Effective properties and micro-mechanical response of filamentary composite wires under longitudinal shear

We propose an asymptotic approach for evaluating effective properties and determining the micro-mechanical response of filamentary composite wires fabricated by cold drawing under longitudinal shear (torsion). Our procedure is based on the homogenization method; a cell problem is solved using the underlying principles of the boundary shape perturbation technique. As the results we derive approximate analytical solutions for the effective shear modulus and for local distributions of the stress field. Developed approach is valid for all values of the componentsʹ volume fractions and properties, in particular, it works well in cases when rapid oscillations of stresses occur on micro level (e.g., in the case of perfectly rigid nearly touching inclusions). Analysis of the local stresses allows to predict the effective initial yield limit corresponding to the beginning of plastification of the composite medium. Obtained results are in good agreement with data of other authors.