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Prediction of Crystallographic Texture Formation in Polycrystalline Samples under Severe Plastic Deformation Based on a Two-Level Statistical Elasto-Viscoplastic Model
Physical Mesomechanics ( IF 1.6 ) Pub Date : 2021-06-17 , DOI: 10.1134/s1029959921030012
K. V. Ostapovich , P. V. Trusov , A. Yu. Yants

Abstract

A multilevel mathematical model is proposed for studying the technological processing of metals and alloys by severe plastic deformation. The model is based on crystal elasto-viscoplasticity and can describe the evolving structure as well as predict crystallographic texture formation. A geometrically nonlinear nonstationary boundary value problem of quasi-static elasto-viscoplastic deformation of macroscopic polycrystalline samples is formulated in rate form, including systems of equations describing physical mechanisms at various structural scale levels. A distinctive feature of the proposed formulation is that it takes into account variable contact conditions on the material surface specified for each moment of the loading process. As a basic constitutive model, a two-level model of a polycrystal is used in which the characteristics of a macroscopic representative volume are calculated by consistent statistical averaging over the values of similar quantities for the contained mesoscopic elements (crystallites). Within the approach used, information on crystallographic textures in different parts of the workpiece is provided in the form of samples of crystal lattice orientations. The associated output data of numerical calculations are reproduced in a reduced form using cluster analysis methods. The developed apparatus is applied to study the drawing of a solid copper cylinder.



中文翻译:

基于两级统计弹粘塑性模型预测严重塑性变形下多晶样品的晶体织构形成

摘要

提出了一个多层次的数学模型来研究金属和合金的剧烈塑性变形工艺加工。该模型基于晶体弹粘塑性,可以描述不断演变的结构并预测晶体结构的形成。宏观多晶样品准静态弹粘塑性变形的几何非线性非平稳边值问题以速率形式表示,包括描述不同结构尺度水平物理机制的方程组。所提出的公式的一个显着特点是它考虑了为加载过程的每个时刻指定的材料表面上的可变接触条件。作为基本的本构模型,使用多晶的两级模型,其中宏观代表性体积的特征是通过对包含的介观元素(微晶)的相似量值的一致统计平均来计算的。在所使用的方法中,工件不同部分的晶体结构信息以晶格取向样本的形式提供。使用聚类分析方法以简化形式再现数值计算的相关输出数据。所开发的装置用于研究实心铜圆柱体的拉拔。工件不同部分的晶体结构信息以晶格取向样本的形式提供。使用聚类分析方法以简化形式再现数值计算的相关输出数据。所开发的装置用于研究实心铜圆柱体的拉拔。工件不同部分的晶体结构信息以晶格取向样本的形式提供。使用聚类分析方法以简化形式再现数值计算的相关输出数据。所开发的装置用于研究实心铜圆柱体的拉拔。

更新日期:2021-06-17
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