TRANSACTIONS
OF THE SOCIETY
OF RHEOLOGY
20:2, 311-317 (1976)
Proposed Nomenclature for Steady Shear Flow
and Linear Viscoelastic Behavior
C. L. SIEGLAFF,
Diamond Shamrock Co., Painesville,
Ohio 44077’
Eighteen years ago Leaderman [Trans. Sot. Rheol., I, 213 (1957)]
Since that time
published a nomenclature for linear viscoelasticity.
the science of rheology has matured and its use in other disciplines
has grown.
In order to facilitate communication
between these
diverse disciplines, a systematic organization of names and symbols
is very desirable.
In 1970, F. R. Eirich, as vice-president of the Society of Rheology,
formed an ad hoc committee to review the status of rheological
nomenclature.
This committee
first convened at the Princeton
The committee then agreed that a uniform
Annual Society meeting.
system of nomenclature
for material properties, such as moduli,
It was also agreed that the existing
viscosities, etc., was needed.
prevalent
usages should
serve as guide lines for proposed
nomenclature.
Subsequent to the original meeting, several approaches to a uniwere explored.
The results were
form system of nomenclature
distilled down to the nomenclature
list proposed in the Rheology
Bulletin, Vol. 43. Several corrections
and comments have been
A major
included in the final nomenclature published in this report.
addition is the use of SI units, as well as the cgs system.
The committee recommends that the Society of Rheology members
adopt this nomenclature
in their communications
to the Society.
The committee
expressly recommends
standardization
of those
symbols and notations
representing
material
constants,
material
functions, and notations for the directions of shearing flow.
The present committee did not consider it necessary or advisable
to develop a dictionary
of (phenomenological)
behavior.
A dictionary of this type by M. Reiner and G. W’. Scott Blair is currently
311
@ 1976 by The Society of Rheology, Inc.
Published by John Wiley & Sons, Inc.
Nomenclature for Simple Steady Shear Flow
vz = j(y) or VI = f(n)
Units
cgs System
SI System
Name
Definition
Name
Symbol
Dimensions
Name
Units
-
geometric direction of 5ow
-
direction of velocity change
-
neutral direction
-
-
-
-
shear stress in simple steady
shear 5ow
-
Pascal
Pa
m-1.kg.s’
or (N/m*)
shear rate
dV./d9
s-1
s-1
s-1
-
s-1
viscosity
u/T
Pascal second
Paas
m-l . kg. s-l
Poise
dyne*s.cm’
-
dyne cm*
-
dyne cm-
or (N . s/m*)
first normal stress function
011 - 022
Pascal
Pa
m-‘.&.s-2
or (N/m’)
second normal stress function
S?Z - 0a.d
PaSC81
Pa
m-1. kg. S-2
or W/m)
dyne cm*
70
first normal stress coefficient
N+i=
-
Pa.9
m-1. kg
-
dyne. 9 +cm4
second normal stress
coefficient
-
-
Pa-s’
m-1. kg
-
dyne. 5%.cm-2
Pascal second
Pa-s
m-1. kg. s-1
Poise
dyne. s. cm-4
Pascal second
Pa-s
,-1 . kg. s-1
Poise
dyne.s.cm*
Pascal second
Pa-s
,-I.
Poise
dyne.s*cm*
limiting viscosity at
zero shear rate
limiting viscosity at
infinite shear rate
iii
(r/q)
4-0
lim (u/q)
+a,
la
viscosity of solvent or
continuous medium
9a
relative viscosity
dimensionless
9.-P
specific viscosity
dimensionless
hl
intrinsic viscosity
-
kg. s-1
dimensionless
dimensionless
ma. kg-r
-
g-r.cma or
specified
units of concentration
Nomenclature for Small Amplitude Oscillatory Motion
Unite
cgs System
SI System
Symbol
w
t
T
1)*
Name
angular frequency
time
relaxation time or retardation time
complex dynamic shear viscosity
Name
Units
Name
Symbol
Dimensions
hertz or radians
per second
second
second
Pascal second
Hz
rad/s
s
s-1
-
,-I.
second
second
poise
S
-
cm’ dyne-i
-
cm* dyne-i
S
Pass
kg. s-2
s-1
s
dyne. s. cm-2
or N .s/m*
‘I’
I!
?
B’
dynamic viscosit.y
out-of-phase component of n*
bulk dynamic complex compliance
-
Pa-i
m.kg-l.s2
or (m’/N)
B'
B"
B(t)
D*
D'
D"
L'(t)
bulk storage compliance
bulk loss compliance
bulk creep compliince
tensile dynamic complex compliance
tensile storage compliance
tensile loss compliance
tensile creep compliance
-
Pa-i
m-kg-r.s*
or (m*/N)
E’
E”
E(t)
G*
G
G”
G(t)
J*
J’
J”
JO)
K”
K’
K”
K(t)
Ir’
*’
d’
tensile dynamic complex modulus
Pascal
Pa
rn-r.kgsor (N/m’)
tensile storage modulus
tensile loss modulus
tensile relaxation modulus
complex dynamic shear modulus
Pascal
Pa
m-‘*kg-s*
or (N/m*)
shear storage modulus
shear loss modulus
shear relaxation modulus
complex dynamic shear compliance
shear storage compliance
shear loss compliance
shear creep compliince
bulk dynamic complex modulus
bulk storage modulus
bulk loss modulus
bulk relaxation modulus
complex dynamic Poisson’s ratio
in-phase component of p*
out-of-phase component of p*
dyne cm-2
-
dyne cm*
2
-
Pascal
Pa’
Pa
dimensionless
rn*kg-r.sz
or (mz/N)
m-r-kg.0
or (N/m*)
-
cm’ dyne-r
%
isi
E
-
3
zz
dyne cm-
z
g
-
-
Nomenclature for Small Deformation Linear Elasticity
Unit.3
cgs System
SI System
Name
Name
Symbol
Symbol
Dimensions
Units
Name
Simple Shear
G
shear modulus; modulus of rigidity
Pascal
Pa
rn-i.kg-sF
or (N/m*)
J
shear compliance
-
Pa-i
makg-i-9
or (m*/N)
Bulk (Isotropic)
K
bulk modulus
Pascal
dyne cm+
-
cm* dyne-r
Compression
Pa
j:
-
dyne cm*
m-kg-i-d
or (m*/N)
-
cm’ dyne-i
,-I.
kg. s-I
or (N/mx)
B
bulk compliance
-
Pa-i
Tensile Extension
E
Young’s modulus (tensile modulus)
Pascal
Pa
m-l.kg-s*
or (N/m*)
-
dyne cm-
D
tensile compliance
-
Pa-*
mekg-i-s*
or (m’/N)
-
cm’ dyne-r
P
Poisson’s ratio
-
-
dimensionless
z
5
3
PROPOSED
NOMENCLATURE
317
available
(IZheoEogy, Vol. 4, Academic Press, New York, 1967).
Also, the systemization
of non-linear nomenclature
was considered
to be premature.
A future committee
should be organized to
consider this vital area of rheology.
The chairman wished to thank the committee members:
R. B. Bird
F. R. Eirich
R. A. Dickie
H. Markovitz
R. R. Myers
for their diligent efforts in compiling the nomenclature
list. Also,
the committee wishes to express its gratitude to the Society members
who made many thoughtful inputs to this endeavor.