Assemblages of layers of fibrous composite materials (see illustration) which can be tailored to provide a wide range of engineering properties, including inplane stiffness, bending stiffness, strength, and coefficients of thermal expansion.
The individual layers consist of high-modulus, high-strength fibers in a polymeric, metallic, or ceramic matrix material. Fibers currently in use include graphite, glass, boron, and silicon carbide. Typical matrix materials are epoxies, polyimides, aluminum, titanium, and alumina. Layers of different materials may be used, resulting in a hybrid laminate. The individual layers generally are orthotropic (that is, with principal properties in orthogonal directions) or transversely isotropic (with isotropic properties in the transverse plane) with the laminate then exhibiting anisotropic (with variable direction of principal properties), orthotropic, or quasi-isotropic properties. Quasi-isotropic laminates exhibit isotropic (that is, independent of direction) inplane response but are not restricted to isotropic out-of-plane (bending) response. Depending upon the stacking sequence of the individual layers, the laminate may exhibit coupling between inplane and out-of-plane response. An example of bending-stretching coupling is the presence of curvature developing as a result of inplane loading. See Composite material, Metal matrix composite
Classical lamination theory describes the mechanical response of any composite laminate subjected to a combination of inplane and bending loads. The laminate in Fig. 1 uses a global x-y-z coordinate system with z perpendicular to the plane of the laminate and positive downward. The origin of the coordinate system is located on the laminate midplane. The laminate has N layers numbered from top to bottom. Each layer has a distinct fiber orientation denoted Θk. The z coordinate to the bottom of the kth layer is designated zk with the top of the layer being zk-1. The thickness, tk, of any layer is then tk = zk - zk-1. The top surface of the laminate is denoted z0, and the total thickness is 2H.
It is assumed that (1) there is perfect bonding between layers; (2) each layer can be represented as a homogeneous material with known effective properties which may be isotropic, orthotropic, or transversely isotropic; (3) each layer is in a state of plane stress; and (4) the laminate deforms according to the Kirchhoff (1850) assumptions for bending and stretching of thin plates: (a) normals to the midplane remain straight and normal to the deformed midplane after deformation, and (b) normals to the midplane do not change length.
The wide variety of coefficients of thermal expansion are possible through changes in the stacking arrangement of a given carbon/epoxy. The coefficient of thermal expansion is the strain associated with a change in temperature of 1°. Most materials have positive coefficients of expansion and thus expand when heated and contract when cooled. The effective axial coefficient of thermal expansion of the carbon/epoxy can be positive, negative, or zero, depending upon the laminate configuration. Laminates with zero coefficient of thermal expansion are particularly important because they do not expand or contract when exposed to a temperature change. Composites with zero (or near zero) coefficient of thermal expansion are therefore good candidates for application in space structures where the temperature change can be 500°F (from -250 to +250°F) [278°C (from -157 to +121°C)] during an orbit in and out of the Sun's proximity. There are many other applications where thermal expansion is a very important consideration.