Lamina micromechanical analysis

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. 

Fig. 11. A unidirectional lamina under longitudinal tension. The micromechanical analysis of the radial, shear and hoop stresses show an increase with fiber volume fraction. From Haener et al.67>...

Fig. 12. A unidirectional lamina under transverse tension. The points of stress concentration are at the dots. The micromechanical analysis shows that the stress concentration factor increases with volume fraction of fiber and fiber to matrix modulus ratio. From Adams et al.70)...

Summary of Results from Micromechanics Analysis of Lamina Elastic Moduli... 

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]. 

Abstract This chapter describes the elastic qualities of advanced fibre-reinforced composites, in terms of characterization, measurement and prediction from the basic constituents, i.e. the fibre and matrix. The elastic analysis comprises applying micromechanics approaches to predict the lamina elastic properties from the basic constituents, and using classical lamination theory to predict the elastic properties of composite materials composed of several laminae stacked at different orientations. Examples are given to illustrate the theoretical analysis and give a full apprehension of its prediction capability. The last section provides an overview on identification methods for elastic proprieties based on full-field measurements. It is shown that these methodologies are very convenient for elastic characterization of anisotropic and heterogeneous materials. 

The mechanical, thermal, and hygrothermal properties of FRP composites are a function of selected constituent materials, namely fiber and matrix, and the fiber, matrix, and void volume fractions that are a result of the manufacturing process. In this analysis, the influence of fiber volume fraction on the failure probability of FRP-rehabilitated piping components is also examined. Procedures for micromechanical and macromechanical analysis of lamina (i.e., determination of lamina elastic moduli and strength properties) from basic constituent properties are well established and readily available in standard texts (Kaw, 2006). Table 5.2 summarizes the constituent properties of carbon fiber, glass fiber, and epoxy matrix utihzed in the reliability analyses presented in this chapter. These standard properties were obtained from Kaw (2006). 

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