13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- Figure 16. Cylindrical specimen after compression Results of numerical modeling are shown in Figure 17. Maximum nominal shear stress criterion was used to initiate damage in cylinder sample. Crack location obtained by simulation is consistent with experimental data. Figure 17. Numerical simulation results on the titanium specimen compression 3. Conclusion The paper is devoted to the study of metal fracture processes under quasi-static loading. There were formulated constitutive equations for elasto-plastic medium with mesodefects. These equations were used for three-dimensional modeling of quasi-static vanadium paddle tension, compression of vanadium oblique cylinder and failure of titanium oblique cylinder sample. Numerical simulation was performed using finite-element package Abaqus by subroutine UMAT which allows user to implement his own constitutive equations. Fracture modeling was carried out using XFEM capability in Abaqus. Simulation results are in a good agreement with experimental data. Acknowledgements This work was supported by grant of President of the Russian Federation for support of young Russian scientists and leading scientific schools (MD-2684.2012.1) and RFBR (grant N 12-01-33072). References [1] V.I. Betekhtin, O.B. Naimark, A.G. Kadomzev, S.N. Grishaev, Experimental and theoretical investigation of defect structure evolution, plastic deformation and fracture, preprint ICMM UB RAS, Perm, 1997. (In Russian) [2] Yu.V. Bayandin, Investigation of self-similar regularities of plastic front formations in metals under intense impact, PhD thesis, ICMM UB RAS, Perm, 2007. (In Russian) [3] O.B. Naimark, Collective properties of defects ensemble and some nonlinear problems of
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