132 ^5 



The existence of unique pressure-deflection or energy-deflection 

 curves for Inflnlteslmally thin plates may be rigorously based on a concept 

 of afflne materials (l6) defined as follows: Two materials A and B are said 

 to be afflne If for any pair of strain states e and t the ratio of corre- 

 sponding stresses is the same for both materials. 



This Is expressed by 



l(«l> «2. «3^ '^B^^V ^2' ^3^ 



where tj, t^, e, are the principal strains in the first state c, 



€j, €2, fg are the principal strains in the second state e', and 

 a ^ and a ^ are the corresponding stresses in materials A and B 

 respectively. 



In the case of uniaxial stresses for example, If LCe) is the load-strain curve 

 for material A, then the load-strain curve for material B must be pL{e), where 

 p is a constant. 



With the help of this notion of afflne materials, a logical basis 

 for the identity of the pressure-deflection and energy-deflection curves may 

 be established for thin circular plates of different radius, thickness, and 

 material. This notion can also serve as a basis for predicting the plastic 

 behavior of other types of structures from the action of a model of different 

 material. When models of the same material are used in a static test quite 

 accurate predictions can be expected for plastic action even from models far 

 removed in scale. The choice of a set of plasticity laws is not required In 

 such an analysis. 



TEST RESULTS 



The quantities of interest to be Introduced as observed values are 

 the dimensions of the plate, the ultimate tensile strength of the material, 

 and the central deflection of the plate as a function of the applied pressure. 

 The apparatus for deforming the diaphragms has been described elsewhere (lU) 

 (15 )■ The tensile strength was measured for a specimen cut from the same 

 stock used to make the diaphragm. The ultimate stresses are given in Table 6, 

 with other information on the diaphragms. 



In Figure 37. for purposes of comparison of different metals, the 

 quantity L/L^, load divided by ultimate load In a tensile test, is plotted on 

 a basis of strain. Values were obtained from tests on specimens taken from 

 the same stock as the plates. 



To unify the pressure-deflection data for the different specimens 

 the non-dimensional quantities derived in the foregoing have been used. 



