An Improved Shear Lag Model for Broken Fibers in Composite Materials

Abstract

A shear lag model is formulated to predict the stresses in a unidirectional fiber reinforced composite. The model is based on assumptions consistent with the finite element method and the principle of virtual work by assuming that the matrix displacements can be interpolated from the fiber displacements. The fibers are treated as one-dimensional springs and the matrix is modeled as three-dimensional finite elements. The resulting finite element equations for the system are transformed into differential equations by taking the discretization length to approach zero. The governing ordinary differential equations are solved using Fourier transformations and an influence function technique. The technique is used to solve for the stresses around a single fiber break in an infinite square or hexagonal array of fibers. The results are compared with previous shear lag models and finite element results. The model predicts stress concentrations that are in good agreement with more detailed finite element analyses.

Strength distribution of large unidirectional composite patches with realistic load sharing

“…The statistics of Hedgepeth and Van Dyke [17] composite failure when ρ is large is wellunderstood in the literature [6,19,33,40,41]. The present work extends this understanding to low ρ. Monte Carlo simulations of large patches containing up to 2 16 fibres confirm that composite strength has a weakest-link structure for ρ ≥ 1.…”

Effect of Environmental Conditions on the Resistance of Damaged Composite Materials

“…Their model consists of seven parallel carbon fibers forming approximate hexagonal packing embedded in an epoxy matrix. Landis et al [4] addressed the question of how to choose effective dimensions of the matrix springs connecting C neighboring fibers by modeling the matrix by finite elements and the fibers by continuous one-dimensional springs. Their model also considered direct interactions of broken fibers with the next to nearest neighbors.…”

“…Their model also considered direct interactions of broken fibers with the next to nearest neighbors. Landis and McMeeking [5] later extended the work of Landis et al [4] to account for the effects of interface sliding, axial matrix stiffness and uneven fiber positioning, on stress concentrations surrounding the broken fiber. Nedele and Wisnom [6,7] also showed that the peak stress concentration on fibers close to the broken fiber occurred slightly out of the rupture plane.…”

A study on the failure behavior and mechanical properties of unidirectional fiber reinforced thermosetting and thermoplastic composites

“…It was found that variability in fiber strength can lead to a nonlinear deformation mechanism of the composites. Landis et al [30,31] developed a three-dimensional shear lag model combining with the Weibull fiber statistics and the influence superposition technique, and applied it to analyze the effect of statistical strength distribution and size effects on the strength of composites. Curtin and colleagues [32e35] proposed an approach to the analysis of the interaction between multiple breaks in fibers, based on the Green's functional model.…”