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Compressive Behavior of Porous Metals with Aligned Unidirectional Pores Compressed in the Direction Perpendicular to the Pore Direction

  • Tomoya TamaiEmail author
  • Daiki Muto
  • Tomonori Yoshida
  • Mahiro Sawada
  • Shinsuke Suzuki
  • Matej Vesenjak
  • Zoran Ren
Article
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Abstract

The compressive behavior of porous A6061 alloy with aligned unidirectional pores was investigated. Porous specimens with various sizes and relative thicknesses (thickness t/length l) of cell walls were prepared via machining after various heat treatments. Compression tests were conducted on porous specimens in the direction perpendicular to the pore direction. Distributions of the equivalent plastic strain were obtained using digital image correlation. Finite element analyses were also conducted to obtain the stress and strain distributions. The compressive stress σ increased with the increase in the compressive strain, and the increase in σ was then suppressed. Using a newly constructed deformation model, it was revealed that a plateau region was initiated by the plastic collapse of the cell walls. After the occurrence of the plastic collapse, three deformation modes were found in the compression of the specimens with various t/l. These modes transitioned from plastic buckling to fracture, and then to rapid densification without plastic buckling and fracture, depending on t/l. The sharp increase in the horizontal strain and the suppression of the decrease in the porosity occurred simultaneously when σ increased sharply again, irrespective of the structure and heat treatment of the specimens; this was observed as the plateau end.

List of symbols

A

Area of pores (mm2)

b

Depth of a cell wall (mm)

D

Initial length of one side of a porous specimen (mm)

ΔDx

Increment in D in x-direction (mm)

ΔDy

Increment in D in y-direction (mm)

d

Pore diameter (mm)

Ec

Elastic gradient of a non-porous specimen (MPa)

Et

Tangent modulus of elasticity (MPa)

l

Length of a cell wall (mm)

M(x′)

Bending moment at the position x′ in a beam (N m)

N

Compressive force on a beam (N)

p

Porosity of a porous specimen (pct)

Q

Load on a cell wall (N)

T

Shear force on a beam (N)

t

Thickness at the center of a cell wall (mm)

t(x′)

Thickness at the position x′ in a beam (mm)

x

Direction perpendicular to the pore orientation

x

Distance from the end of a beam in the longitudinal direction (mm)

y

Direction parallel to the pore orientation

z

Compressive direction

z

Distance from the center of a beam in the direction of the width (mm)

ɛx

Strain perpendicular to the pore orientation (–)

ɛy

Strain parallel to the pore orientation (–)

ɛz

Compressive strain of a porous specimen (–)

\( \overline{{\varepsilon_{\text{p}} }} \)

Equivalent plastic strain in the xz plane of a porous specimen (–)

θ

Inclination angle of a beam (deg)

σ

Compressive stress of a porous specimen (MPa)

σbf

Critical stress for bending fracture of a cell wall (MPa)

σcr

Critical stress for plastic buckling of a cell wall (MPa)

σd

Critical stress for rapid densification (MPa)

σfr

Critical stress for fracture of a cell wall (MPa)

σfs

Bending strength of a cell wall (MPa)

σpc

Critical stress for plastic collapse of a cell wall (MPa)

σpc(x′)

Critical stress for plastic collapse at the position x′ in a beam (MPa)

σY

Yield stress of a non-porous specimen (MPa)

Notes

Acknowledgments

The A6061 alloy used in this study was provided by UACJ Corporation. This study was conducted with the support of a Grant-in-Aid from The Light Metal Educational Foundation, Inc., Strategic Core Technology Advancement Program (Supporting Industry Program) from the Small and Medium Enterprise Agency, Suzuki Foundation, and Overseas Research Travel Grant Program for Master’s/Doctoral Course Students, Waseda University.

References

  1. 1.
    1. J. Banhart: Prog. Mater. Sci., 2001, vol. 46, pp. 559-632.CrossRefGoogle Scholar
  2. 2.
    M. F. Ashby, A. G. Evans, N. A. Fleck, L. J. Gibson, J. W. Hutchinson and H. N. G. Wadley: Metal Foams: A Design Guide, 1st ed., Butterworth-Heinemann, United States of America, pp. 150-156.Google Scholar
  3. 3.
    ISO 13314: Mechanical Testing of Metals, The International Organization for Standardization, Geneva.Google Scholar
  4. 4.
    4. L. J. Gibson and M. F. Ashby: Cellular solids structure and properties, 2nd ed., Pergamon Press, Oxford, 1997, pp. 163-197.CrossRefGoogle Scholar
  5. 5.
    5. A. E. Simone and L. J. Gibson: Acta Mater., 1998, vol. 46, pp. 2139-2150.CrossRefGoogle Scholar
  6. 6.
    6. J. W. Klintworth and W. J. Stronge: Int. J. Mech. Sci., 1988, vol. 30, pp. 273-292.CrossRefGoogle Scholar
  7. 7.
    7. S. D. Papka and S. Kyriakides: J. Mech. Phys. Solids, 1994, vol. 42, pp. 1499-1532.CrossRefGoogle Scholar
  8. 8.
    8. H. Harders, K. Hupfer and J. Rösler: Acta Mater., 2005, vol. 53, pp. 1335-1345.CrossRefGoogle Scholar
  9. 9.
    9. D. Karagiozova and T. X. Yu: Int. J. Mech. Sci., 2004, vol. 46, pp. 1489-1515.CrossRefGoogle Scholar
  10. 10.
    10. X. Yue, K. Matsuo and K. Kitazono: Mater. Trans., 2017, vol. 58, pp. 1587-1592.CrossRefGoogle Scholar
  11. 11.
    11. A.-F. Bastawros, H. Bart-Smith and A.G. Evans: J. Mech. Phys. Solids, 2000, vol. 48, pp. 301-322.CrossRefGoogle Scholar
  12. 12.
    12. B. Gorny, T. Niendorf, J. Lackmann, M. Thoene, T. Troester and H. J. Maier: Mater. Sci. Eng. A, 2011, vol. 528, pp. 7962-7967.CrossRefGoogle Scholar
  13. 13.
    13. H. Bart-Smith, A.-F. Bastawros, D. R. Mumm, A. G. Evans, D. J. Sypeck and H. N. G. Wadley: Acta Mater., 1998, vol. 46, pp. 3583-3592.CrossRefGoogle Scholar
  14. 14.
    14. I. Jeon, T. Asahina, K. Kang, S. Im and T. J. Lu: Mech. Mater., 2010, vol. 42, pp. 227-236.CrossRefGoogle Scholar
  15. 15.
    15. M. Saadatfar, M. Mukherjee, M. Madadi, G. E. Schröder-Turk, F. Garcia-Moreno, F. M. Schaller, S. Hutzler, A. P. Sheppard, J. Banhart and U. Ramamurty: Acta Mater., 2012, vol. 60, pp. 3604-3615.CrossRefGoogle Scholar
  16. 16.
    16. J. Ichikawa, S. Suzuki, T. Hayashida, R. Yahara and H. Nakae: Mater. Trans., 2012, vol. 53, pp. 1790-1794.CrossRefGoogle Scholar
  17. 17.
    D. Muto, T. Yoshida, T. Tamai, and S. Suzuki: Mater. Trans., 2019, vol. 60 (In press).Google Scholar
  18. 18.
    18. S.K. Hyun, K. Murakami, and H. Nakajima: Mater. Sci. Eng. A, 2001, vol. 299, pp. 241-248.CrossRefGoogle Scholar
  19. 19.
    19. T. Ide, M. Tane, T. Ikeda, S. K. Hyun and H. Nakajima: J. Mater. Res., 2006, vol. 21, pp. 185-193.CrossRefGoogle Scholar
  20. 20.
    20. M. Tane, T. Ichitsubo, M. Hirao and H. Nakajima: Mech. Mater., 2007, vol. 39, pp. 53-63.CrossRefGoogle Scholar
  21. 21.
    21. K. Hokamoto, M. Vesenjak and Z. Ren: Mater. Lett., 2014, vol. 137, pp. 323-327.CrossRefGoogle Scholar
  22. 22.
    22. M. Vesenjak, K. Hokamoto, S. Matsumoto, Y. Marumo and Z. Ren: Mater. Lett., 2016, vol. 170, pp. 39-43.CrossRefGoogle Scholar
  23. 23.
    23. M. Vesenjak, K. Hokamoto, M. Sakamoto, T. Nishi, L. Krstulovic-Opara and Z. Ren: Mater. Des., 2016, vol. 90, pp. 867-890.CrossRefGoogle Scholar
  24. 24.
    24. J. Ichikawa, T. Hayashida and S. Suzuki: Mater. Sci. Forum, 2013, vol. 761, pp. 151-155.CrossRefGoogle Scholar
  25. 25.
    25. T. Yoshida, D. Muto, T. Tamai and S. Suzuki: Metall. Mater. Trans. A, 2018, vol. 49A, pp. 2463-2470.CrossRefGoogle Scholar
  26. 26.
    Japanese Industrial Standards Committee: JIS H 4040 Aluminium and Aluminium Alloy Bars and Wires, Japanese Standards Association, Tokyo, 2015.Google Scholar
  27. 27.
    27. E. Tanaka, S. Semoto and Y. Suzuki: J. Jpn. Inst. Met. Mater., 1964, vol. 28, pp. 228-236.CrossRefGoogle Scholar
  28. 28.
    28. M. Mijalković, M. Trajković and B. Milošević: Facta. Univ., 2008, vol. 6, pp. 75-88.CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2019

Authors and Affiliations

  • Tomoya Tamai
    • 1
    Email author
  • Daiki Muto
    • 1
  • Tomonori Yoshida
    • 1
  • Mahiro Sawada
    • 1
  • Shinsuke Suzuki
    • 1
    • 2
  • Matej Vesenjak
    • 3
  • Zoran Ren
    • 3
  1. 1.Faculty of Science and EngineeringWaseda UniversityTokyoJapan
  2. 2.Kagami Memorial Research Institute of Materials Science and TechnologyWaseda UniversityTokyoJapan
  3. 3.Faculty of Mechanical EngineeringUniversity of MariborMariborSlovenia

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