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Small-amplitude oscillatory shear (SAOS) tests provide a complete framework to characterize a viscoelastic material in the linear regime. Large-amplitude oscillatory shear (LAOS) tests in which the material is subjected to large sinusoidal strain amplitudes, and the resulting nonsinusoidal stress waveform is analyzed, have recently become an area of research in the characterization of nonlinear viscoelastic behavior. LAOS tests have been applied on various types of viscoelastic materials and a Fourier-transform analysis has been used to characterize the nonlinearity by the occurrence of higher-order harmonics. Other works have attempted to improve on the existing Fourier-transform method and have also introduced new methods to characterize the nonlinearity, which can provide a physical significance to the parameters involved. While much soft matter has been examined within the various LAOS frameworks, very few attempts have been made to describe the behavior of glassy polymers within the LAOS framework. Here, we report the results of LAOS experiments in which we explore the nonlinear response of a glassy polymethyl methacrylate (PMMA) at 22 °C. We look at the behavior both qualitatively and quantitatively using Lissajous–Bowditch (LB) loops, Fourier-transform rheology (FTR), and Chebyshev-polynomial descriptions of behavior. The stress responses from the LAOS tests are also compared with those predicted by the BKZ nonlinear constitutive model. We report the absolute intensity of the harmonics and their variation with the strain amplitude. For PMMA, the normalized third-harmonic intensity, which is one characteristic of the nonlinearity, does not follow a quadratic dependence on strain amplitude as observed in several other materials. The Chebyshev-polynomial method provides a physical interpretation via the normalized third-order Chebyshev coefficients that were calculated using the MITLAOS MATLAB program. Normalized elastic Chebyshev coefficients showed strain softening, while shear-softening behavior was observed from normalized viscous Chebyshev coefficients for PMMA with an increase in strain amplitude. We have also compared the FTR and Chebyshev methodologies for a purely elastic material and have shown that the Chebyshev analysis can effectively separate the nonlinearity as contributed by elastic and viscous parts, while the harmonic FT analysis characterizes nonlinearity as a combined effect.
Mechanics of Time-Dependent Materials – Springer Journals
Published: Jan 8, 2022
Keywords: Nonlinear rheology; LAOS; Polymethyl methacrylate; Fourier-transform rheology; Lissajous loops; Chebyshev-polynomial method
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