RMZ – MATERIALI IN GEOOKOLJE

= ( (, ) + = (, () (, ) + )(, )) () ()336() = () () = () ()()(, )Kugler, G., Terčelj, M., Peruš, I., Turk, R.()( (), ) = ( (), ) = ( (, ) + (, ) + (, ))() ( = (), (, = ) = ) ( (), (, ) ) () () () ()The idea for ()reconstruction of()the step the system of linear or non-linear ( intermediate ()(, ) + shapes of the rod ((, ) + is equations must = be solved depending (), (, ) = ()) (), ) (, )on () () now = to find ()the approximate () = (, ) func- (, f(z,t) ) + ≈ r(z,t), () for (, which ) + selected function. The simplest()choice () ()( tion for ()(, ) the ) selection of function is certainlythe constant, which upon rotation ( (), () ) = ( (), ) () ( (), ) = ( (), ) = ( (), ) = (, )()( (), ) = ()()( (), ) = ( (), ) (6) around its axes forms cylinder. Unfortunatelythe conditions (7) and (8) can- (, )( + () (), ) (, =where (, l)c(t) is the length from the beginning of = ()not be fulfilled for approximation with = (, ( ) (), + ) ()(, )(, )) = (, )) therod ()to the ( (, ) () () () (), ) = ( (), ) = ( (), ) () end ofthe ()plastic cylinder. Besides that, the radius ofpart. Since the ()( (), contour of deformed rod curvature of the contour at the minimal is (, smooth, = ) = ( ) it immediately follows for cross-section is needed for calculationthe left end side= (, (), (, ) ) (, ) (, ) = (, ) = (, ))( (), ) = ( (), ) = ( (), ) () () () () () of the Bridgman stress correction, [1] ()but () ()for the approximation by cylinder this( (, = (, (), = ) = ( () (), (, )= ) ((, (), ) ) () (7) radius = (, )is infinite. On the other hand, for () () () = an arbitrary function this radius, R,can () = ()(, ) = (, ) () ()(, ))be calculated from ()( (, and for ) the right () = end (, one (), ) = ( (), ) = ( () (),) ) () () () (,(8) = ()(, ) (, )) = (, = (, )(, ) ) = (, (, ) () = ) () 1 + () 1 + () () () ()(10) ( (, ) () = (, ) ( )Due to the constancy () = (, )= of the volume () (, ) (, ) ( ) = during () plastic = ( deformation, ) = () (, ) it also 1 + () follows ) ( where r minis the minimal radius at time t.= (, ) () () (, ) (9) = 1 + ( = ( (, ) + ) = (, )) ( (, ) + (, ))( Calculation )= () = (, ) (, ) (, ) of stress-strain dependence ()1 + The value of (l c(t) ) = which must be greater ( After ) hot tensile testing the measurementsof deformed rods were carried = ( (, ) + (, )) (,than)the length(,of cylinder) () = (, ))of the same() = volume and 1 + ( (, ))radius ) = r = r(l l, t k) on one out by the measurement microscope, hand = ( and must (, ) be smaller + than (,() l d(t) ) on)which automatically save the ( measured )the other hand, is determined (( iteratively.For the function model that fulfils data only those N points for which r i() ) = = table of data (, ))r i= r i(z i). From measured ) ≤ (( ))[1 = the + (( conditions 2(( )(, = )) ) (6), (7), ((+ (8) )) (, )) (( ))[1 + 2(( )) (( ))] ln(1 + ] ln(1and+(9), the(( r)) o, where2((r ))) ois radius of non-deformed polynomial () = or any other suitable functioncouldrod, are taken into account. Additionally beln( ( ) = ln( (( ))) ( (, )) used. = ( ) =(, ) + In (( any (, case ))[1 ) ) due + ) 2(( to the)) two (( points )) ] ln(1which+are the nearestmentioned () = conditions in (, every )iteration) to the interval of N points= (( )) 2(( )))are also con- = ( ) = ln( (( ))) (( ))[1 + 2(( )) (( ))] ln(1 + (( )) 2(( )))() = ( 1 (, ) ) ) = = 1 = RMZ-M&G 2012, 59 + =