Issue 37

U. Muhin et alii, Frattura ed Integrità Strutturale, 37 (2016) 318-324; DOI: 10.3221/IGF-ESIS.37.42 319 i v  - the velocity jump at i- the cut surface i S ;  - a symbol of variation; s  - the yield stress in shear. For rigid-plastic medium (1) is rewritten as follows:           S n i iS i s n s ds v dsv d 1 0 ) (      (2) The first integral (2) is the power of internal resistance, the second - power of the external forces on the borders of the center - the forces of friction between the rolls and the strip, front and rear tension, the third - power cut. When using the Ritz variation equation for the case of rolling Jourdain with tension in the expanded form is written as follows [1]:   0 5 4 3 2 1        N N N N N a j , (3) where: N 1 - the power of internal resistance; N 2 - power sliding friction forces; N 3 - forces cut power; N 4 - power forward tension; N 5 - power adjustable tension; a j - variable parameters. Under the sign of differentiation is the expression for the total power rolling. To describe the process of broadening the focus of the plastic deformation in the calculated use the circuit shown in Fig. 1. Hotbed of plastic deformation is divided into two areas - the zone and the zone timing lag. Form edge (dashed line) approximated by two straight segments - for the zone and the zone timing lag. In accordance with the scheme of the following symbols: y x vvvv , , , 1 0 - entrance and exit strip speed and projection velocity metal side edge on the axis x and y , respectively; 1 0 1 0 , , , , , BBBhhh í í - the thickness and half-width of the entrance and the neutral section and the output, respectively; í x ,  - the length of the deformation zone and the zone of advance. The equations that describe the shape of the side edges of the strip in the hearth of plastic deformation can be written as follows: a) for the area lead í x x  0 ; and b)   x x í for the zone gap   í t îï x x B x B ) ( 1 )( 0       ,    x t t B x B í t í t îò      1 1 1 )( 0   where: . , , , , 0 0 1 0 0  í í í t t t x t B B B B BB B B B B            From kinematic considerations we obtain the following conditions for the edge: a) for the area lead í x x  0 , b) for the zone gap   x x í í t êð x y x B B v v   , í t êð x y x B v v     . For every material point of the current coordinate (x, y) determined in accordance with [2-3] following law changes the flow velocity of the metal: a) for the area lead í x x  0 ; b) for the zone gap   x x í