Comparing interconversion methods between linear viscoelastic material functions

Springer Science and Business Media LLC - Tập 22 - Trang 401-419 - 2017
Stelios Katsourinis1, Evagelia Kontou1
1Department of Applied Mathematical and Physical Sciences, Section of Mechanics, National Technical University of Athens, Athens, Greece

Tóm tắt

A variety of methods applicable to the interconversion of static (creep) and dynamic (relaxation) functions, with regard to appropriate experimental data of various polymers is investigated and compared. The effectiveness of the selected methods was verified by a series of creep experimental data of various polymeric structures. While most of the employed methods are well established in the literature, some further modifications have been introduced for an improvement of the conversion procedure. Furthermore, a new approach is also employed, which is based on the stretched-exponential function, usually applied to represent both relaxation and retardation functions. It is seen that the examined methods produce a similar result, concerning the creep compliance function, having as a beginning storage and loss modulus experimental data. The same observation applies to the retardation spectra, pointing the fact that discrete spectra deviates significantly from the continuous spectra. As a result, it is shown that the creep compliance function, or the relaxation modulus function, can be predicted using experimental dynamic data (relaxation or creep, respectively), as well as anyone of the examined interconversion methods, with an accuracy close to 5%. The use of approximate or exact relations in the whole procedure was proved not to have a significant effect on the final result (referring mostly to the retardation spectra).

Tài liệu tham khảo

Alves, N.M., Gomez Ribelles, J.L., Gomez Tejedor, J.A., Mano, J.F.: Viscoelastic behavior of poly(methyl methacrylate) networks with different cross-linking degrees. Macromolecules 37, 3735–3744 (2004) Baumgaertel, M., Winter, H.H.: Interrelation between continuous and discrete relaxation time spectra. J. Non-Newton. Fluid Mech. 44, 15–36 (1992) Berry, G.C., Plazek, D.J.: On the use of stretched—exponential functions for both linear viscoelastic creep and stress relaxation. Rheol. Acta 36, 320–329 (1997) Bhattacharjee, S., Swamy, A.K., Daniel, J.S.: Continuous relaxation and retardation spectrum method for viscoelastic characterization of asphalt concrete. Mech. Time-Depend. Mater. 16(3), 287–305 (2012). doi:10.1007/s11043-011-9162-9 Chen, D.-L., Chiu, T.-C., Chen, T.-C., Chung, M.-H., Yang, P.-F., Lai, Y.-S.: Using DMA to simultaneously acquire Young’s relaxation modulus and time-dependent Poisson’s ration of a viscoelastic material. Proc. Eng. 79, 153–159 (2014) Emri, I., Tschoegl, N.W.: Generating line spectra from experimental responses. Part 4. Application to experimental data. Rheol. Acta 33, 60–70 (1994) Emri, I., von Bernstorff, B.S., Cvelbar, R., Nikonov, A.: Re-examination of the approximate methods for interconversion between frequency and time-dependent material functions. J. Non-Newton. Fluid Mech. 129, 75–84 (2005) Fernández, P., Rodríguez, D., Lamela, M.J., Fernández-Canteli, A.: Study of the interconversion between viscoelastic behavior functions of PMMA. Mech. Time-Depend. Mater. 15, 169–180 (2011) Ferry, J.D.: Viscoelastic Behavior of Polymers. Wiley, New York (1980) Georgiopoulos, P., Kontou, E., Niaounakis, M.: Thermomechanical properties and rheological behavior of biodegradable composites. Polym. Compos. 35(6), 1140–1149 (2014). doi:10.1002/pc.22761 Grassia, L., D’Amore, A.: The relative placement of linear viscoelastic functions in amorphous glassy polymers. J. Rheol. 53, 339–356 (2009a). doi:10.1122/1.3056631 Grassia, L., D’Amore, A.: On the interplay between viscoelasticity and structural relaxation in glassy amorphous polymers. J. Polym. Sci., Part B, Polym. Phys. 47, 724–739 (2009b) Grassia, L., D’Amore, A., Simon, S.L.: On the viscoelastic Poisson’s ratio in amorphous polymers. J. Rheol. 54, 1009–1022 (2010). doi:10.1122/1.3473811 Guedes, R.M., Marques, A.T., Cardon, A.: Creep or relaxation master curves calculated from experimental dynamic viscoelastic function. Sci. Eng. Compos. Mater. 7(3), 259–267 (1998) Kaschta, J., Schwarzl, F.R.: Calculation of discrete retardation spectra from creep data—I. Method. Rheol. Acta 33, 517–529 (1994) Liu, Y.: A direct method for obtaining discrete relaxation spectra from creep data. Rheol. Acta 40, 256–260 (2001) Ninomiya, K.M., Ferry, J.D.: Some approximate equations useful in the phenomenological treatment of linear viscoelastic data. J. Colloid Interface Sci. 14, 36–48 (1959) Park, S.W., Schapery, R.A.: Methods of interconversion between linear viscoelastic material functions. Part I. A numerical method based on Prony series. Int. J. Solids Struct. 36, 1653–1675 (1999a) Park, S.W., Schapery, R.A.: Methods of interconversion between linear viscoelastic material functions. Part II. An approximate analytical method. Int. J. Solids Struct. 36(11), 1677–1699 (1999b) Plazek, D.J., Ngai, K.L., Rendell, W.: An application of a unified relaxation model to the aging of Polystyrene below its glass temperature. Polym. Eng. Sci. 24, 1111–1116 (1984) Plazek, D.J., Ragupathi, N., Orborn, S.J.: Determination of dynamic storage and loss compliance from creep data. J. Rheol. 23, 477–488 (1979) Sane, S.B., Knauss, W.G.: The time-dependent bulk response of poly (methyl methacrylate). Mech. Time-Depend. Mater. 5, 293–324 (2001) Saprunov, I., Gergesova, M., Emri, I.: Prediction of viscoelastic material functions from constant stress- or stain-rate experiments. Mech. Time-Depend. Mater. 18, 349–372 (2014) Sorvari, J., Malinen, M.: Numerical interconversion between linear viscoelastic material functions with regularization. Int. J. Solids Struct. 44, 1291–1303 (2007) Tschoegl, N.W., Knauss, W.G., Emri, I.: Poisson’s ratio in linear viscoelasticity—a critical review. Mech. Time-Depend. Mater. 6, 3–51 (2002) Williams, G., Watts, D.C.: Non-symmetrical dielectric relaxation behavior arising from a simple empirical decay function. Trans. Faraday Soc. 66, 80 (1970) Williams, G., Watts, D.C.: Further considerations of non symmetrical dielectric relaxation behavior arising from a simple empirical decay function. Trans. Faraday Soc. 67, 1323–1335 (1971)