FEM–MD combined method for evaluation of microscopic stress distribution by considering microscopic heterogeneity and deformation in close vicinity to grain boundary of steels

Abstract

Finite element method (FEM)–molecular dynamics (MD) combined method is proposed for the microscopic stress analysis of steels. In this numerical method, FEM is applied to the stress analysis inside grains, and MD is applied to the calculation of the atomic configuration near the grain boundary in order to consider the microscopic heterogeneity and the deformation near the grain boundary that influences the stress distribution. Slip length between two grains caused by the mismatch of the displacement near the grain boundary is calculated by FEM. Slip resistance, which is necessary to calculate slip length, is obtained by calculating the atomic configuration near the grain boundary by MD. The combination of FEM and MD is realized by using slip resistance in FEM and slip length in MD. The validity of modelling of the deformation near the grain boundary is investigated by comparing the deformation near the grain boundary calculated by FEM–MD combined method to that observed in the experiment in the case of a load applied to the specimen. Calculated slip length coincides with measured slip length. FEM–MD combined method is applied to the investigation of the influence of change in the grain shape caused by the thermal history such as the weld zone upon the strength characteristic. The high stress region tends to increase the incidence of larger grain diameter and it is indicated that grain coarsening due to the weld thermal history increases the possibility of the crack initiation. FEM–MD combined method is expected to be helpful in investigating the mechanism of fracture or the strength characteristic of the complicated microstructure such as the weld zone by evaluating the microscopic stress distribution.

Keywords::

• microscopic heterogeneity
• grain boundary
• stress distribution
• grain shape model
• Voronoi tessellation
• FEM
• molecular dynamics
• weld zone

Acknowledgements

We would like to record our appreciation for financial support received for parts of this study from the Foundation for the Support of the Base for the Teaching and Research of Structural and Functional Advanced Materials (Research Representative: Kakeshita Kazuyuki, Professor Emeritus, Osaka University) a Global COE Programme of the Ministry of Education, Culture, Sports, Science and Technology and from Science Research Foundation, Basic Research (B): Subject Numbers 17360418, 20360393. We would also like to express our gratitude to Mr Arimochi Kazushige, Mr Okaguchi Hideharu and Mr Kawabatake Tomoya of Sumitomo Metals for their kind assistance.

Notes

^1. Present Address: Sumitomo Metal Industries Ltd.