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Journal of Applied Polymer Science, 23, pp. 847-858, 1979
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The origin of residual internal stress in solvent-cast thermoplastic
coatings
Croll, S. G.
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Ser
TH1
$(I
National Research Conseil national
N21d
Council Canada de recherches Canada
LO.
839
L
&a.
,
THE ORIGIN OF RESIDUAL INTERNAL STRESS IN
SOLVENT-CAST THERMOPLASTIC COATINGS
by
S.G. Croll
I
I
Reprinted from
Journal of Applied Polymer Science
VoL
23,
1979
p.
847
-
858
DBR Paper
No.
839
Division of Building Reeearch
Price
25
cents
OTTAWA
NR
453
Des essais sur des revgtements de polystyrSne et de polyisobutyl
msthacrylate coul&s
5
partir de tolusne ont indiqu6 que la
contrainte interne r6siduelle n'est pas influenc6e par
116paisseur
du revgtement sec ou par la concentration
initiale de la solution.
On pr6sente une th&orie selon laquelle on peut pr6dire l'importance
de la contrainte et stipulant que la contrainte ne d6pend nullement
de 116paisseur ou de la concentration
initiale de la solution.
La
contrainte interne est calcul6e selon le volume de solvant qui
s'6vapore aprSs la solidification du revztement. Ce point de
solidification s'identifie
5
la conce3tration de solvant n6cessaire
pour faire diminuer la tempgrature de transition du polym6re
5
1'6tat vitreux
5
la
temp6rature d'essai. I1
y
a donc corr6lation
directe entre le volume de solvant perdu durant le s6chage de la
solution et le changement de volume de la pellicule de polpsre.
The Origin of Residual Internal Stress in Solvent-Cast
Thermoplastic Coatings
1
S.
G.
CROLL, Materials Section, Division of Building Research, National
Research Council of Canada, Ottawa, Canada
KIA
OR6
Synopsis
Experiments on polystyrene and poly(isobuty1 methacrylate) coatings cast from toluene have
shown that residual internal stress is independent of dried coating thickness and initial solution
concentration. A theory is presented that predicts the magnitude of the stress and shows that it
has no dependence on thickness or initial solution concentration. Internal strain is calculated from
the volume of solvent lost after the coating has solidified. This solidification point is identified with
the solvent concentration that is sufficient to depress the glass transition of the polymer to the
prevailing experimental temperature. A one-to-one correlation is confirmed between the volume
of solvent lost from solution during drying and the volume change of the polymer film.
INTRODUCTION
Objects, whether for decorative or protective purposes, are frequently coated
by brush, dip, or spray application of a polymer solution. As the coating dries,
it loses solvent and must consequently shrink. Its thickness can contract, but
the area is constrained by adhesion to the substrate. There is still some solvent
lost after solidification, but the coating can no longer flow to satisfy the change
in volume. Because of this constraint, internal stress arises in the plane of the
coating.
Stresses may have an adverse effect on the adhesive and cohesive properties
of the coating. A previous investigation1 of stresses in a simple, air-dried acrylic
lacquer has shown them to be significant relative to the strength of the coating.
Results on polystyrene coatings presented in this paper show loss of adhesion
owing to the effects of internal stress.
Because of the large quantities involved, considerable economic and raw ma-
terial savings could be made by extending the service life of coatings. One way
of doing this would be to reduce the internal stress. The purpose of this paper
is to provide a basis for understanding the origins of internal stress in simple,
physically drying, thermoplastic coatings and thereby identifying possible means
of removing that stress.
To that end, experiments on polystyrene and poly(isobuty1 methacrylate)
(PIBM) coatings were carried out and compared successfully with a theory that
predicts the final value of the internal stress. The theory identifies the internal
strain, and thus stress, with the volume of solvent lost from the time that the film
solidifies until the final "dry" state. It is assumed that the solidification point
occurs when solvent loss is sufficient to raise the glass transition temperature
of the coating solution to the ambient temperature.
Journal of Applied Polymer Science, Vol. 23,847-858 (1979)
O
1979 John Wiley
&
Sons, Inc.
0021-8995/79/0023-0847$01.00
I
-
848
CROLL
THEORY
Calculation of Residual Internal Stress
The theory presented is concerned only with the equilibrium value of the in-
ternal stress, i.e., the residual stress.
An
algebraic description of the way in which
the stress reaches its final value would be extremely complicated, involving
diffusion through a polymer solution with great changes in concentration,
1
I
evaporation of solvent from the surface, and the nonlinear viscoelastic properties
of a drying polymer solution. It is assumed here that residual internal stress
is due solely to the difference between the volume fraction of solvent at which
the film solidifies,
$,,
and the volume fraction of retained solvent in the "dry"
film,
4.
Prior to solidification, the coating is mobile enough to flow and allow
the volume change demanded by solvent evaporation. The area is constrained
at its original size by adhesion
to
the substrate; thus, the volume change appears
as a change in thickness. After solidification, the polymer can no longer flow,
and further loss
in
solvent produces internal stress in the plane of the coating.
The thickness is still unconstrained and can contract in response to the compo-
nent of stress in that direction.
The volume of solvent lost is responsible for internal bulk strain within the
coating, equivalent to an isotropic linear strain field. The two components of
strain remaining in the plane of the coating give rise to the stress measured ex-
perimentally. Because PIBM and polystyrene are amorphous solids, there will
be no complications due to crystallization in the coating during drying.
The volume of solvent loss from the coating after solidification,
AV,
is given
by
AV
=
4,V
-
&(V
-
AV)
'
(1)
where
V
=
volume of coating at solidification and
4,
is measured in free, un-
strained films, Equation
(1)
can
be
rewritten as
AVlV
=
4,
-
Gr(l
-
AVlV)
(2)
=
internal bulk strain, assuming an exact correspondence with the volume
of solvent lost
=
3t
where
t
=
isotropic linear strain, which is equivalent to the internal bulk
strain.
Thus, the internal linear strain is given by
t
=
4s
-
4r
3(1
-
4r)
(3)
For a Hookean material in this biaxial, plane stress situation, the stress
a
is
given by
E
t
a=-
1
-
v
(4)
where
E
=
Young's modulus of the coating and
v
=
Poisson's ratio. Hence, the
residual internal stress is given by
E
4s
-
dr
6
=
-
1
-
v
3(1
-
&)
(5)
L