The stress field in a [0°/90°] laminated composite plate containing a finite line crack

This paper deals with the construction of an asymptotic solution for the stress field in a laminated composite plate, with (0/90) stacking sequence. The plate contains through the thickness a line crack of length 2c and its perimeter boundaries are sufficiently far away from the crack so that no edge effects are present. The stress field is derived explicitly, and includes a correction factor to account for the laminate effects in the third dimension. The stress σzz is a maximum at an angle of θ ≈ 83 ◦ (see Figure 3). The stress field may now be used to bridge the gap between macro and micro mechanics and to derive a series of fracture criteria, at the micro and macro level, which ultimately will provide us with a better understanding of the formation of the damaged zone ahead of the crack tip. For example, the stress field is used to derive one such approximate fracture criterion for mode I loading and for a self similar type of fracture, similar to that of Griffith. This criterion shows how the periodic length of the material lay-up microstructure effects the fracturing characteristics of the material system. Comparison with some experimental observations for two different material systems shows a fairly good agreement which substantiates the predicted influence. Despite careful design, practically every structure contains stress risers due to the presence of inclusions, holes or cracks. Bolt holes and rivet holes are necessary components for structural joints. It is not surprising, therefore, that the majority of service cracks nucleate in the vicinity of a stress riser. While the subject of stress risers is certainly familiar to engineers, the situation is significantly more complex in the case of high-performance laminated composite materials. The presence of a hole or a crack in the laminate introduces significant stress contributions in the third dimension which create a very complicated three-dimensional (3-D) stress state in the vicinity of such discontinuities. Moreover, this complex state of stress may depend on the stacking sequence of the laminate, the fiber orientation of each lamina as well as the material properties of the fiber and of the matrix. Ultimately, these stress risers form a primary source of damage initiation and property degradation, particularly in the presence of cyclic loading. Experimental investigations carried out by Bakis and Stinchcomb (1986) on graphite- epoxy laminates which have been weakened by a circular hole give us a better insight of this damage growth development under the action of cyclic loading. In general, the progression of this damaged process may be characterized as (i) debonding along fiber-matrix interfaces, (ii) matrix cracking parallel to the fibers, (iii) matrix cracking between fibers, (iv) delamination along the interface of two adjacent laminae with different fiber orientations, and (v) fiber breakage.