Studying the origin of “strain hardening”: Basic difference between extension and shear

This work studies the origin of the so called "strain hardening" observed when comparing the transient stress response of entangled melts to uniaxial extension with that to simple shear. Strain hardening occurs when the transient extensional viscosity measured from a startup uniaxial extension of finite rate deviates upward from the zero-rate transient viscosity. Our theoretical analysis shows that polymer melts would always exhibit strain hardening at sufficient high Hencky rates because the entanglement network can be effectively strengthened during extension and can only be weakened during shear for linear chains. The kinematic difference between simple shear and uniaxial extension has two effects: (a) The force resulting from the startup deformation is measured from an increasingly shrinking area in uniaxial extension instead of a constant area as in simple shear; and (b) the tendency of the entanglement network to yield, i.e., to undergo chain disentanglement is partially suppressed during startup extension at high Hencky rates. In short, the phenomenon of strain hardening reflects the reality that entangled melts are not fluids but temporary solids and that the conventional description of their uniaxial extension in terms of the Cauchy stress contains a geometric condensation factor.