Evaluation of disclination Frank vector in ridge kink microstructure

ABSTRACT

This study conducts dislocation-based modelling and numerical analysis to clarify the presence of disclinations within kinked deformation microstructures using the framework of differential geometry. Although the existence of disclinations has long been postulated, a mathematical foundation for this phenomenon still needs to be provided. In this study, we develop kink deformation models using planar arrays of edge dislocations. The dislocation density is represented using a level-set function, and the governing equations are solved numerically through the finite element method. We then introduce the holonomy method to demonstrate the presence of disclinations by quantitatively measuring the Frank vector. At first, we validate the accuracy of the method by comparing it with the theoretical predictions provided by the grain boundary theory. Subsequently, we performed qualitative validation of the model by comparing the macroscopic deformation observed in experiments. Finally, we evaluate the Frank vector within the ridge kink model, providing quantitative evidence for the presence of disclinations in the kinked deformation microstructure. We also illustrate the distribution of elastic stress fields generated by disclinations at the termination point of the kink interface.

GRAPHICAL ABSTRACT

KEYWORDS:

• Ridge-type kink deformation
• disclinations
• Frank vector
• holonomy method
• differential geometry

Acknowledgements

This work was supported by JST PRESTO Grant Number JPMKPR1997 Japan and JSPS KAKENHI Grant Number JP18H05481.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by JST PRESTO [grant number JPMKPR1997]; JSPS KAKENHI [grant number JP18H05481].