474 - u - 



strain of atout 5'; which is not inconsistent with the measurea strains recorded in Figures 5 and 6 

 for the centre 1 ines. 



3. Strain measurements . 



To obtain estimates of permanent strain punch marks were made on the two centre-lines at 

 approximately 1 inch centres and rubDings of these marks taken before and a't;r trial. Owing to 

 the thinness of the plate these punch marks could only be lightly made and it was found that the 

 rubbings were not in general distinct enough to get sufficiently accurate measurements on 1 inch 

 intervals. The rubbings were accordingly measured up in successive over-lapping pairs at three 

 inch intervals, i.e. hetween punch marks 1 and u, 2 and 5, etc., since in this way errors duK to 

 ill-definition of rubbings contribute only one third the error to the mean strain as compared with 

 measurements over 1 inch gauge length. The mean strains in these successive overlapping thrio- 

 inch intervals arc shown plotted as ordinates in Figures 5 and 6 against tr.e mid-points of the 

 intervals as abscissa. Rubbings of several of the punch marks were too ill-defined to give any 

 reliable measurements and there are corresponding missing points in Figures 5 and 6; it is 

 unfortunate that punch marks near the edges comprised most of this category. 



Due to inaccuracy of measurement no significance can be attached to minor variations from 

 point to point on Figures 6 and 6 but on the other hand the general trend showing strain increasing 

 towards the edges is undoubtedly a result net arising from experimental error. This result was 

 rather unexpected since for an ideal plastic material yielding at a constant stress the analysis 

 of report A shewed the convi-rse effect that for both a circular and an elliptical plate the strain 

 decreases from a maximum at the centre to zero at the edges. A qualitative explanation of the 

 observed result can, however, be given if work hardening is taken into account. 



Thus if we consider an infinitely long plate under uniform lateral pressure each element 

 of the plate is constrained to have no movement parallel to the edges and if work hardens under 

 load the transverse strain will be a single-valued function of the transverse stress. This latter 

 will, however, be constant over the span, in order to satisfy the equation of equilibrium in the 

 place of the plate and thus the strain will also be constant over the span. To account for the 

 strain being actually greater at the edges than at the centre it is only necessary to assume that 

 due to the bolt-holes the plate is rather weaker near the edge, i.e. the stress-strain curve for 

 an element near the edge is assumed to lie below that for an element near the centre. Since 

 equilibrium will still demand a transverse stress constant over the span, a greater strain will 

 be produced at the edges than at the centre. The preceding explanation is regarded as tentative 

 since firstly. Figures 5 and 6 do not rule out the possibility of the strain decreasing rapidly 

 very near the edges and secondly, the theoretical result for no strain hardening quoted from report 

 A refers to a circular or an elliptical plate and the corresponding theoretical solution, yet to 

 be obtained, for a rectangular plate might yield a different result. 



4. Type of failure . 



The cause of cessation of trial, namely by shearing of a clamping bolt, was unexpected 

 since in explosion trials failure at the fixings takes place by tearing of the plate along the 

 line of bolt holes at the centre of one or both of the long edges. Moreover when failure does not 

 occur in explosion trials but the deflection is appreciable the bolt holes are always considerably 

 more elongated than in the static trial. 



It is not thought that the static failure was fortuitous due to a weak bolt since adjacent 

 Dolts were appreciably sheared and it would be improbable that the bolts used for the static trial 

 were v/eaker than any used in the many explosion trials. This apparent relative weakness of the 

 bolts may be due, however, to the fact that in the static trial the pressure was outwards and the 

 bolts were thus subjected not only to shear as in explosion trials but also to tension. If this 

 were the complete explanation it would be expected that that failure would have occurred at a 

 sitHller deflection in the static trial whereas in point of fact the static deflections both 

 inaximifm and mean were 10 - 201 greater than any that have been obtained in explosion trials 

 without rupture. It thus seems necessary to postulate, not only that the bolts have a possibly 

 lower resistance under the conditions of the static trial but that the plate has a lower 

 resistance at the bolt-holes in the explosion trials. Regarding this latter, the suggestion 

 offered is that in explosion trials the plastic wave set up in the clamped edge of the ptate by 

 the deflecting unsupported central portion has difficulty in traversing the relatively weak line 

 of bolt-holes. Consideration of such propagation of a plastic wave across a line of weakness 

 lies outside the scope of the present paper but is a problem it is hoped to consider in the future. 



