Crimped fiber composites: Mechanics of a finite-length crimped fiber embedded in a soft matrix

Composites comprising crimped fibers of finite length embedded in a soft matrix have the potential to mimic the strain hardening behavior of tissues containing fibrous collagen. Unlike continuous fiber composites, such chopped fiber composites would be flow-processable. Here we study the fundamental mechanics of stress transfer between a single crimped fiber and the embedding matrix subjected to tensile strain. Finite element simulations show that fibers with large crimp amplitude and large relative modulus straighten significantly at small strain without bearing significant load. At large strain, they become taut and hence bear increasing load. Analogous to straight fiber composites, there is a region near the ends of each fiber which bears much lower stress than the mid-section. We show that the stress-transfer mechanics can be captured by a shear lag model where the crimped fiber can be replaced with an equivalent straight fiber whose effective modulus is lower than of the crimped fiber, but increases with applied strain. This allows estimating the modulus of a composite at low fiber fraction. The degree of strain hardening and the strain needed for strain hardening can be tuned by changing relative stiffness and crimp geometry.