Skip to main content

Simulation study on cavity growth in ductile metal materials under dynamic loading

Frontiers of Physics volume 8, pages 394–404 (2013)Cite this article

Abstract

Cavity growth in ductile metal materials under dynamic loading is investigated via the material point method. Two typical cavity effects in the region subjected to rarefaction wave are identified: (i) part of material particles flow away from the cavity in comparison to the initial loading velocity, (ii) local regions show weaker negative or even positive pressures. Neighboring cavities interact via coalescence of isobaric contours. The growth of cavity under tension shows staged behaviors. After the initial slow stage, the volume and the dimensions in both the tensile and transverse directions show linear growth rate with time until the global tensile wave arrives at the upper free surface. It is interesting that the growth rate in the transverse direction is faster than that in the tensile direction. The volume growth rate linearly increases with the initial tensile velocity. After the global tensile wave passed the cavity, both the maximum particle velocity in the tensile direction and the maximum particle velocity in the opposite direction increase logarithmically with the initial tensile speed. The shock wave reflected back from the cavity and compression wave from the free surface induce the initial behavior of interfacial instabilities such as the Richtmyer-Meshkov instability, which is mainly responsible for the irregularity in the morphology of deformed cavity. The local temperatures and distribution of hot spots are determined by the plastic work. Compared with the dynamical process, the heat conduction is much slower.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

References

  1. G. T. Gray, P. J. Maudlin, L. M. Hull, Q. K. Zuo, and S. R. Chen, Predicting material strength, damage, and fracture the synergy between experiment and modeling, J. Fail. Anal. Prev., 2005, 5(3): 7

    Article  Google Scholar 

  2. M. M. Carroll, and A. C. Holt, Static and dynamic Pore-Collapse relations for ductile porous materials, J. Appl. Phys., 1972, 27(3): 1626

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. R. Becker, The effect of porosity distribution on ductile failure, J. Mech. Phys. Solids, 1987, 35(5): 577

    Article  ADS  Google Scholar 

  5. 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., 1992, 59(1): 48

    Article  ADS  MATH  Google Scholar 

  6. D. J. Benson, An analysis of void distribution effects on the dynamic growth and coalescence of voids in ductile metals, J. Mech. Phys. Solids, 1993, 41(8): 1285

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  8. T. Pardoen, I. Doghri, and F. Delannay, Experimental and numerical comparison of void growth models and void coalescence criteria for the prediction of ductile fracture in copper bars, Acta Mater., 1998, 46(2): 541

    Article  Google Scholar 

  9. T. Pardoen and J. W. Hutchinson, An extended model for void growth and coalescence, J. Mech. Phys. Solids, 2000, 48(12): 2467

    Article  ADS  MATH  Google Scholar 

  10. V. C. Orsini and M. A. Zikry, Void growth and interaction in crystalline materials, Int. J. Plast., 2001, 17(10): 1393

    Article  MATH  Google Scholar 

  11. V. Tvergaard and J. W. Hutchinson, Two mechanisms of ductile fracture: Void by void growth versus multiple void interaction, Int. J. Solids Struct., 2002, 39(13–14): 3581

    Article  MATH  Google Scholar 

  12. T. I. Zohdi, M. Kachanov, and I. Sevostianov, On perfectly plastic flow in porous material, Int. J. Plast., 2002, 18(12): 1649

    Article  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. E. T. Seppala, J. Belak, and R. Rudd, Onset of void coalescence during dynamic fracture of ductile metals, Phys. Rev. Lett., 2004, 93(24): 245503

    Article  ADS  Google Scholar 

  15. A. K. Zurek, W. R. Thissell, J. N. Johnson, D. L. Tonks, and R. Hixson, Micromechanics of spall and damage in tantalum, J. Mater. Process. Technol., 1996, 60(1–4): 261

    Article  Google Scholar 

  16. A. K. Zurek, J. D. Embury, A. Kelly, W. R. Thissell, R. L. Gustavsen, J. E. Vorthman, and R. S. Hixson, Microstructure of depleted uranium under uniaxial strain conditions, AIP Conf. Proc., 1998, 429: 423

    Article  ADS  Google Scholar 

  17. D. L. Tonks, A. K. Zurek, and W. R. Thissell, Void coalescence model for ductile damage, AIP Conf. Proc., 2002, 620: 611

    Article  ADS  Google Scholar 

  18. J. P. Bandstra, D. M. Goto, and D. A. Koss, Ductile failure as a result of a void-sheet instability: experiment and computational modeling, Mater. Sci. Eng. A, 1998, 249(1–2): 46

    Google Scholar 

  19. J. P. Bandstra, and D. A. Koss, Modeling the ductile fracture process of void coalescence by void-sheet formation, Mater. Sci. Eng. A, 2001, 319–321: 490

    Google Scholar 

  20. J. P. Bandstra, D. A. Koss, A. Geltmacher, P. Matic, and R. K. Everett, Modeling void coalescence during ductile fracture of a steel, Mater. Sci. Eng. A, 2004, 366(2): 269

    Article  Google Scholar 

  21. M. F. Horstemeyer, M. M. Matalanis, A. M. Sieber, and M. L. Botos, Micromechanical finite element calculations of temperature and void configuration effects on void growth and coalescence, Int. J. Plasticity, 2000, 16(7): 979

    Article  MATH  Google Scholar 

  22. E. T. Sepplälä, J. Belak, and R. E. Rudd, Three-dimensional molecular dynamics simulations of void coalescence during dynamic fracture of ductile metals, Phys. Rev. B, 2005, 71(6): 06411

    Google Scholar 

  23. L. M. Dupuy and R. E. Rudd, Surface identification, meshing and analysis during large molecular dynamics simulations, Model. Simul. Mater. Sci. Eng., 2006, 14(2): 229

    Article  ADS  Google Scholar 

  24. W. Pang, G. Zhang, A. G. Xu, and G. Lu, Size effect in void growth and coalescence of face-centered cubic copper crystals, Chin. J. Comp. Phys., 2011, 28: 540 (in Chinese)

    Google Scholar 

  25. W. Pang, P. Zhang, G. Zhang, A. G. Xu, and X. Zhao, The nucleation and growth of nanovoids under high tensile strain rate, Sci. China — Phys. Mech. Astron., 2012, 42: 464

    Google Scholar 

  26. D. Burgess, D. Sulsky, and J. U. Brackbill, Mass matrix formulation of the FLIP particle-in-cell method, J. Comput. Phys., 1992, 103(1): 1

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. S. Bardenhagen, J. Brackbill, and D. Sulsky, The materialpoint method for granular materials, Comput. Methods Appl. Mech. Eng., 2000, 187(3–4): 529

    Article  ADS  MATH  Google Scholar 

  28. N. P. Daphalapurkar, H. Lu, D. Coker, and R. Komanduri, Simulation of dynamic crack growth using the generalized interpolation material point (GIMP) method, Int. J. Fract., 2007, 143(1): 79

    Article  MATH  Google Scholar 

  29. S. Ma, X. Zhang, and X. M. Qiu, Comparison study of MPM and SPH in modeling hypervelocity impact problems, Int. J. Impact Eng., 2009, 36(2): 272

    Article  Google Scholar 

  30. X. F. Pan, A. G. Xu, G. C. Zhang, P. Zhang, J. S. Zhu, S. Ma, and X. Zhang, Three-dimensional multi-mesh material point method for solving collision problems, Commun. Theor. Phys., 2008, 49(5): 1129

    Article  ADS  Google Scholar 

  31. X. F. Pan, A. G. Xu, G. C. Zhang, and J. Zhu, Generalized interpolation material point approach to high melting explosive with cavities under shock, J. Phys. D, 2008, 41(1): 015401

    Article  ADS  Google Scholar 

  32. A. G. Xu, X. F. Pan, G. C. Zhang, and J. Zhu, Materialpoint simulation of cavity collapse under shock, J. Phys.: Condens. Matter, 2007, 19(32): 326212

    Article  Google Scholar 

  33. A. G. Xu, G. Zhang, X. F. Pan, and J. Zhu, Simulation Study of Shock Reaction on Porous Material, Commun. Theor. Phys., 2009, 51(4): 691

    Article  ADS  Google Scholar 

  34. A. G. Xu, G. Zhang, P. Zhang, X. F. Pan, and J. Zhu, Dynamics and thermodynamics of porous HMX-like material under shock, Commun. Theor. Phys., 2009, 52(5): 901

    Article  ADS  Google Scholar 

  35. A. G. Xu, G. C. Zhang, H. Li, Y. Ying, X. Yu, and J. Zhu, Temperature pattern dynamics in shocked porous materials, Sci. China — Phys. Mech. Astron., 2010, 53(8): 1466

    Article  ADS  Google Scholar 

  36. A. G. Xu, G. C. Zhang, Y. Ying, P. Zhang, and J. Zhu, Shock wave response of porous materials: from plasticity to elasticity, Phys. Scr., 2010, 81(5): 055805

    Article  ADS  Google Scholar 

  37. A. G. Xu, G. C. Zhang, H. Li, Y. Ying, and J. Zhu, Dynamical similarity in shock wave response of porous material: From the view of pressure, Comput. Math. Appl., 2011, 61(12): 3618

    Article  MATH  Google Scholar 

  38. F. Auricchio and L. B. da Veiga, On a new integration scheme for von-Mises plasticity with linear hardening, Int. J. Numer. Meth. Eng., 2003, 56(10): 1375

    Article  MATH  Google Scholar 

  39. B. Zhang, et al., Explosion Physics, Beijing: Ordance Industry Press of China, 1997

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009-26, Beijing, 100088, China

    Ai-Guo Xu, Guang-Cai Zhang, Yang-Jun Ying & Xi-Jun Yu

Authors
  1. Ai-Guo Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guang-Cai Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yang-Jun Ying
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xi-Jun Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ai-Guo Xu.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Xu, AG., Zhang, GC., Ying, YJ. et al. Simulation study on cavity growth in ductile metal materials under dynamic loading. Front. Phys. 8, 394–404 (2013). https://doi.org/10.1007/s11467-013-0348-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11467-013-0348-2

Keywords

  • material point method
  • cavity growth
  • dynamic loading
  • interfacial instability