Semi-analytical constitutive model of cracked plies based on linear elastic fracture mechanics

Matrix microcracking of laminated composites lead to stiffness degradation. Microscopic critical stresses are defined according to the linear elastic fracture mechanics and are found to be independent of the crack density. The microscopic critical stresses are constant as long as the material and the thickness of the cracked plies are constant, and can be used to obtain the semi-analytical expression of the equivalent transverse moduli and in-plane shear moduli of the cracked plies versus the crack density. The equivalent longitudinal moduli and in-plane shear moduli of [0/±θ₄/0_1/2]_S laminates are obtained by using the semi-analytical model and the classical laminate theory, and are compared with the available experimental data and conventional finite element analysis (FEA) results.