Abstract
Body forces generated in photoelastic coatings bonded to rotating metallic parts affect the deformation in the parts. This effect becomes considerable when the coating thickness approaches that of the part. As a result, the observed photoelastic strain pattern is not truly indicative of the strains that would be present in an uncoated part. This interaction is considered analytically and experimentally for the case of a flat circular disk with a central hole when the coating covers the entire disk area and (a) coatings of equal thickness are bonded to both sides of the test part, and (b) the coating is bonded to only one side of the test part. Correction factors are derived which are applicable to problems where the strain field is axisymmetrical. The applicability of the derived correction factors in the vicinity of stress concentrations in the rotating part is considered.
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Abbreviations
- r, z, θ:
-
polar coordinates
- t :
-
thickness
- σ:
-
normal stress
- ε:
-
normal strain
- ρ:
-
mass density
- E :
-
modulus of elasticity
- ν:
-
Poisson’s ratio
- γ:
-
thickness ratio,t c /t s
- Φ:
-
mass-density ratio, ρ c / ρ s
- ω:
-
rotational speed (radians per second)
- u :
-
radial displacement at radiusr
- α:
-
see eqs (2a) and (7c)
- \(\bar \in \) :
-
integrated value of ε through coating thickness
- a, b :
-
inner and outer radii of disc
- Ψ:
-
ratio of inner to outer radii,a/b
- X :
-
ratio of variable radius to outer radius,r/b
- N 1 :
-
correction factor for coatings on two sides of part
- f :
-
fringe value of coating (μin./in./fringe)
- K :
-
stress-concentration factor
- F :
-
body force
- δ:
-
distance between neutral surface and interface
- C :
-
bending correction factor from Ref. 2 [see eqs (7a) and (7d)]
- M :
-
bending moment per unit length
- T :
-
body moment [see Fig. 12 (b)]
- T′:
-
see eq (9a)
- D :
-
flexural rigidity of a plate [eq (10a)]
- w :
-
deflection of plate
- ϕ:
-
slope of plate-deflection surface
- N 2 :
-
see eq (18)
- R :
-
derived correction factor for coating on one side of part
- O :
-
denotes structure with no coating
- C :
-
denotes coating on a coated part
- F :
-
denotes body force acting in neutral surface
- T :
-
denotes body moment acting about neutral surface
References
T. C. Lee, C. Mylonas andJ. Duffy, “Thickness Effects in Birefringent Coatings with Radial Symmetry,”and Discussion by Zandman, Proceedings SESA, Vol. 18, No. 2, 1961, 134–142.
S. Timoshenko, “Strength of Materials Part II,” D. Van Nostrand Co. Inc., New York, N. Y.
S. S. Redner, “New Oblique Incidence Method for Direct Photoelastic Measurement of Principal Strains and Related Problems,”Experimental Mechanics,3 (3),1963,67–72.
T. C. Ku, “Stress Concentration in a Rotating Disc with a Central Hole and Two Additional Symmetrically Located Holes,” ASME, June 1960.
F. Zandman, S. S. Redner andE. I. Riegner, “Reinforcing Effect of Birefringent Coatings,”Experimental Mechanics,2 (2),1962,55–64.
D. Post andF. Zandman, “Accuracy of the Birefringent Coating Method for Coatings of Arbitrary Thickness,”Proceedings SESA, Vol. 18, No. 1, 1961, 21–32.
F. Zandman, S. S. Redner andD. Post, “Photoelastic Coating Analysis in Thermal Fields,”Experimentil Mechanics,3 (9),1963,215–221.
J. Duffy, “Effects of the Thickness of Birefringent Coatings,”Proceedings SESA, Vol. 18, No. 1, 1961, 74–82.
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Nickola, W.E. Photoelastic coatings on flat rotating axisymmetrical parts. Experimental Mechanics 4, 99–109 (1964). https://doi.org/10.1007/BF02324938
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DOI: https://doi.org/10.1007/BF02324938