Nonlinear Dynamic Mechanical Moduli for Polycarbonate and Pmma

A multiple integral expansion of the Boltzmann superposition principle when applied to sinusoidal shear oscillations becomes We have evaluated this constitutive equation with hollow cylinders of polycarbonate and polymethylmethacrylate at 1 Hz from T_gto below their 0 transitions. Shear strain amplitude, 70, was increased incrementally from the linear to the nonlinear region. Phase angles and harmonic content were determined with a Rheophasor digital cross correlator. At the maximum strain used, 2-4%, deformation was completely recoverable, after some time, upon returning to the linear region. G₁' and G₁" vs temperature compare excellently to the literature and our own small strain measurements of G₁' and G₁" on rectangular bars in free and forced torsion. H₃' and H₃", and higher harmonic terms were found to be small. All nonlinearity in the range studied can be modeled by G₃' and G₃" is in the range 10^l0-10¹¹ N/m². G₃' is negative and ~ 10 (G₃") for both materials. G₃' and G₃" show a glass transition similar to G₁' For polycarbonate they show a very large transition at the T^p of G₁'. PMMA showed almost no 0 transition in the nonlinear constants. Molecular explanations and implications for impact and fatigue behavior are discussed as well as potential errors in typical dynamic mechanical data due to these nonlinearities.