A 2-DIMENSIONAL ANALYSIS OF MULTIPLE MATRIX CRACKING IN A LAMINATED COMPOSITE CLOSE TO ITS CHARACTERISTIC DAMAGE STATE

The proposed approach incorporates all the stress components of interest in each layer of a cracked cross-ply laminate. Its starting point is a very general distribution of the shearing stress in both types of layer, represented by a series, each term of which is the product of a trigonometric function in the axial coordinate, a hyperbolic function in the thickness coordinate and an undetermined coefficient a(q); all the other stress components in each layer are deduced from the above by using the equilibrium equations, interface continuity conditions and traction boundary conditions. Minimizing the complementary energy of the whole laminate yields an algebraic system whose unknowns (a(q)) are the above coefficients. The validity of the proposed model is assessed by comparing the stress values it gives with those estimated through other semi-analytical models or a finite element method. Moreover, the series convergence is all the faster since the crack density is large, thus enabling careful investigation of the stress field when transverse cracking attains its saturation spacing.