METHOD FOR CALCULATION OF STRESS-STRAIN STATE DUE TO SINGLE TWIN IN GRAIN OF VARIOUS FORMS

Abstract

The paper investigates a stress-strain state in a polycrystalline grain due to presence in its body of a single micro- twin in case of various grain boundary forms. A methodology for calculation of displacement and stress fields for the specified stress-strain state of a polygon-shaped grain has been developed in the paper. Nodal points in a polycrystalline grain that have a maximum stresses contributing to initiation of destruction have been revealed in the paper. The aim of this work has been to study the stress-strain state due to a single micro-twin in the polycrystalline grain and form of grain boundaries. The paper describes polycrystalline grains having a regular polygon shape and containing a single wedge twin in their body. Polycrystalline grain boundaries are presented as walls with complete dislocation. The investigated grains are located far from the surface of twinning material. The developed methodology for calculation of displacement and stresses created by wedge twin is based on the principle of superposition. Calculations on stress tensor components have been carried out for iron (Fe). The presented results of calculations for stress fields have indicated to validity of the used dislocation model. Twin and grain boundaries being stress concentrators are clearly visible on the obtained distributions of stress fields. Maximum normal stresses are observed on the twin boundaries; σ_xy maximum shear stresses are located at nodal points of the twin; σ_zy and σ_xz shear stresses are maximum on the grain boundaries. The conducted investigations have resulted in study of the stress-strain state due to a single wedge-shaped micro-twin in the polycrystalline grain and form of the grain boundaries. Zones of stress concentration in the polycrystalline grain have been identified in the presence of residual mechanical wedge twin. A method for evaluation of the given state has been developed in the paper.