Transverse cracking in fiber-reinforced brittle matrix, cross-ply laminates

The topic addressed in this paper is transverse cracking in the matrix of the 90° layers of a cross-ply laminate loaded in tension. Several aspects of the problem are considered, including conditions for the onset of matrix cracking, the evolution of crack spacing, the compliance of the cracked laminate, and the overall strain contributed by residual stress when matrix cracking occurs. The heart of the analysis is the plane strain problem for a doubly periodic array of cracks in the 90° layers. A fairly complete solution to this problem is presented based on finite element calculations. In addition, a useful, accurate closed form representation is also included. This solution permits the estimation of compliance change and strain due to release of residual stress. It can also be used to predict the energy release rate of cracks tunneling through the matrix. In turn, this energy release rate can be used to predict both the onset of matrix cracking and the evolution of crack spacing in the 90° layers as a function of applied stress. All these results are used to construct overall stress-strain behavior of a laminate undergoing matrix cracking in the presence of initial residual stress.