Metal Foams: A Design Guide

110 Metal Foams: A Design Guide
t
c
t
b
F
d(= c +2t)
Figure 9.6 Sandwich beam loaded in three-point bending
and core are t and c, respectively. The faces have a Young’s modulus, Ef,
and the core has a Young’s modulus, Ec, and a shear modulus Gc. The elastic
and plastic deflection of a sandwich beam are analysed in Chapter 10. The
creep deflection is found from the sum of the bending and shearing deflection
rates. Consider the faces first. The power-law creep response of the faces is
given by:
Pε D Af nf ⊲9.10⊳
where Af and nf are the creep parameters of the face material. Assuming that
plane sections remain plane,
Pε D y P ⊲9.11⊳
and
�
y P
D
Af
� 1/nf
⊲9.12⊳
Assuming also that the moment carried by the faces is much larger than
that carried by the core, then
� h/2 � �1/nf y P
M D 2
yb dy ⊲9.13⊳
c/2
Af
D B 2b
A 1/nf
P
f
1/nf
where
1
B D
2 C 1
nf
� �h
2
� �
2C⊲1/nf⊳ � c �2C⊲1/nf⊳ 2
The bending deflection rate at the center of the beam is then:
� �nf P ⊲ℓ/2⊳
PυbmaxD Af
4bB
nfC2 � �
1
1
nf C 1 nf C 2
⊲9.14⊳
⊲9.15⊳