Beygelzimer Yan, Filippov Alexander, Orlov Dmytro
Donetsk Institute for Physics and Engineering Named After O.O. Galkin, NASU, Kyiv, Ukraine.
Department of the Functional Morphology and Biomechanics, University of Kiel, Kiel, Germany.
Sci Rep. 2024 Aug 18;14(1):19119. doi: 10.1038/s41598-024-70077-3.
Deformation mechanisms of crystalline solids has been the subject of research for more than two centuries. The theory of dislocations dominates modern views but still has significant gaps demanding the introduction of additional concepts for the coherent quantitative description of physical phenomena. In this work, we propose a coherent geometric description of motion and deformation in crystalline solids as piecewise isometric transformations (PWIT). The latter only includes operations that, similar to interatomic spacing in crystalline lattice, do not alter distances between reference points, i.e. translations, rotations and mirror reflections. The difference between solid-body translations and plastic deformations is that the isometric transformations have discontinuities that in real-life materials realise through dislocations (termination of shifts), disclinations (termination of rotations), and twins (mirror reflections). The conceptual description of plastic deformations as PWIT can be useful for the better description of physical phenomena, proposing new hypothesis, and for developing predictive analytical models. In this paper, the use of this conceptual description enables proposing new hypothesis about the nature of such interesting phenomena in severe plastic deformation as (i) stationary 'solid state turbulence' stage in high pressure torsion, and (ii) rate of mass transfer (mechanically assisted diffusion) in simple-shear deformation.
晶体固体的变形机制一直是两个多世纪以来的研究课题。位错理论主导着现代观点，但仍存在重大差距，需要引入额外的概念来对物理现象进行连贯的定量描述。在这项工作中，我们提出了一种将晶体固体中的运动和变形描述为分段等距变换（PWIT）的连贯几何方法。后者仅包括与晶格中的原子间距类似的、不会改变参考点之间距离的操作，即平移、旋转和镜面反射。固体平移和塑性变形之间的区别在于，等距变换具有不连续性，在实际材料中通过位错（位移终止）、 disclinations（旋转终止）和孪晶（镜面反射）来实现。将塑性变形概念描述为PWIT有助于更好地描述物理现象、提出新假设以及开发预测分析模型。在本文中，使用这种概念描述能够就严重塑性变形中一些有趣现象的本质提出新假设，例如（i）高压扭转中的稳态“固态湍流”阶段，以及（ii）简单剪切变形中的传质速率（机械辅助扩散）。
