Superposition of small strains on large deformations as a probe of nonlinear response in polymers

The incremental response ΔG(t) obtained by superposing a deformation, Δγ, on a large deformation, γ₁, has been determined in step shear experiments for a polyisobutylene solution and for a poly(methylmethacrylate) glass in torsion. For both systems ΔG(t) at γ₁ was found to be smaller than the linear viscoelastic modulus, G(t), at zero prestrain. ΔG(t) was found to increase with increasing time, t_e, after imposition of the large deformation. It was also observed that the “apparent relaxation spectrum” associated with ΔG(t) narrows and shifts to shorter times when compared to the spectrum associated with the linear viscoelastic modulus, ΔG(t). The results for the solution art‐well described by the nonlinear constitutive equation of the BKZ elastic fluid theory. It is found that ΔG(t) for the glass falls between the behavior predicted by the BKZ theory and the linear viscoelastic behavior.