Critical compressive stress for continuous fiber unidirectional composites

Dow and Rosen's work in 1965 formed an intellectual framework for compressive strength of unidirectional composites. Compressive strength was explained in terms of micro-buckling, in which filaments are beams on an elastic foundation. While groundbreaking, the discrepancy between model predictions and observed compressive strength is well known. This study builds on Dow and Rosen's model specifically with respect to the dominant shear mode instability. A new method that accounts for matrix thermal residual strain, matrix compressive and shear stresses, with associated reductions in tangent modulus due to matrix non-linearity, is proposed. The method is validated using a specific test case, which is conducted to precisely account for microscopic fiber alignment and matrix non-linearity. Accordingly, a method of measuring and accounting for a continuum of fiber misalignment is developed. Predictions are compared to literature values, with variations in fiber modulus, matrix modulus, and volume fraction. Good agreement is shown, both in terms of trend and magnitude. The approach successfully preserves initial in-plane shear stiffness, while showing that in-plane shear stiffness decreases significantly as compressive stress increases.