Chemistry Reference
In-Depth Information
5γ
0
e
iωt
. Comment on the viscoelastic behavior of the
material as a function of angular frequency.
form of
γ
(
t
)
G
ηω
J
J
0
2
5
iJ
v 5
2
2
i
G
2
1η
2
ω
G
2
1η
2
ω
2
4-20 A Maxwell model (
Eq. 4-59
,
Fig. 4.18b
) is being deformed at a constant
rate
d
(
t
)] at a time
t
after the
imposition of the fixed straining rate? Express your answer in terms of the
constants
G
and
γ
/dt
5
C
. What is the stress on the element [
σ
η
of the Maxwell element and the strain
γ
(
t
) which corre-
sponds to
σ
(
t
).
4-21 Commercial polymer films are usually produced with some orientation.
The orientation is generally different in the longitudinal (machine) direc-
tion than in the transverse direction. How could you tell which is the
machine direction from a stress
strain test? (
Hint:
Refer back to the
effects of orientation mentioned in Section 1.8.)
4-22 The hoop stress,
σ
h
, at the outer surface of a pipe with internal pressure
P
,
outside diameter
d
1
, and inside diameter
d
2
is
2
Pd
2
d
1
2
σ
h
5
d
1
A well-made PVC pipe has outside diameter 150 mm and wall thick-
ness 15 mm. Measurements on this pipe give
K
Ic
5
m
1
/
2
2
.
4 MPa
and
m
2
2
. Assume that the largest flaws are 100-
yield stress,
σ
y
5
50 MN
μ
m cracks and that the calibration factor for the specimens used to mea-
sure fracture toughness is 1.12. The pipe is subjected to a test in which the
internal pressure is gradually raised until the pipe fails. Will the pipe fail
by yielding or brittle fracture in this burst test? At what pressure will the
pipe rupture?
References
[1] T. Bremner, A. Rudin, J. Polym. Sci., Phys. Ed. 30 (1992) 1247.
[2] T.A. Kavassalis, P.R. Sundararajan, Macromolecules 26 (1993) 4146.
[3] V.P. Privalko, Y.S. Lipatov, Makromol. Chem. 175 (1974) 641.
[4] M. Gordon, High Polymers, Addison-Wesley, Reading, MA, 1963.
[5] H. Mark, ChemTech, 220 (April 1984).
[6] L.R.G. Treloar, The Physics of Rubber Elasticity,
third ed., Oxford (Clarendon)
University Press, London and New York, 1975.
[7] M.L. Williams, R.F. Landel, J.D. Ferry, J. Am. Chem. Soc. 77 (1955) 3701.
[8] K.H. Illers, H. Breuer, Kolloid. Z. 17b (1961) 110.
[9] A.M. Donald, E.J. Kramer, J. Polym. Sci., Polym. Phys. Ed. 20 (1982) 899.
