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Plastic instability studied experimentally on a semi-crystalline polymer through thermomechanical heat source identification: the flow stress concept revisited

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Abstract

Micromechanical deformation phenomena such as those leading to macroscopic viscoelastic and plastic behavior must be studied from a thermodynamic viewpoint, as they induce complex and partly irreversible heat effects. Calorimetric measurements of the intrinsic volumetric thermomechanical heat sources (THS) activated in the material bulk during mechanical loads can produce valuable information with respect to that aim. They can be based on infrared imaging if submitted to inverse algorithms that allow a correct reconstruction of THS to be produced. Here, an inverse method relying on a diffusion-advection heat transfer model is applied to experimental temperature maps recorded during tensile tests. These are made on a semi-crystalline polymer that shows a strong development of plastic instabilities. Along with simultaneous kinematic observables produced with a digital image correlation system, the competition between advection and diffusion phenomena may be clearly established. 1-D profiles of the reconstructed THS and measured strain rates illustrate clearly that thermomechanical effects associated with necking onset and propagation follow the kinematic variable in a rather direct manner. Finally, we show for tensile experiments that THS estimations lead to analyze plasticity as a rheological behavior controlled by the flow stress, responsible of necking development and propagation.

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References

  • Adams GW, Farris RJ (1988) Latent energy of deformation of bisphenol A polycarbonate. J Polym Sci B Polym Phys 26:433–445

    Article  Google Scholar 

  • Ahmad SH (1992) Flow stress of high density polyethylene and nylon 66 at high rates of strain. Polym Int 28(4):291–294

    Article  Google Scholar 

  • André S, Meshaka Y, Cunat C (2003) Rheological constitutive equation of solids: a link between models based on irreversible thermodynamics and on fractional order derivative equations. Rheol Acta 42:500–515

  • André S, Baravian C, Renault N, Cunat C (2007) In situ mechanical characterization of polymers with the association of three optical techniques. Appl Phys Lett 91(7):071919

    Article  Google Scholar 

  • André S, Renault N, Meshaka Y, Cunat C (2012) From the thermodynamics of constitutive laws to thermomechanical experimental characterization of materials: an assessment based on inversion of thermal images. Continuum Mech Therm 24(1):1–20

    Article  Google Scholar 

  • Auffray N, Bonnet M, Pagano S (2013) Identification of transient heat sources using the reciprocity gap. Inverse Probl Sci Eng 21(4):721–738

    Article  Google Scholar 

  • Bhalla KS, Zehnder AT, Han X (2003) Thermomechanics of slow stable crack growth: closing the loop between experiments and computational modeling. Eng Fract Mech 70:2439–2458

    Article  Google Scholar 

  • Blaise A, Baravian C, Dillet J, Michot LJ, André S (2012) Characterization of the mesostructure of HDPE under “in-situ” uniaxial tensile test by incoherent polarized steady-light transport. J Polym Sci B Polym Phys 50(5):328–337

  • Blaise A, Andre S, Delobelle P, Meshaka Y, Cunat C (2016) Advantages of a 3-parameter reduced constitutive model for the measurement of polymers elastic Modulus using tensile tests. Mech Time-Depend Mater 20:553–577

    Article  Google Scholar 

  • Callen HB (1985) Thermodynamics and an introduction to thermostatics. Wiley, New York

    Google Scholar 

  • Chrysochoos A, Louche H (2000) An infrared image processing to analyze the calorific effects accompanying strain localization. Int J Eng Sci 38:1759–1788

    Article  Google Scholar 

  • Coussot P (2018) Slow flows of yield stress fluids: yielding liquids or flowing solids? Rheol Acta 57:1–14

    Article  Google Scholar 

  • Cunat C (2001) The DNLR approach and relaxation phenomena. Part I: historical account and DNLR formalism. Mech Time-Depend Mater 5:39–65

    Article  Google Scholar 

  • De Sousa DM, Roberty NC (2012) An inverse source problem for the stationary diffusion–advection–decay equation. Inverse Probl Sci Eng 20(7):891–915

    Article  Google Scholar 

  • Delpueyo D, Balandraud X, Grédiac M (2013) Heat source reconstruction from noisy temperature fields using an optimised derivative Gaussian filter. Infrared Phys Technol 60:312–322

    Article  Google Scholar 

  • Doudard C, Calloch C, Hild F, Roux S (2010) Identification of heat source from infrared thermography: determination of ‘self-heating’ in a dual-phase steel by using a dog bone sample. Mech Mater 42:55–62

    Article  Google Scholar 

  • Farge L, Boisse J, Bihannic I, Diaz A, André S (2017) Anisotropy development during necking of HDPE studied at the microscale with in situ continuous 1D SAXS scans. J Polym Sci B Polym Phys 56(2):170–181

    Article  Google Scholar 

  • Farge L, Boisse J, Dillet J, André S, Albouy P-A, Meneau F (2015) WAXS study of the lamellar/fibrillar transition for a semi-crystalline polymer deformed in tension in relation with the evolution of volume strain, J Polym Sci B Polym Phys 53:1470–1480

  • Kuiken GDC (1994) Thermodynamics of irreversible processes: applications to diffusion and rheology. Wiley Ch7, pp 239–299

  • Maalej T, Maillet D, Fontaine J-R (2012) Estimation of position and intensity of a pollutant source in channel flow using transmittance functions. Inverse Probl 28(5):055010

    Article  Google Scholar 

  • Maj M, Oliferuk W (2012) Analysis of plastic strain localization on the basis of strain and temperature fields. Arch Metall Mater 57(4):1111–1116

    Article  Google Scholar 

  • Meixner J (1954) Thermodynamische theorie der elastichen relaxation. Z Naturforschg 9a:654–663

    Google Scholar 

  • Münster A (1966) Thermodynamique Des Processus Irréversibles. Institut National des Sciences et Techniques Nucléaires and Presses Universitaires de France, Paris-Saclay

    Google Scholar 

  • Nowick AS, Berry BS (1972) Anelastic relaxation in crystalline solids. Academic Press, New York and London, pp 115–129

    Google Scholar 

  • Prigogine I, Defay R (1954) Chemical thermodynamics, Longmans, Green

  • Rap A, Elliott L, Ingham DB, Lesnic D, Wen X (2007) The inverse source problem for the variable coefficients convection-diffusion equation. Inverse Prob Sci Eng 15(5):413–440. https://doi.org/10.1080/17415970600731274

    Article  Google Scholar 

  • Rosenberg E, Brusselle-Dupend N, Epsztein T (2011) A mesoscale quantification method of cavitation in semicrystalline polymers using X-ray microtomography. Mater Sci Eng A 528:6535–6544

    Article  Google Scholar 

  • Salamatina O, Höhne G, Rudnev S, Oleinik E (1994) Work, heat and stored energy in compressive plastic deformation of glassy polymers. Thermochim Acta 247:1–18

    Article  Google Scholar 

  • Tauchert T, Afzal S (1967) Heat generated during torsional oscillations of polymethylmethacrylate tubes. J Appl Phys 38(2):4568–4572

    Article  Google Scholar 

  • Tisza L (1966) Generalized thermodynamics. M.I.T. Press, Cambridge

    Google Scholar 

  • Toussaint E, Balandraud X, Le Cam JB, Grédiac M (2012) Combining displacement, strain, temperature and heat source fields to investigate the thermomechanical response of an elastomeric specimen subjected to large deformations. Polym Test 31:916–925

    Article  Google Scholar 

  • Videcoq E, Quemener O, Lazard M, Neveu A (2008) Heat source identification and on-line temperature control by a branch eigenmodes reduced model. Int J Heat Mass Transf 51:4743–4752

    Article  Google Scholar 

  • Ye J, Andre S, Farge L (2015) Kinematic study of necking in a semicrystalline polymer through 3D digital image correlation. Int J Solids Struct 59:48–72

    Article  Google Scholar 

  • Ye J, Farge L, André S, Neveu A (2016) A numerical study of heat source reconstruction for the advection–diffusion operator: a conjugate gradient method stabilized with SVD. Int J Therm Sci 104:68–85

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Correspondence to Stéphane Andre.

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Ye, J., Andre, S., Farge, L. et al. Plastic instability studied experimentally on a semi-crystalline polymer through thermomechanical heat source identification: the flow stress concept revisited. Rheol Acta 57, 505–520 (2018). https://doi.org/10.1007/s00397-018-1091-y

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  • DOI: https://doi.org/10.1007/s00397-018-1091-y

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