Stress intensity factors for bonded two half planes weakened by thermally insulated cracks
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O R I G I NA L PA P E R
K. B. Hamzah · N. M. A. Nik Long · N. Senu · Z. K. Eshkuvatov
Stress intensity factors for bonded two half planes weakened by thermally insulated cracks
Received: 8 March 2020 / Revised: 26 May 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract The thermally insulated inclined or circular arc cracks problems subjected to axial stress in the upper part of bonded two half planes are considered. The modified complex potential function method with the continuity conditions of the resultant force, displacement, and heat conduction functions is used to develop the new system of hypersingular integral equations (HSIEs) for the problems. The new system of HSIEs is solved numerically for the unknown crack opening displacement function and the known traction along the crack as the right-hand term using the appropriate quadrature formulas. Numerical results for the nondimensional stress intensity factors (SIFs) at all cracks tips are presented. A comparison between the nondimensional SIFs for cracks with and without thermal influence is also given
1 Introduction Most of the engineering structures are exposed to thermal loads, which can affect their strength and life cycles. The emergence of cracks in such materials or structures makes the situation worsen. This phenomenon has led to many types of research works. In recent decades, researchers used the complex potential functions (CPFs) to analyze the behavior of the stress intensity factor (SIF) in order to investigate the stability behavior of materials or planes containing thermally insulated crack problems in an infinite plane [1–4], half plane [5,6], dissimilar elliptic inclusion [7–9], and bonded two half planes [10–14] subjected to remote stress. An insulated penny-shaped crack with uniform heat flow in bonded two half planes was solved using CPFs to calculate SIF [10]. The singular integral equations (SIEs) were derived and solved numerically by using the appropriate interpolation formulas for two-dimensional thermoelastic crack problems in bonded two half planes [11]. The combination of CPFs and the method of analytical continuation was used to formulate a curved The N. M. A. Nik Long would like to thank the Ministry of Education Malaysia for financial support by the Fundamental Research Grant Scheme with Project Number 5540269. K. B. Hamzah · N. M. A. Nik Long (B)· N. Senu Laboratory of Computational Sciences and Mathematical Physics, Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia E-mail: [email protected] K. B. Hamzah Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, 76100 Hang Tuah Jaya, Durian Tunggal, Melaka, Malaysia N. M. A. Nik Long · N. Senu Mathematics Department, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia Z. K. Eshkuvatov Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala Terengganu, Malaysia
K. B. Hamzah et al.
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