Materials for engineering, 3rd Edition - (Malestrom)

214
Materials for engineering
environments at various temperatures have confirmed that the strength of
moist GRP is controlled by moisture sensitivity of the fibres, although different
resins result in different lives for a given stress level.
6.4.6 Mechanical behaviour of cellular solids
The properties of a foam are described in terms of their relative density ρ/ρ s,
where ρ is the density of the foam and ρ s that of the solid of which it is made.
This ratio can vary over two orders of magnitude with foams of differing
density.
Elastic properties
At small strains, foams behave in a linear elastic manner, and their modulus
is given by
E = E
⎛ ρ ⎞
s
⎝ ρ ⎠
s
n
where E s is the modulus of the solid. It is found experimentally that in
tension n ≈ 1.5 and n ≈ 2 in compression, and E can vary over four orders of
magnitude with foams of different relative density. This equation may also
be employed to describe the properties of wood, in which case ρ is the
density of the cell wall material. For moduli parallel to the grain, n = 1,
which corresponds to a rule of mixtures, and, for the perpendicular direction,
n = 2 is a better approximation.
At larger strains, foams deform by elastic buckling of the walls and, from
*
standard beam theory, the elastic collapse stress σ el is given by
σ
*
el
ρ
= 0.05E ⎛ ⎞
s
⎝ ρ ⎠
s
2
If the matrix itself is capable of plastic deformation, then in cellular form it
may exhibit plastic collapse, which is non-reversible, but which will absorb
considerable energy if the material is used for padding purposes, as in the
case of polyurethane automobile crash padding. If the yield strength of the
solid matrix is σ y , then the collapse stress, σ * pl , is given by
σ
*
pl
⎛ ρ ⎞
= 0.3σ
y
⎝ ρ ⎠
s
3/2
6.5 Further reading
D. Hull and T.W. Clyne, An Introduction to Composite Materials, 2 nd edition, Cambridge
University Press, 1996.