First Order Analysis of Stiffness Reduction Due to Matrix Cracking

ABSTRACT: In this paper the reduction in effective elastic constants of composite lami-nates due to matrix cracking is considered. A general easily applicable theory valid for two- and three-dimensional analysis of thin as well as thick laminates is presented. The theory is based on the change of elastic energy in a laminate at the appearance of a matrix crack in one layer. This information combined with a dilute approximation,i.e., different matrix cracks are considered not to interact with each other, is utilized to estimate the re-duction of elastic constants for a certain crack density. The theory is asymptotically exact for nk « 1, where nkis the number of cracks per unit thickness of the cracked ply and a correct value of the slope of the stiffness reduction crack density curve is obtained at nk = 0. Comparisons are made between calculated stiffness reductions and experimental data found in the literature. The agreement for the longitudinal Young’s modulus is seen to be satisfactory at least for crack densities up to nk = 0.5. Comparisons are also made for the inplane Poisson’s ratio. 1