PSI - Issue 45

ScienceDirect Structural Integrity Procedia 00 (2022) 000 – 000 Structural Integrity Procedia 00 (2022) 000 – 000 Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceDirect Available online at www.sciencedirect.com ScienceDirect

www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia

Procedia Structural Integrity 45 (2023) 74–81

© 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Prof. Andrei Kotousov Abstract Numerical procedure for analyzing T -stresses of cracks in two dimensional elasticity was developed using the method of continuously distributed dislocations model. Boundary conditions on the crack surfaces are reduced into singular integral equations in which dislocation densities are unknown. The weight function of the dislocation density is approximated as an expansion of Chebyshev polynomials of the first kind with finite number of terms and the coefficient of each term is determined by satisfying the boundary conditions at suitably selected collocation points. Some crack problems were solved by the proposed method in order to demonstrate rapid convergence of the calculated T -stresses with the increase of the number of the collocation points. © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) 17th Asia-Pacific Conference on Fracture and Strength and the 13th Conference on Structural Integrity and Failure (APCFS 2022 & SIF 2022) T -stress evaluation of cracks by means of continuous dislocations model in two-dimensional elasticity Koji Fujimoto Department of Aeronautics and Astronautics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan Abstract Numerical procedure for analyzing T -stresses of cracks in two dimensional elasticity was developed using the method of continuously distributed dislocations model. Boundary conditions on the crack surfaces are reduced into singular integral equations in which dislocation densities are unknown. The weight function of the dislocation density is approximated as an expansion of Chebyshev polynomials of the first kind with finite number of terms and the coefficient of each term is determined by satisfying the boundary conditions at suitably selected collocation points. Some crack problems were solved by the proposed method in order to demonstrate rapid convergence of the calculated T -stresses with the increase of the number of the collocation points. © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Prof. Andrei Kotousov Keywords: T -stress; Crack; Elasticity; Continuous dislocations model 17th Asia-Pacific Conference on Fracture and Strength and the 13th Conference on Structural Integrity and Failure (APCFS 2022 & SIF 2022) T -stress evaluation of cracks by means of continuous dislocations model in two-dimensional elasticity Koji Fujimoto Department of Aeronautics and Astronautics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan Peer-review under responsibility of Prof. Andrei Kotousov Keywords: T -stress; Crack; Elasticity; Continuous dislocations model 2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Prof. Andrei Kotousov 2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Prof. Andrei Kotousov 1. Introduction It is well known that the stress distribution in the neighborhood of a crack tip is expressed as follows in two-dimensional in-plane elasticity (See Fig. 1). { = I √2 cos 2 (1 － sin 2 sin 3 2 ) − II √2 sin 2 (2 + cos 2 cos 3 2 ) + = I √2 cos 2 (1 + sin 2 sin 3 2 ) + II √2 sin 2 cos 2 cos 3 2 = I √2 sin 2 cos 2 cos 3 2 + II √2 cos 2 (1 − sin 2 sin 3 2 ) 1. Introduction It is well known that the stress distribution in the neighborhood of a crack tip is expressed as follows in two-dimensional in-plane elasticity (See Fig. 1). { = I √2 cos 2 (1 － sin 2 sin 3 2 ) − II √2 sin 2 (2 + cos 2 cos 3 2 ) + = I √2 cos 2 (1 + sin 2 sin 3 2 ) + II √2 sin 2 cos 2 cos 3 2 = I √2 sin 2 cos 2 cos 3 2 + II √2 cos 2 (1 − sin 2 sin 3 2 ) ∙∙∙∙∙ (1) Fig. 1. Field in the vicinity of a crack tip. ∙∙∙∙∙ (1) Fig. 1. Field in the vicinity of a crack tip.

2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Prof. Andrei Kotousov 10.1016/j.prostr.2023.05.016