PSI - Issue 72

Dragana Mihajlović et al. / Procedia Structural Integrity 72 (2025) 195 – 202

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Fig. 3. Distribution of deformation of the MTS Ti-13Nb-13Zr alloy (a) at the beginning of tensile test, (b) under the force of 1.211 kN, (c) under the force of 0.825 kN and (d) MTS of Ti -13Nb-13Zr alloy after tensile test

3.3. Numerical analysis of tensile behaviour of Ti-13Nb-13Zr alloy after anodic oxidation

The von Mises criterion for plastic yielding of materials does not take into account the development of damage in the material and the sudden drop in load capacity that precedes ultimate failure. Fig. 4. presents the force-elongation curves for non-anodized and anodized CG TNZ alloy obtained by applying the complete Gurson model (CGM), Zhang et al. (2000), which is included in the group of micromechanical models, which are used for modelling the ductile fracture of metallic materials, Rakin et al. (2009). This base model has the von Mises plastic yield criterion, but also contains a parameter that quantifies the damage in the material. This parameter is called the volume fraction of voids or porosity, and micromechanical models based on the Gurson yield criterion take into account the mechanism of ductile fracture of the material, which takes place through the formation of voids, their growth under the influence of load, and the coalescence that precedes the final failure. The application of CGM requires a larger number of parameters (8 in total), and for most of these parameters, the values that are most often represented in the literature were used, while the value of the initial volume fraction of cavities f0, as a quantity that, as a rule, has the greatest influence on the results, was varied. Two initial values of the damage parameter (volume fraction of voids) were used: 0.01 and 0.005, and a comparison with the curves obtained using FEM with defined elasto-plastic behaviour of the material and experimental results was given. In the figures, it was seen that the results obtained by applying the von Mises criterion of plastic yielding do not predict a sudden drop in load capacity, which is consistent with the fact that this criterion does not include the modelling of damage development in the material. With the application of CGM, a sudden drop in the bearing capacity of the material is predicted, while in the case of the anodized alloy, the predicted deformation at break is significantly higher than experimentally determined. As mentioned earlier, a possible reason for the greater deviation of the numerical results from the experimental results for the anodized alloy is the early failure of the surface layer, which will be the subject of a detailed analysis in the following period. Also, when analyzing the longitudinal deformation, as a rule, there is a dependence on the choice of the initial measuring length L0; therefore, a comparison of the results in relation to the reduction of the thickness of the test tube, dt, will be shown, Fig. 5.