Tetraglycidyl Methylene Dianiline (TGMDA) Epoxy

Fig. B-19. Composite Matrix Resins

Thermoset resins are currently the matrix of choice for composite materials. The matrix holds the fibers in position, protects the fibers from abrasion, transfers loads between fibers, and provides interlaminar shear strength between the layers. The advantages of thermoset resins are high thermal stability, high rigidity, high dimensional stability, resistance to creep and deformation under load, and ease of processing.

B.5 Composites

A composite material can be defined as a combination of two or more materials that results in better properties than when the individual components are used alone. As opposed to metallic alloys, each material retains its separate chemical, physical, and mechanical properties. The two constituents are normally a fiber and a matrix. Typical fibers include glass, aramid, and carbon, while matrices can be polymers, metals, or ceramics. While the fiber reinforcements can be continuous or discontinuous, aligned or random, it is the continuous aligned composite materials that provide the high strength-to-weight and stiffness-to-weight materials that are used in aerospace.

A typical composite material, shown in Fig. B.20, consists of high strength fibers embedded in a matrix. The longitudinal (0°) tension and compression loads are carried by the fibers, while the matrix distributes the loads between the fibers in tension, and stabilizes and prevents the fibers from buckling in compression. The matrix is also the primary load carrier for interlaminar shear (i.e., shear between the layers) and transverse (90°) tension. Since the matrix transfers load to the fibers at the interface through shear, the fiber-to-matrix interface bond is important in assuring that the load transfer is effective. For example, carbon fibers that are used in epoxy resins are chemically surface treated to maximize the bond between the fiber and matrix. For high temperature metal matrix

Fig. B-20. Fiber Reinforced Composite composites, due to the high processing temperatures required to consolidate the matrix, a reaction can occur between the fiber and matrix at the interface. Therefore, protective coatings (diffusion barriers) are usually applied to the fibers to prevent this reaction which can seriously degrade the fiber strength.

Ceramic matrix composites are a little different. While the objective in polymer and metal matrix composites is to obtain a strong interfacial bond, in ceramic matrix composites, the objective is to obtain a weak bond. The strong bond in polymer and metal matrix composites is needed to strengthen the material, to allow effective load transfer between the matrix and the fibers. However, in ceramic matrix composites, where the ceramic matrix is extremely brittle, the main objective is not to strengthen the ceramic but to toughen it. The weak interfacial bond in ceramic matrix composites allows the fibers to debond, deflect cracks and pull-out of the matrix when the ceramic cracks, slowing the propagating cracks through what are called energy dissipating mechanisms.

As previously stated, the fibers provide the strength. The strength of the 0° aligned composite shown in Fig. B.20 can be calculated by the rule of mixtures:

where composite strength fiber strength volume fraction of fibers matrix strength volume fraction of matrix

For example, if the composite contains a volume fraction of 0.6 carbon fibers with a tensile strength of 750 ksi, embedded in an epoxy matrix (0.4 volume fraction) with a tensile strength of 10 ksi, the tensile strength of this 0° composite is then about:

oc = (750ksi)(0.6) + (10ksi)(0.4) = 450 ksi + 4 ksi = 454 ksi A similar expression can be used for the 0° modulus of elasticity:

Ec = Ef Vf + Em Vm where composite modulus fiber modulus volume fraction of fibers matrix modulus volume fraction of matrix

In our example, assume that the fiber tensile modulus is 44 msi and the matrix modulus is 0.5 msi, then:

Ec = (44msi)(0.6) + (0.5msi)(0.4) = 26.4 msi + 0.2 msi = 26.6 msi

These rather simple calculations emphasize that the fiber properties determine the composite properties, at least when a 0° laminate is loaded in tension along the fiber axis. Referring back to Fig. B.20, it should be obvious that the 90° strength is going to be a lot less than the 0° strength, primarily because the much weaker matrix is carrying most of the load. There are also expressions for calculating the 90° strength and stiffness, but they are not as accurate as the 0° calculations, because one has to make assumptions about the strength of the interface bond between the fibers and matrix.

It should be emphasized that 0° laminates are almost never used in engineering structures, because all of the loads almost never line up with the fiber direction. This fact, combined with the low 90° properties, forces designers to use laminates with fibers aligned in multiple directions, for example +45°, -45°, 0°, and 90°.

Fig. B-21. Quasi-isotropic Laminate Lay-up

If a laminate has equal numbers of layers aligned in the +45°, -45°, 0°, and 90° directions, it is called a quasi-isotropic laminate, as shown in Fig. B.21, because the different directions on the x-y plane have about equal strength and stiffness. By way of example, a carbon fiber/epoxy matrix composite with 50% 0° plies and 50% 90° plies will have about the same strength and modulus as a high strength aluminum alloy, but the composite laminate will weigh about 1/2 that of an equivalent thickness of the high strength aluminum alloy.

Note that if the laminate shown in Fig. B.20 is loaded in the z-direction, the strength is again largely dependent on the matrix strength, rather than the fiber strength. This is a weak link in the composite materials we use today. For the proper design of a composite structure, it is important that the strong fibers pick up the load and not the weak matrix. Therefore, composites need stiff and well-defined load paths in the x- and y-directions, with no out-of-plane loading in the z-direction. It should be noted that there is a considerable amount of work being done to put reinforcements in the z-direction, but very few of these concepts are currently used in production designs.

Recommended Reading

[1] Smith, W.F., Principles of Materials Science and Engineering, McGraw-Hill, 1986.

[2] Callister, W.D., Fundamentals of Materials Science and Engineering, 5th edition, John Wiley & Sons, Inc., 2001.

[3] Askeland, D.R., The Science and Engineering of Materials, 2nd edition, PWS-KENT Publishing Co., 1989.

[4] Campbell, F.C., Manufacturing Processes for Advanced Composites, Elsevier Ltd, 2004.


[1] Courtney, T.H., "Fundamental Structure-Property Relationships in Engineering Materials", in Materials Selection and Design, ASM Handbook Vol. 20, ASM International, 1997.

[2] Callister, W.D., "Phase Transformations", in Fundamentals of Materials Science and Engineering, 5th edition, John Wiley & Sons, Inc., 2001, p. 345.

[3] Thrower, P.A., "Bonding", in Materials in Today's World, Revised edition, McGraw-Hill, Inc., 1992, pp. 25-38.

[4] Thrower, P.A., "Crystal Structures", in Materials in Today's World, Revised Edition, McGraw-Hill, Inc., 1992, pp. 39-53.

[5] Callister, W.D., "Deformation and Strengthening Mechanism", in Fundamentals of Materials Science and Engineering, 5th edition, John Wiley & Sons, Inc., 2001, pp. 197-233.

[6] Smith, W.F., "Ceramic Materials", in Principles of Materials Science and Engineering, McGraw-Hill, 1986, pp. 527-595.

[7] Callister, W.D., "Synthesis, Fabrication, and Processing of Materials", in Fundamentals of Materials Science and Engineering, 5th edition, John Wiley & Sons, Inc., 2001.

[8] Campbell, F.C., "Thermoplastic Composites", in Manufacturing Processes for Advanced Composites, Elsevier Ltd, 2004, p. 358.

[9] Smith, W.F., "Polymeric Materials", in Principles of Materials Science and Engineering, McGraw-Hill, 1986, p. 303.

Appendix C

Mechanical and Environmental Properties

This appendix provides some definitions, or explanations, of some of the important mechanical properties and environmental degradation mechanisms that can occur in structural materials. It should be pointed out that these are very brief explanations, often simplified, and that much more extensive explanations can be found in texts dedicated to these subjects.

C.1 Static Strength Properties1

The tensile properties of a material are determined by applying a tension load to a specimen and measuring the elongation or extension. A typical stressstrain curve for a metal is shown in Fig. C.1. The load can be converted to engineering stress (a) by dividing the load by the original cross-sectional area of the specimen.

Ao = original cross-sectional area in in.2

Ultimate Tensile

Failing Stress

0.002 Offset

Ultimate Tensile

Failing Stress

0.002 Offset

Failing Strain

Fig. C-1. Typical Stress-Strain Curve

The engineering strain (e) can be calculated dividing the change in gage length by the original gage length.

where l = gage length l0 = original gage length

As shown in Fig. C.1, the ultimate tensile strength is the maximum stress that occurs during the test. For metals without a definite yield point, the yield strength is determined by drawing a straight line parallel to the initial straight line portion of the stress-strain curve. The line is normally offset by a strain of 0.2% (0.002). Yield strength is generally a more important design parameter than ultimate strength, since the possibility of plastic yielding is unacceptable for almost all structures.

The modulus of elasticity (E) is determined by taking the slope of the initial straight line portion of the stress-strain curve. The higher the modulus of elasticity, the stiffer is the material.

E = Aa/Ae expressed in msi (millions of pounds/in.2).

Percent elongation and reduction of area are measures of ductility, with higher values indicating greater ductility. Since percent elongation is sensitive to the gage length, it is important to record the gage length used when reporting percent elongation. In general, shorter gage lengths result in higher values for percent elongation. Percent elongation can be determined by:

% Elongation = {(lf — l0)/l0} x 100 where l0 = original gage length lf = final length of the gage section

Likewise, reduction in area can be determined by the tensile test.

A0 = original area of the gage section

Af = final area of the gage section

Static compressive properties are determined in a similar manner, except the specimen is loaded in compression rather than tension.

C.2 Failure Modes12

Failure modes can be classified into four general categories: ductile failures, brittle failures, decohesive or intergranular failures, and fatigue failures.

Ductile failures are associated with large amounts of plastic deformation. As a result of plastic deformation, localized necking or distortion is often present. Ductile failures occur by tearing of the metal with a large expenditure of energy. Microscopically, ductile failures occur by a process of microvoid nucleation and growth (Fig. C.2). Microvoids form at stress concentrations, and are most frequently initiated by constituent particles, followed by void formation and growth around the particles, or by particle cracking. In aluminum alloys, the constituent particles that most often initiate mircovoids are quite large (> 1 ^m) particles of Al7Cu2Fe, Mg2Si, and (Fe, Mn)Al2. Note that these particles contain iron and silicon. Many improvements in the properties of aluminum alloys have been a result of lowering iron and silicon impurity levels.

The mircovoids then coalesce, and grow, to produce larger voids until the remaining area becomes too small to support the load and failure occurs. Shear lips, due to slip mechanisms, often occur at angles approaching 45° to the applied tensile stress, to form the well-known cup and cone fracture appearance.

Brittle fractures are generally flat, with little or no evidence of localized necking. Glasses and crystalline ceramics, when fractured at room temperature, fracture in a purely brittle manner, with no evidence of plastic deformation.

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