169 



slope of the instantaneoua profile of the diaphragm. As the wave sweeps 

 over each annular material element in the flat central region, in effect 

 it tilts it into the shape of an annular trtincated conical element behind 

 the wave. During this process, it is assumed that, because of the thinness 

 of the diaphragm, no significant amount of work is done in bending. Moreover, 

 no impulsive thinning is supposed to take place in the bend of the wave. We 

 further suppose that the only streeses of importance at the bending wave are 

 radial and circumferential principal stresses just ahead of the wave, and 

 behind the wave in the tilted region, a normal sttfess component along the 

 generator of the tilted element, a shear stress component, and a circumferential 

 normal stzess component. 



Now the material passed over by the wave shall be supposed to have 

 come to rest. The stresses v/hich exist in this region are supposed to be 

 such as to just hold the material in equilibrium - although their tendency 

 to cause further plastic flow or not is a subject for further investigation, 

 and might constitute a partial theoretical test of the model. 



'tiithin the central region which is as yet unaffected by the 

 plastic bending wave, the diaphragm is still supposed to be flat, and therefore 

 in the absence of normal force components it reta 'jis its uniform normal 

 velocity v. At the same tine, the material in the flat central region is 

 supposed to be flowing radially outward and thinning. To avoid the extreme 

 complexities of considering the probably non-uniform distributions of tension 

 and thinning in an actual diaphragm, we introduce in this region a distribu- 

 tion of constraint forces which do no work and which produce a uniform thinning 

 over the region during the motion. These constraints must be considered to 

 yield a non-uniform stress system which is superimposed on the streeses arising 

 from the uniform plastic deformation of this region.* Their 



♦Henceforth these latter are denoted as "plastic stress<,s" to distinguish them 

 from the stresses arising from the constraints. 



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