13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- in plate vanadium specimen under quasi-static tension, compression of inclined cylindrical specimen were carried out in the finite-element package Simulia Abaqus using procedure UMAT. The big attention was paid on the calculation of plastic work and heat dissipation under investigated process. The results were compared with original experimental data, and with the results obtained using standard (incorporated in Abaqus) elasto–plastic model. 2. Mathematical model Mesoscopic defects (mesoshears) can be described by the following tensor [3] 1 2 S s lb bl , (1) where l - a unit normal to the shear plane, b - unit vector in the shear direction, S - shift intensity. Averaging s over an elementary volume allows us to introduce the tensor parameter p, which can be considered as a deformation caused by the defects: n p s , (2) where n - defect density. Application of dimension analysis allowed us to allocate the scale invariant structural parameter as 3 n c L L , (3) where nL - the mean size of the defect, cL - the mean distance between the defects. Solution of the self-consistency equation between the tensor micro- and macroparameters s and p allows us to establish three characteristic mode of [2,3]. For values of * 1.3, dependence of ( ) p (the case of uniaxial loading) is monotone and the reaction of defect formation is reversible (Fig.1). There is a metastability respect to the parameter p, associated with the orientational degrees of mesoshears freedom in the range of * 1 c . For c the jump of p becomes infinite; this characterizes unstable reaction of solid on the microshear formation. Figure 1. Typical response of a material on the defect growth Material susceptibility to the defect growth in the deformation process in terms of should be determined by the current values of the structural scale i.e. the values of . It is also shown that these scales are determined by non-linear kinetics of p and thus, the defect density distribution determines the structural sensitivity to its further growth. The growth of the scales cL , nL means
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