Abstract
The constraint associated with the direction of the thickness of a thin photoelastic circular-ring model is experimentally proved to occur and it is compared with the theoretical result; the constraint is induced by thermal loads. The method for dealing with the constraint and for obtaining a transient thermal stress under plane-stress conditions is applied to study the thermal stress of the circular ring partly cooled from the inside cylindrical surface. It is found that the thermal stress of the fully cooled circular ring is not always greater than the partly cooled one.
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Abbreviations
- B :
-
R 1 γ/k=Biot number
- E :
-
modulus of elasticity
- F :
-
ϰτ/R1 2=Fourier number
- f :
-
material fringe value
- J n(x):
-
Bessel function of first kind
- k :
-
thermal conductivity
- N e :
-
experimental fringe order
- N t :
-
theoretical fringe order
- P :
-
R 2/R 1
- P n :
-
eigenvalues of {pJ 1(p)+BJ 0(p)}/{pY 1(p)+BY 0(p)}=J 1(pP)/Y 1(pP)
- R 1 :
-
inner radius
- R 2 :
-
outer radius
- T :
-
temperature
- T i :
-
initial temperature of circular ring
- T * :
-
T/T i
- t :
-
thickness of circular ring
- Y n(x):
-
Bessel function of second kind
- α:
-
coefficient of thermal expansion
- γ:
-
convective-heat-transfer coefficient
- ϰ:
-
thermal diffusivity
- λ:
-
thickness-constraint coefficient
- ν:
-
Poisson's ratio
- ϱ:
-
r/R 1
- σ:
-
thermal stress
- σ* :
-
σ/αETi
- τ:
-
time
- ϕ:
-
cooled angle subscript 0=fully cooled circular ring
References
Burger, C.P., “Photoelastic Modeling of Stress Caused by Thermal Shock,”Experimental Mechanics,16 (3),95–99 (March 1976).
Iwaki, T. andMiyao, K., “Transient Thermal Stresses in a Strip with an Eccentric Hole,”Experimental Mechanics,24 (1),22–27 (March 1984).
Gerard, G. andGilbert, A.C., “Photothermoelasticity: An Exploratory Study,”J. Appl. Mech.,79 (3),355–360 (1957).
Rothstein, R.J. andKirkwood, W.F., “Photothermoelastic Analysis of Stresses in Multiconnected Flat Circular Rings,”Experimental Mechanics,4, (8),237–243 (Aug. 1964).
Tsukada, Y. andAmada, S., “An Improved Photoelastic Method for Thermal Stress Measurement,”Trans. Jap. Soc. Mech. Eng. (In Japanese),40 (332),926–933 (April 1974).
Tsuji, M., et al., “Photothermoelastic Investigation of Transient Thermal Stresses in Circular Plates, with a Hole Heated by Fluid,”Trans. Jap. Soc. Mech. Eng. (in Japanese),46, (405A),514–524 (May 1980).
Hirai, N. andSaito, A., “Photothermoelastic Measurement by Means of High Frequency Induction Heating Apparatus,”J. Thermal Stresses,6,153–165 (1983).
Iwaki, T., “Effect of Thickness of Circular Ring on Transient Photothermoelastic Experiment,”Trans. Jap. Soc. Mech. Eng. (in Japanese),52, (474A),332–337 (Feb. 1986).
Emery, A.F. et al., “Temperature Distributions and Thermal Stresses in a Partially Filled Annulus,”Experimental Mechanics,6 (12),602–608 (Dec. 1966).
Iwaki, T., “A Simple Measurement of Thermal Diffusivity,”Experimental Techniques,8, (8),20–21 (Aug. 1984).
Carslaw, H.S. and Jaeger, J.C., Conduction of Heat in Solids, Oxford University Press, 332–333 (1959).
Johns, D.J., Thermal Stress Analyses, Pergamon Press, 35–37, (1965).
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Iwaki, T. Transient thermal stresses in fully and partly cooled circular rings. Experimental Mechanics 26, 163–168 (1986). https://doi.org/10.1007/BF02320010
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DOI: https://doi.org/10.1007/BF02320010