Thermal stresses were studied in freezing of biomaterials containing significant amounts of water. An apparent specific heat formulation of the energy equation and a viscoelastic model for the mechanics problem were used to analyze the transient axi-symmetric freezing of a long cylinder. Viscoelastic properties were measured in an Instron machine. Results show that, before phase change occurs at any location, both radial and circumferential stresses are tensile and keep increasing until phase change begins. The maximum principal tensile stress during phase change increases with a decrease in boundary temperature (faster cooling). This is consistent with experimentally observed fractures at a lower boundary temperature. Large volumetric expansion during water to ice transformation was shown to be the primary contributor to large stress development. For very rapid freezing, relaxation may not be significant, and an elastic model may be sufficient.
Issue Section:
Research Papers
1.
Aklonis, J. J., and MacKnight, W. J., 1983, Introduction to Polymer Viscoelasticity, Wiley, New York.
2.
Chen, P., and Fridley, R. B., 1972, “Analytical method for determining viscoelastic constants of agricultural materials,” Transactions of the ASAE, pp. 1103–1106.
3.
Choi, Y., 1985, “Food thermal property prediction as affected by temperature and composition,” Ph.D. thesis, Purdue University.
4.
Christensen, R. M., 1971, Theory of Viscoelasticity, An Introduction, Academic Press.
5.
Chuma, Y., Uchida, S., and Shemsanha, K. H. H., 1983, “Cryogenic properties of fruits and vegetables,” Transactions of the ASAE, pp. 1258–1263.
6.
Comini, G., Bunacina, C., and Brina, S., 1974, “Thermal properties of food-stuffs,” Bull. Int. Inst. Refrig., Annexe, 3:163.
7.
Diller
K. R.
1992
, “Modeling of bioheat transfer processes at high and low temperature
,” Advances in Heat Transfer
, 22
:177
–357
.8.
Fahy
G. M.
Saur
J.
Williams
R. J.
1990
, “Physical problems with the vitrification of large biological systems
,” Cryobiology
, 27
:492
–510
.9.
Fennema, O., Powrie, W. D., and Marth, E. H., 1973, Low-Temperature Preservation of Foods and Living Matter, Marcel Dekker, New York.
10.
Finney
E. E.
Hall
C. W.
1967
, “Elastic properties of potatoes
,” Transactions of the ASAE
, 10
:4
–8
.11.
Fung, Y. C., 1990, Biomechanics: Motion, Flow, Stress, and Growth, Springer-Verlag.
12.
Gold, L. W., and Sinha, N. K., 1980, “The rheological behavior of ice at small strains,” in: Physics and Mechanics of Ice, P. Tryde, ed., pp. 117–128.
13.
Hamza
H.
Muggeridge
D. B.
1984
, “An analysis of the viscoelastic fracture toughness and crack growth in ice
,” Cold Regions Science and Technology
, Vol. 9
, pp. 249
–258
.14.
Hunt
C. J.
Song
Y. C.
Bateson
E. A. J.
Pegg
D. E.
1994
, “Fractures in cryopreserved arteries
,” Cryobiology
, Vol. 31
, pp. 506
–515
.15.
Kim, N.-K., 1993, “Mathematical modeling of cryogenic food freezing,” Ph.D. Dissertation, University of Georgia.
16.
Kim
N. K.
Hung
Y. C.
1994
, “Freeze-cracking in foods as affected by physical properties
,” Journal of Food Science
, Vol. 59
, pp. 669
–674
.17.
Kroener
C.
Luyet
B.
1966
, “Formation of cracks during the vitrification of glycerol solutions and disappearance of the cracks during rewarming
,” Biodynamica
, Vol. 10
, pp. 48
–52
.18.
Laverty, J., 1991, “Physio-chemical problems associated with fish freezing,” in: Food Freezing: Today and Tomorrow, W. B. Bald, ed., Springer-Verlag, London.
19.
Lin
S.
Gao
D. Y.
Yu
X. C.
1990
, “Thermal stresses induced by water solidification in a cylindrical tube
,” ASME Journal of Heat Transfer
, Vol. 112
, pp. 1079
–1082
.20.
Mellor
M.
Cole
D. M.
1982
, “Deformation and failure of ice under constant stress or constant strain-rate
,” Cold Regions Science and Technology
, Vol. 5
, pp. 201
–219
.21.
Michel, B., 1978, Ice Mechanics, Les Presses de L’universite´ Laval, Que´bec.
22.
Michel, B., 1980, “Mechanical model of creep of polycrystalline ice with cracking activity,” in: Physics and Mechanics of Ice, P. Tryde, ed., Springer-Verlag, pp. 246–264.
23.
Morrow
C. T.
Mohsenin
N. N.
1981
, “Consideration of selected agricultural products as viscoelastic materials
,” Journal of Food Science
, Vol. 31
(5)
, pp. 689
–698
.24.
Mott
L. F.
1964
, “The prediction of product freezing time
,” Australian Refrigeration, Air Conditioning and Heating
, 18
:16
–18
.25.
O¨zis¸ik, M. N., 1980, Heat Conduction, Wiley, New York.
26.
Pitt, R. E., 1992, “Viscoelastic properties of fruits and vegetables,” in: Viscoelastic Properties of Foods, M. A. Rao and J. F. Steffe, eds., Elsevier Applied Science, London.
27.
Rabin
Y.
Steif
P. S.
1996
, “Analysis of thermal stresses around a cryosurgical probe
,” Cryobiology
, 33
:276
–290
.28.
Rabin
Y.
Steif
P. S.
Taylor
M. J.
Julian
T. B.
Wolmark
N.
1996
, “An experimental study of the mechanical response of frozen biological tissues at cryogenic temperatures
,” Cryobiology
, 33
:472
–482
.29.
Rahman, S., 1995, Food Properties Handbook, CRC Press, Inc.
30.
Rao, M. A., and Steffe, J. F., 1992, Viscoelastic Properties of Foods, Elsevier Applied Science, New York.
31.
Rubinsky
B.
Cravalho
E. G.
Mikic
B.
1980
, “Thermal stresses in frozen organs
,” Cryobiology
, 17
:66
–73
.32.
Schapery, R. A., 1993, “Viscoelastic deformation behavior of ice based on micromechanical models,” in: Ice Mechanics, J. P. Dempsey et al., eds., ASME, pp. 15–33.
33.
Shi, X., 1996, “Thermomechanics of fracture in freezing of biomaterials.” Ph.D. Dissertation, Cornell University, Ithaca, NY.
34.
Shi, X., Datta, A. K., and Mukherjee, S., 1998a, “Thermal fracture in a biomaterial during rapid freezing,” Journal of Thermal Stresses, in press.
35.
Shi, X., Datta, A. K., and Throop, J., 1998b, “Mechanical property changes during freezing of biomaterials,” Transactions of the ASAE, in press.
36.
Spring
U.
Morland
L. W.
1982
, “Viscoelastic solid relations for the deformation of ice
,” Cold Regions Science and Technology
, 5
:221
–243
.37.
Thom
F.
Matthes
G.
Richter
E.
Hackensellner
H. A.
1983
, “The ductility of mammalian tissue in dependence on the deformation temperature
,” Cryo-Letters
, 4
:341
–348
.
This content is only available via PDF.
Copyright © 1998
by The American Society of Mechanical Engineers
You do not currently have access to this content.
