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Thermal stresses on the surface of tube-sheet plates of 10 and 33 1/3 percent ligament efficiency

Details of the experimental techniques employed are presented, together with the assumptions and calculations required to obtain the variation with time of the stresses at the ligament edges on the tube-sheet surface

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Abstract

A thermal shock ΔT was applied to the surface of tube-sheet models of 10 percent and 33 1/3 percent ligament efficiency. By means of a thin slice cemented with a reflective cement, it was posible to obtain photo-elastically the surface-stress variation with time. By extrapolation, maximum stresses of 0.93 and 1.04\(E_p \alpha _p - \Delta T_p /(1 - v_p )\) were obtained at zero time for the 10 percent and 33 1/3 percent ligament efficiencies, respectively.

Details of the experimental techniques employed are presented, together with the assumptions and calculations required to obtain the variation with time of the stresses at the ligament edges on the tube-shee surface.

Using the effective elastic constants and stress-intensification factors for tube sheets subjected to isotropic biaxial-plane stress, thermal stresses of 1.18 and 1.31\(E_p \alpha _p \Delta _p \Delta T_v /(1 - v_p )\) were calculated for ligament efficiency of 10 and 33 1/3 percent, respectively. It is felt that these are uppe limits for the thermal stresses.

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Abbreviations

x, y :

coordinates in the plane of the surface

ϕ:

angular position around a hole, measured fromy-axis

z :

coordinate perpendicular to plane of surface

H :

thickness of reflelctive slice

t :

model time

t p :

prototype time

T :

temperature of model at any distancez at any timet

T 0 :

initial ambient temperature

T−T 0 :

temperature change, °C

T s :

Temperature of surface

T a :

average temperature betweenz=0 andz=H

ΔH :

T s =T 0 , thermal shock in model, ° C

ΔT p :

thermal shock in prototype, ° C

f :

model material fringe value, psi/fringe/in

E :

model modulus of elasticity, psi

α:

model coefficient of thermal expanison, in./in./° C

ν:

model Poisson’s ratio

E p ,α p ,v p :

prototype constants

n 0 :

initial fringe order at ligament edges

n t :

fringe order at ligament edges after thermal shock

n ea :

n t −n o , fringe order averaged through thicknessH

σ ea :

stress at ligament edge averaged through thicknessH

σ es :

(Ts/Ta)σ ea = ligament edge stress at surfacez=0

σ p :

prototype stress at ligament edges on the surface

m/m p :

ratio of thermal diffusivity of model to prototype

v*,E*:

effective elastic constants for tube sheets

F x=y :

stress-intensification factor for tube sheets subjected to plane-biaxial stressσ x =σ y

\((\sigma _\phi /\sigma _y )_{x = y}\) :

ratio of hole-boundary stress to hominal plane biaxial stress,σ x =σ y , based on unperforated plate

References

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Authors and Affiliations

  1. Westinghouse Research Laboratoires, Pittsburgh, Pa.

    M. M. Leven & R. L. Johnson

Authors
  1. M. M. Leven
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  2. R. L. Johnson
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Leven, M.M., Johnson, R.L. Thermal stresses on the surface of tube-sheet plates of 10 and 33 1/3 percent ligament efficiency. Experimental Mechanics 4, 356–365 (1964). https://doi.org/10.1007/BF02322794

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  • DOI: https://doi.org/10.1007/BF02322794

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