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

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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.

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References

  1. Gibson, L.J., Ashby, M.F.: Cellular Solids: Structure and Properties, 2nd edn. Cambridge University Press, Cambridge (1997)

    Book  MATH  Google Scholar 

  2. Lu, G.X., Yu, T.X.: Energy Absorption of Structures and Materials. Woodhead Publishing Ltd, Cambridge (2003)

    Book  Google Scholar 

  3. Maiti, S.K., Gibson, L.J., Ashby, M.F.: Deformation and energy absorption diagrams for cellular solids. Acta Metall. 32, 1963–1975 (1984)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  7. Liu, Q.L., Subhash, G.: A phenomenological constitutive model for foams under large deformations. Polym. Eng. Sci. 44, 463–473 (2004)

    Article  Google Scholar 

  8. Reid, S.R., Peng, C.: Dynamic uniaxial crushing of wood. Int. J. Impact Eng. 19, 531–570 (1997)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  16. Hu, L.L., Yu, T.X.: Dynamic crushing strength of hexagonal honeycombs. Int. J. Impact Eng. 37, 467–474 (2010)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  22. Dannemann, K.A., Lankford, J.: High strain rate compression of closed-cell aluminium foams. Mater. Sci. Eng. A 293, 157–164 (2000)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  24. Deshpand, V.S., Fleck, N.A.: High strain rate compressive behaviour of aluminium alloy foams. Int. J. Impact Eng. 24, 277–298 (2000)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  33. Gaitanaros, S., Kyriakides, S.: Dynamic crushing of aluminum foams: part II—analysis. Int. J. Solids Struct. 51, 1646–1661 (2014)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

  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)

    Article  Google Scholar 

Download references

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).

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Correspondence to Zhijun Zheng.

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Wang, P., Zheng, Z., Liao, S. et al. Strain-rate effect on initial crush stress of irregular honeycomb under dynamic loading and its deformation mechanism. Acta Mech. Sin. 34, 117–129 (2018). https://doi.org/10.1007/s10409-017-0716-1

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  • DOI: https://doi.org/10.1007/s10409-017-0716-1

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