Abstract

Transmissive windows designed to operate at low temperatures are subject to repeated thermal cycling, which may crack the window. This paper derives a simple expression for the stresses developed at the edge of a circular window. These stresses depend upon the lowest service temperature, the elastic moduli of window and holder, the mismatch in the coefficients of thermal expansion, and the holder and window thicknesses. For a given material pair, there is a critical holder thickness that will initiate fracture in the window. A graph is provided to facilitate the determination of holder thickness.

© 1973 Optical Society of America

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References

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  1. F. B. Hildebrand, E. Reissner, G. B. Thomas, “Notes on the Foundations of the Theory of Small Displacements of Orthotropic Shells,” NACA Technical Note 1833 (1949).
  2. V. Biricikoglu, A. Kalnins, Intern. J. Solids Structures 7, 431 (1971).
    [CrossRef]
  3. M. Goland, E. Reissner, J. Appl. Mech. 66, A-17 (1944).

1971 (1)

V. Biricikoglu, A. Kalnins, Intern. J. Solids Structures 7, 431 (1971).
[CrossRef]

1944 (1)

M. Goland, E. Reissner, J. Appl. Mech. 66, A-17 (1944).

Biricikoglu, V.

V. Biricikoglu, A. Kalnins, Intern. J. Solids Structures 7, 431 (1971).
[CrossRef]

Goland, M.

M. Goland, E. Reissner, J. Appl. Mech. 66, A-17 (1944).

Hildebrand, F. B.

F. B. Hildebrand, E. Reissner, G. B. Thomas, “Notes on the Foundations of the Theory of Small Displacements of Orthotropic Shells,” NACA Technical Note 1833 (1949).

Kalnins, A.

V. Biricikoglu, A. Kalnins, Intern. J. Solids Structures 7, 431 (1971).
[CrossRef]

Reissner, E.

M. Goland, E. Reissner, J. Appl. Mech. 66, A-17 (1944).

F. B. Hildebrand, E. Reissner, G. B. Thomas, “Notes on the Foundations of the Theory of Small Displacements of Orthotropic Shells,” NACA Technical Note 1833 (1949).

Thomas, G. B.

F. B. Hildebrand, E. Reissner, G. B. Thomas, “Notes on the Foundations of the Theory of Small Displacements of Orthotropic Shells,” NACA Technical Note 1833 (1949).

Intern. J. Solids Structures (1)

V. Biricikoglu, A. Kalnins, Intern. J. Solids Structures 7, 431 (1971).
[CrossRef]

J. Appl. Mech. (1)

M. Goland, E. Reissner, J. Appl. Mech. 66, A-17 (1944).

Other (1)

F. B. Hildebrand, E. Reissner, G. B. Thomas, “Notes on the Foundations of the Theory of Small Displacements of Orthotropic Shells,” NACA Technical Note 1833 (1949).

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Figures (3)

Fig. 1
Fig. 1

The geometry of the window and holder assembly.

Fig. 2
Fig. 2

Section of holder element.

Fig. 3
Fig. 3

The variation of maximum interface shear stress as a function of the holder thickness.

Equations (19)

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d / d r ( r S w ) - r N w = 0 ;
N w = E w h ( β - α w T ) ,
S w = G w h 3 / 12 · d β / d r ,
W w ( r , z ) = z β ( r ) .
γ 2 = 12 E w / h 2 G w
d / d r ( r d β / d r ) - γ 2 r ( β - α w T ) = 0 ,
β ( r ) = A I 0 ( γ r ) + α w T ,
N w = E w h A I 0 ( γ r ) ,
S w = γ G w h 3 / 12 · A I 1 ( γ r ) .
W w = h / 2 · [ A I o ( γ r ) + α w T ] .
d σ / d z = τ / t ,
σ = E ( d W / d z - α T ) .
W = α T h / 2 - S / 2 E t             ( z = h / 2 ) .
S = S w ( a ) ,
W = W w ( a ) .
A = ( α - α w ) T I 0 ( γ α ) + γ h ( G w h / 12 t ) I 1 ( γ a ) .
τ max = ( 6 t / h ) · G w ( α - α w ) T ( G w / E ) + ( 12 t / γ h 2 ) · [ I 0 ( γ a ) / I 1 ( γ a ) ] .
( γ h / 2 ) · G w ( α - α w ) T [ I 1 ( γ a ) / I 0 ( γ a ) ] .
Lexan tube with wall thickness t = 0.050 cm , τ = 4400 psi ; fiberglass tube with wall thickness t = 0.038 cm , τ = 939 psi .

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