A bridge between finite element and shear lag analyses for fiber pull out

The strength of fiber-reinforced composites is often dependent on the strength of the fiber-matrix interface bond. Thermal, chemical, and other means have been used to modify the surface of fibers, resulting in increased fiber-matrix interface bond strength. One potential mechanism for improving interfacial strength is through increased surface roughness. It is desirable to develop physics-based models capable of predicting the effect of surface treatment on interfacial bond strength. It is anticipated that experimental, numerical, and analytical efforts will be needed to contribute toward this endeavor. A shear-lag approach has been used to model the transfer of load from fiber to matrix in fiber pull out, microbond, and axisymmetric macrobond tests. However, the shear lag parameter, β, must be fitted to experimental results to use this approach. Finite element analyses could be useful in interpreting experimental results, and predicting the effect of surface roughness on load transfer. However, shear lag models do not capture the singularity that is present along the fiber-matrix interface at the free surface of the matrix, meaning that finite element and shear lag analyses do not agree near the location that fiber-matrix debond is most likely to begin. In this paper, a numerical approach is presented that allows the shear lag parameter, β, to be extracted from finite element results. This allows a bridge between numerical and analytical approaches that does not currently exist. Axisymmetric finite element analyses of fiber pull out and axisymmetric macrobond configurations are discussed in light of this approach. The effect of the different boundary conditions in these two test configurations are considered for a range of ratios for matrix and fiber Young's moduli. It is anticipated that this approach will be essential in future research efforts to simulate the effect of fiber surface texture on pull out strength.