Metal Foams: A Design Guide

elations take the form
P Ł � Ł �n D ˛
Ps
s
Properties of metal foams 53
where P is a property, ˛ a constant and n a fixed exponent.
The scaling relations are particularly useful in the early stages of design
when approximate analysis of components and structures is needed to decide
Table 4.2
(a) Scaling laws for the mechanical properties of foams
Mechanical properties Open-cell foam Closed-cell foam
Young’s modulus
(GPa), E
E D ⊲0.1–4⊳Es
�
s
� 2
E� D ⊲0.1–1.0⊳Es ð
� �2 �
0.5 C 0.3
Shear modulus
(GPa), G
G ³ 3
E 8
3
G ³ 8 E
Bulk modulus (GPa),
K
K ³ 1.1E K ³ 1.1E
Flexural modulus
(GPa), Ef
Ef ³ E Ef ³ E
Poisson’s ratio 0.32–0.34 0.32–0.34
Compressive strength
(MPa), c
�
c D ⊲0.1–1.0⊳ c,s
�3/2 s
�c
D ⊲0.1–1.0⊳ c,s ð
� �2/3 �
0.5 C 0.3
Tensile strength
(MPa), t
Endurance limit
(MPa), e
Densification
strain, εD
t ³ ⊲1.1–1.4⊳ c t ³ ⊲1.1–1.4⊳ c
e ³ ⊲0.5–0.75⊳ c e ³ ⊲0.5–0.75⊳ c
εD � D ⊲0.9–1.0⊳ ð
�
1–1.4 C 0.4
s
s
� 3 �
Loss coefficient, s
³ ⊲0.95–1.05⊳ ð
⊲ / s⊳
� �
Hardness (MPa), H H D c 1 C 2
s
Initiation toughness.
(J/m 2 ) JIC
JŁ IC ³ ˇ � �
Ł p
y,sℓ
s
s
s
εD � D ⊲0.9–1.0⊳ ð
�
1–1.4 C 0.4
s
s
s
� �
s
� �
� 3 �
s
³ ⊲0.95–1.05⊳ ð
⊲ / s⊳
� �
H D c 1 C 2
s
JŁ IC ³ ˇ � �
Ł p
y,sℓ
s