Advertisement

Acta Mechanica Sinica

, Volume 34, Issue 1, pp 117–129 | Cite as

Strain-rate effect on initial crush stress of irregular honeycomb under dynamic loading and its deformation mechanism

  • Peng Wang
  • Zhijun ZhengEmail author
  • Shenfei Liao
  • Jilin Yu
Research Paper

Abstract

The seemingly contradictory understandings of the initial crush stress of cellular materials under dynamic loadings exist in the literature, and a comprehensive analysis of this issue is carried out with using direct information of local stress and strain. Local stress/strain calculation methods are applied to determine the initial crush stresses and the strain rates at initial crush from a cell-based finite element model of irregular honeycomb under dynamic loadings. The initial crush stress under constant-velocity compression is identical to the quasi-static one, but less than the one under direct impact, i.e. the initial crush stresses under different dynamic loadings could be very different even though there is no strain-rate effect of matrix material. A power-law relation between the initial crush stress and the strain rate is explored to describe the strain-rate effect on the initial crush stress of irregular honeycomb when the local strain rate exceeds a critical value, below which there is no strain-rate effect of irregular honeycomb. Deformation mechanisms of the initial crush behavior under dynamic loadings are also explored. The deformation modes of the initial crush region in the front of plastic compaction wave are different under different dynamic loadings.

Keywords

Cellular material Constant-velocity compression Direct impact Cross-sectional stress Initial crush stress Strain rate effect 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants 11372308, 11372307) and the Fundamental Research Funds for the Central Universities (Grant WK2480000001).

References

  1. 1.
    Gibson, L.J., Ashby, M.F.: Cellular Solids: Structure and Properties, 2nd edn. Cambridge University Press, Cambridge (1997)CrossRefzbMATHGoogle Scholar
  2. 2.
    Lu, G.X., Yu, T.X.: Energy Absorption of Structures and Materials. Woodhead Publishing Ltd, Cambridge (2003)CrossRefGoogle Scholar
  3. 3.
    Maiti, S.K., Gibson, L.J., Ashby, M.F.: Deformation and energy absorption diagrams for cellular solids. Acta Metall. 32, 1963–1975 (1984)CrossRefGoogle Scholar
  4. 4.
    Tang, L.Q., Shi, X.P., Zhang, L., et al.: Effects of statistics of cell’s size and shape irregularity on mechanical properties of 2D and 3D Voronoi foams. Acta Mech. 225, 1361–1372 (2014)CrossRefzbMATHGoogle Scholar
  5. 5.
    Song, Y.Z., Wang, Z.H., Zhao, L.M., et al.: Dynamic crushing behavior of 3D closed-cell foams based on Voronoi random model. Mater. Des. 31, 4281–4289 (2010)CrossRefGoogle Scholar
  6. 6.
    Hanssen, A.G., Hopperstad, O.S., Langseth, M., et al.: Validation of constitutive models applicable to aluminum foams. Int. J. Mech. Sci. 44, 359–406 (2002)CrossRefGoogle Scholar
  7. 7.
    Liu, Q.L., Subhash, G.: A phenomenological constitutive model for foams under large deformations. Polym. Eng. Sci. 44, 463–473 (2004)CrossRefGoogle Scholar
  8. 8.
    Reid, S.R., Peng, C.: Dynamic uniaxial crushing of wood. Int. J. Impact Eng. 19, 531–570 (1997)CrossRefGoogle Scholar
  9. 9.
    Li, Q.M., Meng, H.: Attenuation or enhancement—a one-dimensional analysis on shock transmission in the solid phase of a cellular material. Int. J. Impact Eng. 27, 1049–1065 (2002)CrossRefGoogle Scholar
  10. 10.
    Harrigan, J.J., Reid, S.R., Tan, P.J., et al.: High rate crushing of wood along the grain. Int. J. Mech. Sci. 47, 521–544 (2005)CrossRefGoogle Scholar
  11. 11.
    Tan, P.J., Reid, S.R., Harrigan, J.J., et al.: Dynamic compressive strength properties of aluminium foams. Part I—experimental data and observations. J. Mech. Phys. Solids 53, 2174–2205 (2005)CrossRefGoogle Scholar
  12. 12.
    Zhao, H., Elnasri, I., Li, H.J.: The mechanism of strength enhancement under impact loading of cellular materials. Adv. Eng. Mater. 8, 877–883 (2006)CrossRefGoogle Scholar
  13. 13.
    Elnasri, I., Pattofatto, S., Zhao, H., et al.: Shock enhancement of cellular structures under impact loading: Part I experiments. J. Mech. Phys. Solids 55, 2652–2671 (2007)CrossRefGoogle Scholar
  14. 14.
    Pattofatto, S., Einasri, I., Zhao, H., et al.: Shock enhancement of cellular structures under impact loading: Part II analysis. J. Mech. Phys. Solids 55, 2672–2686 (2007)CrossRefGoogle Scholar
  15. 15.
    Ma, G.W., Ye, Z.Q., Shao, Z.S.: Modeling loading rate effect on crushing stress of metallic cellular materials. Int. J. Impact Eng. 36, 775–782 (2009)CrossRefGoogle Scholar
  16. 16.
    Hu, L.L., Yu, T.X.: Dynamic crushing strength of hexagonal honeycombs. Int. J. Impact Eng. 37, 467–474 (2010)CrossRefGoogle Scholar
  17. 17.
    Tan, P.J., Harrigan, J.J., Reid, S.R.: Inertia effects in uniaxial dynamic compression of a closed cell aluminium alloy foam. Mater. Sci. Technol. 18, 480–488 (2002)CrossRefGoogle Scholar
  18. 18.
    Zou, Z., Reid, S.R., Tan, P.J., et al.: Dynamic crushing of honeycombs and features of shock fronts. Int. J. Impact Eng. 36, 165–176 (2009)CrossRefGoogle Scholar
  19. 19.
    Liao, S.F., Zheng, Z.J., Yu, J.L.: Dynamic crushing of 2D cellular structures: local strain field and shock wave velocity. Int. J. Impact Eng. 57, 7–16 (2013)CrossRefGoogle Scholar
  20. 20.
    Barnes, A.T., Ravi-Chandar, K., Kyriakides, S., et al.: Dynamic crushing of aluminum foams: part I—experiments. Int. J. Solids Struct. 51, 1631–1645 (2014)CrossRefGoogle Scholar
  21. 21.
    Zheng, Z.J., Wang, C.F., Yu, J.L., et al.: Dynamic stress–strain states for metal foams using a 3D cellular model. J. Mech. Phys. Solids 72, 93–114 (2014)CrossRefGoogle Scholar
  22. 22.
    Dannemann, K.A., Lankford, J.: High strain rate compression of closed-cell aluminium foams. Mater. Sci. Eng. A 293, 157–164 (2000)CrossRefGoogle Scholar
  23. 23.
    Wang, P.F., Xu, S.L., Li, Z.B., et al.: Experimental investigation on the strain-rate effect and inertia effect of closed-cell aluminum foam subjected to dynamic loading. Mater. Sci. Eng. A 620, 253–261 (2015)CrossRefGoogle Scholar
  24. 24.
    Deshpand, V.S., Fleck, N.A.: High strain rate compressive behaviour of aluminium alloy foams. Int. J. Impact Eng. 24, 277–298 (2000)CrossRefGoogle Scholar
  25. 25.
    Tan, P.J., Reid, S.R., Harrigan, J.J., et al.: Dynamic compressive strength properties of aluminium foams. Part II—‘shock’ theory and comparison with experimental data and numerical models. J. Mech. Phys. Solids 53, 2206–2230 (2005)CrossRefGoogle Scholar
  26. 26.
    Lopatnikov, S.L., Gama, B.A., Haque, M.J., et al.: Dynamics of metal foam deformation during Taylor cylinder–Hopkinson bar impact experiment. Compos. Struct. 61, 61–71 (2003)CrossRefGoogle Scholar
  27. 27.
    Lopatnikov, S.L., Gama, B.A., Haque, M.J., et al.: High-velocity plate impact of metal foams. Int. J. Impact Eng 30, 421–445 (2004)CrossRefGoogle Scholar
  28. 28.
    Lopatnikov, S.L., Gama, B.A., Gillespie, J.W.: Modeling the progressive collapse behavior of metal foams. Int. J. Impact Eng. 34, 587–595 (2007)CrossRefGoogle Scholar
  29. 29.
    Zheng, Z.J., Liu, Y.D., Yu, J.L., et al.: Dynamic crushing of cellular materials: continuum-based wave models for the transitional and shock modes. Int. J. Impact Eng. 42, 66–79 (2012)CrossRefGoogle Scholar
  30. 30.
    Karagiozova, D., Langdon, G.S., Nurick, G.N.: Propagation of compaction waves in metal foams exhibiting strain hardening. Int. J. Solids Struct. 49, 2763–2777 (2012)CrossRefGoogle Scholar
  31. 31.
    Wang, L.L., Yang, L.M., Ding, Y.Y.: On the energy conservation and critical velocities for the propagation of a “steady-shock” wave in a bar made of cellular material. Acta. Mech. Sin. 29, 420–428 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Zheng, J., Qin, Q.H., Wang, T.J.: Impact plastic crushing and design of density-graded cellular materials. Mech. Mater. 94, 66–78 (2016)CrossRefGoogle Scholar
  33. 33.
    Gaitanaros, S., Kyriakides, S.: Dynamic crushing of aluminum foams: part II—analysis. Int. J. Solids Struct. 51, 1646–1661 (2014)CrossRefGoogle Scholar
  34. 34.
    Sun, Y.L., Li, Q.M., McDonald, S.A., et al.: Determination of the constitutive relation and critical condition for the shock compression of cellular solids. Mech. Mater. 99, 26–36 (2016)CrossRefGoogle Scholar
  35. 35.
    Ding, Y.Y., Wang, S.L., Zheng, Z.J., et al.: Dynamic crushing of cellular materials: a unique dynamic stress-strain state curve. Mech. Mater. 100, 219–231 (2016)CrossRefGoogle Scholar
  36. 36.
    Zheng, Z.J., Yu, J.L., Li, J.R.: Dynamic crushing of 2D cellular structures: a finite element study. Int. J. Impact Eng. 32, 650–664 (2005)CrossRefGoogle Scholar
  37. 37.
    Yu, J.L., Wang, P., Liao, S.F., et al.: Local strain and stress calculation methods of irregular honeycombs under dynamic compression. In: Proceedings of the ASME 35th International Conference on Ocean, Offshore and Arctic Engineering, Busan, June 19–24 (2016)Google Scholar
  38. 38.
    Liao, S.F., Zheng, Z.J., Yu, J.L.: On the local nature of the strain field calculation method for measuring heterogeneous deformation of cellular materials. Int. J. Solids Struct. 51, 478–490 (2014)CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Peng Wang
    • 1
    • 2
  • Zhijun Zheng
    • 1
    Email author
  • Shenfei Liao
    • 3
  • Jilin Yu
    • 1
  1. 1.CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern MechanicsUniversity of Science and Technology of ChinaHefeiChina
  2. 2.Institute of Systems EngineeringChina Academy of Engineering PhysicsMianyangChina
  3. 3.Institute of Fluid PhysicsChina Academy of Engineering PhysicsMianyangChina

Personalised recommendations