We report the first-ever complete measurement of MAOStress material functions, which reveal that stress can be more fundamental than strain or strain rate for understanding linearity limits as a function of Deborah number. The material used is a canonical viscoelastic liquid with a single dominant relaxation time: polyvinyl alcohol (PVA) polymer solution cross-linked with tetrahydroborate (Borax) solution. We outline experimental limit lines and their dependence on geometry and test conditions. These MAOStress measurements enable us to observe the frequency dependence of the weakly nonlinear deviation as a function of stress amplitude. The observed features of MAOStress material functions are distinctly simpler than MAOStrain, where the frequency dependence is much more dramatic. The strain-stiffening transient network model was used to derive a model-informed normalization of the nonlinear material functions that accounts for their scaling with linear material properties. Moreover, we compare the frequency dependence of the critical stress, strain, and strain-rate for the linearity limit, which are rigorously computed from the MAOStress and MAOStrain material functions. While critical strain and strain-rate change by orders of magnitude throughout the Deborah number range, critical stress changes by a factor of about 2, showing that stress is a more fundamental measure of nonlinearity strength. This work extends the experimental accessibility of the weakly nonlinear regime to stress-controlled instruments and deformations, which reveal material physics beyond linear viscoelasticity but at conditions that are accessible to theory and detailed simulation.
REFERENCES
1.
Hyun
, K.
, M.
Wilhelm
, C. O.
Klein
, K. S.
Cho
, J. G.
Nam
, K. H.
Ahn
, S. J.
Lee
, R. H.
Ewoldt
, and 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
). 2.
Philippoff
, W.
, “Vibrational measurements with large amplitudes
,” Trans. Soc. Rheol.
10
, 317
–334
(1966
). 3.
Wilhelm
, M.
, “Fourier-transform rheology
,” Macromol. Mater. Eng.
287
, 83
–105
(2002
). 4.
Ewoldt
, R. H.
, A. E.
Hosoi
, and G. H.
McKinley
, “New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear
,” J. Rheol.
52
, 1427
–1458
(2008
). 5.
Rogers
, S. A.
, B. M.
Erwin
, D.
Vlassopoulos
, and M.
Cloitre
, “A sequence of physical processes determined and quantified in LAOS: Application to a yield stress fluid
,” J. Rheol.
55
, 435
–458
(2011
). 6.
Rogers
, S. A.
, “In search of physical meaning: Defining transient parameters for nonlinear viscoelasticity
,” Rheol. Acta
56
, 501
–525
(2017
). 7.
Komatsu
, H.
, T.
Mitsui
, and S.
Onogi
, “Nonlinear viscoelastic properties of semisolid emulsions
,” Trans. Soc. Rheol.
17
, 351
–364
(1973
). 8.
Giacomin
, A. J.
, and J. M.
Dealy
, Using large-amplitude oscillatory shear, in Rheological Measurement, edited by A. A. Collyer and D. W. Clegg (Springer, Dordrecht, 1998), pp. 327–356.9.
Neidhöfer
, T.
, S.
Sioula
, N.
Hadjichristidis
, and M.
Wilhelm
, “Distinguishing linear from star-branched polystyrene solutions with Fourier-transform rheology
,” Macromol. Rapid Commun.
25
, 1921
–1926
(2004
). 10.
Kate Gurnon
, A.
, and 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
). 11.
Dealy
, J. M.
, and J.
Wang
, Melt Rheology and Its Applications in the Plastics Industry (Springer, Netherlands, 2013), pp. 19–47. 12.
Randall
, A. M.
, and C. G.
Robertson
, “Linear-nonlinear dichotomy of the rheological response of particle-filled polymers
,” J. Appl. Polym. Sci.
131
, 40818
(2014
). 13.
Joyner
, H. S.
, “Nonlinear (large-amplitude oscillatory shear) rheological properties and their impact on food processing and quality
,” Annu. Rev. Food Sci. Technol.
12
, 591
–609
(2021
). 14.
Rogers
, S. A.
, B. M.
Erwin
, D.
Vlassopoulos
, and M.
Cloitre
, “Oscillatory yielding of a colloidal star glass
,” J. Rheol.
55
, 733
–752
(2011
). 15.
Wang
, S. Q.
, S.
Ravindranath
, and P. E.
Boukany
, “Homogeneous shear, wall slip, and shear banding of entangled polymeric liquids in simple-shear rheometry: A roadmap of nonlinear rheology
,” Macromolecules
44
, 183
–190
(2011
). 16.
Ravindranath
, S.
, S. Q.
Wang
, M.
Olechnowicz
, V. S.
Chavan
, and R. P.
Quirk
, “How polymeric solvents control shear inhomogeneity in large deformations of entangled polymer mixtures
,” Rheol. Acta
50
, 97
–105
(2011
). 17.
Merger
, D.
, and M.
Wilhelm
, “Intrinsic nonlinearity from LAOStrain—Experiments on various strain- and stress-controlled rheometers: A quantitative comparison
,” Rheol. Acta
53
, 621
–634
(2014
). 18.
Läuger
, J.
, and H.
Stettin
, “Effects of instrument and fluid inertia in oscillatory shear in rotational rheometers
,” J. Rheol.
60
, 393
–406
(2016
). 19.
Hyun
, K.
, and 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
). 20.
Ewoldt
, R. H.
, and N. A.
Bharadwaj
, “Low-dimensional intrinsic material functions for nonlinear viscoelasticity
,” Rheol. Acta
52
, 201
–219
(2013
). 21.
Kumar
, M. A.
, R. H.
Ewoldt
, and C. F.
Zukoski
, “Intrinsic nonlinearities in the mechanics of hard sphere suspensions
,” Soft Matter
12
, 7655
–7662
(2016
). 22.
Singh
, P. K.
, J. M.
Soulages
, and R. H.
Ewoldt
, “Frequency-sweep medium-amplitude oscillatory shear (MAOS)
,” J. Rheol.
62
, 277
–293
(2017
). 23.
Bharadwaj
, N. A.
, K. S.
Schweizer
, and R. H.
Ewoldt
, “A strain stiffening theory for transient polymer networks under asymptotically nonlinear oscillatory shear
,” J. Rheol.
61
, 643
–665
(2017
). 24.
Carey-De La Torre
, O.
, and R. H.
Ewoldt
, “First-harmonic nonlinearities can predict unseen third-harmonics in medium-amplitude oscillatory shear (MAOS)
,” Korea Aust. Rheol. J.
30
, 1
–10
(2018
). 25.
Natalia
, I.
, R. H.
Ewoldt
, and E.
Koos
, “Questioning a fundamental assumption of rheology: Observation of noninteger power expansions
,” J. Rheol.
64
, 625
–635
(2020
). 26.
Lennon
, K. R.
, G. H.
Mckinley
, and J. W.
Swan
, “Medium amplitude parallel superposition (MAPS) rheology. Part 1 : Mathematical framework and theoretical examples
,” J. Rheol.
64
, 551
–579
(2020
). 27.
Lennon
, K. R.
, J. D. J.
Rathinaraj
, M. A.
Gonzalez Cadena
, A.
Santra
, G. H.
McKinley
, and J. W.
Swan
, “Anticipating gelation and vitrification with medium amplitude parallel superposition (MAPS) rheology and artificial neural networks
,” Rheol. Acta
62
, 535
–556
(2023
). 28.
Shanbhag
, S.
, and Y. M.
Joshi
, “Kramers–Kronig relations for nonlinear rheology. Part I: General expression and implications
,” J. Rheol.
66
, 973
–982
(2022
). 29.
Cziep
, M. A.
, M.
Abbasi
, M.
Heck
, L.
Arens
, and M.
Wilhelm
, “Effect of molecular weight, polydispersity, and monomer of linear homopolymer melts on the intrinsic mechanical nonlinearity 3Q0(
) in MAOS
,” Macromolecules
49
, 3566
–3579
(2016
). 30.
Song
, H. Y.
, S. J.
Park
, and K.
Hyun
, “Distinguishing between linear and star polystyrenes with unentangled arms by dynamic oscillatory shear tests
,” ACS Macro Lett.
12
, 968
–973
(2023
). 31.
Martinetti
, L.
, O.
Carey-De La Torre
, K. S.
Schweizer
, and R. H.
Ewoldt
, “Inferring the nonlinear mechanisms of a reversible network
,” Macromolecules
51
, 8772
–8789
(2018
). 32.
Wu
, Y.
, P.
Huang
, Y.
Yu
, C.
Shi
, H.
Chen
, H.
Wang
, J.
Yang
, Z.
Leng
, and W.
Huang
, “Nonlinear rheological performance characterization of styrene-butadiene-styrene and crumb rubber composite modified bitumen using large amplitude oscillatory shear tests
,” J. Cleaner Prod.
385
, 135712
(2023
). 33.
Lee
, S.
, M.
Kim
, H. Y.
Song
, and K.
Hyun
, “Characterization of the effect of clay on morphological evaluations of PLA/biodegradable polymer blends by FT-rheology
,” Macromolecules
52
, 7904
–7919
(2019
). 34.
Hyun
, K.
, E. S.
Baik
, K. H.
Ahn
, S. J.
Lee
, M.
Sugimoto
, and K.
Koyama
, “Fourier-transform rheology under medium amplitude oscillatory shear for linear and branched polymer melts
,” J. Rheol.
51
, 1319
–1342
(2007
). 35.
Song
, H. Y.
, S. Y.
Park
, S.
Kim
, H. J.
Youn
, and K.
Hyun
, “Linear and nonlinear oscillatory rheology of chemically pretreated and non-pretreated cellulose nanofiber suspensions
,” Carbohydr. Polym.
275
, 118765
(2022
). 36.
Song
, H. Y.
, S. J.
Park
, and K.
Hyun
, “Characterization of dilution effect of semidilute polymer solution on intrinsic nonlinearity Q0 via FT rheology
,” Macromolecules
50
, 6238
–6254
(2017
). 37.
Liu
, J.
, L.
Lou
, W.
Yu
, R.
Liao
, R.
Li
, and C.
Zhou
, “Long chain branching polylactide: Structures and properties
,” Polymer
51
, 5186
–5197
(2010
). 38.
Natalia
, I.
, R. H.
Ewoldt
, and E.
Koos
, “Particle contact dynamics as the origin for noninteger power expansion rheology in attractive suspension networks
,” J. Rheol.
66
, 17
–30
(2022
). 39.
Wagner
, M. H.
, V. H.
Rolón-Garrido
, K.
Hyun
, and M.
Wilhelm
, “Analysis of medium amplitude oscillatory shear data of entangled linear and model comb polymers
,” J. Rheol.
55
, 495
–516
(2011
). 40.
Bharadwaj
, N. A.
, and R. H.
Ewoldt
, “Constitutive model fingerprints in medium-amplitude oscillatory shear
,” J. Rheol.
59
, 557
–592
(2015
). 41.
Saengow
, C.
, A. J.
Giacomin
, and C.
Kolitawong
, “Exact analytical solution for large-amplitude oscillatory shear flow from Oldroyd 8-constant framework: Shear stress
,” Phys. Fluids
29
, 043101
(2017
). 42.
Martinetti
, L.
, and R. H.
Ewoldt
, “Time-strain separability in medium-amplitude oscillatory shear
,” Phys. Fluids
31
, 021213
(2019
). 43.
Song
, H. Y.
, H. J.
Kong
, S. Y.
Kim
, and K.
Hyun
, “Evaluating predictability of various constitutive equations for MAOS behavior of entangled polymer solutions
,” J. Rheol.
64
, 673
–707
(2020
). 44.
Ramlawi
, N.
, N. A.
Bharadwaj
, and R. H.
Ewoldt
, “The weakly nonlinear response and nonaffine interpretation of the Johnson–Segalman/Gordon–Schowalter model
,” J. Rheol.
64
, 1409
–1424
(2020
). 45.
Singh
, P. K.
, and R. H.
Ewoldt
, “On simultaneous fitting of nonlinear and linear rheology data: Preventing a false sense of certainty,” arXiv:2202.02867 (2022).46.
Pipkin
, A. C.
, Lectures on Viscoelasticity Theory, Applied Mathematical Sciences Vol. 7 (Springer New York, New York, 1986).47.
Dealy
, J. M.
, and K. F.
Wissbrun
, Melt Rheology and Its Role in Plastics Processing (Springer, Netherlands, 1999). 48.
Giacomin
, A.
, R.
Bird
, L.
Johnson
, and A.
Mix
, “Large-amplitude oscillatory shear flow from the corotational Maxwell model
,” J. Non-Newtonian Fluid Mech.
166
, 1081
–1099
(2011
). 49.
Davis
, W. M.
, and C. W.
Macosko
, “Nonlinear dynamic mechanical moduli for polycarbonate and PMMA
,” J. Rheol.
22
, 53
–71
(1978
). 50.
Jongschaap
, R. J.
, K. H.
Knapper
, and J. S.
Lopulissa
, “On the limit of linear viscoelastic response in the flow between eccentric rotating disks
,” Polym. Eng. Sci.
18
, 788
–792
(1978
). 51.
Pearson
, D. S.
, and W. E.
Rocherfort
, “Behavior of concentrated polystyrene solutions in large-amplitude oscillating shear fields
,” J. Polym. Sci.: Polym. Phys. Ed.
20
, 83
–98
(1982
). 52.
Dimitriou
, C. J.
, R. H.
Ewoldt
, and 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
). 53.
Piñeiro-Lago
, L.
, N.
Ramlawi
, I.
Franco
, C. A.
Tovar
, L.
Campo-Deaño
, and R. H.
Ewoldt
, “Large amplitude oscillatory shear stress (LAOStress) analysis for an acid-curd Spanish cheese: Afuega’l Pitu atroncau blancu and roxu (PDO)
,” Food Hydrocolloids
142
, 108720
(2023
). 54.
Läuger
, J.
, and H.
Stettin
, “Differences between stress and strain control in the non-linear behavior of complex fluids
,” Rheol. Acta
49
, 909
–930
(2010
). 55.
Ewoldt
, R. H.
, “Defining nonlinear rheological material functions for oscillatory shear
,” J. Rheol.
57
, 177
–195
(2013
). 56.
Lee
, J. C.-W.
, Y.-T.
Hong
, K. M.
Weigandt
, E. G.
Kelley
, H.
Kong
, and S. A.
Rogers
, “Strain shifts under stress-controlled oscillatory shearing in theoretical, experimental, and structural perspectives: Application to probing zero-shear viscosity
,” J. Rheol.
63
, 863
–881
(2019
). 57.
Hassager
, O.
, “Stress-controlled oscillatory flow initiated at time zero: A linear viscoelastic analysis
,” J. Rheol.
64
, 545
–550
(2020
). 58.
Griebler
, J. J.
, G. J.
Donley
, V.
Wisniewski
, and S. A.
Rogers
, “Strain shift measured from stress-controlled oscillatory shear: Evidence for a continuous yielding transition and new techniques to determine recovery rheology measures
,” J. Rheol.
68
, 301
–315
(2024
). 59.
Atalik
, K.
, and R.
Keunings
, “On the occurrence of even harmonics in the shear stress response of viscoelastic fluids in large amplitude oscillatory shear
,” J. Non-Newtonian Fluid Mech.
122
, 107
–116
(2004
). 60.
Singh
, P. K.
, J. M.
Soulages
, and R. H.
Ewoldt
, “On fitting data for parameter estimates: Residual weighting and data representation
,” Rheol. Acta
58
, 341
–359
(2019
). 61.
Graham
, M. D.
, “Wall slip and the nonlinear dynamics of large amplitude oscillatory shear flows
,” J. Rheol.
39
, 697
–712
(1995
). 62.
Bird
, R. B.
, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids
, 2nd ed. (Wiley
, New York
, 1987
), Vol. 1.63.
Vrentas
, J. S.
, D. C.
Venerus
, and C. M.
Vrentas
, “Finite amplitude oscillations of viscoelastic fluids
,” J. Non-Newtonian Fluid Mech.
40
, 1
–24
(1991
). 64.
Nam
, J. G.
, K.
Hyun
, K. H.
Ahn
, and S. J.
Lee
, “Prediction of normal stresses under large amplitude oscillatory shear flow
,” J. Non-Newtonian Fluid Mech.
150
, 1
–10
(2008
). 65.
Ewoldt, R. H., M. T. Johnston, and L. M. Caretta
, “Experimental challenges of shear rheology: How to avoid bad data,”
in Complex Fluids in Biological Systems
, Springer Biological Engineering Series, edited by S. Spagnolie (Springer, New York, 2015
), pp. 207–241. 66.
Savins
, J. G.
, “Shear thickening phenomena in poly(vinyl)alcohol-borate complexes
,” Rheol. Acta
7
, 87
–93
(1968
). 67.
Inoue
, T.
, and K.
Osaki
, “Rheological properties of poly(vinyl alcohol)/sodium borate aqueous solutions
,” Rheol. Acta
32
, 550
–555
(1993
). 68.
Osaki
, K.
, T.
Inoue
, and K. H.
Ahn
, “Shear and normal stresses of a poly(vinyl alcohol)/sodium borate aqueous solution at the start of shear flow
,” J. Non-Newtonian Fluid Mech.
54
, 109
–120
(1994
). 69.
Narita
, T.
, K.
Mayumi
, G.
Ducouret
, and P.
Hébraud
, “Viscoelastic properties of poly(vinyl alcohol) hydrogels having permanent and transient cross-links studied by microrheology, classical rheometry, and dynamic light scattering
,” Macromolecules
46
, 4174
–4183
(2013
). 70.
Hossain
, M. T.
, and R. H.
Ewoldt
, “Protorheology
,” J. Rheol.
68
, 113
–144
(2024
). 71.
72.
Martinetti
, L.
, J. M.
Soulages
, and R. H.
Ewoldt
, “Continuous relaxation spectra for constitutive models in medium-amplitude oscillatory shear
,” J. Rheol.
62
, 1271
–1298
(2018
). 73.
Corman
, R. E.
, and R. H.
Ewoldt
, “Mapping linear viscoelasticity for design and tactile intuition
,” Appl. Rheol.
29
, 141
–161
(2019
). 74.
Ewoldt
, R. H.
, and G. H.
McKinley
, “Mapping thixo-elasto-visco-plastic behavior
,” Rheol. Acta
56
, 195
–210
(2017
). 75.
Macosko
, C. W.
, Rheology: Principles, Measurements, and Applications
(VCH Publishers. Inc., New York, 1994
).76.
Coleman
, B. D.
, and W.
Noll
, “Foundations of linear viscoelasticity
,” Rev. Mod. Phys.
33
(2), 239
(1961
). 77.
Coleman
, B. D.
, and W.
Noll
, “Erratum: Foundations of linear viscoelasticity
,” Rev. Mod. Phys.
36
, 1103
(1964
). 78.
Riesz
, F.
, “Untersuchungen über systeme integrierbarer funktionen
,” Math. Ann.
69
, 449
–497
(1910
). 79.
Bourbaki
, N.
, Topological Vector Spaces
(Springer
, Berlin
, 1987
), Vol. 1.80.
White
, J. L.
, “Dynamics of viscoelastic fluids, melt fracture, and the rheology of fiber spinning
,” J. Appl. Polym. Sci.
8
, 2339
–2357
(1964
). 81.
Hatzikiriakos
, S. G.
, and J. M.
Dealy
, “Wall slip of molten high density polyethylene. I. Sliding plate rheometer studies
,” J. Rheol.
35
, 497
–523
(1991
). 82.
Lennon
, K. R.
, M.
Geri
, G. H.
McKinley
, and J. W.
Swan
, “Medium amplitude parallel superposition (MAPS) rheology. Part 2: Experimental protocols and data analysis
,” J. Rheol.
64
, 1263
–1293
(2020
). 83.
Bharadwaj
, N. A.
, and R. H.
Ewoldt
, “Single-point parallel disk correction for asymptotically nonlinear oscillatory shear
,” Rheol. Acta
54
, 223
–233
(2015
). You do not currently have access to this content.
