INTERFACE STRESSES IN FIBER-REINFORCED MATERIALS WITH REGULAR FIBER ARRANGEMENTS

Residual stresses at fiber/matrix interfaces are frequently responsibl e for crack nucleation in composite materials: interface failure can o ccur in the case of a weak interface and a higher thermal expansion co efficient of the fiber. Radial matrix cracking may be observed if the matrix is brittle and possesses the higher thermal expansion coefficie nt. The quantitative assessment of interface stresses is a key factor in developing reliable fiber reinforced composites. Of further special interest is the state of stress at the surface of the composite where interface-nucleated cracks may originate and propagate into the compo site. In this paper the theory of linear elasticity is used to analyze the stresses inside and at the surface of fiber-reinforced composites . All three states of plane deformation are considered: plane strain, plane stress and generalized plane strain. They are investigated analy tically using the so-called shell-model (for plane strain and plane st ress) and the BHE-model (for generalized plane strain). Moreover, they are treated numerically by means of a finite element analysis. In the shell-model a single fiber in a finite matrix under an additional ext ernal pressure is considered. First, Duhamel-Neumann's form of Hooke's law is applied and a general expression for the thermomechanical stre sses in cylindrical systems is obtained. The result reduces to Lame's solution in the absence of thermal stresses. Next, this solution is ev aluated by means of the appropriate boundary conditions to give explic it, analytical expressions for the thermomechanical stresses as functi ons of thermal and elastic mismatch as well as of external pressure. N umerical results of the shell- and the BHE-model are compared with int erface stresses obtained from the finite element method for regular cu bic and hexagonal fiber arrangements: interface stresses are shown to depend weakly on Poisson's ratio. For equal values of Poisson's ratio, generalized plane strain and plane strain results are identical. The dependence of interface stresses on volume fraction and on the arrange ment of fibers is examined for the range of practically important elas tic mismatches in composites. For small volume fractions up to 40 vol. % of fibers the shell- and the BHE-model are shown to predict the inte rface stresses very well over a wide range of elastic mismatches and f or different fiber arrangements. At higher volume fractions, however, the stresses are influenced by the interaction with neighboring fibers . An external pressure. which is nearly independent of the elastic mis match, is introduced into the shell-model to take this influence into account. This allows the prediction of interface stresses in real comp osites with isolated or regularly arranged fibers. The analytical form ulae can be used to assess the influence of residual stresses for the design of new fiber-reinforced composites.