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Obtaining Fourier series graphically from large amplitude oscillatory shear loops

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Abstract

Large amplitude oscillatory shear (LAOS) flow has been used to characterize the nonlinear viscoelasticity of polymer melts and solutions. Results are frequently reported with shear stress versus strain loops, or with shear stress versus shear rate loops. A Fourier analysis of the stress response to LAOS is often desired for comparison with theory, or for quantitative comparison between resins. A method is presented which employs the discrete Fourier transform to obtain the Fourier series coefficients from LAOS loops.

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References

  • Dealy JM, Petersen JF, Tee TT (1973) A concentriccylinder rheometer for polymer melts. Rheol Acta 12:550–558

    Google Scholar 

  • Giacomin AJ, Samurkas T, Dealy JM (1989) A novel sliding plate rheometer for molten plastics. Polym Eng Sci 29:499–504

    Google Scholar 

  • Lammiman KA, Roberts JE (Nov 1961) Notes on the measurement of visco-elasticity in materials of high viscosity. Laboratory Practice 816–824

  • MacSporran WC, Spiers RP (1982) The dynamic performance of the Weissenberg rheogoniometer II. Large amplitude oscillatory shearing — fundamental response. Rheol Acta 21:193–200

    Google Scholar 

  • Matsumoto T, Segawa Y, Warashina Y, Onogi S (1973) Nonlinear behavior of viscoelastic materials. II. The method of analysis and temperature dependence of nonlinear viscoelastic functions. Trans Soc Rheol 17:47–62

    Google Scholar 

  • Onogi S, Matsumoto T (1981) Rheological properties of polymer solutions and melts containing suspended particles. Polym Eng Rev 1:45–87

    Google Scholar 

  • Onogi S, Masuda T, Matsumoto T (1970) Non-linear behavior of viscoelastic materials. I. Disperse systems of polystyrene solution and carbon black. Trans Soc Rheol 14:275–294

    Google Scholar 

  • Philippoff W (1966) Vibrational measurements with large amplitudes. Trans Soc Rheol 10:317–334

    Google Scholar 

  • Ramirez RW (1985) The FFT fundamentals and concepts. Prentice-Hall, New Jersey

    Google Scholar 

  • Tanaka A, Onogi S (1983) Nonlinear viscoelastic properties of crystalline polymers. Pol Eng Rev 3:235–275

    Google Scholar 

  • Tee TT, Dealy JM (1975) Nonlinear viscoelasticity of polymer melts. Trans Soc Rheol 19:595–615

    Google Scholar 

  • Tielking JT, Hanson RR, Giacomin AJ (Oct-Dec, 1990) Viscoelastic properties of aircraft tire materials. Tire Sci Technol 18:262–281

    Google Scholar 

  • Tsai AT, Soong DS (1985) Measurement of fast transient and steady-state responses of viscoelastic fluids with a sliding cylinder rheometer executing coaxial displacements. J Rheol 29:1–18

    Google Scholar 

  • Tsang WKW, Dealy JM (1981) The use of large transient deformations to evaluate rheological models for molten polymers. J Non-Newt Fluid Mech 9:203–222

    Google Scholar 

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Giacomin, A.J., Oakley, J.G. Obtaining Fourier series graphically from large amplitude oscillatory shear loops. Rheola Acta 32, 328–332 (1993). https://doi.org/10.1007/BF00434197

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  • DOI: https://doi.org/10.1007/BF00434197

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