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**Published:** Jan 1991

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**Source: **STP1110-EB

The effect of the stress-free edge on the growth of local delaminations initiating from a matrix crack in a composite laminate is investigated using a three-dimensional finite element analysis. Two glass epoxy layups, (0^{2}/90^{4})^{s} and (±45/90^{4})^{s}, were modeled with a matrix crack in the central group of eight 90° plies, and delaminations initiating from the matrix cracks in the 0/90 and -45/90 interfaces, respectively. The analysis indicated that high tensile interlaminar normal stresses were present at the intersection (corner) of the matrix crack with the stress-free edge, suggesting that an opening (Mode I) delamination may initiate at these intersections.

In order to analyze the strain energy release rates associated with delaminations that may form at the corners, three different configurations of the local delamination were assumed. One configuration was a uniform through-width strip growing normal to the matrix crack in the direction of the applied load. The other two configurations were triangular shaped delaminations, originating at the intersection of the matrix crack with the free edge, and growing away from the corner. The analysis of the uniform delamination indicated that the magnitude of both the total strain energy release rate, *GT*, and its components increased near the free edges. This edge effect was symmetric for the (0^{2}/90^{4})^{s} layup. However, for the (±45/90^{4})^{s} layup, the *G* distribution across the front was asymmetric, with the total *G* and its components having higher values near one free edge than the other. For both layups, the *G*^{I} component was large at small delamination lengths, but vanished once the delamination had reached a length of one-ply thickness.

The second and third delamination configurations consisted of triangular-shaped delaminations with straight fronts inclined at angles of 10.6 and 45°, respectively, to the matrix crack. The total *G* along the delamination front decreased sharply near the matrix crack for both configurations and increased sharply near the free edge for the 10.6° configuration. However, the total *G* distribution was fairly uniform in the middle of the delamination front for the 10.6° configuration. These inclined models suggest that if the exact geometry of the delamination front could be modeled, a uniform *G* distribution may be obtained across the entire front. However, because the contour of the delamination front is unknown initially, it may only be practical to model the uniform through-width delamination and use the peak values of *G* calculated near the free edges to predict delamination onset. For the layups modeled in this study, the total *G* values near the free edge agreed fairly well with a previously derived closed-form solution. However, a convergence study may need to be conducted to have confidence that peak values of *G* calculated from three-dimensional finite element analyses near the free edges are quantitatively correct.

**Keywords:**

composite materials, fracture, fatigue (materials), matrix cracking, delamination, finite element analysis, free edge

**Author Information:**

Salpekar, SA *Research scientist, Analytical Services and Materials, Inc., Hampton, VA*

O'Brien, TK *Senior scientist, Aerostructures Directorate, U.S. Army Aviation Research and Technology Activity (AVSCOM), NASA Langley Research Center, Hampton, VA*

**Committee/Subcommittee:** D30.06

**DOI:** 10.1520/STP17724S