3 Micromechanical Analysis of a Lamina Chapter Objectives Develop concepts of volume and weight fraction(mass fraction)of fiber and matrix,density,and void fraction in composites. Find the nine mechanical and four hygrothermal constants:four elastic moduli,five strength parameters,two coefficients of thermal expansion,and two coefficients of moisture expansion of a unidirec- tional lamina from the individual properties of the fiber and the matrix,fiber volume fraction,and fiber packing. Discuss the experimental characterization of the nine mechanical and four hygrothermal constants. 3.1 Introduction In Chapter 2,the stress-strain relationships,engineering constants,and fail- ure theories for an angle lamina were developed using four elastic moduli, five strength parameters,two coefficients of thermal expansion(CTE),and two coefficients of moisture expansion(CME)for a unidirectional lamina. These 13 parameters can be found experimentally by conducting several tension,compression,shear,and hygrothermal tests on unidirectional lamina (laminates).However,unlike in isotropic materials,experimental evaluation of these parameters is quite costly and time consuming because they are functions of several variables:the individual constituents of the composite material,fiber volume fraction,packing geometry,processing,etc.Thus,the need and motivation for developing analytical models to find these param- eters are very important.In this chapter,we will develop simple relationships for the these parameters in terms of the stiffnesses,strengths,coefficients of thermal and moisture expansion of the individual constituents of a compos- ite,fiber volume fraction,packing geometry,etc.An understanding of this 203 2006 by Taylor Francis Group,LLC203 3 Micromechanical Analysis of a Lamina Chapter Objectives • Develop concepts of volume and weight fraction (mass fraction) of fiber and matrix, density, and void fraction in composites. • Find the nine mechanical and four hygrothermal constants: four elastic moduli, five strength parameters, two coefficients of thermal expansion, and two coefficients of moisture expansion of a unidirec￾tional lamina from the individual properties of the fiber and the matrix, fiber volume fraction, and fiber packing. • Discuss the experimental characterization of the nine mechanical and four hygrothermal constants. 3.1 Introduction In Chapter 2, the stress–strain relationships, engineering constants, and fail￾ure theories for an angle lamina were developed using four elastic moduli, five strength parameters, two coefficients of thermal expansion (CTE), and two coefficients of moisture expansion (CME) for a unidirectional lamina. These 13 parameters can be found experimentally by conducting several tension, compression, shear, and hygrothermal tests on unidirectional lamina (laminates). However, unlike in isotropic materials, experimental evaluation of these parameters is quite costly and time consuming because they are functions of several variables: the individual constituents of the composite material, fiber volume fraction, packing geometry, processing, etc. Thus, the need and motivation for developing analytical models to find these param￾eters are very important. In this chapter, we will develop simple relationships for the these parameters in terms of the stiffnesses, strengths, coefficients of thermal and moisture expansion of the individual constituents of a compos￾ite, fiber volume fraction, packing geometry, etc. An understanding of this 1343_book.fm Page 203 Tuesday, September 27, 2005 11:53 AM © 2006 by Taylor & Francis Group, LLC