Biaxial Yield for Nonlinearly Viscoelastic Materials with a Strain Clock

Abstract

A constitutive equation with a dilatation dependent reduced time is used to model the mechanical response of solid amorphous polymers such as polycarbonate. Such constitutive equa- tions have the property that stress relaxation occurs faster with increasing dilatation. In previous work, it has been shown that this constitutive equation can account for yield in materials undergoing uniaxial strain or stress control histories. In the present work, yield is discussed when materials described by this constitutive equation undergo homogeneous biaxial and triaxial strain histories. Four sets of conditions are considered: in-plane biaxial constant strain rate histories and in-plane biaxial constant stress rate histories, for both plane stress and plane strain states. Yield is defined in a manner analogous to that in the corresponding strain and stress control conditions in the uniaxial case.