Lamina composite materials

Laminates aie materials made up of plies or laminae stacked up like a deck of cards and bonded together. Plywood is a common example of a laminate. It is made up of thin pHes of wood veneer bonded together with various glues. Laminates ate a form of composite material, ie, they ate constmcted from a continuous matrix and a reinforcing material (1) (see also Reinforced plastics). 

Unlike most conventional materials, there is a very close relation between the manufacture of a composite material and its end use. The manufacture of the material is often actually part of the fabrication process for the structural element or even the complete structure. Thus, a complete description of the manufacturing process is not possible nor is it even desirable. The discussion of manufacturing of laminated fiber-reinforced composite materials is restricted in this section to how the fibers and matrix materials are assembled to make a lamina and how, subsequently, laminae are assembled and cured to make a laminate. 

For the composite spoiler design, the bottom is a variable-thickness skin on one side in Figure 1-33, but with composite materials that construction is not difficult. We do not have to chem-mill a composite material to change its thickness. All we do is stop building up the material in layers in the middle, but continue to build it up at the sides. That s a very natural process for composite materials and does not involve a costly machining operation. Instead of machined extruded stiffeners, a honeycomb core is placed on the inside of the laminae. That honeycomb... 

The values in Figures 2-11 and 2-12 are not entirely typical of all composite materials. For example, follow the hints in Exercise 2.6.7 to demonstrate that E can actually exceed both E., and E2 for some orthotropic laminae. Similarly, E, can be shown to be smaller than both E. and E2 (note that for boron-epoxy in Figure 2-12 E, is slightly smaller than E2 in the neighborhood of 6 = 60°). These results were summarized by Jones [2-6] as a simple theorem the extremum (largest and smallest) material properties do not necessarily occur in principal material coordinates. The moduli Gxy xy xyx exhibit similar peculiarities within the scope of Equation (2.97). Nothing should, therefore, be taken for granted with a new composite material its moduli as a function of 6 must be examined to truly understand its character. 

A key element in the experimental determination of the stiffness and strength characteristics of a lamina is the imposition of a uniform stress state in the specimen. Such loading is relatively easy for isotropic materials. However, for composite materials, the orthotropy introduces coupling between normal stresses and shear strains and between shear stresses and normal and shear strains when loaded in non-principal material coordinates for which the stress-strain relations are given in Equation (2.88). Thus, special care must be taken to ensure obtaining... 

Another test used to determine the shear modulus and shear strength of a composite material is the sandwich cross-beam test due to Shockey and described by Waddoups [2-17]. The composite lamina... 

In Section 2.2, the stress-strain relations (generalized Hooke s law) for anisotropic and orthotropic as well as isotropic materials are discussed. These relations have two commonly accepted manners of expression compliances and stiffnesses as coefficients (elastic constants) of the stress-strain relations. The most attractive form of the stress-strain relations for orthotropic materials involves the engineering constants described in Section 2.3. The engineering constants are particularly helpful in describing composite material behavior because they are defined by the use of very obvious and simple physical measurements. Restrictions in the form of bounds are derived for the elastic constants in Section 2.4. These restrictions are useful in understanding the unusual behavior of composite materials relative to conventional isotropic materials. Attention is focused in Section 2.5 on stress-strain relations for an orthotropic material under plane stress conditions, the most common use of a composite lamina. These stress-strain relations are transformed in Section 2.6 to coordinate systems that are not aligned with the principal material... 

Robert C. Reuter, Jr., Concise Property Transformation Relations for an Anisotropic Lamina, Journal of Composite Materials, April 1971, pp. 270-272. 

Hong T. Hahn and Stephen W. Tsai, Nonlinear Elastic Behavior of Unidirectional Composite Laminae. Journal of Composite Materials, January 1973, pp. 102-118. 

Note that no assumptions involve fiber-reinforced composite materials explicitly. Instead, only the restriction to orthotropic materials at various orientations is significant because we treat the macroscopic behavior of an individual orthotropic (easily extended to anisotropic) lamina. Therefore, what follows is essentially a classical plate theory for laminated materials. Actually, interlaminar stresses cannot be entirely disregarded in laminated plates, but this refinement will not be treated in this book other than what was studied in Section 4.6. Transverse shear effects away from the edges will be addressed briefly in Section 6.6. 

Obviously, the foregoing description of problems in the mechanics of composite materials is incomplete. Some topics do not fit well within the logical framework just described. Other topics are too advanced for an introductory book, even at the graduate level. Thus, the rest of this chapter is devoted to a brief discussion of some basic lamina and laminate analysis and behavior characteristics that are not included in preceding chapters. 

Composite materials have many distinctive characteristics reiative to isotropic materials that render application of linear elastic fracture mechanics difficult. The anisotropy and heterogeneity, both from the standpoint of the fibers versus the matrix, and from the standpoint of multiple laminae of different orientations, are the principal problems. The extension to homogeneous anisotropic materials should be straightfor-wrard because none of the basic principles used in fracture mechanics is then changed. Thus, the approximation of composite materials by homogeneous anisotropic materials is often made. Then, stress-intensity factors for anisotropic materials are calculated by use of complex variable mapping techniques. 

Composite materials typically have a low matrix Young s modulus in comparison to the fiber modulus and even in comparison to the overall laminae moduli. Because the matrix material is the bonding agent between laminae, the shearing effect on the entire laminate is built up by summation of the contributions of each interlaminar zone of matrix material. This summation effect cannot be ignored because laminates can have 100 or more layersi The point is that the composite material shear moduli and G are much lower relative to the direct modulus than for isotropic materials. Thus, the effect of transverse shearing stresses. 

Shear-stress-shear-strain curves typical of fiber-reinforced epoxy resins are quite nonlinear, but all other stress-strain curves are essentially linear. Hahn and Tsai [6-48] analyzed lamina behavior with this nonlinear deformation behavior. Hahn [6-49] extended the analysis to laminate behavior. Inelastic effects in micromechanics analyses were examined by Adams [6-50]. Jones and Morgan [6-51] developed an approach to treat nonlinearities in all stress-strain curves for a lamina of a metal-matrix or carbon-carbon composite material. Morgan and Jones extended the lamina analysis to laminate deformation analysis [6-52] and then to buckling of laminated plates [6-53]. 

Fibers are often regarded as the dominant constituents in a fiber-reinforced composite material. However, simple micromechanics analysis described in Section 7.3.5, Importance of Constituents, leads to the conclusion that fibers dominate only the fiber-direction modulus of a unidirectionally reinforced lamina. Of course, lamina properties in that direction have the potential to contribute the most to the strength and stiffness of a laminate. Thus, the fibers do play the dominant role in a properly designed laminate. Such a laminate must have fibers oriented in the various directions necessary to resist all possible loads. 

Tension, compression, and shear are the three fundamental modes in which a composite lamina may fail. As the composite material is made up of multiple laminae (layers and plies) of various orientations, the stresses in the lamina s principal directions vary from lamina to lamina. As the load is increased, so do the various stresses in the laminae, and failure values may be attained in a certain lamina in a certain principal direction without the overall laminate experiencing actual failure in other words, the failure of the composite laminate is a progressive phenomenon. This progressive damage evolution is subcritical for a while, but eventually leads to ultimate failure of the composite laminate. 

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