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A mechanical method of tensile strength prediction for liquids with the application of a new model for void nucleation

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Abstract

A new model for void nucleation, employed in the mechanical method of tensile strength prediction for liquids, is presented in this paper based on classical nucleation theory and energy conservation analysis. The dependence of surface tension on void radius, which is presented in the method of Tolman’s correction, could influence the total energy for void nucleation, including the surface energy and the work of external tensile load. NAG (nucleation and growth) scheme is used in the present mechanical model to study the tensile process of the Al melt. The calculation results of material strength and void evolution of the melt under a high strain rate by using present mechanical method are studied and compared with those by MD (molecular dynamics) simulation.

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References

  1. Bull, T.H.: The tensile strengths of viscous liquids under dynamic loading. Br. J. Appl. Phys. 7(11), 416 (1956)

    Article  Google Scholar 

  2. Erlich, D.C., Wooten, D.C., Crewdson, R.C.: Dynamic tensile failure of glycerol. J. Appl. Phys. 42(13), 5495–5502 (1971)

    Article  Google Scholar 

  3. Huneault, J., Higgins, A.J.: Shock wave induced cavitation of silicon oils. J. Appl. Phys. 125, 245903 (2019)

    Article  Google Scholar 

  4. Cai, Y., Wu, H.A., Luo, S.N.: Cavitation in a metallic liquid: homogeneous nucleation and growth of nanovoids. J. Chem. Phys. 140, 214317 (2014)

    Article  Google Scholar 

  5. Agranat, M.B., Anisimov, S.I., et al.: Strength properties of an aluminum melt at extremely high-tension rates under the action of femtosecond laser pulses. JETP Lett. 91, 571 (2010)

    Article  Google Scholar 

  6. de Resseguier, T., Signor, L., et al.: Experimental investigation of liquid spall in laser shock-loaded tin. J. Appl. Phys. 101, 013506 (2007)

    Article  Google Scholar 

  7. Kanel, G.I., Savinykh, A.S., et al.: Dynamic strength of tin and lead melts. JETP Lett. 102, 548–551 (2015)

    Article  Google Scholar 

  8. Bogach, A.A., Utkin, A.V.: Strength of water under pulsed loading. J. Appl. Mech. Tech. Phys. 41, 752 (2000)

    Article  Google Scholar 

  9. Carlson, G.A., Levine, H.S.: Dynamic tensile strength of glycerol. J. Appl. Phys. 46, 1594 (1975)

    Article  Google Scholar 

  10. Carlson, G.A.: Dynamic tensile strength of mercury. J. Appl. Phys. 46, 4069 (1975)

    Article  Google Scholar 

  11. Ashitkov, S.I., Komarov, P.S., et al.: Strength of liquid tin at extremely high strain rates under a femtosecond laser action. JETP Lett. 103(8), 544–548 (2016)

    Article  Google Scholar 

  12. Mayer, A.E., Mayer, P.N.: Continuum model of tensile fracture of metal melts and its application to a problem of high-current electron irradiation of metals. J. Appl. Phys. 118(3), 235414–235477 (2015)

    Article  Google Scholar 

  13. Mayer P., Mayer A. Evolution of Size Distribution of Pores in Metal Melts at Tension with High Strain Rates. In: Gdoutos E. (eds) Proceedings of the First International Conference on Theoretical, Applied and Experimental Mechanics. ICTAEM 2018. Structural Integrity, vol 5. Springer, Cham. (2019)

  14. Cai, Y., Wang, L., et al.: Homogeneous crystal nucleation in liquid copper under quasi-isentropic compression. Phys. Rev. B 92, 014108 (2015)

    Article  Google Scholar 

  15. Cai, Y., Huang, J., Wu, H.A., et al.: Tensile strength of liquids: equivalence of temporal and spatial scales in cavitation. J. Phys. Chem. Lett. 7, 806 (2016)

    Article  Google Scholar 

  16. Carroll, M.M., Holt, A.C.: Static and dynamic pore-collapse for ductile porous materials. J. Appl. Phys. 43, 1627–1636 (1972)

    Article  Google Scholar 

  17. Seaman, L., Curran, D.R.: Inertia and temperature effects in void growth. AIP Conf. Proc. 620, 607(2002)

  18. Curran, D.R., Seaman, L., Shockey, D.A.: Dynamic failure of solids. Phys. Rep. 147(5–6), 253–388 (1987)

    Article  Google Scholar 

  19. Molinari, A., Wright, T.W.: A physical model for nucleation and early growth of voids in ductile materials under dynamic loading. J. Mech. Phys. Solids 53(7), 1476–1504 (2005)

    Article  MATH  Google Scholar 

  20. Czarnota, C., Jacques, N., et al.: Modelling of dynamic ductile fracture and application to the simulation of plate impact tests on tantalum. J. Mech. Phys. Solids 56(4), 1624–1650 (2008)

    Article  Google Scholar 

  21. Gibbs, J.W.: The Scientific Papers of J. Willard Gibbs. Dover, New York (1961)

    Google Scholar 

  22. Turnbull, D., Fisher, J.C.: Rate of nucleation in condensed systems. J. Chem. Phys. 17, 71 (1949)

    Article  Google Scholar 

  23. Christian, J.W.: The Theory of Transformation in Metals and Alloys. Pergaman, New York (1965)

    Google Scholar 

  24. Zeldovich, Y.B.: On the theory of new phase formation: cavitation. In: Ostriker, J.P., Barenblatt, G.I., Sunyaev, R.A. (eds.) Selected Works of Yakov Borisovich Zeldovich, Volume I: Chemical Physics and Hydrodynanics, pp. 120–137. Princeton University Press, Princeton (1992)

    Chapter  Google Scholar 

  25. Tolman, R.C.: The effect of droplet size on surface tension. J. Chem. Phys. 17(3), 333–337 (1949)

    Article  Google Scholar 

  26. Vitos, L., Ruban, A.V., Skriver, H.L., Kollár, J.: The surface energy of metals. Surf. Sci. 411, 186–202 (1998)

    Article  Google Scholar 

  27. Zhao, F.Q., Ma, X.B., Pan, H., Liu, J.X.: Modeling of dynamic elasto-plastic growth of a nano-void with surface energy, inertia and thermal softening effects. AIP Adv. 9(10), 105313 (2019)

    Article  Google Scholar 

  28. Carroll, M.M., Kim, K.T., Nesterenko, V.F.: The effect of temperature on viscoplastic pore collapse. J. Appl. Phys. 59(6), 1962–1962 (1986)

    Article  Google Scholar 

  29. Zhao, F.Q., Pan, H., Zhang, F.G., Liu, J.X.: A viscoplastic model for void growth under dynamic loading conditions. AIP Adv. 9(12), 125119 (2019)

    Article  Google Scholar 

  30. Yu, Qiao, Ling, et al. Pressurized Liquid in Nanopores: A Modified Laplace-Young Equation[J]. Nano Letters, 9(3):984–988 (2009)

  31. Young, T.: An essay on the cohesion of fluids. Philos. Trans. R. Soc. 95, 65–87 (1805)

    Article  Google Scholar 

  32. Gutzow I.S., Schmelzer J.W.P. Kinetics of Crystallization and Segregation: Nucleation in Glass-Forming Systems. In: The Vitreous State. Springer, Berlin, Heidelberg. (2013)

  33. Schmelzer, J.W.P., Gutzow, I., et al.: Curvature-dependent surface tension and nucleation theory. J. Colloid Interface Sci. 178(2), 657–665 (1996)

    Article  Google Scholar 

  34. Lu, H.M., Jiang, Q.: Surface tension and its temperature coefficient for liquid metals. J. Phys. Chem. B 109(32), 15463 (2005)

    Article  Google Scholar 

  35. Heermann, D.W.: Classical nucleation theory with a Tolman correction. J. Stat. Phys. 29(3), 631–640 (1982)

    Article  MathSciNet  Google Scholar 

  36. Asim, U.B., Siddiq, M.A., Demiral, M.: Void growth in high strength aluminium alloy single crystals—a CPFEM based study. Model. Simul. Mater. Sci. Eng. 25(3), 035010 (2017)

    Article  Google Scholar 

  37. Asim, U.B., Siddiq, M.A., Kartal, M.E.: Representative volume element (RVE) based crystal plasticity study of void growth on phase boundary in titanium alloys. Comput. Mater. Sci. 161, 346 (2019)

    Article  Google Scholar 

  38. Asim, U.B., Siddiq, M.A., Kartal, M.E.: A CPFEM based study to understand the void growth in high strength dual-phase titanium alloy (Ti–10V–2Fe–3Al). Int. J. Plast. 122, 188–211 (2019)

    Article  Google Scholar 

  39. Siddiq, M.A.: A porous crystal plasticity constitutive model for ductile deformation and failure in porous single crystals. Int. J. Damage Mech. 28(2), 233 (2018)

    Article  MathSciNet  Google Scholar 

  40. Siddiq, M.A., Arciniega, R., Sayed, T.E.: A variational void coalescence model for ductile metals. Comput. Mech. 49(2), 185–195 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  41. Franc, J.P.: The Rayleigh–Plesset equation: a simple and powerful tool to understand various aspects of cavitation. In: d’Agostino, L., Salvetti, M.V. (eds.) Fluid Dynamics of Cavitation and Cavitating Turbopumps, vol. 496. CISM International Centre for Mechanical Sciences, Udine (2007)

    Chapter  Google Scholar 

  42. Johnson, J.N.: Dynamic fracture and spallation in ductile solids. J. Appl. Phys. 52(4), 2812–2825 (1981)

    Article  Google Scholar 

  43. Grady, D.E.: The spall strength of condensed matter. J. Mech. Phys. Solids 36(3), 353–384 (1988)

    Article  Google Scholar 

  44. Wu, X.Y., Ramesh, K.T., Wright, T.W.: The dynamic growth of a single void in a viscoplastic material under transient hydrostatic loading. J. Mech. Phys. Solids 51(1), 1–26 (2003)

    Article  MATH  Google Scholar 

  45. Ashitkov, S.I., Inogamov, N.A., et al.: Strength of metals in liquid and solid states at extremely high tension produced by femtosecond laser heating. AIP Conf. Proc. 1464, 120 (2012)

    Article  Google Scholar 

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Acknowledgements

This work was funded by the Science Challenge Project (Grant No. TZ2018001).

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Fuqi Zhao, Hongqiang Zhou, Fengguo Zhang, Anmin He & Pei Wang

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  1. Fuqi Zhao
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Correspondence to Fuqi Zhao or Pei Wang.

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Zhao, F., Zhou, H., Zhang, F. et al. A mechanical method of tensile strength prediction for liquids with the application of a new model for void nucleation. Arch Appl Mech 91, 4223–4237 (2021). https://doi.org/10.1007/s00419-021-02000-5

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