13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- 3. Numerical simulation Numerical simulation was carried out using the finite element package Abaqus. Material behavior is described by a statistical – thermodynamic model introducing above using the procedure UMAT. Arrays of material constants, strain, strain increments and the time step passed as input data to the procedure. Increment of stress tensor components and increment of defect density tensor components are determined from the system of constitutive equations. Values of these components at the next time step are defined as the sum of values on the previous step and the appropriate increment. There were considered numerical experiments on the quasi-static tensile of vanadium paddle, containing a central crack, compression of an oblique cylindrical vanadium sample and fracture of an oblique cylindrical titanium sample. Quasi-static tensile experiment was carried out on the sample, the geometry of which is shown in Fig. 2. The specimen contains a central crack; its length is 3 mm. Figure 2. Geometry of specimen. All sizes are in millimeters. The extended finite element method (XFEM) capability in Abaqus was used to model crack propagation. XFEM models a crack as an enriched feature by adding degrees of freedom in elements with special displacement functions. XFEM does not require the mesh to match the geometry of the discontinuities. It can be used to simulate initiation and propagation of a discrete crack along an arbitrary, solution – dependent path without the requirement of remeshing [5]. A maximum principal stress criterion was used to model the damage initiation. Stress state of the sample with a central crack after deformation is shown in Fig 3. Figure 4 displays the zoomed stress field near crack tip. The stress increases near the crack tip. Figure 3. Component σxx (in the tension direction) of the stress tensor
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