A recursive concentric cylinder model for composites containing coated fibers

A simple recursive algorithm which considers only two concentric cylinders ut a time is presented in order to calculate Five effective clastic constants and two linear thermal expansion coefficients for a uniaxially aligned composite which contains an arbitrary number of coatings on its fibers. The micro stresses and the micro displacements are determined under combined applied radial and axial load and temperature change. During composite fabrication, each coating can be processed at a different temperature so that the zero-thermal-stress temperature is not unique for the composite. When layer properties vary with load and temperature, an incremental recursive analysis can be done by adjusting the zero stress temperatures at each step in order to induce initial stresses. The material for each constituent is assumed to be transversely isotropic with its axis oriented in the fiber direction. Approximate expressions for the equivalent axial and the transverse shear moduli are given in order to replace effectively two concentric cylinders with a single homogeneous cylinder It is shown that the effective shear modulus of two concentric cylinders measured from a torsion test does not correspond to any of the effectivoshear moduli. The three remaining effective elastic constants and the two thermal expansion coefficients for two cylinders are the same as those given for a two-phase composite. The recursive method is applied to a titanium matrix composite reinforced with CVD SiC filaments (AVCO SCS-6). The inhomogeneous structure of the fiber is shown to influence the stress distribution and the composite elastic properties.