The application of the Eshelby equivalent inclusion method for unifying modulus and transformation toughening |
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| Institution: | 1. Institute of Strength Physics and Materials Science SB RAS, 2/4 pr. Akademicheskii, 634055, Tomsk, Russia;2. National Research Tomsk Polytechnic University, 30 Leninа Avenue, 634050, Tomsk, Russia;3. Department of Mechanical and Aerospace Engineering, New Mexico State University, P.O. Box 30001, Las Cruces, NM 88003, USA;1. Department of Mechanics, School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China;2. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi''an Jiaotong University, Xi''an 710049, China;3. Department of Mechanical, Aerospace and Civil Engineering, Brunel University, Uxbridge, London, UK;1. Institute of Soft Matter Mechanics, College of Mechanics and Materials, Hohai University, Nanjing 211100, P.R. China;2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, P.R. China;3. State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100048, P.R. China;4. Jiangsu Key Laboratory of Construction Materials, School of Materials Science and Engineering, Southeast University, Nanjing 211189, P.R. China |
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| Abstract: | When a crack is lodged in an inclusion, both difference between the modulus of the inclusion and matrix material and stress-free transformation strain of the inclusion will cause the near-tip stress intensity factor to be greater (amplification effect) or less (shielding or toughening effect) than that prevailing in a homogeneous material. In this paper, the inclusion may represent a second phase particle in composites and a transformation or microcracked process zone in brittle materials, which may undergo a stress-free transformation strain induced by phase transformation, microcracking, thermal expansion mismatch and so forth. A close form of solution is derived for predicting the toughening (or amplification) effect. The derivation is based on Eshelby equivalent inclusion approach that provides rigorous theoretical basis to unify the modulus and transformation contributions to the near-tip field. As validated by numerical examples, the developed formula has excellent accuracy for different application cases. |
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