Abstract
This chapter includes a short review of large amplitude oscillatory shear (LAOS), the details on the analysis methods for LAOS, and the fluid mechanics of LAOS. The first section is the short review of LAOS. The second one deals with analysis methods for the interpretation of LAOS data such as FT-rheology and stress decomposition. The third one introduces how to calculate the analytical solution of LAOS for various constitutive models and the problems involved in the analytical solutions. The last one introduces semi-analytical method for LAOS which is a trial to overcome the limitation of the analytical approaches.
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References
J.-E. Bae, K.S. Cho, Semi-analytical methods for the determination of the nonlinear parameter of nonlinear viscoelastic constitutive equations from LAOS data. J. Rheol. 59, 525–555 (2015)
J.-E. Bae, M. Lee, K.S. Cho, K.H. Seo, D.G. Kang, Comparison of stress-controlled and strain-controlled rheometers for large amplitude oscillatory shear. Rheol. Acta 52, 841–857 (2013)
N.A. Bharadwaj, R.H. Ewoldt, The general low-frequency prediction for asymptotically nonlinear material functions in oscillatory shear. J. Rheol. 58, 891–910 (2014)
M. Boisly, M. Kästner, J. Brummund, V. Ulbricht, Large Amplitude Oscillatory Shear of the Prandtl Element Analysed by Fourier Transform Rheology. Appl. Rheol. 24, 1–11 (2014)
A. Calin, M. Wilhelm, C. Balan, Determination of the nonlinear parameter (mobility factor) of the Giesekus constitutive model using LAOS procedure. J. Non-Newtonian Fluid Mech. 165, 1564–1577 (2010)
K.S. Cho, K. Hyun, K.H. Ahn, S.J. Lee, A geometrical interpretation of large amplitude oscillatory shear response. J. Rheol. 49, 747–758 (2005)
K.S. Cho, K.-W. Song, G.-S. Chang, Scaling relations in nonlinear viscoelastic behavior of aqueous peo solutions under large amplitude oscillatory shear flow. J. Rheol. 54, 27–63 (2010)
K.S. Cho, J.W. Kim, J.-E. Bae, J.H. Youk, H.J. Jeon, K.-W. Song, Effect of temporary network structure on linear and nonlinear viscoelasticity of polymer solutions. Korea–Aust. Rheol. J. 27, 151–161 (2015)
C.J. Dimitriou, R.H. Ewoldt, G.H. McKinley, Describing and prescribing the constitutive response of yield stress fluids using large amplitude oscillatory shear stress (LAOStress). J. Rheol. 57, 27–70 (2013)
B.M. Erwin, S.A. Rogers, M. Cloitre, D. Vlassopoulos, Examining the validity of strain-rate frequency superposition when measuring the linear viscoelastic properties of soft materials. J. Rheol. 54, 187–195 (2010)
R.H. Ewoldt, Defining nonlinear rheological material functions for oscillatory shear. J. Rheol. 57, 177–195 (2013)
R.H. Ewoldt, N.A. Bharadwaj, Low-dimensional intrinsic material functions for nonlinear viscoelasticity. Rheol. Acta 52, 201–219 (2013)
R.H. Ewoldt, G.H. McKinley, On secondary loops in LAOS via self-intersection of Lissajous-Bowditch curves. Rheol. Acta 49, 213–219 (2010)
R.H. Ewoldt, A.E. Hosoi, G.H. McKinley, New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear. J. Rheol. 52, 1427–1458 (2008)
R.H. Ewoldt, P. Winter, J. Maxey, G.H. McKinley, Large amplitude oscillatory shear of pseudoplastic and elastoviscoplastic materials. Rheol. Acta 49, 191–212 (2010)
A.J. Giacomin, J.G. Oakley, Obtaining Fourier series graphically from large amplitude oscillatory shear loops. Rheol. Acta 32, 328–332 (1993)
A.J. Giacomin, T. Samurkas, J.M. Dealy, A novel sliding plate rheometer for molten plastics. Polym. Eng. Sci. 29, 499–504 (1989)
A.J. Giacomin, R.B. Bird, L.M. Johnson, A.W. Mix, Large–Amplitude oscillatory shear flow from the co-rotational maxwell model. J. Non-Newtonian Fluid Mech. 166, 1081–1099 (2011)
A.J. Giacomin, C. Saengow, M. Guay, C. Kolitawong, Padé approximants for large amplitude oscillatory shear flow. Rheol. Acta 54, 679–693 (2015)
X. Gong, Y. Xu, S. Xuan, C. Guo, L. Zong, W. Jiang, The investigation on the nonlinearity of plasticine-like magnetorehological material under oscillatory shear rheometry. J. Rheol. 56, 1375–1391 (2012)
A.K. Gurnon, N.J. Wagner, Large amplitude oscillatory shear (LAOS) measurements to obtain constitutive equation model parameters: giesekus model of banding and nonbanding wormlike micelles. J. Rheol. 56, 333–351 (2012)
E. Helfand, D.C. Pearson, Calculation of the nonlinear stress of polymers in oscillatory shear fields. J. Polym. Sci. Polym. Phys. Ed. 20, 1249–1258 (1982)
K. Hyun, A study on the nonlinear response of viscoelastic complex fluids under large amplitude oscillatory shear flow, Ph.D. thesis supervised by Prof. S. J. Lee, (Seoul National University, Seoul, 2005)
K. Hyun, M. Wilhelm, Establishing a new mechanical nonlinear coefficient Q from FT-Rheology: first investigation of entangled linear and comb polymer model systems. Macromolecules 42, 411–422 (2009)
K. Hyun, S.H. Kim, K.H. Ahn, S.J. Lee, Large amplitude oscillatory shear as a way to classify the complex fluids. J. Non-Newtonian Fluid Mech. 107, 51–65 (2002)
K. Hyun, K.H. Ahn, S.J. Lee, M. Sugimoto, K. Koyama, Degree of branching of polypropylene measured from Fourier-transform rheology. Rheol. Acta 46, 123–129 (2006)
K. Hyun, E.S. Baik, K.H. Ahn, S.J. Lee, M. Sugimoto, K. Koyama, Fourier–transform rheology under medium amplitude oscillatory shear for linear and branched polymer melts. J. Rheol. 51, 1319–1342 (2007)
K. Hyun, M. Wilhelm, C.O. Klein, K.S. Cho, J.G. Nam, K.H. Ahn, S.J. Lee, R.H. Ewoldt, G.H. McKinley, A review of nonlinear oscillatory shear tests: analysis and application of large amplitude oscillatory shear (LAOS). Prog. Polym. Sci. 36, 1697–1753 (2011)
K. Hyun, W. Kim, S.J. Park, M. Wilhelm, Numerical simulation results of the nonlinear coefficient Q from FT-rheology using a single mode pom-pom model. J. Rheol. 57, 1–25 (2013)
A.I. Isayev, C.M. Wong, Parallel superposition of small- and large-amplitude oscillations upon steady shear flow of polymer fluids. J. Polym. Sci. Polym. Phys. Ed. 26, 2303–2327 (1988)
M. Kempf, D. Ahirwal, M. Cziep, M. Wilhelm, Synthesis and linear and nonlinear melt rheology of well-defined comb architectures of PS and PpMS with a low and controlled degree of long-chain branching. Macromolecules 46, 4978–4994 (2013)
H. Kim, K. Hyun, D.-J. Kim, K.S. Cho, Comparison of interpretation methods for large amplitude oscillatory shear response. Korea–Aust. Rheol. J. 18, 91–98 (2006)
R.G. Larson, Constitutive equations for polymer melts and solutions (Butterworths, UK, 1988)
J. Läuger, H. Stettin, Differences between stress and strain control in the non-linear behavior of complex fluids. Rheol. Acta 49, 909–930 (2010)
X. Li, S.-Q. Wang, X. Wang, Nonlinearity in large amplitude oscillatory shear (LAOS) of different viscoelastic materials. J. Rheol. 53, 1255–1274 (2009)
H.T. Lim, K.H. Ahn, J.S. Hong, K. Hyun, Nonlinear viscoelasticity of polymer nanocomposites under large amplitude oscillatory shear flow. J. Rheol. 57, 767–789 (2013)
T. Matsumoto, Y. Segawa, Y. Warashina, S. Onogi, Nonlinear behavior of viscoelastic materials. II. the method of analysis and temperature dependence of nonlinear viscoelastic functions. Trans. Soc. Rheol. 17, 47–62 (1973)
J.G. Nam, K. Hyun, K.H. Ahn, S.J. Lee, Prediction of normal stresses under large amplitude oscillatory shear flow. J. Non-Newtonian Fluid Mech. 150, 1–10 (2008)
J.G. Nam, K.H. Ahn, S.J. Lee, K. Hyun, First normal stress difference of entangled polymer solutions in large amplitude oscillatory shear flow. J. Rheol. 54, 1243–1266 (2010)
T. Neidhöfer, M. Wilhelm, B. Debbaut, Fourier-transform rheology experiments and finite-element simulations on linear polystyrene solutions. J. Rheol. 47, 1351–1371 (2003)
A. Papon, S. Merabia, L. Guy, F. Lequeux, H. Montes, P. Sotta, D.L. Long, Unique nonlinear behavior of nano-filled elastomers: from the onset of strain softening to large amplitude shear deformations. Macromolecules 45, 2891–2904 (2012)
E.-K. Park, K.-W. Song, Rheological evaluation of petroleum jelly as a base material in ointment and cream formulations with respect to rubbing onto the human body. Korea–Aust. Rheol. J. 22, 279–289 (2010)
A.R. Payne, The dynamic properties of carbon black-loaded natural rubber vulcanizates. Part I. J. Appl. Polym. Sci. 6, 57–63 (1962)
D.S. Pearson, W.E. Rochefort, Behavior of concentrated polystyrene solutions in large-amplitude oscillatory shear fields, J. Polym. Sci., Part B: Polym. Phys. Ed., 20, 83–98 (1982)
W. Pilippoff, Vibrational measurements with large amplitudes. Trans. Soc. Rheol. 10, 317–334 (1966)
F. Renou, J. Stellbrink, G. Petekidis, Yielding processes in a colloidal glass of soft star-like micelles under large amplitude oscillatory shear (LAOS). J. Rheol. 54, 1219–1242 (2010)
S.A. Rogers, A sequence of physical processes determined and quantified in LAOS: An instantaneous local 2D/3D approach. J. Rheol. 56, 1129–1151 (2012)
S.A. Rogers, B.M. Erwin, D. Vlassopoulos, M. Cloitre, A sequence of physical processes and quantified in LAOS: application to a yield stress fluid. J. Rheol. 55, 435–458 (2011)
C. Saengow, A.J. Giacomin, C. Kolitawong, Exact analytical solution for large-amplitude oscillatory shear flow. Macromol. Theory Simul. 24, 352–392 (2015)
R. Salehiyan, Y. Yoo, W.J. Choi, K. Hyun, Characterization of morphologies of compatibilized polypropylene/ polystyrene blends with nanoparticles via nonlinear rheological properties from FT-rheology. Macromolecules 47, 4066–4076 (2014)
E. Senses, P. Akcora, An interface-driven stiffening mechanism in polymer nanocomposites. Macromolecules 46, 1868–1874 (2013)
H.G. Sim, K.H. Ahn, S.J. Lee, Large amplitude oscillatory shear behavior of complex fluids investigated by a network model: a guide for classification. J. Non-Newtonian Fluid Mech. 112, 237–250 (2003)
J.W. Swan, R.N. Zia, J.F. Brady, Large amplitude oscillatory microrheology. J. Rheol. 58, 1–41 (2014)
T.T. Tee, J.M. Dealy, Nonlinear viscoelasticity of polymer melts. J. Rheol. 19, 595–615 (1975)
D. van Dusschoten, M. Wilhelm, H.W. Spiess, Two-dimensional Fourier transform rheology. J. Rheol. 45, 1319–1339 (2001a)
D. van Dusschoten, M. Wilhelm, H.W. Spiess, Two-dimensional Fourier transform rheology. J. Rheol. 45, 1319–1339 (2001b)
I. Vittorias, M. Parkinson, K. Klimke, B. Debbaut, M. Wilhelm, Detection and quantification of industrial polyethylene branching topologies via Fourier-transform rheology, NMR and simulation using the pom-pom model. Rheol. Acta 46, 321–340 (2007)
M.H. Wagner, R. Rubio, H. Bastian, The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release. J. Rheol. 45, 1387–1412 (2001)
M.H. Wagner, V.H. Rolón-Garrido, K. Hyun, M. Wilhelm, Analysis of medium amplitude oscillatory shear data of entangled linear and model comb polymer. J. Rheol. 55, 495–516 (2011)
M. Wilhelm, D. Maring, H.-W. Spiess, Fourier-transform rheology. Rheol. Acta 37, 399–405 (1998)
M. Wilhelm, P. Reinheimer, M. Ortseifer, High sensitivity Fourier-transform rheology. Rheol. Acta 38, 349–356 (1999)
M. Wilhelm, P. Reinheimer, M. Ortseifer, T. Neidhöfer, H.W. Spiess, The crossover between linear and nonlinear mechanical behavior in polymer solutions as detected by Fourier-transform rheology. Rheol. Acta 39, 241–247 (2000)
H.M. Wyss, K. Miyazaki, J. Mattsson, Z. Hu, D.R. Reichman, D.A. Weitz, Strain-rate frequency superposition: a rheological probe of structural relaxation in soft materials. Phys. Rev. Lett. 98, 238303 (2007)
W. Yu, P. Wang, C. Zhou, General Stress decomposition in nonlinear oscillatory shear flow. J. Rheol. 53, 215–238 (2009)
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Cho, K.S. (2016). Large Amplitude Oscillatory Shear. In: Viscoelasticity of Polymers. Springer Series in Materials Science, vol 241. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-7564-9_11
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DOI: https://doi.org/10.1007/978-94-017-7564-9_11
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