Mechanics of Composite Materials

Abstract

presentation of its subject which, by having collected in one place a comprehensive assortment of methods and techniques of measurement, will be of value to any person interested in comparing the possibilities and limitations of each. It is most certainly recommended to the audience for which it is written. Mechanics of Composite Materials. By Robert M. Jones. McGraw-Hill Book Company, New York. 1975. xiv + 355 Pages. Cost $21.00. REVIEWED BY C. W. BERT* With the rapid development of high-performance fibers and their increasing use in critical structural applications, there is a great need for a text which covers the topics peculiar to the mechanics of such structures: micromechanics, macroscopic anisotropy, and flexural-extensional coupling. Professor Jones has drawn from his extensive industrial and pedagogical experience in the relatively new field of composite material mechanics to write a textbook which serves this need very well. The introductory chapter gives an up-to-date overview of the types, terminology, manufacture, current applications, and future potential of composites. Chapter 2 is devoted to macroscopic stiffness and strength behavior of a single layer. Chapter 3 is concerned with micromechanics, i.e., prediction of the composite stiffness and strength behavior from known properties and geometric configuration of its constituent materials (the fibers or other reinforcements and the matrix). Chapter 4 covers laminate mechanics, i.e., prediction of laminate behavior from known properties, arrangement, and orientation of the individual layers. Problems of stable static deflection, static buckling under in-plane loads, and free vibration of laminated, composite-material plates are presented in Chapter 5. Chapter 6 treats briefly the following miscellaneous topics: fatigue, fracture mechanics, effects of holes, transverse shear effects, and environmental effects.

Estimation of the reinforcement factor ξ for calculating the transverse stiffness E2 with the Halpin–Tsai equations using the finite element method

“…The H-T equations can be found in many books on mechanical behaviour of composite materials [1][2][3][4]. The H-T equation for the transverse modulus…”

“…Analogous equations are formulated for G 12 and ν 23 [1][2][3][4]. For the longitudinal modulus E 1 and ν 12 the well-known rule of mixtures holds [1].…”

“…Among these properties, one of the most relevant is the transverse stiffness E 2 of a unidirectional lamina with oriented continuous fibers. It is well known that approaches based on a strength of materials analysis underestimate the true value of E 2 , leading to a lower bound of E 2 (Reuss boundary) [2]. In the past a large number of models have been proposed in the literature to obtain more accurate estimations of E 2 and other elastic constants, many based in formal approaches of the theory of elasticity (see the excellent reviews in [1,2]).…”

“…These models account for the matrix-dominant effect on the homogenized value E 2 for a lamina, such as the Ekvall model [2] that considers the triaxial stress state in the matrix due to fiber restraint.…”

“…Originally, the value of ξ for oriented continuous fibers was derived by Halpin and Tsai from correlation with analytical solutions that assume an idealized geometrical distribution or pattern (e.g. Adams and Doner solution for a square array of fibers solved by a finite-difference scheme [1,2]). Some approximate equations for ξ are also given in the literature to modify the value of ξ for high volume fractions, as recalled in Section 2.…”