PSI - Issue 52

ScienceDirect Available online at www.sciencedirect.com ScienceDirect Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2022) 000–000 Available online at www.sciencedirect.com Procedia Structural Integrity 52 (2024) 133–142 Structural Integrity Procedia 00 (2022) 000–000

www.elsevier.com/locate/procedia

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.2023.12.014 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 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 © 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 The concept of crack arrest design is proposed to enhance the safety of structures reducing the probability of crack propagation. The goal of crack arrest methods is to create compression stresses at the crack tip vicinity to stop the crack propagation. The thermal field at the crack tip vicinity can create such compression stresses. If a cracked electrically conductive structure is subjected to an electric load, a high temperature is induced by the Joule heating effect in regions subjected to higher electric current densities. A reliable computational method based on gradient theory is developed in the present paper. Due to a high concentration of electro thermal-mechanical fields at the crack tip vicinity, the size effects are considered for both mechanical equation and the thermal transport. The strain gradients are included into the constitutive equations for the double stress tensor and electric displacements. Due to occurrence of higher order derivatives in governing equations of gradient theories it is needed to develop the collocation mixed FEM. The collocation mixed FEM is applied to our multiphysical problem with size effects for mechanical and thermal fields, where the C 0 continuous approximations are applied independently to displacements and strains and also to temperature and temperature gradients. Keywords: Size effect, gradient theory elasticity and heat conduction, mixed finite element method, crack problem 1. Introduction The fracture and the fatigue properties of structures are important to their mechanical integrity, reliability and durability in practical engineering applications. The fracture mechanics help us to avoid brittle fracture. It would be very helpful to have a concept of crack arrest to enhance the safety of structures reducing the probability of crack propagation (Tagawa et al. 2020). The basic idea in the crack arrest is to create compression stresses at the crack tip vicinity to stop the crack propagation. There are familiar arrest methods, where a small hole is made in front of cracks to change stress properties (Wu et al. 2010). However, the arrest mechanism of the arrest-holes on running crack is Abstract The concept of crack arrest design is proposed to enhance the safety of structures reducing the probability of crack propagation. The goal of crack arrest methods is to create compression stresses at the crack tip vicinity to stop the crack propagation. The thermal field at the crack tip vicinity can create such compression stresses. If a cracked electrically conductive structure is subjected to an electric load, a high temperature is induced by the Joule heating effect in regions subjected to higher electric current densities. A reliable computational method based on gradient theory is developed in the present paper. Due to a high concentration of electro thermal-mechanical fields at the crack tip vicinity, the size effects are considered for both mechanical equation and the thermal transport. The strain gradients are included into the constitutive equations for the double stress tensor and electric displacements. Due to occurrence of higher order derivatives in governing equations of gradient theories it is needed to develop the collocation mixed FEM. The collocation mixed FEM is applied to our multiphysical problem with size effects for mechanical and thermal fields, where the C 0 continuous approximations are applied independently to displacements and strains and also to temperature and temperature gradients. Keywords: Size effect, gradient theory elasticity and heat conduction, mixed finite element method, crack problem 1. Introduction The fracture and the fatigue properties of structures are important to their mechanical integrity, reliability and durability in practical engineering applications. The fracture mechanics help us to avoid brittle fracture. It would be very helpful to have a concept of crack arrest to enhance the safety of structures reducing the probability of crack propagation (Tagawa et al. 2020). The basic idea in the crack arrest is to create compression stresses at the crack tip vicinity to stop the crack propagation. There are familiar arrest methods, where a small hole is made in front of cracks to change stress properties (Wu et al. 2010). However, the arrest mechanism of the arrest-holes on running crack is Fracture, Damage and Structural Health Monitoring Crack Propagation Arrest by the Joule Heating in Micro/Nano-Sized Structures Jan Sladek a *, Vladimir Sladek a , Miroslav Repka a a Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia Fracture, Damage and Structural Health Monitoring Crack Propagation Arrest by the Joule Heating in Micro/Nano-Sized Structures Jan Sladek a *, Vladimir Sladek a , Miroslav Repka a a Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia * Corresponding author. Tel.: +421904885687; fax: +421254773548. E-mail address: jan.sladek@savba.sk * Corresponding author. Tel.: +421904885687; fax: +421254773548. E-mail address: jan.sladek@savba.sk