This sutdy has been made of the compress-release behaviour of cotton assemblies and polyurethane rubberfoams by measuring the relation of compressional stress-strain and compressional stress relaxation. There are similarties of property between cotton and urethane since they are consisted of polymer materials and have their randomized inter-surfaces. The experiment has been made to make clear characteristics which are obscure in cotton assemblies only. The main task here is appointed to find the effects of inner friction upon their compress-release behaviour.
First, to analyse the compressional stress
P and specimens′ height
h curve for cotton or urethane which deform largely, taking account of the usual stress-strain relationships available for small deformation of specimens, we define the stresst ratio γ from the
P-h curve as follow: Drawing a tangent line from a point
S upon the curve, let the reading of intercept made by the line and
h-axis be
H, and γ=(
H-h)/
H (1) becomes the strain ratio of the deformed specimens
S. Applied it to our specimens, the following results are obtained:
(1) For both the cotton and urethane, γ is nearly constant in the range of wide pressure. Thus the elastic modulus
E of the specimens as a whole may be expressed E=(1/γ)
P (2) This result means that the specimens become more stiff proportionally to
P. and it seems suitable to take 1/γ for an index of stiffness of those highly deformed materials such as cotton or urethane, For cotton γ is 0.26, urethane 0.29.
(2) From the above it may be assumed that the variation of the height of compress specimens is caused by the slipping of intersurfaces.
Secondary, measuring the relaxation of stress
P after stopping to compress, special attention is paid to a instanteneous reduction of pressure.
3) The instanteneous reduced pressure
P0 is proportional to inital pressure
P for both specimens, that is:
P0=a
fP (3) where
af is constant, and for cotton
af=0.84 urethane 0.87. It is assumed that the quantity
F≡
P-
P0 represents a rapid reduction of mutual slippage against the surfaces which exists during the compression. Namely,
F=(1-
af)
P=
fP is equal to frictional force that resists to slip among the surfaces. For cotton
f=0.16, urethane 0.13.
(4) On release-process, appling the same frictional force as for the compress-process. The relation between compress pressure
P and release pressure
P′ at the same specimens height may be lead to:
P′=(1-4
f)
P (4) This relation gives an approximation showing the range of the pressures 0 to 2.4kg/cm
2.
(5) The loss factor φ of the compress-release process of specimens are defined as φ=(
W1-
W2)/
W1, where
W1 is the absorbed energy of the specimens during compression and
W2 is exhausted one of the specimens on release process. Appling the result of (4) to the φ the following equation is obtainable: φ=(
P-P′)/
P=4
f (5) For cotton the estimated value of φ and the observed one are 0.64 and 0.72 and, for urethane 0.52 and 0.53 respectively.
It may safely be concluded that the hysteresis loss on the compress-release process of fibre assemblies or porous materials are largely depend on friction caused by slipping of the inter-surfaces which compose the material.
The stress relaxation obtained from release process does not behave so simply as with
P′.
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