Analytical technique is developed for prediction of reverse buckling in thin curved shells. Test data indicate technique predicts actual reverse buckling pressure within 10 percent, and should be useful for analytical prediction of reversed condition failure for problems such as explosive decomposition through vacuum failure

Martindale, D. L.

Urbanac, C.

English

NASA Technical Reports Server

rTh 
Hoop 
Direction 
Die First Stage
December 1970	 Brief 70-10582 
NASA TECH BRIEF 
NASA Tech Briefs announce new technology derived from the U.S. space program. They are issued to encourage commercial 
application. Tech Briefs are available on a subscription basis from the National Technical Information Service, Springfield, 
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nology Utilization Division, NASA, Code UT, Washington, D.C. 20546. 
Analytical Prediction of Reverse Buckling Pressure for Thin Shells 
Upper Die Cavity 
Oil Pressure
Die
Meridional 
Direction 
Oil Pressure 
Lower Die Cavity 
Second Stage
Elongational Directions 
	
An analytical technique has been developed for the 	 forming and reverse snap buckling pressures and the 
	
prediction of reverse buckling in thin curved shells.	 dome heights. The elongation in the shell takes place 
	
Empirical equations were obtained froni burst-disk
	 in the meridional and hoop directions (see fig.); merid-
	
testing. Major considerations were material, material	 ional and hoop elongations were assumed to be 
	
thickness, dome diameter, dome height, forming	 equal, then combined and subtracted from the initial 
	
pressure, and reverse buckling pressure. Test data	 material elongation to provide a residual elongation. 
	
indicated that this technique predicts the actual reverse	 The residual elongation was used to determine the 
	
buckling pressure within 10%, and should be of use 	 equivalent yield stress from data (a curve) established 
	
for analytical prediction of reversed condition failure 	 from other research (see Ref.). The forming pressure 
	
for problems such as explosive decomposition through 	 required could then be calculated from the equation 
vacuum failure. 	 for a hemispherical pressure vessel. 
	
This method is based on empirical information ob-	 The reverse snap buckling pressure is a nonlinear 
	
tained from tests in forming hemispheres by extrap-	 function; an empirical curve was established, but was 
	
olation from test data on reverse snap buckling of the 	 limited to a geometrical parameter A equal to ten 
	
hemisphere. Initial data were obtained oo elongation 	 where A is a nondirnensional ratio of the chord, 
	
and yield strength of Inconel 600 foil along with the 	 thickness, radius and Poissons ratio. For the tech-
(continued overleaf) 
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Government nor any person acting on behalf of the United States
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nique 'being described, A varied from 30 to 44, but 
combined data indicated a good correlation. 
Chord lengths were obtained by measuring the 
reflected image of the hemisphere on a comparator, 
and the material thickness was obtained by measuring 
with pin micrometers. The radius, half angle, and arc 
length were calculated from equations. The dome-
wall (diaphragm) thickness from the chord to the 
crown varied from approximately 17% to 33% respec-
tively. The mean thickness value was empirically deter-
mined to be at the centroid of the dome where one-
half the included angle is equal to 38°. This averages 
out to 23.5% thinning of the initial material thick-
ness. The variations in thinning from chord to crown 
indicate that the cold work varies directly as the 
thinning rate. For these reverse buckling calculations, 
the empirical thinning value of 23.5% indicated reverse 
buckling pressures within 10% of tested values. 
Reference: 
Kaplan, A.; and Fung, Y. C.: A Nonlinear Theory 
of Bending and Buckling of Thin Elastic Shallow 
Spherical Shells, NASA-TN-3212, 1954.
Notes: 
I. Future mathematical solutions will be developed 
to predict the individual thinning value. Additional 
testing and refinement of the equations should 
enhance the accuracy in predicting the forming 
and reverse snap buckling pressures. 
2. Requests for further information may be directed 
to:
Technology Utilization Officer 
Kennedy Space Center 
Code AD-PAT 
Kennedy Space Center, Florida 32899 
Reference: B70-10582 
Patent status: 
Inquiries about obtaining rights for the commercial 
use of this invention may be made to: 
Patent Counsel 
Mail Code AD-PAT 
John F. Kennedy Space Center 
Kennedy Space Center, FL 32899 
Source: C. Urbanac and D. L. Martindale of 
AMETEK/Straza
under contract to

Kennedy Space Center
(KSC-105 IS)
1^1 
. 
Brief 70-10582	 Category 06


Analytical prediction of reverse buckling pressure for thin shells

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