Influence of the crack morphology on the fatigue crack growth rate: A continuously-kinked crack model based on fractals |
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| Authors: | Andrea Carpinteri Andrea Spagnoli Sabrina Vantadori Danilo Viappiani |
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| Affiliation: | 1. State Key Laboratory for Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, PR China;2. Center for Rock Instability & Seismicity Research, Northeastern University, Shenyang 110819, PR China;3. Department of Civil Engineering, Monash University, Melbourne, Victoria 3800, Australia;1. Aerospace Division, Defence Science and Technology Group, 506 Lorimer Street, Fishermans Bend, Victoria 3207, Australia;2. Dept. Engineering & Architecture, University of Parma, Parco Area delle Scienze 181/A, Parma 43124, Italy;3. Centre of Expertise for Structural Mechanics, Dept. Mechanical and Aerospace Engineering, Monash University, Victoria 3800, Australia;1. School of Civil Engineering and Communication, North China University of Water Resources and Electric Power, Zhengzhou 450046, China;2. State Key Laboratory of Shield Machine and Boring Technology, Zhengzhou 450001, China;3. Geotechnical and Structural Engineering Research Center, Shandong University, Jinan 250061, China;4. School of Civil Engineering, Shandong Jianzhu University, Jinan 250101, China;1. State Key Laboratory of Advanced Special Steel, School of Materials Science and Engineering, Shanghai University, Shanghai 200072, China;2. Mechanical Department, Tongling University, Tongling 244000, Anhui, China;1. ARC Centre of Excellence for Geotechnical Science and Engineering, Civil, Surveying and Environmental Engineering, The University of Newcastle, Callaghan, NSW 2308, Australia;2. State Key Laboratory for Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221008, PR China;3. School of Civil & Hydraulic Engineering, Dalian University of Technology, Dalian 116024, PR China |
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| Abstract: | Threshold condition and rate of fatigue crack growth appear to be significantly affected by the degree of deflection of cracks. In the present paper, the reduction of the fatigue crack growth rate for a so-called ‘periodically-kinked crack’ as compared to that for a straight counterpart is quantified via the Paris–Erdogan law modified according to some simple theoretical arguments. It is shown that such a reduction increases as the value of the kinking angle increases. Then, a so-called ‘continuously-kinked crack’ (the kink length tends to zero) is considered and modelled as a self-similar invasive fractal curve. The sequence of kinking angles in the crack is such that the fatigue crack path is ‘on average’ straight. Using the Richardson’s expression for self-similar fractals, the fractal dimension of the crack is expressed as a function of the kinking angle. It is shown that the fatigue crack growth rate in the Paris range depends not only on the above fractal dimension and in turn on the kinking angle, but also, in an explicit fashion, on the crack length. Some experimental results related to concrete and showing a crack size effect on the fatigue crack growth rate are analysed. |
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