The stress field of an infinite set of discrete dislocations

ABSTRACT

The two-dimensional stress fields induced by a set of infinitely many parallel edge dislocations are difficult to estimate as those of individual dislocations decay slowly. A simple numerical method to compute them is proposed. The method is based on series summation using a convergence factor, $\exp (-s{r}^2)$ that decays rapidly with radial distance r from the field point, and letting the positive parameter $s\downarrow 0$ numerically through Richardson extrapolation. The present method is more general than a lattice summation method with explicit spurious stress cancellation that is widely used in the literature. Furthermore, the spurious long-range stresses are cancelled in the present method without explicit evaluation.

KEYWORDS:

• Dislocation
• series summation
• spurious stress
• numerical method

Acknowledgments

The authors gratefully acknowledge funding from the Science and Engineering Research Board (SERB) through sanction order No. PDF/2019/000944.

Disclosure statement

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

Additional information

Funding

The authors gratefully acknowledge funding from the Science and Engineering Research Board (SERB) through sanction order No. PDF/2019/000944.

Notes on contributors

Sivasambu Mahesh

Sivasambu Mahesh is faculty member in the department of Aerospace Engineering, Indian Institute of Technology Madras.

Shyam M. Keralavarma

Shyam M. Keralavarma is faculty member in the department of Aerospace Engineering, Indian Institute of Technology Madras.