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Acta Mechanica

Erschienen in:

09.08.2019 | Original Paper

Fractional single-phase lag heat conduction and transient thermal fracture in cracked viscoelastic materials

verfasst von: Wenzhi Yang, Zengtao Chen

Erschienen in: Acta Mechanica | Ausgabe 10/2019

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Abstract

In the present article, a thermo-viscoelastic model is developed to investigate fractional single-phase lag heat conduction and the associated transient thermal mechanical behavior of a cracked viscoelastic material under a thermal shock. To avoid the negative temperature distribution around cracks, which violates the second law of thermodynamics, the time-fractional single-phase lag heat conduction is introduced to analyze the transient temperature field around the cracks. The Fourier and Laplace transforms, coupled with the singular integral equations, are employed to solve the governing partial differential equations numerically. Both the results of temperature field and stress intensity factors (SIFs) show that the fractional single-phase lag heat conduction model is more accurate and reasonable compared to the conventional hyperbolic heat conduction. A significant difference in transient fracture behavior exists between viscoelastic and elastic materials. A sharp pulse of the SIFs at the early stage is observed and should be consider carefully to meet the requirement of increased application of viscoelastic composites under thermal loading.

Vorheriger Artikel Two-scale analysis of the permeability of 3D periodic granular and fibrous media

Nächster Artikel Contact of faces of a rectilinear crack under complex loading and various contact conditions

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Drury, J.L., Mooney, D.J.: Hydrogels for tissue engineering: scaffold design variables and applications. Biomaterials 24(24), 4337–4351 (2003)

Guo, M., Pitet, L.M., Wyss, H.M., Vos, M., Dankers, P.Y., Meijer, E.: Tough stimuli-responsive supramolecular hydrogels with hydrogen-bonding network junctions. J. Am. Chem. Soc. 136(19), 6969–6977 (2014)

Luo, F., Sun, T.L., Nakajima, T., Kurokawa, T., Zhao, Y., Sato, K., Ihsan, A.B., Li, X., Guo, H., Gong, J.P.: Oppositely charged polyelectrolytes form tough, self-healing, and rebuildable hydrogels. Adv. Mater. 27(17), 2722–2727 (2015)

Sun, J.-Y., Zhao, X., Illeperuma, W.R., Chaudhuri, O., Oh, K.H., Mooney, D.J., Vlassak, J.J., Suo, Z.: Highly stretchable and tough hydrogels. Nature 489(7414), 133 (2012)

Haag, S., Bernards, M.: Polyampholyte hydrogels in biomedical applications. Gels 3(4), 41 (2017)

Haraguchi, K.: Nanocomposite hydrogels. Curr. Opin. Solid State Mater. Sci. 11(3–4), 47–54 (2007)

Guedes, R.: Durability of polymer matrix composites: viscoelastic effect on static and fatigue loading. Compos. Sci. Technol. 67(11–12), 2574–2583 (2007)

Zhai, S., Zhang, P., Xian, Y., Zeng, J., Shi, B.: Effective thermal conductivity of polymer composites: theoretical models and simulation models. Int. J. Heat. Mass. Transf. 117, 358–374 (2018)

Chen, H., Ginzburg, V.V., Yang, J., Yang, Y., Liu, W., Huang, Y., Du, L., Chen, B.: Thermal conductivity of polymer-based composites: fundamentals and applications. Prog. Polym. Sci. 59, 41–85 (2016)

10.

Ji, H., Sellan, D.P., Pettes, M.T., Kong, X., Ji, J., Shi, L., Ruoff, R.S.: Enhanced thermal conductivity of phase change materials with ultrathin-graphite foams for thermal energy storage. Energy Environ. Sci. 7(3), 1185–1192 (2014)

11.

Li, X., Li, C., Xue, Z., Tian, X.: Analytical study of transient thermo-mechanical responses of dual-layer skin tissue with variable thermal material properties. Int. J. Therm. Sci. 124, 459–466 (2018)

12.

Van Hees, J., Gybels, J.: C nociceptor activity in human nerve during painful and non painful skin stimulation. J. Neurol. Neurosurg. Psychiatry 44(7), 600–607 (1981)

13.

Liu, Y.J., Xu, N.: Modeling of interface cracks in fiber-reinforced composites with the presence of interphases using the boundary element method. Mech. Mater. 32(12), 769–783 (2000)

14.

Zhi-He, J., Naotake, N.: Transient thermal stress intensity factors for a crack in a semi-infinite plate of a functionally gradient material. Int. J. Solids Struct. 31(2), 203–218 (1994)MATH

15.

Erdogan, F., Wu, B.: The surface crack problem for a plate with functionally graded properties. J. Appl. Mech. 64(3), 449–456 (1997)MATH

16.

Bao, G., Wang, L.: Multiple cracking in functionally graded ceramic/metal coatings. Int. J. Solids Struct. 32(19), 2853–2871 (1995)MATH

17.

Wang, B., Mai, Y.: A cracked piezoelectric material strip under transient thermal loading. J. Appl. Mech. 69(4), 539–546 (2002)MATH

18.

Ueda, S.: Thermally induced fracture of a piezoelectric laminate with a crack normal to interfaces. J. Therm. Stress. 26(4), 311–331 (2003)

19.

Ueda, S.: Thermal stress intensity factors for a normal crack in a piezoelectric material strip. J. Therm. Stress. 29(12), 1107–1125 (2006)

20.

Cattaneo, C.: A form of heat-conduction equations which eliminates the paradox of instantaneous propagation. C. R. 247, 431 (1958)MATH

21.

Vernotte, P.: Some possible complications in the phenomena of thermal conduction. C. R. 252, 2190–2191 (1961)

22.

Shaw, S., Mukhopadhyay, B.: A discontinuity analysis of generalized thermoelasticity theory with memory-dependent derivatives. Acta Mech. 228(7), 2675–2689 (2017)MathSciNetMATH

23.

Mondal, S., Pal, P., Kanoria, M.: Transient response in a thermoelastic half-space solid due to a laser pulse under three theories with memory-dependent derivative. Acta Mech. 230, 179–199 (2019)MathSciNetMATH

24.

Youssef, H.M.: Two-dimensional thermal shock problem of fractional order generalized thermoelasticity. Acta Mech. 223(6), 1219–1231 (2012)MathSciNetMATH

25.

Sur, A., Kanoria, M.: Fibre-reinforced magneto-thermoelastic rotating medium with fractional heat conduction. Procedia Eng. 127, 605–612 (2015)

26.

Sur, A., Kanoria, M.: Modeling of memory-dependent derivative in a fibre-reinforced plate. Thin Wall Struct. 126, 85–93 (2018)

27.

Mondal, S., Sur, A., Kanoria, M.: Transient response in a piezoelastic medium due to the influence of magnetic field with memory-dependent derivative. Acta Mech. 230, 2325–2338 (2019)MathSciNet

28.

Sur, A., Pal, P., Mondal, S., Kanoria, M.: Finite element analysis in a fiber-reinforced cylinder due to memory-dependent heat transfer. Acta Mech. 230, 1607–1624 (2019)

29.

Purkait, P., Sur, A., Kanoria, M.: Elasto-thermodiffusive response in a spherical shell subjected to memory-dependent heat transfer. Wave Random Complex Media 1–23 (2019). https://doi.org/10.1080/17455030.2019.1599464

30.

Li, W., Song, F., Li, J., Abdelmoula, R., Jiang, C.: Non-Fourier effect and inertia effect analysis of a strip with an induced crack under thermal shock loading. Eng. Fract. Mech. 162, 309–323 (2016)

31.

Hu, K., Chen, Z.: Thermoelastic analysis of a partially insulated crack in a strip under thermal impact loading using the hyperbolic heat conduction theory. Int. J. Eng. Sci. 51, 144–160 (2012)MathSciNetMATH

32.

Chang, D., Wang, B.: Transient thermal fracture and crack growth behavior in brittle media based on non-Fourier heat conduction. Eng. Fract. Mech. 94, 29–36 (2012)

33.

Zhang, X., Chen, Z., Li, X.: Thermal shock fracture of an elastic half-space with a subsurface penny-shaped crack via fractional thermoelasticity. Acta Mech. 229(12), 4875–4893 (2018)MathSciNet

34.

Zhang, X., Li, X.: Transient thermal stress intensity factors for a circumferential crack in a hollow cylinder based on generalized fractional heat conduction. Int. J. Therm. Sci. 121, 336–347 (2017)

35.

Wang, B.: Transient thermal cracking associated with non-classical heat conduction in cylindrical coordinate system. Acta. Mech. Sin. 29(2), 211–218 (2013)MathSciNetMATH

36.

Zhang, X., Xie, Y., Li, X.: Transient thermoelastic response in a cracked strip of functionally graded materials via generalized fractional heat conduction. Appl. Math. Model. 70, 328–349 (2019)MathSciNet

37.

Xue, Z., Chen, Z., Tian, X.: Thermoelastic analysis of a cracked strip under thermal impact based on memory-dependent heat conduction model. Eng. Fract. Mech. 200, 479–498 (2018)

38.

Xue, Z., Chen, Z., Tian, X.: Transient thermal stress analysis for a circumferentially cracked hollow cylinder based on memory-dependent heat conduction model. Theor. Appl. Fract. Mech. 96, 123–133 (2018)

39.

Kaminski, W.: Hyperbolic heat conduction equation for materials with a nonhomogeneous inner structure. J. Heat Transf. 112(3), 555–560 (1990)

40.

Mitra, K., Kumar, S., Vedevarz, A., Moallemi, M.: Experimental evidence of hyperbolic heat conduction in processed meat. J. Heat Transf. 117(3), 568–573 (1995)

41.

Braznikov, A., Karpychev, V., Luikova, A.: One engineering method of calculating heat conduction process. Inzhenerno Fizicheskij Zhurnal 28(4), 677–680 (1975)

42.

Bai, C., Lavine, A.: On hyperbolic heat conduction and the second law of thermodynamics. J. Heat Transf. 117(2), 256–263 (1995)

43.

Körner, C., Bergmann, H.: The physical defects of the hyperbolic heat conduction equation. Appl. Phys. A 67(4), 397–401 (1998)

44.

Rubin, M.: Hyperbolic heat conduction and the second law. Int. J. Eng. Sci. 30(11), 1665–1676 (1992)MathSciNetMATH

45.

Zhang, W., Cai, X., Holm, S.: Time-fractional heat equations and negative absolute temperatures. Comput. Math. Appl. 67(1), 164–171 (2014)MathSciNetMATH

46.

Ezzat, M.A., El-Karamany, A.S.: Fractional thermoelectric viscoelastic materials. J. Appl. Polym. Sci. 124(3), 2187–2199 (2012)

47.

Tarasov, V.E., Aifantis, E.C.: On fractional and fractal formulations of gradient linear and nonlinear elasticity. Acta Mech. 230, 2043–2070 (2019). https://doi.org/10.1007/s00707-019-2373-x MathSciNetCrossRef

48.

Cajić, M., Lazarević, M., Karličić, D., Sun, H., Liu, X.: Fractional-order model for the vibration of a nanobeam influenced by an axial magnetic field and attached nanoparticles. Acta Mech. 229, 4791–4815 (2018)MathSciNet

49.

Atanackovic, T.M., Pilipovic, S.: On a constitutive equation of heat conduction with fractional derivatives of complex order. Acta Mech. 229, 1111–1121 (2018)MathSciNetMATH

50.

Ezzat, M., El-Karamany, A., El-Bary, A.: Generalized thermo-viscoelasticity with memory-dependent derivatives. Int. J. Mech. Sci. 89, 470–475 (2014)

51.

Ezzat, M., El-Karamany, A., El-Bary, A.: Thermo-viscoelastic materials with fractional relaxation operators. Appl. Math. Model. 39(23–24), 7499–7512 (2015)MathSciNet

52.

Ezzat, M.A., El-Bary, A.A.: On thermo-viscoelastic infinitely long hollow cylinder with variable thermal conductivity. Microsyst. Technol. 23, 3263–3270 (2017)

53.

Sladek, J., Sladek, V., Zhang, C., Schanz, M.: Meshless local Petrov–Galerkin method for continuously nonhomogeneous linear viscoelastic solids. Comput. Mech. 37(3), 279–289 (2006)MATH

54.

Cheng, Z., Meguid, S., Zhong, Z.: Thermo-mechanical behavior of a viscoelastic FGMs coating containing an interface crack. Int. J. Fract. 164(1), 15–29 (2010)MATH

55.

Choi, H.J., Thangjitham, S.: Thermally-induced interlaminar crack-tip singularities in laminated anisotropic composites. Int. J. Fract. 60(4), 327–347 (1993)

56.

Carslaw, H.S., Jaeger, J.C.: Conduction of Heat in Solids. Clarendon Press, Oxford (1959)MATH

57.

Erdogan, F.: Interface cracking of FGM coatings under steady-state heat flow. Eng. Fract. Mech. 59, 361–380 (1998)

58.

Zhou, Y., Li, X., Yu, D.: A partially insulated interface crack between a graded orthotropic coating and a homogeneous orthotropic substrate under heat flux supply. Int. J. Solids Struct. 47, 768–778 (2010)MATH

59.

Christensen, R.M., Freund, L.: Theory of viscoelasticity. J. Appl. Mech. 38, 720 (1971)

60.

Eringen, A.C.: Continuum Physics. Academic Press Inc, New York (1975). 632 p

61.

Delale, F., Erdogan, F.: Effect of transverse shear and material orthotropy in a cracked spherical cap. Int. J. Solids Struct. 15(12), 907–926 (1979)MATH

62.

Miller, M.K., Guy, J.: WT: numerical inversion of the Laplace transform by use of Jacobi polynomials. SIAM J. Numer. Anal. 3(4), 624–635 (1966)MathSciNetMATH

63.

Paulino, G., Jin, Z.-H.: Viscoelastic functionally graded materials subjected to antiplane shear fracture. J. Appl. Mech. 68(2), 284–293 (2001)MATH

Titel: Fractional single-phase lag heat conduction and transient thermal fracture in cracked viscoelastic materials
verfasst von: Wenzhi Yang
Zengtao Chen
Publikationsdatum: 09.08.2019
Verlag: Springer Vienna
Erschienen in: Acta Mechanica / Ausgabe 10/2019
Print ISSN: 0001-5970
Elektronische ISSN: 1619-6937
DOI: https://doi.org/10.1007/s00707-019-02474-z

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