An exact solution for stresses in cracked composite laminates and evaluation of the characteristic damage state

Abstract

An exact solution for stresses in cracked composite laminates with lay-up [0m∘/90n∘] is developed in this paper. The inter-laminar shear stresses between the 90° and 0° plies are assumed to be in the form of series expansion of sinusoidal functions. This leads to the stress components in laminates having corresponding series expressions from the equilibrium equations together with boundary conditions for inter-laminar stresses. The principle of minimum potential energy is used to derive algebraic equations for the unknown coefficients. Furthermore, cyclic differential function is introduced to express analytically the resulting stresses in the laminates. As an application, reduction of Young’s modulus and change in Poisson’s ratio for different laminates are evaluated and compared with available experimental and predicted results. Distributions of inter-laminar stresses are also presented in this paper, with results showing that the present solution is accurate and suitable for the analysis of characteristic damage state for composite laminates.