Abstract
If a viscoelastic body is in a stressed state, then relaxation of all constraints will cause it to assume a different configuration in the final unstressed condition. Thus one sees a general elastic recovery. The term ‘recoverable strain’ is usually used more restrictively. Suppose a sample is undergoing a steady shear flow at shear rate. γ, where the first normal stress difference is N1 and the shear stress is σ. If the shear stress is annihilated at t = 0, and the normal force constraints are maintained, then the sample will recoil in shear. Suppose the bottom plate defining the shear sample (z = 0) is fixed, and the top layer of fluid (z = h) recoils through a distance d; the sample thickness is maintained at h always, so the elastic recoil is constrained.1 For a Lodge—type rubber—elastic liquid,.1 we can show that
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Abbreviations
- a :
-
constant
- C-1 :
-
strain tensor
- d :
-
recoil distance
- D :
-
die diameter
- D ∞ :
-
final diameter of extrudate
- D :
-
rate of strain tensor
- F 0, F 1 :
-
deformation gradients
- G :
-
modulus
- h :
-
thickness
- h f :
-
final sheet half-thickness
- h i :
-
see Fig. 4.2
- i :
-
unit vector along x-direction
- I :
-
unit tensor
- L :
-
die length
- L :
-
velocity gradient
- m :
-
stretching parameter (eqn (4.34))
- n :
-
shear-thinning (power law) index
- N 1 :
-
first normal stress difference
- p :
-
pressure
- P :
-
pressure gradient
- R i, R 0 :
-
pressure gradient
- R :
-
inside and outside radii
- S R :
-
recoverable shear (eqn (4.1))
- S :
-
parameter = (t — t’)
- t, t’ :
-
times
- t :
-
traction vector (Fig. 4.5)
- U :
-
potential
- v :
-
velocity vector
- w̄:
-
mean speed in tube
- W :
-
potential function
- W e :
-
Weissenberg number λẏw
- x :
-
present position vector
- x* :
-
position vector
- y :
-
coordinate
- β :
-
neo-Leonov parameter (eqn. (4.31))
- γ :
-
shear strain
- γ ∞ :
-
recoil strain
- ẏ:
-
shear rate
- ẏm :
-
mean shear rate in die (8w̄ for tube)
- Δ/Δt :
-
(upper) convected derivative symbol (eqn (4.25))
- ε :
-
PTT parameter (eqn (4.27))
- ε̇:
-
elongational rate of strain
- η :
-
viscosity
- η E :
-
Trouton or elongation viscosity
- λ :
-
relaxation time
- ∧ :
-
ratio of lengths, sideways swelling
- µ :
-
rigidity
- ζ :
-
PTT parameter (eqn (4.27))
- σ :
-
shear stress
- σ :
-
stress tensor
- τ :
-
extra stress tensor (eqn (4.23))
- ϕ :
-
Leonov function
- χ :
-
swelling ratio ( = D f/D)
References
A. S. Lodge, Elastic Liquids, Academic Press, London, 1964.
J. J. Benbow and E. R. Howells, Polymer, 1961, 2, 429.
R. I. Tanner, Engineering Rheology, Oxford University Press, 1985.
W. W. Graessley, S. D. Glasscock and R. L. Crawley, Trans. Soc. Rheol., 1970, 14, 519.
A. S. Lodge, D. J. Evans and D. B. Scully, Rheol. Acta, 1965, 4, 140.
R. I. Tanner, J. Polym. Sci. (A2), 1970, 8, 2067.
L. A. Utracki, Z. Bakerdjian and M. R. Kamal, J. Appl. Polym. Sci., 1975, 19, 481.
D. C. Huang and J. L. White, University of Tennessee, Polymer Science and Engineering Report No. 113, 1978.
J. R. A. Pearson and R. Trottnow, J. Non—Newt. Fluid Mech., 1978, 4, 195.
H. B. Phuoc and R. I. Tanner, J. Fluid Mech., 1980, 98, 253.
R. I. Tanner, J. Non—Newt. Fluid Mech., 1980, 6, 289.
M. J. Crochet, A. R. Davies and K. Walters, Numerical Simulation of Non Newtonian Flow, Elsevier, Amsterdam, 1984.
M. B. Bush, R. I. Tanner and N. Phan-Thien, J. Non—Newt. Fluid Mech., 1985, 18, 143.
M. J. Crochet and R. Keunings, J. Non—Newt. Fluid Mech., 1982, 10, 85.
A. I. Leonov, Rheol. Acta, 1976, 15, 85.
R. Larson, Rheol. Acta, 1983, 22, 435.
H. Giesekus, Proc. IX Int. Congr. Rheol., B. Mena et al. (Eds), Elsevier, Amsterdam, Vol. 1, 1985, p. 39.
R. I. Tanner, R. E. Nickel and R. W. Bilger, Computer Meth. Appl. Mech. Eng., 1975, 6, 155.
J. Meissner, Pure Appl. Chem., 1975, 42, 553.
R. I. Tanner, in Numiform ’86, Proc. Second Int. Conf. on Numerical Methods in Industrial Forming Processes, Gothenburg, 1986, A. Samuelsson et al. (Eds), Balkema, Rotterdam, p. 59.
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© 1993 Springer Science+Business Media Dordrecht
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Tanner, R.I. (1993). Recoverable Elastic Strain and Swelling Ratio. In: Collyer, A.A., Clegg, D.W. (eds) Rheological Measurement. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2898-0_4
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