|Large Plastic Deformations and Ductile Fracture of Polycrystals: Multiscale Modeling|
Very far, in the Land of High Pressures, behind the Severe Plastic Deformations Hill, lies a mysterious country called Ideal Plasticity. Some think that there is only one Strain-Strength Curve leading there, some believe that there are several, while others think that there is no such a country at all. Many went there; only a few reached it, most fractured on the way. People tell wonders about it: As if metals live there in a complete idyll, deforming without fracturing and hardening. As if those who lived there, became super-plastic, their grains became small and pure, and they started to react to external influences in a completely different way. People admire those who returned from this country, and respectfully add "Nano" to their titles.
From a legend told by an old alloy Ti-6-4 who survived a severe plastic deformation to a young inexperienced alloy.
Below are some of my contributions in this area.
Proposing a continuum model of grain refinement and damage of polycrystalline materials under severe plastic deformation (SPD). The model makes two natural assumptions: (1) the self-similarity of grain refinement and micro-damage, and (2) the complementarity of these two processes. The model uses a system of kinetic equations to explain the formation of structure during an SPD process. Analyzing these equations gives the following conclusions:
Y. Beygelzimer. Grain refinement versus voids accumulation during severe plastic deformations of polycrystals: A mathematical simulation, Mechanics of Materials, Vol. 37, No. 7, pp. 753--767 (2005).
Developing a continuum theory of plastic deformation in structurally-inhomogeneous porous bodies. Based on this theory, proposing a mathematical model of metal forming of porous and powder materials. Developing a new model for predicting the ductility of materials under deformation.
Y. Beygelzimer, V. Varyukhin, B. Efros. Physical mechanics of hydrostatic treatment of materials. Donetsk: DonFTI NANU, 192 pages, 2000 (in Russian).
Y. Beygelzimer. Constitutive Equations of a Porous Body with a Structurally-Inhomogeneous Matrix, Proceedings of International Workshop on Modelling of Metal Powder Forming Processes, Grenoble, France, July 21--23, 1997, pp. 57--67.
Y. Beygelzimer, B. Efros, V. Varyukhin, A. Khokhlov. A continuum model of a structurally-inhomogeneous porous body and its application for the study of stability and viscous fracture of materials deformed under pressure. Engineering Fracture Mechanics, Vol. 48, No. 5, pp. 629--640 (1994).
Proposing a computational model of elastic-plastic deformation of micro-inhomogeneous materials, which accounts for rotations of structural elements. Introducing new geometrical structures into plasticity theory ("thick yield surface", "cloud of internal stress") which effectively describe elastic-plastic deformation of micro-inhomogeneous materials. The picture below demonstrates a cloud of internal stress.
Y. Beygelzimer, A. Spuskanyuk. The thick yield surface: An idea and approach for investigating its structure. Philosophical Magazine A, Vol. 79, No. 10, pp. 2437--2459 (1999).
Y. Beygelzimer, A. Spuskanyuk, V. Varyukhin. On The Loading Surface of Microinhomogeneous Materials, Resent Development in Computer Modeling of Powder Metallurgy Processes, IOS Press, pp. 17--28, 2001.