Abstract
Cavity bifurcation is an important mechanism of damage and fracture failure of various materials. The thermal cavitation problem of a composite sphere composed of two kinds of viscoelastic materials subjected to a uniform temperature field was studied in this paper. Based on the finite deformation dynamics theory, a nonlinear mathematical model describing cavity movement in a composite sphere was established by employing the Kelvin–Voigt constitutive equation of thermo-viscoelasticity. Adopting the dimensionless transformation, a parametric cavitated bifurcation solution describing the cavity radius with the temperature was obtained. The dynamic variation curves of the cavity radius, which increase with external temperature, radius ratios, and material parameters, were also discussed. It was proved that the dynamic growth of an infinitely large sphere, including a small sphere, can be achieved by a finitely composite sphere.
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References
Baghani, M., Eskandari, A.H., Zakerzadeh, M.R.: Transient growth of a micro-void in an infinite medium under thermal load with modified Zerilli–Armstrong model. Acta Mech. 227(4), 943–953 (2016). https://doi.org/10.1007/s00707-015-1490-4
Banerjee, S., Roychoudhuri, S.K.: Spherically symmetric thermo-visco-elastic waves in a visco-elastic medium with a spherical cavity. Comput. Math. Model. 30, 91–98 (1995)
Bishop, R.F., Hill, R., Mott, N.F.: The theory of indentation and hardness tests. Proc. Phys. Soc. 57(3), 147–159 (1945). https://doi.org/10.1088/0959-5309/57/3/301
Cahn, R.W., Haasen, P., Kramer, E.J.: Plastic deformation and fracture of materials. Mater. Sci. Technol. 6, 568–633 (1993)
Cohen, T., Molinari, A.: Dynamic cavitation and relaxation in incompressible nonlinear viscoelastic solids. Int. J. Solids Struct. 69–70, 544–552 (2015). https://doi.org/10.1016/j.ijsolstr.2015.04.029
Durban, D., Fleck, N.A.: Spherical cavity expansion in a Drucker–Prager solid. J. Appl. Mech. 64(4), 743–750 (1997)
Durban, D., Masri, R.: Dynamic spherical cavity expansion in a pressure sensitive elastoplastic medium. Int. J. Solids Struct. 41(20), 5697–5716 (2004)
Feng, Q., Tong, J.Y., Zheng, Y.R.: Service induced degradation and rejuvenation of gas turbine blades. Mater. China 31(12), 21–34 (2012)
Forrestal, M.J., Luk, K.: Dynamic spherical cavity-expansion in a compressible elastic-plastic solid. J. Appl. Mech. 55(2), 275–279 (1988)
Forrestal, M.J., Tzou, D.Y.: A spherical cavity-expansion penetration model for concrete targets. Int. J. Solids Struct. 34(31–32), 4127–4146 (1997)
Ghazali, S., Algarni, M.: A study on the plasticity and fracture of the AISI 4340 steelalloy under different loading conditions and considering heat-treatment effects. Int. J. Fract. 225, 69–87 (2020). https://doi.org/10.1007/s10704-020-00466-y
Gurson, A.L.: Continuum theory of ductile rupture by void nucleation and growth: part I—yield criteria and flow rules for porous ductile media. J. Eng. Mater. Technol. 99(1), 2–15 (1977). https://doi.org/10.1115/1.3443401
Hasanlou, S., Vaseghi, M.: Modeling and experimental investigation of fracture behavior of hot-rolled hypereutectoid Si-Mn TRIP steel: heat-treatment efect. Met. Mater. Int. 28, 1349–1360 (2022). https://doi.org/10.1007/s12540-021-01045-z
Hill, R.: The Mathematical Theory of Plasticity, pp. 103–106. Clarendon, Oxford (1950)
Hopkins, H.G.: Dynamic expansion of spherical cavities in metals. Prog. Solid Mech. 1(3), 20–23 (1960)
Huang, Y., Hutchinson, J.W., Tvergaard, V.: Cavitation instabilities in elastic-plastic solids. J. Mech. Phys. Solids 39, 223–241 (1991)
Hunter, S.C., Crozier, R.J.M.: Similarity solution for the rapid uniform expansion of a spherical cavity in a compressible elastic-plastic solid. Q. J. Mech. Appl. Math. 21(4), 467–486 (1968)
Kar, A., Kanoria, M.: Generalized thermo-visco-elastic problem of a spherical shell with three-phase-lag effect. Appl. Math. Model. 33, 3287–3298 (2009)
Luk, V.K., Forrestal, M.J., Amos, D.E.: Dynamic spherical cavity expansion of strain-hardening materials. J. Appl. Mech. 58, 1–6 (1991)
McClintock, F.A.: A criterion for ductile fracture by the growth of holes. J. Appl. Mech. 35(2), 363–371 (1968). https://doi.org/10.1115/1.3601204
Ning, J.G., Li, W.: Influence of the temperature on the cavitation instability under plane strain condition. Acta Mech. Solida Sin. 24(3), 356–363 (2003)
Ren, J.S., Cheng, C.J.: Bifurcation for void growth in incompressible thermo-hyperelastic materials. Chin. Q. Mech. 28(3), 426–430 (2007)
Rice, J.R., Tracey, D.M.: On the ductile enlargement of voids in triaxial stress fields. J. Mech. Phys. Solids 17(3), 201–217 (1969). https://doi.org/10.1016/0022-5096(69)90033-7
Shang, X.C., Wu, P.F.: Quasi-static analysis of microvoid growth in elastic-viscoplastic materials under thermal shock. J. Therm. Stresses (2018). https://doi.org/10.1080/01495739.2018.1466668
Shang, X.C., Zhang, Z.B.: Characterization of microscopic damage in aluminum alloy materials under intense thermal shock. J. Mater. Eng. 35(2), 1–4 (2011)
Shang, X.C., Zhang, R.: Analysis of cavitation problem of heated elastic composite ball. Appl. Math. Mech. Engl. Ed. 32(5), 587–594 (2011). https://doi.org/10.1007/s10483-011-1440-9
Shi, X.Y., Shang, X.C.: Growth of a spherical micro-void in an infinite elastoplastic body under thermal load. Acta Mech. 225(11), 3237–3245 (2014). https://doi.org/10.1007/s00707-013-1030-z
Wu, P.F.: Analysis of microvoid growth and cavitation in visco-elastic-plastic solids under thermal shock. Ph.D. thesis, University of Science and Technology, Beijing (2018)
Wu, P.F., Shang, X.C.: Dynamic analysis on microvoid growth in viscoelastoplastic materials under thermal shock. J. Therm. Stresses 45(5), 415–434 (2022). https://doi.org/10.1080/01495739.2022.2059038
Xue, C.C., Yang, M.M.: Fracture toughness and fracture mechanism of EH47 high-strength steel subjected to different temperatures. Metall. Mater. Trans. A 53A, 3588–3603 (2022). https://doi.org/10.1007/s11661-022-06763-6
Zhang, Y., Huang, Z.P.: Void growth and cavitation in nonlinear viscoelastic solids. Acta Mech. Sin. 19, 380–384 (2003)
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We are also very grateful to the reviewers for their suggestions and opinions on the revision of the manuscript.
Funding
The research of this thesis was supported by the National Natural Science Foundation Project (No. 10772024) and the Open Fund Project of State Key Laboratory of Explosive Science and Technology (No. 185 KFJJ12-12M).
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YaJuan Chen and XinChun Shang wrote the main manuscript text and figures. All authors reviewed the manuscript.
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Chen, Y., Shang, X. Analysis of thermal cavitation in a viscoelastic composite sphere under a uniform temperature field. Mech Time-Depend Mater (2023). https://doi.org/10.1007/s11043-023-09630-y
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DOI: https://doi.org/10.1007/s11043-023-09630-y