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

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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 (mm

^{2})*b*Depth of a cell wall (mm)

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

- Δ
*D*_{x} Increment in

*D*in*x*-direction (mm)- Δ
*D*_{y} Increment in

*D*in*y*-direction (mm)*d*Pore diameter (mm)

*E*_{c}Elastic gradient of a non-porous specimen (MPa)

*E*_{t}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)

*ɛ*_{x}Strain perpendicular to the pore orientation (–)

*ɛ*_{y}Strain parallel to the pore orientation (–)

*ɛ*_{z}Compressive strain of a porous specimen (–)

- \( \overline{{\varepsilon_{\text{p}} }} \)
Equivalent plastic strain in the

*x*–*z*plane of a porous specimen (–)*θ*Inclination angle of a beam (deg)

*σ*Compressive stress of a porous specimen (MPa)

*σ*_{bf}Critical stress for bending fracture of a cell wall (MPa)

*σ*_{cr}Critical stress for plastic buckling of a cell wall (MPa)

*σ*_{d}Critical stress for rapid densification (MPa)

*σ*_{fr}Critical stress for fracture of a cell wall (MPa)

*σ*_{fs}Bending strength of a cell wall (MPa)

*σ*_{pc}Critical stress for plastic collapse of a cell wall (MPa)

*σ*_{pc}(*x*′)Critical stress for plastic collapse at the position

*x*′ in a beam (MPa)*σ*_{Y}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.

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