Abstract
A 3D model of fiber microbuckling assuming a square packed fiber array has been developed and analyzed under the assumption of fiber in-plane microbuckling. In this model, the fiber equilibrium equation is first developed as a function of uniaxial loading, material properties, and fiber/matrix interfacial stresses. By utilizing 3D boundary element modeling, the 3D stress distribution along the fiber/matrix interface is determined. The interfacial stresses obtained from the 3D boundary element analysis are then incorporated into the 3D equilibrium equation of fiber microbuckling to provide a closedform analytical solution of the 3D compressive fiber strength in unidirectional composites. Results show that the in-plane shear stress component is predominant, while one of the two out-of-plane stress components, which cannot be captured by a 2D model, is not negligible. Furthermore it is found that the in-plane interfacial shear stress is strongly dependent upon fiber spacing. These results indicate that the results for a 2D model are quite different from those of the 3D model. Therefore, the 3D model of compressive behavior of unidirectional composites is necessary in order to properly model the real interfacial stress distribution in a unidirectional composite subjected to axial compressive load. Because of the strong dependence of interfacial shear stress upon fiber spacing, more accurate calculation of in-plane interfacial shear stresses and theoretical fiber microbuckling strength will result from a 2D model if fiber spacing in the model is set to match that of a 3D model for a given 3D model-based fiber volume fraction.