A simple method for predicting the singular stress distribution of Mode I interlamellar crack embedded in unidirectionally-fiber-reinforced composites

Elastic-plastic analysis was carried out for a Mode I interlamellar crack embedded in unidirectionally-fiber-reinforced composites by means of the finite element method. The stress distribution in the vicinity of a crack tip was calculated for various crack lengths and various combinations of elastic constants for fiber and matrix. When both fiber and matrix are elastic, the stress intensified region ahead of the crack tip was divided into three regions. In the region nearest the crack tip (Region I), the distribution of stress, σ_y, which is the normal stress perpendicular to the crack plane, was given by the stress intensity factor, K_com. K_com is obtained assuming that the composite is actually composed of two parts which have different elastic constants. On the other hand, the stress distribution in the farthermost part in the stress intensified region was given by the stress intensity factor, K_homo (Region III). K_homo is obtained regarding the composite as homogeneously orthotropic. Between these regions, the stress distribution was undulated (Region II). As K_com and K_homo can be evaluated analytically using elastic constants of fiber and matrix and Region II always appears at a distance from the crack tip equal to the thickness of matrix, the stress distribution can be predicted without carrying out numerical analyses such as a finite element analysis. When the matrix is assumed to be elastic-perfectly plastic, the length of yield region and the stress outside the yield region can be estimated from the yield stress of the matrix and the stress distribution predicted for the case where the matrix does not yield.