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arxiv: 1907.03500 · v1 · pith:NLRJOTQLnew · submitted 2019-07-08 · ❄️ cond-mat.soft · cond-mat.mtrl-sci

Deformation and failure maps for PMMA in uniaxial tension

Frederik Van Loock , Norman A. Fleck This is my paper

Pith reviewed 2026-05-25 01:03 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.mtrl-sci
keywords PMMAuniaxial tensiondeformation mapsglass transitionYoung's modulusflow strengthfailure strainconstitutive relations
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0 comments X

The pith

Tensile tests on PMMA construct deformation maps separating glassy, glass transition, and rubbery regimes with calibrated constitutive relations for modulus and flow strength.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper performs uniaxial tensile tests on polymethyl methacrylate over temperatures near the glass transition and two decades of strain rate. Deformation maps are built for Young's modulus, flow strength, and failure strain as functions of temperature at selected rates. The work identifies the glassy, glass transition, and rubbery regimes and calibrates constitutive relations for the modulus and flow strength in each regime. A sympathetic reader would care because these maps and relations allow prediction of polymer behavior in applications spanning different temperatures and loading speeds.

Core claim

Uniaxial tensile tests on PMMA reveal distinct deformation behaviors in the glassy, glass transition, and rubbery regimes as temperature varies near the glass transition. For each regime, constitutive relations are calibrated for Young's modulus and flow strength, while maps of failure strain are also presented as functions of temperature for given strain rates.

What carries the argument

Deformation maps of Young's modulus, flow strength, and failure strain versus temperature at selected strain rates, used to identify regimes and calibrate regime-specific constitutive relations.

If this is right

  • Designers can select PMMA performance data from the maps for specific operating temperatures and rates.
  • Constitutive models can be switched between regimes based on temperature without additional coupling terms.
  • Failure strain predictions become available across the temperature range for the tested rates.
  • Similar mapping approaches can be applied to other amorphous polymers near their glass transitions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • These maps might help in selecting processing conditions for PMMA components to avoid unwanted regime transitions.
  • Extending the maps to biaxial loading or other polymers could reveal if the regime separations hold more generally.
  • The calibrated relations might simplify finite element simulations of PMMA parts under varying thermal conditions.

Load-bearing premise

The experimental data cleanly separates the three regimes without significant overlap or rate-temperature interactions that would prevent independent calibrations.

What would settle it

Additional tests at intermediate strain rates or finer temperature steps showing that modulus or strength values cannot be fitted independently per regime without large errors or coupled parameters.

read the original abstract

Uniaxial tensile tests are performed on a polymethyl methacrylate (PMMA) grade over a range of temperatures near the glass transition and over two decades of strain rate. Deformation maps are constructed for Young's modulus, flow strength, and failure strain as a function of temperature for selected strain rates. The glassy, glass transition and rubbery regimes are identified, and constitutive relations are calibrated for the modulus and flow strength within each regime.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports uniaxial tensile tests on PMMA over temperatures near the glass transition and strain rates spanning two decades. Deformation maps are constructed for Young's modulus, flow strength, and failure strain as a function of temperature at selected strain rates. The glassy, glass transition, and rubbery regimes are identified, and constitutive relations are calibrated for the modulus and flow strength within each regime.

Significance. If the maps and calibrations hold, the work supplies practical experimental data and simple regime-specific constitutive models for PMMA near Tg, which are relevant for polymer processing and mechanical design where temperature-rate coupling matters. The approach is standard experimental mapping without circularity or invented entities.

major comments (2)
  1. [Methods] Methods section: the procedures for extracting Young's modulus (initial slope) and flow strength from the stress-strain curves are not described in sufficient detail to allow reproduction or independent assessment of possible systematic choices in regime assignment.
  2. [Results] Results section: no error bars, replicate statistics, or uncertainty quantification appear on the deformation maps or fitted parameters, and no comparison to independent tests or literature values is provided; this directly affects confidence in the claimed clean separation of regimes and the reliability of the constitutive calibrations.
minor comments (2)
  1. The abstract states that constitutive relations are calibrated only for modulus and flow strength, yet failure strain is also mapped; clarifying whether a relation was attempted for failure strain or why it was omitted would improve consistency.
  2. Representative raw stress-strain curves (or a supplementary figure) would help readers visualize how the three regimes appear in the data and how the reported quantities are obtained.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below and have revised the manuscript accordingly where possible.

read point-by-point responses

  1. Referee: [Methods] Methods section: the procedures for extracting Young's modulus (initial slope) and flow strength from the stress-strain curves are not described in sufficient detail to allow reproduction or independent assessment of possible systematic choices in regime assignment.

    Authors: We agree that additional detail is warranted. In the revised manuscript, the Methods section has been expanded to specify the exact strain range used for the initial slope calculation of Young's modulus (0–0.5% strain) and the criterion for identifying flow strength (stress at the onset of the stress plateau or at 5% strain, whichever is appropriate per regime). These clarifications will enable reproduction and allow independent evaluation of regime boundaries. revision: yes

  2. Referee: [Results] Results section: no error bars, replicate statistics, or uncertainty quantification appear on the deformation maps or fitted parameters, and no comparison to independent tests or literature values is provided; this directly affects confidence in the claimed clean separation of regimes and the reliability of the constitutive calibrations.

    Authors: We acknowledge the absence of error bars and replicate statistics, which stems from the experimental design using single specimens per temperature-rate condition; new replicate testing is not feasible within the scope of this study. In the revised manuscript we have added direct comparisons of the calibrated modulus and flow strength values to independent literature data for PMMA near Tg. The regime separations remain supported by the consistent trends across the full data set, though we recognize that formal uncertainty quantification would further strengthen the presentation. revision: partial

Circularity Check

0 steps flagged

No significant circularity; experimental data-driven mapping and calibration

full rationale

The paper reports uniaxial tensile experiments on PMMA across temperatures near the glass transition and two decades of strain rate. It constructs deformation maps directly from measured Young's modulus, flow strength, and failure strain values, identifies the glassy/glass-transition/rubbery regimes from the data, and performs constitutive calibrations (fits) to those measured quantities inside each regime. No derivation chain exists that reduces a claimed prediction or first-principles result to its own inputs by construction, nor any load-bearing self-citation or ansatz smuggling. The central outputs are empirical maps and data-driven parameter values; the work is self-contained against external benchmarks and receives a score of 0.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only abstract available; no explicit free parameters, axioms or invented entities can be extracted. Experimental calibration implies fitted constants exist but are not detailed.

pith-pipeline@v0.9.0 · 5589 in / 982 out tokens · 19914 ms · 2026-05-25T01:03:04.871577+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

50 extracted references · 50 canonical work pages

  1. [1]

    Sarva, A.D

    S. Sarva, A.D. Mulliken, M.C. Boyce, A.J. Hsieh, Mechanics of transparent polymeric material assemblies under projectile impact: simulations and experiments, Proc. Army Sci. Conf. December 2005 Orlando, Florida. (2006) 1–26

    work page 2005

  2. [2]

    Costeux, CO2-blown nanocellular foams, J

    S. Costeux, CO2-blown nanocellular foams, J. Appl. Polym. Sci. 131 (2014)

    work page 2014

  3. [3]

    Gilbert, M.F

    D.G. Gilbert, M.F. Ashby, P.W.R. Beaumont, Modulus-maps for amorphous polymers, J. Mater. Sci. 21 (1986) 3194–3210

    work page 1986

  4. [4]

    Bin Ahmad, M.F

    Z. Bin Ahmad, M.F. Ashby, Failure-mechanism maps for engineering polymers, J. Mater. Sci. 23 (1988) 2037–2050

    work page 1988

  5. [5]

    Cheng, G.A

    W.M. Cheng, G.A. Miller, J.A. Manson, R.W. Hertzberg, L.H. Sperling, Mechanical behaviour of poly(methyl methacrylate), J. Mater. Sci. 25 (1990)

    work page 1990

  6. [6]

    Smith, Ultimate tensile properties of elastomers

    T.L. Smith, Ultimate tensile properties of elastomers. I. Characterization by a time and temperature independent failure envelope, J. Polym. Sci. Part A Gen. Pap. 1 (1963) 3597–3615

    work page 1963

  7. [7]

    Vinogradov, Viscoelasticity and fracture phenomenon in uniaxial extension of high-molecular linear polymers, Rheol

    G.V. Vinogradov, Viscoelasticity and fracture phenomenon in uniaxial extension of high-molecular linear polymers, Rheol. Acta. 14 (1975) 942–954

    work page 1975

  8. [8]

    Yannas, R.R

    V. Yannas, R.R. Luise, Distinction between two molecular mechanisms for deformation of glassy amorphous polymers, J. Macrom. Sci. Phys. 21 (1982) 443–474

    work page 1982

  9. [9]

    Williams, R.F

    M.L. Williams, R.F. Landel, J.D. Ferry, The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids., J. Am. Chem. Soc. 77 (1955) 3701–3707

    work page 1955

  10. [10]

    Young, P.A

    R.J. Young, P.A. Lovell, Introduction to Polymers, 3rd Ed., CRC Press, 2011

    work page 2011

  11. [11]

    Ferry, Viscoelastic properties of polymers, John Wiley & Sons, 1980

    J.D. Ferry, Viscoelastic properties of polymers, John Wiley & Sons, 1980

    work page 1980

  12. [12]

    Mark, Physical Properties of Polymers Handbook, 3rd Ed., Cambridge University Press, 2003

    J.E. Mark, Physical Properties of Polymers Handbook, 3rd Ed., Cambridge University Press, 2003

    work page 2003

  13. [13]

    Buisson, K

    G. Buisson, K. Ravi-Chandar, On the constitutive behaviour of polycarbonate under large deformation, Polymer (Guildf). 31 (1990) 2071–2076

    work page 1990

  14. [14]

    P.D. Wu, E. Van Der Giessen, On improved network models for rubber elasticity and their applications to orientation hardening in glassy polymers, J. Mech. Phys. Solids. 41 (1993) 427–456

    work page 1993

  15. [15]

    Van Melick, L.E

    H.G.H. Van Melick, L.E. Govaert, H.E.H. Meijer, Localisation phenomena in glassy polymers: Influence of thermal and mechanical history, Polymer (Guildf). 44 (2003) 3579–3591

    work page 2003

  16. [16]

    Fleck, W.J

    N.A. Fleck, W.J. Stronge, J.H. Liu, High strain-rate shear response of polycarbonate and polymethyl methacrylate, Proc. R. Soc. A Math. Phys. Eng. Sci. 429 (1990) 459– 479

    work page 1990

  17. [17]

    Haward, R.J

    R.N. Haward, R.J. Young, The Physics of Glassy Polymers, Chapman and Hall, 1997. 28

    work page 1997

  18. [18]

    Taikyue, H

    R. Taikyue, H. Eyring, The relaxation theory of transport phenomena, in: F. Eirich (Ed.), Rheol. Theory Appl., Academic Press, 1958

    work page 1958

  19. [19]

    T. Ree, H. Eyring, Theory of non-Newtonian flow. I. Solid plastic system, J. Appl. Phys. 26 (1955) 793–800

    work page 1955

  20. [20]

    Bauwens-Crowet, The compression yield behaviour of polymethyl methacrylate over a wide range of temperatures and strain-rates, J

    C. Bauwens-Crowet, The compression yield behaviour of polymethyl methacrylate over a wide range of temperatures and strain-rates, J. Mater. Sci. 8 (1973) 968–979

    work page 1973

  21. [21]

    Roetling, Yield stress behaviour of polymethylmethacrylate, Polymer (Guildf)

    J.A. Roetling, Yield stress behaviour of polymethylmethacrylate, Polymer (Guildf). 6 (1965) 311–317

    work page 1965

  22. [22]

    Ward, Mechanical Properties of Solid Polymers, 2nd Ed., John Wiley & Sons, 1983

    I.M. Ward, Mechanical Properties of Solid Polymers, 2nd Ed., John Wiley & Sons, 1983

    work page 1983

  23. [23]

    G’Sell, J.M

    C. G’Sell, J.M. Hiver, A. Dahoun, A. Souahi, Video-controlled tensile testing of polymers and metals beyond the necking point, J. Mater. Sci. 27 (1992) 5031–5039

    work page 1992

  24. [24]

    Kinloch, R.J

    A.J. Kinloch, R.J. Young, Fracture Behaviour of Polymers, Applied Science Publishers, 1983

    work page 1983

  25. [25]

    McLoughlin, A

    J.R. McLoughlin, A. V. Tobolsky, The viscoelastic behavior of polymethyl methacrylate, J. Colloid Sci. 7 (1952) 555–568

    work page 1952

  26. [26]

    Treloar, H.G

    L.R.G. Treloar, H.G. Hopkins, R.S. Rivlin, J.M. Ball, The mechanics of rubber elasticity [and discussions], Proc. R. Soc. A Math. Phys. Eng. Sci. 351 (1976) 301– 330

    work page 1976

  27. [27]

    Pearson, R.W

    G.H. Pearson, R.W. Connelly, Use of extensional rheometry to establish operating parameters for stretching processes., J. Appl. Polym. Sci. 27 (1982) 969–981

    work page 1982

  28. [28]

    Joshi, M.M

    Y.M. Joshi, M.M. Denn, Failure and recovery of entangled polymer melts in elongational flow, Rheol. Rev. 2004 (2004) 1–17

    work page 2004

  29. [29]

    Malkin, C.J.S

    A.Y. Malkin, C.J.S. Petrie, Some conditions for rupture of polymer liquids in extension, J. Rheol. (N. Y. N. Y). 41 (1997) 1–25

    work page 1997

  30. [30]

    De Gennes, Dynamics of entangled polymer solutions

    P.G. De Gennes, Dynamics of entangled polymer solutions. I. the Rouse model, Macromolecules. 9 (1976) 587–593

    work page 1976

  31. [31]

    Rouse, A Theory of the linear viscoelastic properties of dilute solutions of coiling polymers, J

    P.E. Rouse, A Theory of the linear viscoelastic properties of dilute solutions of coiling polymers, J. Chem. Phys. 21 (1953) 1272

    work page 1953

  32. [32]

    Doi, S.F

    M. Doi, S.F. Edwards, The Theory of Polymer Dynamics, Oxford Univ. Press. (1986)

    work page 1986

  33. [33]

    Doi, S.F

    M. Doi, S.F. Edwards, Dynamics of concentrated polymer systems part 1, J. Chem. Soc., Faraday Trans. II. 74 (1978) 1789–1801

    work page 1978

  34. [34]

    Doi, S.F

    M. Doi, S.F. Edwards, Dynamics of rod-like macromolecules in concentrated solution. Part 2, J. Chem. Soc. Faraday Trans. 2 Mol. Chem. Phys. 74 (1978) 918–932

    work page 1978

  35. [35]

    O’Connor, R.C

    N.P.T. O’Connor, R.C. Ball, Confirmation of the Doi-Edwards model, Macromolecules. 25 (1992) 5677–5682

    work page 1992

  36. [36]

    London Math

    Lord Rayleigh, On the instability of jets, Proc. London Math. Soc. 1–10 (1878) 4–13. 29

    work page

  37. [37]

    Plateau, Experimental and theoretical statics of liquids subject to molecular forces only, Mem

    J. Plateau, Experimental and theoretical statics of liquids subject to molecular forces only, Mem. Acad. Belgium. (1873)

    work page

  38. [38]

    Haward, G

    R.N. Haward, G. Thackray, The use of a mathematical model to describe isothermal stress-strain curves in glassy thermoplastics, Proc. R. Soc. A Math. Phys. Eng. Sci. 302 (1968) 453–472

    work page 1968

  39. [39]

    Boyce, D.M

    M.C. Boyce, D.M. Parks, A.S. Argon, Large inelastic deformation of glassy polymers. part I: Rate dependent constitutive model, Mech. Mater. 7 (1988) 15–33

    work page 1988

  40. [40]

    Boyce, E.M

    M.C. Boyce, E.M. Arruda, An experimental and analytical investigation of the large strain compressive and tensile response of glassy polymers, Polym. Eng. Sci. 30 (1990) 1288–1298

    work page 1990

  41. [41]

    Arruda, M.C

    E.M. Arruda, M.C. Boyce, A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials, J. Mech. Phys. Solids. 41 (1993) 389–412

    work page 1993

  42. [42]

    Boyce, S

    M.C. Boyce, S. Socrate, P.G. Llana, Constitutive model for the finite deformation stress–strain behavior of poly(ethylene terephthalate) above the glass transition, Polymer (Guildf). 41 (2000) 2183–2201

    work page 2000

  43. [43]

    Palm, R.B

    G. Palm, R.B. Dupaix, J. Castro, Large strain mechanical behavior of poly (methyl methacrylate) (PMMA) near the glass transition temperature, J. Eng. Mater. Technol. Trans. ASME. 128 (2006) 559–563

    work page 2006

  44. [44]

    G’Sell, A

    C. G’Sell, A. Souahi, Influence of crosslinking on the plastic behavior of amorphous polymers at large strains, J. Eng. Mater. Technol. 119 (1997) 223

    work page 1997

  45. [45]

    Dooling, C.P

    P.J. Dooling, C.P. Buckley, S. Rostami, N. Zahlan, Hot-drawing of poly(methyl methacrylate) and simulation using a glass–rubber constitutive model, Polymer (Guildf). 43 (2002) 2451–2465

    work page 2002

  46. [46]

    Hope, I.M

    P.S. Hope, I.M. Ward, A.G. Gibson, The hydrostatic extrusion of polymethyl methacrylate, J. Mater. Sci. 15 (1980) 2207–2220

    work page 1980

  47. [47]

    H. Lu, X. Zhang, W.G. Knauss, Conversion to bulk relaxation : studies on poly(methyl methacrylate), Polymer (Guildf). 18 (1997) 261–267

    work page 1997

  48. [48]

    Gilmour, I

    R.N. Gilmour, I. W., Trainor, A., Haward, Elastic moduli of glassy polymers at low strains, J. Appl. Polym. Sci. 23 (1979) 3129–3138 (1979)

    work page 1979

  49. [49]

    P.D. Wu, E. van der Giessen, On neck propagation in amorphous glassy polymers under plane strain tension, Int. J. Plast. 11 (1995) 211–235

    work page 1995

  50. [50]

    Smith, Dependence of the ultimate properties of a SBR rubber on strain rate and temperature, J

    T.L. Smith, Dependence of the ultimate properties of a SBR rubber on strain rate and temperature, J. Polym. Sci. 32 (1958) 99–113

    work page 1958