Quasi-static analysis of microvoid growth in elastic-viscoplastic materials under thermal shock

References

• R. W. Cahn, P. Haasen, and E. J. Kramer, “Plastic Deformation and Fracture of Materials,” in Materials Science and Technology, vol. 6, Hael Mughrabi, Ed. New York, NY, USA: VCH, 1993, p. 568–633.
   Google Scholar
• Q. Feng, G. J. Ton, and Y. Zheng, “Service induced degradation and rejuvenation of gas turbine blades,” Mater. China., vol. 31, no. 12, pp. 21–34, 2012.
   Google Scholar
• J. W. Sanders, M. Dadfarnia, J. F. Stubbins, and P. Sofronisac, “On the fracture of high temperature alloys by creep cavitation under uniaxial or biaxial stress states,” J. Mech. Phys. Solids., vol. 98, pp. 49–62, Jan. 2017. DOI: 10.1016/j.jmps.2016.05.019.
   Web of Science ®Google Scholar
• X. C. Shang and Z. B. Zhang, “Characterization of microscopic damage in aluminum alloy materials under intense thermal shock,” J. Mater. Eng., vol. 35, no. 2, pp. 1–4, 2011.
   Google Scholar
• R. F. Bishop, R. Hill, and N. F. Mott, “The theory of indentation and hardness tests,” Proc. Phys. Soc., vol. 57, no. 3, pp. 147–159, May. 1945. DOI: 10.1088/0959-5309/57/3/301.
   Google Scholar
• R. Hill, The Mathematical Theory of Plasticity, Oxford: Clarendon Press, 1950, p. 103–106.
   Google Scholar
• F. A. McClintock, “A criterion for ductile fracture by the growth of holes,” J. Appl. Mech, vol. 35, no. 2, pp. 363–371, Jun. 1968. DOI: 10.1115/1.3601204.
   Web of Science ®Google Scholar
• J. R. Rice and D. M. Tracey, “On the ductile enlargement of voids in triaxial stress fields,” J. Mech. Phys. Solids., vol. 17, no. 3, pp. 201–217, Jun. 1969. DOI: 10.1016/0022-5096(69)90033-7.
   Web of Science ®Google Scholar
• A. L. Gurson, “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., vol. 99, no. 1, pp. 2–15, Jan. 1977. DOI:10.1115/1.3443401.
   Web of Science ®Google Scholar
• V. Tvergaard, “Material failure by void growth to coalescence,” Adv. Appl. Mech., vol. 27, pp. 83–151, Jan. 1990. DOI:10.1016/S0065-2156(08)70195-9.
   Web of Science ®Google Scholar
• Y. Huang, J. W. Hutchinson, and V. Tvergaard, “Cavitation instabilities in elastic-plastic solids,” J. Mech. Phys. Solids., vol. 39, no. 2, pp. 223–241, Jan. 1991. DOI: 10.1016/0022-5096(91)90004-8.
   Web of Science ®Google Scholar
• H. S. Yu, Cavity Expansion Methods in Geomechanics, Chap. 3, Norwell, MA, USA: Kluwer Academic Publishers, 2000, p. 50–84.
   Google Scholar
• H. G. Hopkins, “Progress in sold mechanics,” in Dynamic Expansion of Spherical Cavity in Metals, vol. 1, I. N. Sneddon and R. Hill, Eds. Amsterdam: North-Holland, 1960.
   Google Scholar
• D. Durban and N. A. Fleck, “Spherical cavity expansion in a Drucker-Prager solid,” J. Appl. Mech., vol. 64, no. 4, pp. 743–750, Dec. 1997. DOI: 10.1115/1.2788978.
   Web of Science ®Google Scholar
• D. Durban and R. Masri, “Dynamic spherical cavity expansion in a pressure sensitive elastoplastic medium,” Int. J. Solids Struct., vol. 41, no. 20, pp. 5697–5716, Oct. 2004. DOI: 10.1016/j.ijsolstr.2004.03.009.
   Web of Science ®Google Scholar
• S. C. Hunter and R. J. M. Crozier, “Similarity solution for the rapid uniform expansion of a spherical cavity in a compressible elastic-plastic solid,” Quarter. J. Mech. Appl. Math., vol. 21, no. 4, pp. 467–486, Nov. 1968. DOI: 10.1093/qjmam/21.4.467.
   Google Scholar
• M. J. Forrestal and V. K. Luk, “Dynamic spherical cavity-expansion in a compressible elastic-plastic solid,” J. Appl. Mech., vol. 55, no. 2, pp. 275–279, Jun. 1988. DOI: 10.1115/1.3173672.
   Web of Science ®Google Scholar
• M. J. Forrestal and D. Y. Tzou, “A spherical cavity-expansion penetration model for concrete targets,” Int. L Solids Struct., vol. 34, no. 31–32, pp. 4127–4146, Nov. 1997. DOI: 10.1016/S0020-7683(97)00017-6.
   Web of Science ®Google Scholar
• V. K. Luk, M. J. Forrestal, and D. E. Amos, “Dynamic spherical cavity expansion of strain-hardening materials,” J. Appl. Mech., vol. 58, no. 1, pp. 1–6, Mar. 1991. DOI: 10.1115/1.2897150.
   Web of Science ®Google Scholar
• M. Ortiz and A. Molinari, “Effect of strain hardening and rate sensitivity on the dynamic growth of a void in a plastic material,” J. Appl. Mech, vol. 59, no. 1, pp. 48–53, Mar. 1992. DOI: 10.1115/1.2899463.
   Web of Science ®Google Scholar
• Y. Zhang and Z. P. Huang, “Void growth and cavitation in nonlinear viscoelastic solids,” Acta. Mech. Sin., vol. 19, no. 4, pp. 380–384, Aug. 2003. DOI: 10.1007/BF02487816.
   Web of Science ®Google Scholar
• T. Cohen and A. Molinari, “Dynamic cavitation and relaxation in incompressible nonlinear viscoelastic solids,” Int. J. Solids Struct., vol. 69–70, pp. 544–552, Sep. 2015. DOI: 10.1016/j.ijsolstr.2015.04.029.
   Web of Science ®Google Scholar
• Y. Tanigawa and M. Kosako, “Transient thermal stress analysis of an infinite medium with a spherical cavity due to a nonuniform heat supply,” Int. J. Eng. Sci., vol. 24, no. 3, pp. 309–321, Dec. 1986. DOI: 10.1016/0020-7225(86)90088-1.
   Web of Science ®Google Scholar
• T. Hata, “Thermal shock in a hollow sphere caused by rapid uniform heating,” J. Appl. Mech, vol. 58, no. 1, pp. 64–69, Mar. 1991. DOI: 10.1115/1.2897180.
   Web of Science ®Google Scholar
• H. H. Sherief and F. A. Megahed, “Two-dimensional problems for thermoelasticity with two relaxation times in spherical regions under axisymmetric distributions,” Int. J. Eng. Sci, vol. 37, no. 3, pp. 299–314, Feb. 1999. DOI: 10.1016/S0020-7225(98)00070-6.
   Web of Science ®Google Scholar
• F. L. Huang and Z. P. Wang, “Modelling fracture process in a ductile solid under intense impulsive loading using a model of the void growth with temperature-dependency,” Eng. Fract. Mech., vol. 55, no. 4, pp. 657–674, Nov. 1996. DOI: 10.1016/0013-7944(95)00252-9.
   Web of Science ®Google Scholar
• X. C. Shang, R. Zhang, and H. L. Ren, “Analysis of cavitation problem of heated elastic composite ball,” Appl. Math. Mech. Engl. Ed., vol. 32, no. 5, pp. 587–594, May. 2011. DOI: 10.1007/s10483-011-1440-9.
   Google Scholar
• X. Y. Shi and X. C. Shang, “Growth of a spherical micro-void in an infinite elastoplastic body under thermal load,” Acta Mech., vol. 225, no. 11, pp. 3237–3245, Nov. 2014. DOI: 10.1007/s00707-013-1030-z.
   Web of Science ®Google Scholar
• Y. J. Chen and X. C. Shang, “Research on the thermal cavitation problem of a preexisting microvoid in a viscoelastic sphere,” Math. Probl. Eng., vol. 2013, no. 8, pp. 1–226, Oct. 2013. DOI: 10.1155/2013/456375.
   Google Scholar
• M. Baghani, A. H. Eskandari, and M. R. Zakerzadeh, “Transient growth of a micro-void in an infinite medium under thermal load with modified Zerilli-Armstrong model,” Acta Mech., vol. 227, no. 4, pp. 943–911, Apr. 2016. DOI: 10.1007/s00707-015-1490-4.
   Web of Science ®Google Scholar
• P. Perzyna, “The study of the dynamic behavior of rate sensitive plastic materials,” Arch. Mech. Stos., vol. 15, no. 15, pp. 113–130, 1963.
   Google Scholar
• A. M. Freudenthal, Handbuch der Physik, vol. VI, Berlin-Gottingen-Heidelberg: Springer Verlag, 1958.
   Google Scholar
• T. Wierzbicki, “Impulsive loading of a spherical container with rigid-plastic and strain rate sensitive material,” Arch. Mech. Stos., vol. 15, pp. 775–790, 1963.
   Google Scholar
• H. Takuda, K. Mori, I. Masuda, Y. Abe, and M. Matsuo, “Finite element simulation of warm deep drawing of aluminum alloy sheet when accounting for heat conduction,” J. Mater. Process. Technol., vol. 120, no. 1–3, pp. 412–418, Jan. 2002. DOI: 10.1016/S0924-0136(01)01180-3.
   Web of Science ®Google Scholar
• J. Zheng and Z. P. Wang, “Dynamic damage and failure in visco-plastic materials,” Eng. Fract. Mech., vol. 52, no. 6, pp. 1065–1077, Dec. 1995. DOI: 10.1016/0013-7944(95)00061-Y.
   Web of Science ®Google Scholar