143 



A METHOD FOR DETERMINING THE ENERGY ABSORPTION 

 OF THIN STEEL DIAPHRAGMS UNDER HYDROSTATIC PRESSURE 



By M.A. Greenfield 



In Part I of the Progress Report (1 )* for TMB Research Project El 39, 

 dated February 19'+'+. it was stated that two Independent methods are used at 

 the David Taylor Model Basin to calculate the energy absorbed by a thin steel 

 diaphragm which has been deformed into a plastic state. The first method ex- 

 presses the energy in terms of the forces acting on the diaphragm. If p is 

 the pressure on the diaphragm and v is the volume bounded by the initial and 

 final positions of the diaphragm, then the work done on the diaphragm is jpdv. 



The second method expresses the energy in terms of the physical 

 properties of the steel and the measured strains corresponding to a given 

 deformation. 



Each method can be used either for statically or dynamically de- 

 formed diaphragms. 



The present report describes the second method in some detail. It 

 also gives a comparison of both methods as applied to a diaphragm which was 

 deformed by hydrostatic pressure. This diaphragm was l/8 inch thick and had 

 a diameter of 20 inches. 



Since the diaphragm is deformed plastically the following laws (2) 

 of plastic flow will be adopted in making the analysis. 



a. The directions of the principal extensions coincide with 

 those of the principal stresses at all times. 



b. The volume of the material remains constant. 



c. The principal shearing stresses remain proportional to 

 the corresponding 'principal shearing strains. 



Let cTj, a^, cTg be the true stresses and e^, e^, e .^ be the natural 

 strains. The natural strain is related to the conventional strain ? by the 

 relation 



6 = ln(l + ?) [T] 



Rule (b) may be expressed as 



and Rule (c ) as 



3] 



'"^ Niunbers in parenthesis indicate references at the end of 

 this paper. 



