PSI - Issue 33

Evgeny Lomakin et al. / Procedia Structural Integrity 33 (2021) 809–817 Lomakin E.V., Fedulov B.N. / Structural Integrity Procedia 00 (2019) 000–000

816

8

possible to state that the tip of the cut deforms as circular cut with very small radius. At the first stage of loading, the sharp tip of the cut deformed into smooth one, that cause the modification of further plasticity region development. Analysis of limits loads (Fig. 8) also shows difference in obtained values even for classical solution without dilatation and when parameter C=0. It is possible to see that there is no difference in limit load values for numerical solutions with different angles of cut ( γ ). This fact also can be explained by the analysis performed for rounded tips of cuts where plastic region avoids linear free edges, thus angle has no meaning [8]. Nevertheless, if we consider statically admissible solution simply assuming �� � ���� , where 2h is the width of wakened section, the corresponding values of limit loads are less than numerical results. However, this fact is correct in terms of limit load theorems. Limit load analysis must not show right kinematics, it only promises to determine the unique estimation of limit load values by kinematically and statically admissible solutions.

Fig. 8. Normalized limit loads predicted by numerical and analytical solutions

Conclusion An approach to analyze plastic deformation of the material with characteristics dependent on stress state type is considered. The usage of triaxiality ratio parameter in plasticity criterion and the study of its influence on materials plastic flow has been carried out. The example of limit analysis problem has been demonstrated by means of analytical methods and using numerical one with fewer assumptions. All numerical results are within the range of the limit load values obtained in kinematically and statically admissible analytical solutions. Acknowledgements This research was supported by the Russian Science Foundation (grant No. 20-11-20230). References [1] Reynolds, Osborne. "LVII. On the dilatancy of media composed of rigid particles in contact. With experimental illustrations." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 20.127 (1885): 469-481. [2] Drucker, Daniel Charles, and William Prager. "Soil mechanics and plastic analysis or limit design." Quarterly of applied mathematics 10.2 (1952): 157-165. [3] Green, R. J. "A plasticity theory for porous solids." International Journal of Mechanical Sciences 14.4 (1972): 215-224. [4] Mises, R. V. "Mechanik der festen Körper im plastisch-deformablen Zustand." Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse 1913.4 (1913): 582-592.