Residual elastic fields in fiber reinforced composites

A derivation of the residual elastic deformation fields expected when the inclusions are long, straight cylindrical fibers in a stress-free effective medium (EM) was presented. The interfacial tractions were shown to be directly proportional to the magnitude of the temperature drop from the stress-free processing temperature to ambient temperature. Analysis of the embedding process and determination of the elastic fields were followed by a calculation of the temperature drop on cooling, Delta Tp, needed to initiate plastic flow in the matrix at the interface of the matrix and inclusion. This quantity was shown to be directly proportional to the yield stress and inversely proportional to the shear modulus of the matrix and inversely proportional to the difference in volumetric thermal expansion coefficients of the matrix and fiber. These results were also compared with the corresponding expression for spherical inclusions. Examples were presented for Delta Tp for an aluminum matrix reinforced by fibers of representative ceramic materials (Al sub 2 O sub 3 ).