The stress in twisted fiber relaxes as elongated, so the twisting moment changes with time under the condition of constant twist. The torsional relaxation in macroscopic meanings is measured and studied with the specimen of raw silk. The twisting moment
M decreases with elapsed time
t from the initial moment at constant twist
T (relaxation in narrow sense) and increases showing a negative value after removing the twist (recovery), an inverse moment remaining permanently. The momentrelaxation in fiber is represented in the following types of empirical formula;
M=
A-
Blog
t or
M=
At-c,
c being almost constant below a certain twist.
A and
B are the functions of
T and so
M=
aeαT-
bTβ logt for example (500_??_
T_??_3000), where
a,
b,
a and β are constant.
a=4.65,
b=0.0281; α=3.69×10
-4, β=0.415 and
c=7.44×10
-2 for relaxation of raw silk (
M in mg•cm,
T in m
-1,
t in min.) The relative moment-relaxation is shown in the similar type of formula as above;
M/
M1=1-
b′log
t or
M/
M1=
t-c, where
b′ is scarcely dependent on the twist (constant in
T_??_2000). (
M1=
A i.e. moment of 1 min after twisting or untwisting). As mean value
b′=0.0663 for relaxation, 0.168 for recovery. The relations among
M,
T and
t are illustrated in the isochronal curves and the surface of moment-relaxation.
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