Torsion of an Elastomeric Cylinder Undergoing Microstructural Changes

Abstract

A constitutive theory which accounts for scission and cross linking processes in polymers during deformation is used to analyze the torsion of a circular bar. In each increment of deformation at a material element of the torsion bar, some volume fraction of material undergoes scission and then re-cross links to form a new network with a new reference state. The scission process reduces the ability of the material to transmit stress. The newly formed networks restore the ability of the material to transmit stress. The total stress is assumed to be the superposition of the stress in the remainder of the original material, determined by its deformation from its original configuration, and the stress in each newly formed network, determined by the deformation in that network from the configuration at which it formed. The interaction of this material response with the inhomogeneous deformation during torsion is studied. The analysis shows the evolution of regions of original and modified material, the softening effects associated with the process of scission and re-cross linking and the occurrence of residual stress and deformation on removal of load.