The effect of moisture on the nonlinearly viscoelastic behavior of an epoxy
Tóm tắt
The shear and bulk relaxation moduli required to characterize a homogeneous, isotropic, and linearly viscoelastic material were determined using a confined compression experiment and by introducing a new iterative scheme that accounts for the fact that the hoop and radial strains are not step functions. In addition, the coefficients of thermal and hygral expansion of the epoxy being considered were determined along with its diffusive behavior. Fickian diffusion of moisture was confirmed by coupling radial diffusion in an epoxy disk with optical interference measurements of the out-of-plane displacements. These properties are essential components of the modified free-volume model of nonlinear viscoelasticity established by Popelar and Liechti (J. Eng. Mater. Technol. 119:205–210, 1997, Mech. Time-Depend. Mater. 7(2):89–141, 2003). For the nonlinear component of the model, its distortional parameters were evaluated from Arcan pure shear test results at one strain rate and temperature/humidity state. The nonlinear viscoelasticity model was then used to predict the shear stress-strain response under other conditions. The dilatational parameters were extracted from uniaxial tensile test results at one strain rate and temperature humidity state and predictions under other conditions compared favorably with the results from experiments. This exercise adds to a growing list of glassy polymers whose nonlinear stress-strain behavior can be modeled by this modified free-volume model.
Tài liệu tham khảo
Adolf, D.B., Chambers, R.S., Caruthers, J.M.: Extensive validation of a thermodynamically consistent, nonlinear viscoelastic model for glassy polymers. Polymer 45, 4599–4621 (2004)
Arcan, M., Hashin, Z., Voloshin, A.: A method to produce uniform plane stress states with applications to fiber-reinforced materials. Exp. Mech. 18(2), 141–146 (1978)
Arzoumanidis, G.A., Liechti, K.M.: Linear viscoelastic property measurement and its significance to some nonlinear viscoelasticity models. Mech. Time-Depend. Mater. 7, 209–250 (2003)
Bradshaw, R.D., Brinson, L.C.: A sign control method for fitting and interconverting material functions for linearly viscoelastic solids. Mech. Time-Depend. Mater. 1(1), 85–108 (1997)
Canal, L.P., Michaud, V.: Micro-scale modeling of water diffusion in adhesive composite joints. Compos. Struct. 111, 340–348 (2014)
Caruthers, J.M., Adolf, D.B., Chambers, R.S., Shrikhande, P.: A thermodynamically consistent, nonlinear viscoelastic approach for modeling glassy polymers. Polymer 45, 4577–4597 (2004)
Chevellard, G., Ravi-Chandar, K., Liechti, K.: Modeling the nonlinear viscoelastic behavior of polyurea using a distortion modified free volume approach. Mech. Time-Depend. Mater. 16(2), 181–203 (2012). https://doi.org/10.1007/s11043-011-9146-9
Cost, T.L., Becker, E.B.: A multidata method of approximate Laplace transform inversion. Int. J. Numer. Methods Eng. 2(2), 207–219 (1970)
Doolittle, A.K.: Studies in Newtonian flow II: the dependence of the viscosity of liquids on free-space. J. Appl. Mech. 22, 1471–1475 (1951)
Drozdov, A.D.: Accretion of ageing, viscoelastic bodies under conditions of volume solidification. Mech. Solids 23, 98–103 (1988)
Emri, I., Tschoegl, N.: Generating line spectra from experimental responses. Part I: relaxation modulus and creep compliance. Rheol. Acta 32(3), 311–322 (1993)
Ferreira Vieira de Mattos, D.: Effect of moisture on mixed-mode traction-separation relations of a glass/epoxy interface. PhD Dissertation, University of Texas Austin (2017)
Fillers, R.W., Tschoegl, N.W.: The effect of pressure on the mechanical properties of polymers. Trans. Soc. Rheol. 21, 51–100 (1977)
Fujita, H.: Diffusion in polymer-diluent systems. In: Fortschritte Der Hochpolymeren-Forschung, pp. 1–47. Springer, Berlin (1961)
Guth, E., Wack, P.E., Anthony, R.L.: Significance of the equation for state for rubber. J. Appl. Phys. 17, 347–351 (1946)
Knauss, W.G., Emri, I.: Non-linear viscoelasticity based on free volume consideration. Comput. Struct. 13, 123–128 (1981)
Knauss, W.G., Emri, I.: Volume change and the nonlinearly thermo-viscoelastic constitution of polymers. Polym. Eng. Sci. 27(21), 86–100 (1987)
Knauss, W.G., Kenner, V.H.: On the hygrothermomechanical characterization of polyvinyl acetate. J. Appl. Phys. 51(10), 5131–5136 (1980)
Leaderman, H.: Elastic and Creep Properties of Filamentous Materials and Other High Polymers. The Textile Foundation, Washington (1943)
Losi, G.U., Knauss, W.G.: Free volume theory and nonlinear thermoviscoelasticity. Polym. Eng. Sci. 32(8), 542–557 (1992)
Lustig, S.R., Shay, R.M. Jr, Caruthers, J.M.: Thermodynamic constitutive equations for materials with memory on a material time scale. J. Rheol. 40(1), 69–106 (1996)
Ma, Z., Ravi-Chandar, K.: Confined compression: a stable homogeneous deformation for constitutive characterization. Exp. Mech. 40, 38–45 (2000)
Makhmutov, I., Sorina, T., Suvorova, Y.V., Surgucheva, A.: Failure of composites taking into account the effects of temperature and moisture. Mech. Compos. Mater. 19(2), 175–180 (1983)
Masurovsky, E.B., Bunge, R.P.: Fluoroplastic coverslips for long-term nerve tissue culture. Stain Technol. 43(3), 161–165 (1968)
Medvedev, G.A., Caruthers, J.M.: A comparison of constitutive descriptions of the thermo-mechanical behavior of polymeric glasses. In: Roth, C.B. (ed.) Polymer Glasses. Taylor and Francis, London (2017)
Odegard, G., Bandyopadhyay, A.: Physical aging of epoxy polymers and their composites. J. Polym. Sci., Part B, Polym. Phys. 49(24), 1695–1716 (2011)
Park, S.J., Liechti, K.M., Roy, S.: Simplified bulk experiments and hygrothermal nonlinear viscoelasticity. Mech. Time-Depend. Mater. 8, 303–344 (2004)
Popelar, C.F., Liechti, K.M.: Multiaxial nonlinear viscoelastic characterization and modeling of a structural adhesive. J. Eng. Mater. Technol. 119, 205–210 (1997)
Popelar, C.F., Liechti, K.M.: A distortion-modified free volume theory for nonlinear viscoelastic behavior. Mech. Time-Depend. Mater. 7(2), 89–141 (2003)
Schapery, R.A.: A simple collocation method for fitting viscoelastic models to experimental data. In: GALCIT Solid Mechanics Reports, vol. SM-61-23A. California Institute of Technology (1962)
Schapery, R.A.: Application of thermodynamics to thermomechanical, fracture, and birefringent phenomena in viscoelastic media. J. Appl. Phys. 35, 1451–1465 (1964)
Schapery, R.A.: A method of viscoelastic stress analysis using elastic solutions. J. Franklin Inst. 279, 268–289 (1965)
Schapery, R.A.: On the characterization of nonlinear viscoelastic materials. Polym. Eng. Sci. 9, 295–310 (1969)
Schapery, R.A.: Nonlinear facture analysis of viscoelastic composite materials based on a generalized j integral theory. In: Akasak, K.K.T. (ed.) Proc. Japan-U.S. Conference Composite Materials, Tokyo (1981)
Tschoegl, N.W.: The Phenomenological Theory of Linear Viscoelastic Behavior: An Introduction. Springer, Berlin (2012)
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)
Viktorova, I.: Description of the delayed fracture of inelastic materials taking temperature into account. Mech. Compos. Mater. 19(1), 35–38 (1983)
Williams, M.L., Landel, R.F., Ferry, J.D.: The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J. Am. Chem. Soc. 77, 3701–3707 (1955)