129 



PLASTIC DEFORMATION OF AND ABSORPTION OP ENERGY 

 BY THIN CIRCULAR PLATES UNDER NORMAL LOADING 



By A.N. Gleyzal 



INTRODUCTION 



The deformation of thin circular plates by static and by explosive 

 pressures has been the subject of Intensive Investigation at the David Taylor 

 Model Basin (15) (10) (14)* In this connection tests have been made on metal 

 diaphragms rigidly supported at the rim and subjected to static pressures on 

 one face. Two quantities derivable from the test results are of particular 

 interest. These are the deflection of a diaphragm at its center and the en- 

 ergy required to deform a diaphragm as it distends under static pressure. 



It was believed that unification of the test results on the basis 

 of these two quantities for diaphragms of different dimensions and material 

 could be accomplished by plotting the quantities in terms of non-dimensional 

 coordinates involving the dimensions, and perhaps the yield stress or the ul- 

 timate tensile strength of the material as obtained from tensile tests. Rea- 

 sonably good predictions of deflection and of energy absorbed for any thin 

 circular plate under pressure might be possible from curves based on these 

 selected coordinates, provided the material of the plate had a plastic be- 

 havior similar to that of the plates used in the tests. Predictions of high 

 accuracy would be expected for plates of materials similar to those tested. 

 With these considerations in mind data on diaphragms of different materials 

 are reported here and analyzed. 



THEORETICAL CONSIDERATIONS 



Deflection measurements on the circular plates show that, for stat- 

 ic pressures of sufficient magnitude to cause plastic flow, the plates form 

 very nearly spherical caps. Thus, for a particular pressure, the tension is 

 nearly constant throughout the plate. Moreover, calculations show that this 

 tension tends to be constant as the pressure is increased; this constancy may 

 be ascribed to the balancing of two effects; i.e., the strain-hardening of 

 the material and the decrease of thickness as the pressure is increased. Thus 

 under sufficiently large pressures the thin plates act somewhat as membranes 

 with constant tension. 



Suppose pressure Is applied, as in Figure 56, to one face of a cir- 

 cular membrane with tension r.** It may readily be shown (15) that the pres- 

 sure p and the center deflection z are related by the equation 



Numbers in parenthesis indicate references at the end of this paper. 



In a thin plate the tension at a point is the product of the thickness 

 and the stress at the point 



