RMZ – MATERIALI IN GEOOKOLJE

() = (, )() () ()Calculation () = of stress-strain dependence from tensile tests at high temperatures using ... 337 = = (, )(, ) () = (, ) (, ) sidered. For reconstruction of contour ing 1 + () ()()is true V p= V o–V e. For the part of(), ) = the (continuous (), ) = ( function (), is ) needed and the rod which is in the plastic state ( two ) = ( (, ) + (, ) + (, ))thus, cubic splines were applied for additional conditions are valid, namely(, ) interpolation = (, ()which ) ()yields continuous () function r r(z). ()it cannot (be ) longer = than s 1V p⁄πr 2 (l l) (The next step is and cannot be shorter than s 2= l d–l l, (), ) = ( (), ) now the calculation of the volume of respectively.(, ) the rod which undergoes plastic deformation. () Here the Simpson () integration Let construct the function = (, ) = ( (, ) + ()(, )) method [2] = was employed (, )for numericalintegration () ()of equation (2). In thepresent work two different functional(13) () = () = (, ) (, ))(models (), )were= (chosen, (), ) =namely( (),catenary )and constant. ()On deformed part of the(, )rod K equidistant points separated for which on the interval s 1≤ s ≤ s 2has the= (, ) (, ) Δz, were (, selected ) (and ) =( ) () from that () for the root, which is found by bisection. Further,the parameters of the functional final1 +lengthof deformed (( ))[1 + 2(( )) (( ))] ln(1 + (( )) 2 rod, l(t k), wefind (, )( ) = (, )model = ln( which fulfil (( the )))conditions () () (6)–(8) must be determined in every( ) = (11) bisection step. We have the system oflinear equations = () for the polynomial After a number of trials we found that model (constant in the present work) () = (, )( the (, value ) + of Δz = (, 0.5 ) mm ) is most suit-able. In order to meet the condition (4), for the catenary; where the last one isand the system of non-liner equations = = 1 + = ()we find for each value of l l= iΔz corresponding value of l dsolved by the Newton method [2]. Thein every step iteration is interrupted when g(s) < ε, = (, ) (, ) () = i∈[1, 1 + K] by (, bisection. )) For those two where ε is prescribed accuracy. Firstvalues which are at that particular ( ) we determine r minand then from (10)moment in elastic state we calculated the radius of curvature of the contourvolume of ( the ( ) rod, ) = V e, asat the minimal cross-section, R. Both+ 2((of them are combined into the vector. )) (( ))] ln(1 + (( )) 2(( )))Described procedure is iterated until(12) V p> ε 1or l l+ l d+ s