Experimental assessment of the eigenstress state in two-ply yarns and its effect on tensile properties

Propaedeutical to a better understanding of the mechanics of cables, with potential applications in material science and biology, tensile tests were performed on two-ply yarns made of rubber rods, manufactured by transforming the twist on two adjacent straight rods into tortuosity for the resulting double-helix shape. Modeling of the yarn as a pair of Kirchhoff rods in reciprocal contact, fails to provide results in agreement with experiments, especially when the helix slope angle α tends to π/4, representing the geometric limit for material interpenetration. This discrepancy could not be justified by considering the viscosity of the rods, their cross-sectional distortion, or cohesive/frictional contact. Our contribution starts from the experimental observation that the rods are in an eigenstress state already in the reference balanced configuration. This is characterized by a high twist, dictated by the ratio between torsional and bending rod stiffness, which increases as α decreases, growing unboundedly as α→π/4. Experiments confirm that twisting can significantly increase the tensile stiffness of straight rubber rods, in agreement with non-linear elasticity theory. Tensile tests on the yarns can be reproduced excellently only if the twist-induced stiffening is considered.