�ݺ�ߣ

Predictionof Long-Term Service Performance of
Polymeric Materials From Short-Term Tests:
Creep and Prediction of the Stress Shift Factor
of a Longitudinal Polymer Liquid Crystal zyx
ALI E. zyxwvu
AKINAYl, WITOLD BROSOW’, zyxwv
and zyxw
ROBERT MAKSIMOV zyx
’LAPOM,Department o
f Materials Science
University o
f
zyxwv
North Texas
Denton, TX 76203-531
0
21nstituteo
f PolymerMechanics of the University of Latvia
23 Aizkraukles i
e
4 1006 Riga, Latvia
The material studied is a longitudinal polymer liquid crystal (PLC).The creep
behavior of the PLC is examined in the region of nonlinear viscoelasticity. The
creep compliance D curves at nine different stress zyxw
(T levels, from 10 to 50 J.cm3
at a constant temperature are determined and shifted along the log time axis for
uRf = 1
0 J . to produce the D versus t/a, master curve. A fairly general
formula for stress shift factor zyxwv
a
,
,based on free volume vf and the chain relaxation
capability (CRC) derived by one of the authors is applied. The formula predicts
values that agree with the experimental ones within the limits of the experimental
accuracy.Thus, experimentsat several stress levels zyxw
can serve for prediction of long-
term behavior from short-term tests. The same value of the Doolittle constant B is
obtained separatelyfrom temperature shift and stress shift experimentsfor the PLC.
1
. INTRODUCTION
redictionof long-termbehavioron the basis o
f short-
Pterm tests is possibly one of the most important
areas o
f polymer science and technology. Viscoelas-
ticity, that is, time and temperature dependence of
mechanical properties of polymers, might be consid-
ered an inconvenience.In fact, viscoelasticityprovides
us with the capability of long-term service perform-
ance prediction.
Since polymer liquid crystals (PLCs) have excellent
mechanical, thermal and electrical properties, there
are investigations of their alignments under a me-
chanical field or a magnetic field (14)’ their unusual
phase behaviors (5-7), their blends zyxwvu
(8, 9) and also
their surface tensions (10-12).
Usually, either longitu-
dinal or comb PLCs are investigated: for a classifi-
cation o
f PLCs see Brostow (13,1
4
)
.
In this paper we
shall discuss an equation derived by one o
f the au-
thors for the correspondencebetween time and stress
(TSC),
which shallbe used to predict long-termbehav-
ior of a PLC. It is a longitudinal PLC,with the LC se-
quences in the main chain and oriented along the
chain backbone (15).That PIX: forms four coexisting
phases in its servicetemperature range (7).
Before discussing the application of the TSC, we
shall give a brief summary of long-term predictions
from short-term tests on the basis of correspondence
principles, starting with the time-temperature cor-
respondence m)
principle. From mechanical meas-
urements made at severaltemperatures one can create
a master curve for a chosen temperature Trefextend-
ing over several decades of time (16-18).Temperature
shift factor a
, or log a
,is used to shift the individual
curves, thus producing the master curve. Already half
a century ago a connection between morphology and
TIY: principle applicabilitywas studied (19).
The first
attempt to predict quantitative long-term properties o
f
amorphous polymers came h m Williams, Landel and
Ferry 0in 1955.They provided a formulafor a-JT)
(
2
0
)
.
Unless an a,(T) equation is available,quite &en-
sive experimentation at a number of temperatures is
necessary. However, as discussedby Ferry himself (16),
the WLF equation is limited in its use range, expected
to work above the glass transition temperature Tg,but
not belowTgnor for temperaturesT >Tg+ 50 K. More-
over, there are sduystalline viscoelastic materials to
whichTM= does applybut the specificform of the a,(T)
relationshipproduced by WLF does not. Starting from
POLYMERENGINEERINGAND SCIENCE, JUNE2001, Vol. 41, No. 6 977

Ali E. Akinay, zyxwvut
WitoldBrostow, zyxwv
and Robert Maksimov
the Doolittle equation (21), one of the authors has
derived the followingformula (22.23): zyxwvu
InaT zyxwvutsr
= zyxwvuts
A + B/(G- 1) (1)
Equatron zyxwvutsrqpo
1is applicablebelow and aboveTg Here is
the reduced volume, which will be defined below: A
and B are material constants; B is Doolittle viscosity
constantrelating viscosity -q to free volume vf.A primi-
tive and unfounded assumption reduces the general
Eq 1 to the WLF equation. Work on several kinds of
polymers, including various polyethylenes (24, 251, a
number o
f polyurethanes (26) as well zyxwvu
as a PLC (27,
18)which containsfour phases in its service tempera-
ture range zyxwvuts
(7),shows that zyxwvut
Q 1works well and "TC is
applicable if only a reliable equation of state is avail-
able (seebelow).
Equation 1 involves two important assumptions.
First, the response of the material to an external me-
chanicalforce is treated as a collectiverather than in-
dividual reaction of polymer chain segments.This has
been assumed by Kubat (28-30) to explainexperimen-
tal stress relaxation curves and confirmed by molec-
ular dynamics computer simulations (31, 32). The
other assumption is the adoption of the concept of the
chain relaxation capability (CRC)(21,22).CRC canbe
defined as the amount of external energy dissipated
by relaxation in a unit o
f time per unit weight of poly-
mer. zyxwvutsrqp
Equutbn 1has to be used in conjunction with an
equation o
f state. The next section covers the connec-
tion of vf to CRC, an equation of state used with Eq 1
aswell as the present theory, and also the effect of the
stress level on CRC.
2. THEORY USED
2.1. Free Volume and Its Role
Let us list important processes that occur in a poly-
meric material when a mechanical force is applied to
it: transmission of energy across a chain and to its
neighbors where segmental motions as well as entan-
glements play a role; conformational rearrangements
in the chains, and elastic energy storage resulting from
bond stretching and angle changes. All these proc-
esses inside the polymeric material require vf. The
larger vf creates a larger maneuvering ability of the
chains and thus higher CRC (15,22). The vf can be
then defined (33)as
.
I
= u - u* (2)
where v is the total specific volume (for instance in
cm3g1)and v* is the characteristic(incompressibleor
hard-core)volume correspondingto a very high pres-
sure and zero thermodynamic temperature. The re-
duced volumeQ and the other reduced parameters are
defined as follows:
G = u/v*; T = TIT*: p= P/P* (3)
whereT and P are the thermodynamictemperature and
pressure: T* and P* are the characteristic (hard-core)
parameters for a given material. The former is related
to the strength of interactions in the material. P* is a
complicated function of the intermolecular interac-
tions and of the material structure represented by the
binary radial distributionfunctiong(R)(34).
2.2. The Equation of State
Equations 1-3 can be used only in conjunction with
a specific equation of state. Good results have been
obtained repetitively (26, 24, 27, 35, 18, 25)by using
the Hartmann equation (36,37), which is valid for
both polymer melts and solids:
(4)
j3 3= T3P - ~n
u
-
2
.
3
.The Correspondenceof Stress and Time
We know that the stress level u affects free volume
and thus CRC. As early as 1948, OShaughnessy re-
ported that compliancevalues of rayon from creep ex-
periments for different stress levels can coalesce into
a single master curve when plotted against time or a
function of time (38).Later, more studies were per-
formed, as discussed in Goldman's book (17).How-
ever, a reliable formula for the stress shift factorau as
a function of stress u to predict long-termbehavior of
polymers was not available. Now, one o
f the authors
has derived such a formula using the CRC concept;
details of the derivation are provided elsewhere (15).
The resulting equation is
a, = [U(U)/Vre.l +
B[(G- l)-' - (Ere.- 1)-'] + C(U - u
~
,
,
J
) (5)
where vref= v(uRf,
T
,
,
)
, B is the Doolittle constant as
before, while C is a constant representing the effects
of varying stress on the chain conformations and
structure of the material. Positive C corresponds to a
viscosity increase under stress. Thus, experiments at
several stress levels can serve for prediction of long-
term behavior in a similar way as experiments at sev-
eral temperatures are used.
The objective o
f the present paper is to test the va-
lidity of Eq 5.As already noted, PLCs form multiphase
systems. Our test is based on results for a longitudi-
nal PLC. If this would provide satisfactoryresults, one
or two phase systems should then obey Eq 5 even
more easily.
3
.EXPERIMElV'TAL
The stress dependence of the creep compliance of
PET/O.GPHB has been investigated at the room tem-
perature 20 2 1°C. Here PET = poly(ethy1enetereph-
thalate)),PHB = p-hydroxybenzoic acid (LC);
0.6 = the
mole fraction of PHB. The PLC used in the study has
already been well characterized in previous papers (7,
39).Experimentalcreep curves were measured for 2 h
at nine stress levelsin the range from 10to 50J .cm3
with 5 J . ~ m - ~
intervals by using an MTS universal
testing machine (1J * cm3 = 1 MPa).The elongation
was determined with the strain gauge, MTS Model
632.11 c-20,as reported by Brostow et at (18).
978 POLYMER ENGINEERING AND SCIENCE,JUNE 2007, Vol.47, No. 6

Prediction zyxwvu
o
f Long-TermService zyxwv
Performance zyxw
4. EXPERIMENTAL RESULTSzyxwvu
The time dependence of creep compliance D zyxwvu
as a
function o
f logarithmic time at room temperature has
been investigated at several stress values. zyxwvu
Figure zyxwvu
1
shows D versus log time curves at different stress lev-
els in the range from 10 to 50 J zyxwv
* ~ m - ~ .
As reported
previously (271,
isochronous stress-strain curves at t
= 0 (the zyxwvuts
strain at the loading time] are linear up to 30
J . ~ m - ~ .
Then a deviation from linearity is observed,
first only slight, but the effect increases with increas-
ing stress level. Moreover, significant nonlinear vis-
coelasticity was observed at t = 120 min (total strain
before unloading). As an approximation to nonlinear
creep, a multiple integral representation using several
kernels between the stress levels 30-50 J .cm3 has
been applied (27).
While an accurate representation
can be achieved with a large number of parameters,
clearlythis is not a predictiveapproach.
5. APPLICATION OF THE TSC PRINCIPLE
AND OF EQUATION 5
We now apply the TSC to the results shown in Fig.
1. We choose as the reference stress level aRf= 10J '
~ m - ~
for which zyxwvut
a
,
, = 1by definition. Then, we shift the
results of a
l
l other stress levels building a single mas-
ter curve.The results are shown in Fig. 2. The respec-
tive shifting distance is the stress shift factor q.
We
conclude that the TSC principle is well applicable to
the creep complianceof our multi-phase system.
We now investigatethe validity of Eq 5.The charac-
teristic parameters v* = 0.682 cm3g1,'
P = 1400 K
and P* = 3850 J . cm-3 for our PLC have been deter-
mined from the experimentalPVT data (35).These pa-
rameters and Eq 4 have been used to compute and
v values for the corresponding stress levels. The re-
sults are then applied to Eq 5
.B and C values com-
puted by fitting to the experimental data are equal to
5.10 and -0.56, respectively.
Y

0
3.0
2.6
-
?
E
i
SE
n
0
0
Y

2.2
1.8
0
I P
0
1010 015 h20i
I
I 0
m
025 X30 +351
I X
X
0.5 1.5 2.5 3.5 4.5
log (W
Ftg. 1. Experimental creep compliancefor PJT/O.GPHB as a
fundion o
f log time between 1
0 zyx
and 50 J . cm3stress levels
with5 J.crn3interualsatT= 20°C.
A good agreement between experimentaland calcu-
lated a
,is achieved-as represented in Fig.3.The dis-
continuous line is fitted to the experimental a
,
,values
by using Eq 5in conjunctionwith Eq 4.A good confor-
mity is then obtained between the experimental and
1.9
1.5
0 2 4 6 8
log(ta,/s)
Rg. 2. Themaster m efor PET/O.GPHBo
f creep complinnceD as afunction of log t .%for ore.
= 10J .mi3.Points are experimen-
t
a
lvalues andsymbols are the same as i
n F
X
g
. 1. The broken curuekjittedby usingEq 5.
POLYMER ENGINEERINGAND SCIENCE,JUNE 2001, Vol.41, No. 6 979

Ali zyxwvut
E.Akinay, Witold zyxwvuts
Brostow, zyxwvu
and Robert Maksimov zyxw
2 r zyxwvutsr
I "u
C
-
fj zyx
-7
-10 L I I , I I I
0 10 20 30 40 50 60
CJzyxwvutsrqponmlkjih
I (J.cmJ)
FSg. 3. The stress sh@ f d r a,, zyxwvutsr
(
u
)for the PET/O.GPHB
for
line is computedfromEq 5i
n conjunctionwith% 2.
a
,
, = 10J .~ m - ~ .
circle^ CUE values; the broken zyxwvu
the predicted master curve in Rg. 2. The dotted line in
Q. 2 represents the values calculated from Eq 5. We
see that prediction is within the limits of experimental
accuracy.
The best fit to the experimental temperature shift
factor a
,for the same PLC from creep measurements
for Tmf= 20°C up to 120°Chas already been achieved
from Eq 1 with B = 5.093 (18).This proves the as-
sumption made in (15)that the Doolittleconstant B in
Eqs I and 5is indeed a material constant-regardless
of its origin (such as from either a, or a
,experiments).
Moreover, the negative value of C = - 0.56 computed
from Eq 5is also in harmony with the logarithmicvis-
cosity of binary molten blends of the same PLC as a
function of logarithmic shear rate (8).The addition of
the PLC to four compatible engineering polymers
has resulted then in lowering of the viscosity. A par-
ticularly large effect was obtained when isotactic
polypropylene was the second component. A further
decrease in viscosity was observed with increasing
shear rate. Hence, the inverse proportionality between
viscosity and shear rate is well represented by the
negative value of C, which reflects effects of stress on
the chain conformations.
Therefore, we have reached our main purpose. Just
as temperature, stress can serve equally well for the
prediction of long-term behavior from short-term
tests. We have tested with good results Eq 5,which
thus provides the capability of using time-stress
equivalence for reliable long-term quantitative predic-
tions. The validity of the model is confirmed further by
the same value of the Doolittle constant B obtained
separatelyfrom temperature shift (18) and stress shift
experiments for the same PLC material.
A C K N O ~ E D O S
One of us (AEA)would like to thank TUBITAK
(BAYG-NATO),Ankara, for financial support. Partial
support has also been provided by the State of Texas
Advanced Research zyxwvut
Program (GrantNo. 003594-0075-
1999)and by the Robert A. Welch Foundation (Grant
No. B-1203).Discussions on the nature of liquid crys-
tallinity with: Dr. Michael Hess, Gerhard Mercator
University, Duisburg; Dr. Andreas Schonhals, Bunde-
sanstalt fiir Materialforschung und-prtifung (BAM),
Berlin; and Prof. Jiirgen Springer, Technical Univer-
sity of Berlin, are appreciated. Discussions with Dr.
Anatoly Goldman,Alcoa CSI, CrawFordsville,Indiana,
and with Dr. Bruce Hartmann,Naval SurfaceW
a
r
f
a
r
e
Center,West Bethesda, Maryland, on the free volume-
mechanical properties connection are acknowledged
as well. A preprint from Dr. Joao Mano and Prof. An-
tonio M. Cunha, University of Minho, Gu'
names. was
useful.
REFERENCES
1. M. Zisenis, B. Prstzl, and J. Springer, Polymer. M e .
2
.M. Zisenis and J. Springer, Polymer,85,3156 (1994).
3
.D.Ferri, D. Wolff, J. Springer, D. Francescangeli, M.
Laus. A. S. Angeloni, G. Galli, and E. Chiellini, J.Po@-
mersCi Phys.,36.
2
1 (1998).
4.W.Brostow, E.A. Faitelson. M. G. Kamensky, V. P.
Korkhov. and Y. P. Rodin, Potymer, 40, 1441 (1999).
5
.F.T
.Niesel and J. Springer, Macromol. Rapid Commun.,
15,7(
1
9
9
4
)
.
6
.A.Schonhals, D. Worn, and J. Springer, MacromL, 28,
6254(1995).
7
.W. Brostow, M. Hess, and B. L. Lopez, MacromoZ., 27,
2262(1994).
8.W.Brostow, T.Sterzynski, and S. Triouleyre, PoZyymer,
97, 1
5
6
1 (
1
9
9
6
)
.
9.W. Brostow, N. A. DSouza, B. Gopalanarayanan. and
E. G. Jacobs, Polym Eng. Sci.40,490(
2
0
0
0
)
.
1
0
.M.Selimovic, A. Bismarck, M. Phffemoschke, and J.
Springer, Acta Polyrn,SO, 1
5
6 (1999).
11. A. Bismarck, M. Pfaffernoschke, B. Song. and J.
Springer, J.Appl. PoZymer Sci,71,1893(1999).
1
2
.A. Bismarck, M. E. Kumru, B. Song. J Springer, E.
Moss, and J. Karger-Kocsis, Composites, SO, 135
(
1
9
9
9
)
.
Sci &kg..
71.4
1 (1994).
1
3
.W. Brostow,Polymer,31,979(1990).
1
4
.W. Brostow, "Polymer Liquid Crystals." in Physical Prop-
erties o
f Polymers Handbook,Ch. 33,J. E. Mark, ed.,
American Institute of Physics Press, Woodbury, N.Y.
(1996).
1
5
.W. Brostow, Mater. Res. Inmuat., 3,
347(
2
0
0
0
)
.
1
6
.J.D. Ferry, Vismelastic Properties o
f Polymers,3rd Edi-
tion, Wiley. New York (
1
9
8
0
)
.
1
7
.A.Y. Goldman, Prediction o
f the &formation hoperties
o
f Polymeric and Composite MateriaIs, American Chemi-
cal Society,Washington, D.C. (1994).
1
8
.W. Brostow, N.A. DSouza,J. Kubat, and R D. Maksi-
mov, J. Chern Plys., 110,9706 (1999).
1
9
.F.Schwanl and A. J. Staverman,J. Appl. Phys..13,
838(1952).
2
0
.M. L.Williams, R. F. Landel, and J. D. Ferry, J. A m
Chem Soc., 17,3701 (
1
9
5
5
)
.
2
1
.A.K
.Doolittle, J.AppL P
h
y
s
.
.21. 1741 (
1
9
5
1
)
.
22.W.Brostow, Mater. Chem & Phys., 13,47(1985).
23.W.Brostow. Ch. 10 in W. Brostow and R. D. Comeli-
ussen, eds., Failure o
f Plastics,Hanser, Munich-Vienna-
New York (1986).
2
4
.Yu M. Boiko, W. Brostow. A. Ya. Goldman, and A. C.
Ramamurthy, P
o
l
y
m
e
r
,
96. 1383(1995).
25.J. Mano. R. A. Sousa. R. L. Reis, A. M. Cunha, and
M. J. Bevis, Polymer,42,6187
(2001).
26.W.Brostow, J. V. Durn, G. F. Lee. and K. Madejczyk,
M a c r o m o W s . 24.479(1991).
980 POLYMERENGINEERINGAND SCIENCE, JUNE 2001, Vol.41, No. 6

Prediction zyxwvu
o
f Long-TermService Performane
27. zyxwvutsrqpo
J. Kubat and zyxwvutsrq
R. D. Maksimov,"Creep and zyxwvuts
Stress Relax-
ation", in zyxwvutsrqp
Mechanical and Z%etmophysicalProperties o
f
Polymer Liquid Crystals, p. 407,W. Brostow, ed.,Chap-
man zyxwvutsrqp
& Hall, London (1998).
28.J. Kubat, zyxwvutsr
Phys.StatusSolidi B,111,599 (1982).
29.J. Kubat and M. Rigdahl, Ch. 4in Ref. 1
7
.
30.M. J. Kubat, F. J. Jansson. M. Delin, J. Kubat, R. W.
Rychwalski, and S. Uggla, J. Appl. Phys.,la, 5179
(1992).
31.W. Brostow and J. Kubat, Phys. zyxwvuts
Reu.B, 47,
7659(1993).
32.S.Blonski, W. Brostow, and J. Kubat, Phys. Rev.B, 49,
6494(1994). zyxwvutsr
POLYMERENGINEERINGAND SCIENCE,JUNE 2001, Vol.41, No. 6
33.P.J. Flory, Fmaday Soc. Disc., 49,
7 (1970).
34.W. Brostow and W. Szymanski, J. Rheology, 30,877
35.J. M. Berry, W. Brostow, M. Hess, and E.G.Jacobs,
36.B. Hartmann and M. A. Haque, J.AppL Phys., 58,
2831
37.B. Hartmann and M. A. Haque, J. AppL Polymer Sci,
38.M. T.OShaughnessy, TewtileRes. J.,18,263 (1948).
39.W.Brostow, T.Dziemianowicz, W. Romanski, and W.
(1986).
Polymer, 39,4081(1998).
(1985).
30, 1553 (1985).
Werber, PoZyym Eng. Sci,28, 785 (1988).
981

�ݺ�ߣ

Prediction_of_long_term_service_performa.pdf

More Related Content

Prediction_of_long_term_service_performa.pdf