A CLOSED FORM MATHEMATICAL FORMULATION FOR CALCULATIONS OF PEEL STRESS, σz, AND INTERLAMINAR SHEAR STRESS, τyz IN A THIN COMPOSITE LAMINATE

This paper presents a closed form mathematical formulation for calculations of peel stress σz and interlaminar shear stress τyz in a thin composite laminate. The existence of σz has been acknowledged in the composite literature, such as, Ref.[1] and Ref.[2], etc. Some analytical formulations are presented in the literature for calculation of these stresses. The numerical techniques such as finite difference and finite element however, have been extensively used in the literature for calculations of these stresses. The interlaminar normal stress, σz, is hypothesized by Pagano and Pipes, Ref.[1] to exhibit the distribution shown in Figure 1. Ref.[2] uses results of Ref.[1] and states that, “ ... σz goes to zero in the region where classical lamination theory applies and perhaps to infinity at the free edges;...”. Ref.[3] uses the Moire technique to confirm the existence of the interlaminar stresses. This paper presents, a closed form mathematical formulation for calculations of interlaminar stresses, σz, and τyz. Using this formulation, it will be shown that for a thin laminate, the distribution of σz is identical to the hypothesized distribution of σz as stated by Pagano and Pipes, Figure 1, Ref.[1]. However, it will be shown that, for a laminate with a finite thickness, these stresses do not go to infinity, Figure 2. It will be shown that the thiner the laminate is, the higher these stresses are. In a laminated composite structure, the smallest laminate thickness is the thickness of a single ply. Therefore if the laminate thickness is not zero, the σz, and τyz stresses are finite, however, very large near the free edges. These stresses drop to zero very rapidly as they get away from the free edges. This formulation is then applied to a thin composite laminate. Peel and shear stresses are calculated and compared to the test results. It will be shown that the locations of maximum stresses as calculated by these equations are similar to the locations of delaminations observed in the test lab. The paper will then proceed to discuss the available techniques, such as the third axes fiber application to increase the laminate strength through the thickness. It will be shown that, via test results, although this technique is successful in stiff structures, however it is not useful in flexible structures. Following that, a third technique, applicable to the flexible structures is presented. This technique is used to strengthen a composite laminate against σz and τyz. The test results will then be presented. It will be shown that, significant increase in the laminate fatigue life and increase in static strength is obtained using this technique. Finally, conclusions are made.