Thermal Expansion of Elastic-Plastic Composite Materials

Abstract

Exact relationships are derived between instantaneous overall thermal stress or strain vectors and instantaneous overall mechanical stiffness or compliance, for two binary composite systems in which one of the phases may deform plastically. Also, the local instantaneous thermal strain and stress concentration factors are related in an exact and on local fields in the two composite materials..'-'.''. '".'' . ' . ".'", . € " caused in a prestressed fibrous composite by a small uniform thermal -change can be related in an exact way to thermoelastic constants of the phases and to instantaneous overall compliance. No restrictions need to be imposed on the type of prestress or on the matrix constitutive law except for plastic incompressibility, but the fiber must be isotropic or transversely isotropic and remain elastic. This result has been applied in analysis of a composite cylinder element (DVORAK and WUNG 1984) subjected to axisymmetric mechanical loading, uniform thermal changes, and variations in matrix yield stress.The present paper develops the connections between overall instank,22taneous mechanical and thermal properties in a more general way. First, it is shown that the overall thermal stress and strain vectors for an 1, ELASTIC FIBROUS COMPOSITEA binary composite material consists of a matrix reinforced by aligned and bonded cylindrical fibers. Both phases are assumed to be homogeneous and transversely isotropic about the fiber direction x 3 . In the transverse x 1 x 2 -plane, the cross sections and distribution of the phases can be arbitrary providing that the composite is statistically homogeneous, transversely isotropic, and free of voids.A representative volume element V of the composite is selected and subjected to a certain loading or deformation history which is imposed through application of uniform overall stresses To or strains To to the surface S of volume V. Also, a certain uniform thermal change has been applied such that the current temperature in V is constant and equal to 0o . At this particular point of the loading sequence simultaneous increments of d and de, or d -and de, are applied to V.The response of the composite to these load increments is described by constitutive equations:where M,L are (6x6) overall stiffness and compliance matrices, and m,t are (6x) overall thermal strain and stress vectors*.While M and L are known, we wish to determine the vectors m and 1.To this end it is necessary to specify the constitutive equations for field averages of the phases: which are analogous to (1); f,m indicate the "fiber" and "matrix"phases. In elastic composites, these phases are interchangeable and f,m are used merely for convenience of notation.Since both the composite and each of the phases are transversely isotropic about x 3 , it is possible to write a subset of (1) and (2) which relates the first two stress and strain invariants. With top bars and subscripts r,f,m omitted in (1) and (2) In the second step of the procedure, the tractions 1 and dr must All strain and stress increm...

High Temperature Advanced Structural Composites. Volume 3. Mechanics

“…In addition to the earlier studie4 of coated fiber composites described in (1), we mention here The present paper is a continuation of our the work of Avery and Herakovich (1986) who earlier study of stress fields in composites reinconsidered a single composite cylinder, with a forced by coated inclusions (Benveniste et aL, cylindrically orthotropic fiber, under uniform 1989), which will be referred to as (I) in the thermal change. Pagano and Tandon (1988) treat sequel In that work we evaluated the overall a thermomechanically loaded system reinforced by properties of such composites, and examined in randomly oriented short coaled fibers in which the detail the local fields in fibrous composites with constituents may be transversely isotropic.…”

“…(1989). (1986), Thermal stresses in a coated sing orthntrupifir, loadeituby c an ri short fiber composite. J. Appl.…”

“…Interest in problems of this kind is linearly anisotropic, coated inclusions; (b) to exmotivated by the use of coated carbon fibers which tend the validity of the Levin-type relationship to may possess circumferential or radial orthotropy; composites of this kind; and (c) for the fibrous see for example, Avery and Herakovich (1986), systems considered in (I) and (II). and for the , and other references cited in (I) micromechanics model used therein, to establish and (II).…”

“…and C.T. Herakovich (1986). Effect of fiber aniThe T, £ and i tensors in (46) and (48) Benveniste, Y.…”

“…the local fields in the coating and inclusion, and in Available solutions of problems of this kind the adjacent matrix can be evaluated by using the can be found in the papers by Walpole (1978) and solution of a single coated particle in an infinite Hatta and Taya (1986). Walpole considers a commatrix and particle interaction is taken into posite with dilute reinforcement under mechanical account through the yet unknown average matrix loading.…”