Abstract
Birefringent coatings carry a portion of the load that would otherwise be carried by the structure. Thus, strains at the structure-coating interface are somewhat less than those in an uncoated part. In addition, strain gradients through the coating thickness must be taken into account to determine the surface strains that would be developed in an uncoated part. Correction factors are derived for plane stress, flexure of plates, torsion of shafts and cylindrical pressure vessels, and the case of combined plane and flexural loads is treated. For plane and flexural loading, the correction factors are equally applicable to regions surrounding common geometrical discontinuities.
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Abbreviations
- x,y,z :
-
cartesian coordinates; principal directions
- dx, dy :
-
infinitesimal elements of length inx andy directions
- t :
-
thickness
- σ:
-
normal stress
- ε:
-
normal strain
- E :
-
modulus of elasticity
- ν:
-
Poisson's ratio
- C 1 ,C 2 ,C 3 ,C 4 :
-
correction factors
- R :
-
radius of curvature of neutral surface
- δ:
-
distance between neutral surface and interface
- γ:
-
thickness ratiot c /t s
- M :
-
bending moment per unit width of plate
- α:
-
see eqs (8) and (19a)
- β:
-
see eq (10a)
- \(\bar \varepsilon\) :
-
integrated value of ε through coating thickness
- T :
-
torque
- a,b,c :
-
radii, see Figs. 4 and 6
- L :
-
length, see Fig. 4
- ϕ:
-
angle of twist
- J :
-
polar moment of inertia
- G :
-
shear modulus of elasticity:\(G = E/2\left( {1 + v} \right)\)
- ρ:
-
radial coordinate for cylindrical shafts
- r,θ,Z :
-
cylindrical coordinates
- P :
-
internal pressure
- Q :
-
pressure at structure-coating interface for coated pressure vessel
- x,y,z :
-
pertaining to values in thex,y,z directions
- 0:
-
pertaining to a structure having no coating
- s :
-
pertaining to the structural part in a composite structure-coating member
- c :
-
pertaining to the coating in a composite structure-coating member
- (s,c):
-
pertaining to both the structure and coating in a composite member
- r,θ,Z :
-
pertaining to values in ther,θ,Z directions
References
Zandman, F., “Analyse des Contraintes par Vernis Photoelastique” (“Stress Analysis with Photoelastic Coatings”), Groupement pour l'Avancement des Methodes d'Analyse des Contraintes (French SESA), 2, No. 6, 1956 (oral presentation 1955).
Zandman, F., and Wood, M. R., “PhotoStress, a New Technique for Photoelastic Stress Analysis for Observing and Measuring Surface Strains on Actual Structures and Parts,” Product Engineering, 167–178 (Sept. 1956).
Zandman, F., “Stress Analysis of a Guided Missile Tail Section with the Photoelastic Coating Technique,” Proc. SESA,XVII,No. 2 (1960).
Post, D., and Zandman, F., “The Accuracy of the Birefringent Coating Method for Coatings of Arbitrary Thickness,” XVIII,No. 1 (1961).
Timoshenko, S., andMacCullough, G. H., “Elements of Strength of Materials,”D. Van Nostrand Co., Inc., N. Y. (1949).
Zandman, F., Redner, S., and Riegner, E. I., “Partial Evaluation of the Photoelastic Coating Technique and discussion of Some Special Cases,” Tatnall Measuring Systems Co. Report, Phoenixville, Pa. (1958).
Timoshenko, S., “Strength of Materials,”II, D. Van Nostrand Co., N. Y. (1949).
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formerly Tatnall Measuring Systems Co.
E. I. Riegner, formerly with Budd, is now associated with Vertol Division of Boeing Co.
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Zandman, F., Redner, S.S. & Riegner, E.I. Reinforcing effect of birefringent coatings. Experimental Mechanics 2, 55–64 (1962). https://doi.org/10.1007/BF02325694
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DOI: https://doi.org/10.1007/BF02325694