SiC/Al composite.

gimbal by General Electric Co. [12] used 40 vol.% SiC-particulate-reinforced 6061 Al in low-expansion and joint areas combined with graphite/ epoxy in ultra-low expansion areas and won first place in Materials Engineering 1985 competition. The low-expansion behavior of this composite is also being used in place of beryllium for guidance components [13] (Fig. 9). This composite material is being considered for connecting rods since the expansion is similar to steel, and this will reduce the large-end, crankshaft clearance problems encountered with aluminum alloys in this application. The expansion characteristics of the whisker composites are similar to the particulate composites, with some degree of anisotropy due to the whisker alignment and some restriction by the reinforcement limit of 25% whisker mentioned earlier.

E.

Other Reinforcements

In the early 1980s, composites were made with short, polycrystalline alumina fibers (trade name SAFFIL). These alumina fibers were first used by Toyota Motor Company to reinforce the ring land area of diesel pistons [14]. This development was brought about by the advent of improved grades of the fiber at relatively low cost with high volume availability. These pistons were made by a squeeze-casting process that was described by Dinwoodie, et al [15]. The short fibers did not increase the ultimate strength of the matrix alloy at room temperature; however, the strength is retained to

1 METAL MATRIX COMPOSITES

11

temperatures approximately 573 K rather than 473 K for the base alloy. The elastic modulus of the composite is substantially increased over that of the matrix at all temperatures. In addition, the incorporation of the fibers decreases the coefficient of thermal expansion. This combination of properties has made the piston a technical success. The pistons have become a commercial success because the earlier version of the Toyota piston was squeeze-cast with a Ni-resist ring inserted into the mold before casting. The replacement of the metal ring with a fiber preform ring did not increase the manufacturing costs and produced a lighter piston for a comparable cost. Because of this success, other manufacturers have reported on production of other pistons reinforced with short fibers [16]. However, to date, there have not been any similar inroads into manufacturing components with metal matrix composites in the United States. It seems that the philosophy of the Japanese industry is to take chances on using new materials to develop an understanding of the production of these materials. American industry is too worried about "the bottom line" and will not commit to new materials. American R & D commitments are for the next quarter, whereas the Japanese are committed for multiyear programs.

III.

Cast Composites

In 1985, Schuster [17] presented data for SiC-particulate-reinforced aluminum composites made by casting techniques. The particles are coated for protection, injected into a stirred melt of aluminum, and then cast into a mold. The primary reason for working with the casting technique is the potential for low-cost billet manufacture and the possibility of replacing standard castings with reinforced castings. Casting to date has been carried out in sand molds, permanent steel molds, and investment molds. There is a limit on the amount of reinforcement due to increase in viscosity as the particles are added. Reinforcement levels as high as 35 vol.% have been attempted; however, the reinforcement level is normally kept to a maximum of 20 vol.%. These composites do not have prior particle boundaries due to the powder processing, but they do have a cast microstructure which must be dealt with before and during metalworking. These composites have isotropic modulus values lower than those of the PM processed particulate composites. The yield strengths, ultimate strength, and ductility of the cast and metalworked composites are lower than the PM composites that have undergone comparable metalworking. These composites have expansion properties and wear resistance that are functions of the SiC particle content.

12

W.C. HARRIGAN, JR.

During 1988, billet sizes for cast composites have increased from nominal 9.1 kg (20 lb) to 45 kg (100 lb) by increasing the length of the 15-cm (6-in) diameter billet. The 45-kg billet is approximately 1 m long and exceeds the maximum container size for most extrusion presses. This billet must be cut to be extruded. Late in 1988 a larger billet diameter, 18 cm (7 in), became available, and reinforcement was changed from SiC to A1203 for the wrought alloy versions of the composite. The cast microstructure of these composites is characterized by the ceramic reinforcement being associated with the last liquid to freeze. Even though the particles are wet by the aluminum, they are rejected by the primary solidifying phase and are segregated to the eutectic regions of the castings [18, 19]. Another consequence of this segregation is the presence of microshrinkage at or near the ceramic/metal interface. This microshrinkage casting defect has been overcome almost completely by hot isostatic pressing (HIP) of the castings, either billets or net castings, but this process adds cost [20]. Aluminum oxide-reinforced composites also have a spinnel formation at the alumina/aluminum interface. This reaction depletes magnesium from the alloy and changes the heat-treat response of the alloys [21, 22].

IV. Continuous Fiber Composites Continuous fiber composites derive most of their properties from the reinforcing fibers. These are the materials that one generally thinks of when the term composite is used. These composites have very high strength and modulus values in the fiber direction. At angles of 10° from the fiber direction, the strength values of the composite are approximately 50% of the 0° values [23]. At 90° from the fiber direction, the strength values are less than 10% of the 0° values. The modulus of the composites is not as sensitive to the fiber orientation [23], If multiple loading directions are anticipated, the fibers can be aligned in order to resist the loads. However, this placing the fibers in many directions decreases the maximum strength and stiffness values in any direction. A.

Large-Diameter Fiber Composites

From 1960 to 1970 a large effort was made to develop continuous fibers for reinforcements. These fibers included boron on tungsten, silicon carbide on tungsten, and single-crystal alumina. The boron and silicon carbide fibers

13

1 METAL MATRIX COMPOSITES TABLE III PROPERTIES OF FILAMENTS

Filament E-Glass Boron Silicon carbide Alumina

Tensile strength (GPa)

Elastic modulus (GPa)

Density ratio (g/cc)

Strength/Density (107 cm)

3.45 3.10 2.41 2.41

72.4 400 379 483

2.5 2.6 3.4 3.98

1.38 1.19 0.72 0.62

were produced by vapor deposition on to a heated tungsten substrate [24]. These fibers were approximately 100 microns in diamter, and later these diameters grew to 140,200, and even 280 microns. Typical properties of these fibers are listed in Table III. Many studies have been conducted to define the performance of thesefibersin matrices, such as aluminum, copper, nickel, and titanium. The fibers were oriented in a single direction as well as in elaborate multidirection configurations such as (0, ±45, 90, ±45, 0). Many prototype parts and structures have been successfully produced and tested; however, the only structure that has found its way into service is a tube. Boron/Aluminum tubes make up the mid-fuselage structure in the space shuttle. The continuing development of large-diameter fiber composites has been complicated by several interrelated problems. The cost of the fibers is high, but it can be reduced if a market develops and large quantities of the fibers are produced. There is only one producer of the fiber in the United States. A second source for large diameter silicon carbide fibers emerged in 1989, BP with the sigmafiber.If this form of metal matrix composite is to develop, the cost of the fiber must come down and the fiber must be available as a product for second source development. The sigma fiber impacts this development issue. B. Graphite Fiber Composites In 1970 researchers at the Aerospace Corporation successfully produced graphite fiber/aluminum composites [25, 26]. The fine diameter of the graphite fibers, (~10 microns), made composite fabrication by diffusionbonding techniques with individual filaments (so successful with the boron/ aluminum system) impossible. The composite was produced by vapordepositing titanium and boron onto the graphite fibers and then liquidmetal-infiltrating the coated graphite fiber tow [27]. The codeposition of

14

WC. HARRIGAN, JR.

titanium and boron produces a coating that allows molten metals such as aluminum, magnesium, copper, lead, and tin to wet the graphite fiber bundle, yet it protects the graphite fiber from attack by the metal. This process produces a continuous infiltrated tow offibersthat resembles a wire. This wire is cut into lengths, aligned in mats, and diffusion-bonded into structures. During the 1970s researches built and tested many stiffness and specific strength critical structures. None of these structures were translated into service, due to shear, compression, and traverse strength limitations of the graphite/metal composites. In 1980 researchers at Lockheed Missiles and Space Corporation identified the ultra-low expansion, high thermal conductivity, and high stiffness combination of properties that makes graphite/aluminum (or magnesium) composites attractive for thermally stable spacecraft structures [28]. The ultra-low, zero, or negative expansion characteristics of these composites are brought about by the combination of the negative expansion of the high-modulus graphite fibers and the positive expansion of the metal matrix. This program led to the production of graphite/aluminum composite high-gain antenna booms for the Hubble space telescope. One of these structures is shown in Fig. 10. Much of the effort of the 1980s has been to develop processes to manufacture zero-expansion tube structures with the graphite/aluminum or magnesium composites. An example of one of these structures is shown in Fig. 11. This triangular truss was designed to have a negative expansion in the tubes to counteract the positive expansion of the end fittings. This truss was tested for thermal stability and was found to have a net negative 0.15 ppm/°F expansion coefficient, i.e. zero.

FIG. 10. Photograph of graphite/aluminum composite 3-m long high-gain antenna boom for the Hubble space telescope.

15

1 METAL MATRIX COMPOSITES

FIG. 11. Photograph of zero expansion tube truss made from P100 graphite/aluminum tubes and B4C/aluminum composite end fittings. Truss dimensions: length = 1.2 meter, triangle dimension = 0.9 meter.

The continuing development of the ultra-high (650 GPa and higher) modulus-pitch-based graphite fibers has led to the development of graphitefiber-enhanced thermal conductivity. The highly graphitized fibers exhibit thermal conductivity that is higher than that of pure silver. Sheets of graphite/fiber aluminum composites have thermal conductivity that rivals pure copper at a fraction of the weight. These sheets also have much superior strength and stiffness. The cost of the very high modulus fibers is extremely high, $750 to $2000 per kilogram; however, the unique properties of the composites made with these fibers have not prevented the further development of this composite. These composites are being considered for use in space structures and as protection systems for electronic circuits. Both of these applications involve expensive, unique systems that can justify the high cost of these fibers.

References 1. F. R. Billman, J. C. Kuli, G. J. Hildeman, J. T. Petit, and J. D. Walker, "Processing of P/M Aluminum Alloys 7090 and 7091," Presented at The Third Conference on Rapid Solidification Processing: Principles and Technology, December 1982. 2. S. S. Brenner, J. Appl Phys. 33, 33 (1962). 3. S. S. Brenner, J. Metals 14(11), 808 (1962).

16

W.C. HARRIGAN, JR.

4. W. H. Sutton, "Whisker Composite Materials—A Prospectus for the aerospace designer," Astronautics and Aeronautics, August 1966, 46. 5. W. H. Sutton and J. Chorn, Metals Engin. Quart. 3(1), 44 (1963). 6. A. P. Divecha, P. Lare, and H. Hahn, "Silicon Carbide Whisker-Metal Matrix Composites," AFML-TR-69-7, May 1969. 7. D. L. McDaniels, Met. Trans. 16A, 1105 (1985). 8. R. J. Arsenault, Mat. Sei. Eng. 64, 171 (1984). 9. C. R. Crow, R. A. Gray, and D. F. Hasson, in "Proceedings of ICCM Y" (W. C. Harrigan, Jr., J. Strife, and A. K. Dhingra, eds.) p. 843, AIME, 1985. 10. A. P. Divecha, S. G. Fishman, and S. D. Karmarkar, /. Metals 9, 12 (1981). 11. H. Gaegle, private communication, 1985. 12. 1985 Top Twenty Awards, Materials Engineering, November (1985). 13. W. R. Mohn, "Dimensionally Stable SXA Engineered Metallic Composites for Guidance Systems and Optics Applications," Presented at ASM Materials Week Conference, October 1986. 14. T. Donomoto, K. Funatani, N. Miura, and N. Miyake, Society of Automotive Engineers Paper No. 830252, March 1983. 75. J. Dinwoodie, E. Moore, C. A. J. Langman, and S. Symes, in "Proceedings of ICCM Y" (W. C. Harrigan, Jr., J. Strife, and A. K. Dhingra, eds.), p. 671, AIME, 1985. 16. M. Toaz and M. Smalc, Diesel Progress North America, p. 56, June 1985. 17. D. Schuster, "Cast Metal Matrix Composites," Presented at ASM Materials Week Conference, October 1986, Orlando, Florida. 18. P. K. Rohatgi, F. M. Yarandi, and F. Liu, in "Cast Reinforced Metal Composites" (S. G. Fishman and A. K. Dhingra, eds.), p. 249, ASM International, 1988. 19. J. W. McCoy and F. E. Wawner, in "Cast Reinforced Metal Composites" (S. G. Fishman and A. K. Dhingra, eds.) p. 237, ASM International, 1988. 20. D. J. Lloyd and Chamberlain, in "Cast Reinforced Metal Matrix Composites" (S. G. Fishman and A. K. Dhingra eds.) p. 263, ASM International, 1988. 21. C. M. Friend, T. Horsfall, S. D. Luxton, and R. J. Young, in "Cast Reinforced Metal Matrix Composites" (S. G. Fishman and A. K. Dhingra, eds.) p. 309, ASM International, 1988. 22. "Boron Filament Process Development, Boron Trichloride-Tungsten Process," Vol. 1, AFML-TR-67-120, May 1967. 23. P. W. Jackson and D. Cratchley, J. Mech. Phys. Solids 14, 49 (1966). 24. J. C. Whithers, L. C. Handel, and R. T. Schwartz, in "Advanced Fibrous Reinforced Composites," 10th SAMPE Symposium, San Diego, California, November 1966. 25. R. T. Pepper, R. C. Rossi, J. W. Upp, and W. C. Riley, Aerospace Corporation Report Number TR-0059(9250-03)-l, August 1970. 26. R. T. Pepper, J. W. Upp, R. C. Rossi, and E. G. Kendall, Met. Trans. 2, 117 (1971). 27. W. C. Harrigan, Jr., and R. Flowers, in "Failure Modes in Composites IV" (J. A. Cornie and F. W. Crossman, eds.), p. 319, AIME, 1977.