Simulation der Lokalisierung und des Portevin-Le-Chatelier-Effekts auf der Gundlage zellularer Automaten und des Relaxationselementeverfahrens
Final Report Abstract
In this project the Portevin-Le Chatelier-Effect has been investigated on the mesoscopic level on the basis of the relaxation element method (REM) in combination with other methods of computer aided-simulations of the material (finite element method, boundary element method and cellular automata). With the help of REM one can predict the selforganization of band structures in ductile materials. The method is applied for the description of plastic deformation in polycrystals. A plastically deformed grain is considered to be a stress concentrator on the mesoscopic scale. As a result of plastic flow in local places the stress-state of the conglomerate of grains is calculated. Experimental investigations with optical system of surface characterization allowed to detect the propagating bands of localized plastic deformation in the specimen. The main results obtained during this project show the large predictive possibilities and perspectives of the developed approach. They are in good agreement with the known experimental data: • The effect of serrated flow is the consequence of the formation of meso- and macrobands of localized deformation; • In the changing field of stresses the jump-like propagation of the process of strain localization takes place along the working part of the specimen; • An increase in the rate of the loading suppresses the effect of serrated flow; • Depending on the value of the rigidity of the machine, different types of oscillations on the stress-strain curve could be observed (serrated type of PLC-oscillations refers to rigid type of the machine (high value of rigidity) and stair-case type refers to soft machine (with low value of rigidity)). The following peculiarities of the development of plastic strain localization have been elucidated: • The formation of the macroband proceeds on the mechanism of Lüders band propagation and is accompanied by a decrease in the external stress. • The structure of the formed macrobands consists of a number of mesobands, oriented along the maximum tangential stresses. • Accumulation of the field of internal stresses in a polycrystal results in the effect of work-hardening. • When all conditions are kept the same, a decrease in Young’s modulus enhances the effect of intermittent flow. • The reason of PLC-effects could be the difference between the stress level of the starting movement of pinned dislocations and the lower stress of their free movement. The performed experiments and numerical simulations of PLC-effects in aluminium alloys with hard Al2O3-inclusions have shown that only a qualitative comparison of stressstrain diagrams, obtained in experiment and in simulations up to now is possible. In order to achieve the quantitative match of the curves one should take into account a number of factors in the model. One of them is taking into account the proper grain shapes. For simplicity reasons we took equal grain sizes, having the shape of squares, for which an analytical solution within the framework of the relaxation element method has been derived. In order to obtain the stress-strain curves, which could be compared with experimental ones, one should take into account the decrease in the cross-section of the specimen. That will be done in the follow up proposals. In the future it is planned to extend the developed approach to 3D-objects and in combination with the FEM to develop an algorithm for the prediction of plastic strain localization during sheet forming applications. The method could be applied in the prediction of fracture, multiple cracking as well as ductile and brittle fracture description.
Publications
- "Simulation of the Evolution of band Structures in Polycrystals on the Basis of Relaxation Element Method and Cellular Automata", Proceedings of the Seventh International Conference Cellular Automata for Research and Industry, ACRI 2006, September 20-23, 2006, Perpignan, France, Eds.: S. El Yacoubi, B. Chopard, S. Bandini, Lecture Notes in Computer Science 4173/2006, Springer-Verlag, Berlin Heidelberg, pp. 367-372 (2006)
G.V. Lasko, Ye.Ye. Deryugin, S. Schmauder
- Field of stresses in an isotropic plane with circular inclusion under tensile stress, online proceedings of the Conference on Damage in Composite Materials 2006, 18-19 September, Stuttgart, Germany
Ye.Ye. Deryugin, G.V. Lasko, S. Schmauder
(See online at https://doi.org/10.4236/eng.2012.49074) - Simulation of jerky flow in polycrystals by the relaxation element method (in Russian), Physical Mesomechanics 9, No. 5 (2006) 21-24
Ye.Ye. Deryugin, V.E. Panin, G.V. Lasko, S. Schmauder
- Study of local characteristics of jerky for particle reinforced aluminium as multilevel system (in Russian), Physical Mesomechanics 9, No. 5 (2006) 27-32
Ye.Ye. Deryugin, V.E. Panin, S. Schmauder, B.I. Suvorov
- "Modelling of Mesomechanics of Portevin-Le Chatelier Effect by Relaxation Element Method", Proc. International Conference on Computational & Experimental Engineering and Sciences 3-8 January 2007 (ICCE07), 1707-1713
Ye.Ye. Deryugin, G.V. Lasko, S. Schmauder
- Modelling and simulation of the localized plastic deformation by relaxation element method, Comput. Mech. 40, No. 4 (2007) 791-801
Ye.Ye. Deryugin, G.V. Lasko, S. Schmauder
- "Influence of stress macroconcentrators on the strain localization in Al6061/Al2O3 composites", Aluminum Alloys: Fabrication, Characterization and Applications, TMS (The Minerals, Metals & Materials Society), 2008, Eds.: Y. Weimin, K. Subodh, pp. 41-47 (2008)
Y. Deryugin, V.E. Panin, V.I. Suvorov, G.V. Lasko, S. Schmauder
- "Simulation of PLC-Effects in A16061/Al2O3 Alloys", TMS (The Minerals, Metals & Materials Society), 2008, Ed.: W. Yin, K. Subodh, 2008, Ernest Morial Convention Center, New Orleans, USA, March 9-13, 2008, Aluminum Alloys: Fabrication, Characterization and Applications, pp. 131-137 (2008)
G.V. Lasko, Y.Y. Deryugin, S. Schmauder
- "Simulation of the effect of intermittent flow in polycrystals on the basis of cellular automata and relaxation element method", Proceedings of the Eight International Conference Celullar Automata for Research and Industry, ACRI 2008, September 23-26, 2008, Yokohama, Japan, Eds.: H. Umeo et al, Lecture Notes in Computer Science 5191/2008, Springer-Verlag, Berlin Heidelberg, pp. 268-273 (2008)
Y.Y. Deryugin, G.V. Lasko, S. Schmauder
- Relaxation Element Method in mechanics of deformed solid, in book: ”Computational Materials”; ed. by Wilhelm U. Oster, Nova Science Publishers, Inc., Hauppauge NY, (2009) pp. 479-545.
Y.Y. Deryugin, G.V. Lasko, S. Schmauder
