Tak.in,t; a:lvanta[:" of the i;!ri:::T: of ey-P'Trinon'-ril ■l-xt". :v.'-.i] -vA't at 

 Nl'UnC, curves v;ore dovolopod rulatip;;: th- r-J.io o;' iV/[\r '.o i? ;.;p/'V , 

 rui- ;.'iac;ii nod , KlrcGi^-relived, and as f.-Jjricauud lif.irisphor'is . '.vith 

 these curver. av;'.Jlablp, it is passible to develop prediction type curves 

 by first assii'nii:^ coll£:;:;e depths ar.d thle';nesses - thus sfjlvinj* for 

 cllov.'aMe deviations in sphericity /.Ai^ , this can th.en be plotted as a 

 far:ily of curves relati:v^ thickness or 'vei;jht-to-displacev.':nt ratio 

 (\'j/\S)to A • -y cross plotting froni this ftsiily of curves it is possible 

 to develop curves relatir.g collapse depth to WyP) ratio for a rjlven or 

 assuruei^ A. 



This s;une procedure i-.'as utilized herein for studying ALVIfi. Fig 1 

 shov;s the eriiplrical reduction factor curve based on U'i-l'JO - ;!i-150 steels, 

 (strain hardening materials) , The curves shown are the ].o.;or boi/nd 

 envelopes of experimental results froifi machined, stress reli.&ved and 

 ncn stress relieved riOd-;l3. It should be noted that the non stress 

 relieved models vere fabricated frori pressed petals thus they contain a 

 consii'erable number of jeaTii welds anJ larj^/j areas of residi^al \iol.'lin;^ 

 stresses. In Figures 2 and 3, ai-e presented typical stress strain curves 

 and plasti'city factor cr.rves, for titanium. Utilizing the curves of 

 Fi£7Jres 1, 2, and 3 the curve of Fig-iU^es l can be developed (as described 

 aoove) v.-hich relate Ai t.^v'-Z/j-^ratio for give.'i coilr;.pse depths. Figure A 

 is only one of a number of such curves that v;e:e d',veloped for different 

 collapse depth. P^inally the curves of Fij^ire 5 '.vere developed by cross 

 plotting from t'ne curve cf Figure /,, an 2 the ot}:er :;u:iil,ar curves for 

 ether collapse depths. 



