PSI - Issue 52

ScienceDirect Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2023) 000–000 Structural Integrity Procedia 00 (2023) 000–000 Available online at www.sciencedirect.com Available online at www.sciencedirect.com Available online at www.sciencedirect.com Available online at www.sciencedirect.com Procedia Structural Integrity 52 (2024) 323–339 Structural Integrity Procedia 00 (2023) 000–000

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© 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 Professor Ferri Aliabadi Abstract A method for calculating a stress intensity factor at a tip of cracks in an elastic plate with rectilinear anisotropy is studied based on the body force method, an indirect BEM. The crack is replaced by continuously embedded pairs of concentrated forces and accurate stress intensity factor solutions are obtained by introducing a fundamental density function which expresses the exact stress singularity at an each crack tip. Solutions to the problem of multiple interfering cracks are computed and results are presented in numeric tables and graphs by changing the material properties and a direction of material principal axes as well as crack locations. Keywords: Crack interference; rectilinear anisotropy; stress intensity factor; infinite plate; body force method; Fracture, Damage and Structural Health Monitoring Analysis of mutual interference among line cracks in an orthotropic plate Akihide Saimoto a, ∗ , Yohei Sonobe a , Takuya Kitamura a , Yuichirou Ambe a a Graduate School of Engineering, Nagasaki University, 1-14 Bunkyo-machi, Nagasaki 8528521, Japan Abstract A method for calculating a stress intensity factor at a tip of cracks in an elastic plate with rectilinear anisotropy is studied based on the body force method, an indirect BEM. The crack is replaced by continuously embedded pairs of concentrated forces and accurate stress intensity factor solutions are obtained by introducing a fundamental density function which expresses the exact stress singularity at an each crack tip. Solutions to the problem of multiple interfering cracks are computed and results are presented in numeric tables and graphs by changing the material properties and a direction of material principal axes as well as crack locations. Keywords: Crack interference; rectilinear anisotropy; stress intensity factor; infinite plate; body force method; The stress intensity factor (SIF) at a crack tip was computed for the problem of multiple line cracks interfering with each other in an infinite plate of rectilinearly anisotropic elasticity. The body force method (BFM), a type of indirect boundary element method, was employed for numerical analysis. The BFM is based on a principle of superposition and was originally proposed by Nisitani (1967). In this study, the elastic field due to a pair of point forces, which is obtained by di ff erentiating those due to an isolated force acting in an infinite plate with orthogonal anisotropy, is used as a fundamental solution for crack problems. When treating a stress boundary condition imposed on the crack lines, not a traction at representative points (collocation method) but a resultant force over a predefined interval set on the crack line is employed. This technique is known as resultant force method preferably used by Isida (1978), dramatically improves the solution accuracy. Sih et al. (1965) clarified a relationship between the SIF and the singular elastic fields at a crack tip in an anisotropic elastic material, and presented a closed form solutions for problems of an anisotropic infinite plate with a single line crack subjected to a uniaxial tension at infinity and for the case where an isolated line crack is subjected to a concentrated force in its plane, based on Savin (1961)’s result. Prominent numerical solutions to crack problems in anisotropic media are finite element studies such as by Walsh (1972), Mandell et al. (1974), Foschi and Barrett (1976), Soni and Stern (1976), Wang et al. (2020) and the boundary element based studies by Snyder and Cruse (1975), Kamel and Liaw (1991) , Sollero and Aliabadi (1993), Sollero and Aliabadi (1995), Hwu et al. (2020) and so on. Recently, Ayatollahi et al. (2022) published a review paper on Fracture, Damage and Structural Health Monitoring Analysis of mutual interference among line cracks in an orthotropic plate Akihide Saimoto a, ∗ , Yohei Sonobe a , Takuya Kitamura a , Yuichirou Ambe a a Graduate School of Engineering, Nagasaki University, 1-14 Bunkyo-machi, Nagasaki 8528521, Japan Abstract A method for calculating a stress intensity factor at a tip of cracks in an elastic plate with rectilinear anisotropy is studied based on the body force method, an indirect BEM. The crack is replaced by continuously embedded pairs of concentrated forces and accurate stress intensity factor solutions are obtained by introducing a fundamental density function which expresses the exact stress singularity at an each crack tip. Solutions to the problem of multiple interfering cracks are computed and results are presented in numeric tables and graphs by changing the material properties and a direction of material principal axes as well as crack locations. Keywords: Crack interference; rectilinear anisotropy; stress intensity factor; infinite plate; body force method; 1. Introduction The stress intensity factor (SIF) at a crack tip was computed for the problem of multiple line cracks interfering with each other in an infinite plate of rectilinearly anisotropic elasticity. The body force method (BFM), a type of indirect boundary element method, was employed for numerical analysis. The BFM is based on a principle of superposition and was originally proposed by Nisitani (1967). In this study, the elastic field due to a pair of point forces, which is obtained by di ff erentiating those due to an isolated force acting in an infinite plate with orthogonal anisotropy, is used as a fundamental solution for crack problems. When treating a stress boundary condition imposed on the crack lines, not a traction at representative points (collocation method) but a resultant force over a predefined interval set on the crack line is employed. This technique is known as resultant force method preferably used by Isida (1978), dramatically improves the solution accuracy. Sih et al. (1965) clarified a relationship between the SIF and the singular elastic fields at a crack tip in an anisotropic elastic material, and presented a closed form solutions for problems of an anisotropic infinite plate with a single line crack subjected to a uniaxial tension at infinity and for the case where an isolated line crack is subjected to a concentrated force in its plane, based on Savin (1961)’s result. Prominent numerical solutions to crack problems in anisotropic media are finite element studies such as by Walsh (1972), Mandell et al. (1974), Foschi and Barrett (1976), Soni and Stern (1976), Wang et al. (2020) and the boundary element based studies by Snyder and Cruse (1975), Kamel and Liaw (1991) , Sollero and Aliabadi (1993), Sollero and Aliabadi (1995), Hwu et al. (2020) and so on. Recently, Ayatollahi et al. (2022) published a review paper on ∗ Corresponding author. Tel.: + 81-95-819-2493 ; fax: + 81-95-819-2534. E-mail address: s-aki@nagasaki-u.ac.jp Fracture, Damage and Structural Health Monitoring Analysis of mutual interference among line cracks in an orthotropic plate Akihide Saimoto a, ∗ , Yohei Sonobe a , Takuya Kitamura a , Yuichirou Ambe a a Graduate School of Engineering, Nagasaki University, 1-14 Bunkyo-machi, Nagasaki 8528521, Japan Abstract A method for calculating a stress intensity factor at a tip of cracks in an elastic plate with rectilinear anisotropy is studied based on the body force method, an indirect BEM. The crack is replaced by continuously embedded pairs of concentrated forces and accurate stress intensity factor solutions are obtained by introducing a fundamental density function which expresses the exact stress singularity at an each crack tip. Solutions to the problem of multiple interfering cracks are computed and results are presented in numeric tables and graphs by changing the material properties and a direction of material principal axes as well as crack locations. Keywords: Crack interference; rectilinear anisotropy; stress intensity factor; infinite plate; body force method; 1. Introduction The stress intensity factor (SIF) at a crack tip was computed for the problem of multiple line cracks interfering with each other in an infinite plate of rectilinearly anisotropic elasticity. The body force method (BFM), a type of indirect boundary element method, was employed for numerical analysis. The BFM is based on a principle of superposition and was originally proposed by Nisitani (1967). In this study, the elastic field due to a pair of point forces, which is obtained by di ff erentiating those due to an isolated force acting in an infinite plate with orthogonal anisotropy, is used as a fundamental solution for crack problems. When treating a stress boundary condition imposed on the crack lines, not a traction at representative points (collocation method) but a resultant force over a predefined interval set on the crack line is employed. This technique is known as resultant force method preferably used by Isida (1978), dramatically improves the solution accuracy. Sih et al. (1965) clarified a relationship between the SIF and the singular elastic fields at a crack tip in an anisotropic elastic material, and presented a closed form solutions for problems of an anisotropic infinite plate with a single line crack subjected to a uniaxial tension at infinity and for the case where an isolated line crack is subjected to a concentrated force in its plane, based on Savin (1961)’s result. Prominent numerical solutions to crack problems in anisotropic media are finite element studies such as by Walsh (1972), Mandell et al. (1974), Foschi and Barrett (1976), Soni and Stern (1976), Wang et al. (2020) and the boundary element based studies by Snyder and Cruse (1975), Kamel and Liaw (1991) , Sollero and Aliabadi (1993), Sollero and Aliabadi (1995), Hwu et al. (2020) and so on. Recently, Ayatollahi et al. (2022) published a review paper on ∗ Corresponding author. Tel.: + 81-95-819-2493 ; fax: + 81-95-819-2534. E-mail address: s-aki@nagasaki-u.ac.jp Fracture, Damage and Structural Health Monitoring Analysis of mutual interference among line cracks in an orthotropic plate Akihide Saimoto a, ∗ , Yohei Sonobe a , Takuya Kitamura a , Yuichirou Ambe a a Graduate School of Engineering, Nagasaki University, 1-14 Bunkyo-machi, Nagasaki 8528521, Japan 1. Introduction The stress intensity factor (SIF) at a crack tip was computed for the problem of multiple line cracks interfering with each other in an infinite plate of rectilinearly anisotropic elasticity. The body force method (BFM), a type of indirect boundary element method, was employed for numerical analysis. The BFM is based on a principle of superposition and was originally proposed by Nisitani (1967). In this study, the elastic field due to a pair of point forces, which is obtained by di ff erentiating those due to an isolated force acting in an infinite plate with orthogonal anisotropy, is used as a fundamental solution for crack problems. When treating a stress boundary condition imposed on the crack lines, not a traction at representative points (collocation method) but a resultant force over a predefined interval set on the crack line is employed. This technique is known as resultant force method preferably used by Isida (1978), dramatically improves the solution accuracy. Sih et al. (1965) clarified a relationship between the SIF and the singular elastic fields at a crack tip in an anisotropic elastic material, and presented a closed form solutions for problems of an anisotropic infinite plate with a single line crack subjected to a uniaxial tension at infinity and for the case where an isolated line crack is subjected to a concentrated force in its plane, based on Savin (1961)’s result. Prominent numerical solutions to crack problems in anisotropic media are finite element studies such as by Walsh (1972), Mandell et al. (1974), Foschi and Barrett (1976), Soni and Stern (1976), Wang et al. (2020) and the boundary element based studies by Snyder and Cruse (1975), Kamel and Liaw (1991) , Sollero and Aliabadi (1993), Sollero and Aliabadi (1995), Hwu et al. (2020) and so on. Recently, Ayatollahi et al. (2022) published a review paper on 1. Introduction ∗ Corresponding author. Tel.: + 81-95-819-2493 ; fax: + 81-95-819-2534. E-mail address: s-aki@nagasaki-u.ac.jp Structural Integrity Procedia 00 (2023) 000–000 www.elsevier.com / locate / procedia

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 Professor Ferri Aliabadi 10.1016/j.prostr.2023.12.032 2210-7843 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of Professor Ferri Aliabadi. ∗ Corresponding author. Tel.: + 81-95-819-2493 ; fax: + 81-95-819-2534. E-mail address: s-aki@nagasaki-u.ac.jp 2210-7843 © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of Professor Ferri Aliabadi. 2210-7843 © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of Professor Ferri Aliabadi. 2210-7843 © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of Professor Ferri Aliabadi.