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Determination of material parameters and texture of a polycrystalline aggregate from ultrasonic measurements
Authors:J Lewandowski  
Affiliation:1. Asthma and Allergy Department, Dr. von Hauner Children''s Hospital, Ludwig Maximilians University, 80337 Munich, Germany;2. Institute for Asthma and Allergy Prevention, Helmholtz Centre Munich, Neuherberg, Germany;1. School of Mechanical and Electrical Engineering, China JiLiang University, Hangzhou 310018, China;2. Tederic Machinery Co., Ltd., Hangzhou, China;3. School of Mechanical and Electrical Engineering, Shanghai DianJi University, Shanghai 201306, China;1. The State Key Laboratory of Fluid Power and Mechatronic Systems, College of Mechanical Engineering, Zhejiang University, Hangzhou, 310027, China;2. The Key Laboratory of 3D Printing Process and Equipment of Zhejiang Province, College of Mechanical Engineering, Zhejiang University, Hangzhou, 310027, China;1. Peter the Great St. Petersburg Polytechnic University, 29 Politekhnicheskaya St., St. Petersburg 195251, Russia;2. Institute for Problems in Mechanical Engineering of the RAS, 61 V.O. Bolshoy Ave., St. Petersburg 199178, Russia;1. Department of Civil Engineering, Monash University, VIC 3800, Australia;2. Newmont Cooperation, Melbourne, Australia;1. Japan Atomic Energy Agency, 4002 Narita, O-arai, Ibaraki 311-1393, Japan;2. Mitsubishi FBR Systems, Inc., 2-34-17, Jingumae Shibuya-ku, Tokyo 150-0001, Japan;3. TEPCO SYSTEMS CORPORATION, 2-37-28, Eitai Koto-ku, Tokyo 135-0034, Japan;4. Mitsubishi Heavy Industries, Ltd., 5-717-1 Fukahori, Nagasaki, Nagasaki 851-0392, Japan
Abstract:The propagation of ultrasonic waves in a polycrystalline aggregate is considered for a bulk sample with orthorhombic symmetry made of cubic crystals of the highest symmetry. The probability density function of the crystallite orientation and the stiffness moduli of a single grain (crystallite) of the polycrystalline aggregate are found from four ultrasonic velocities and the rules of orthorhombic symmetry. Moreover, Jaynes’ principle of maximum Shannon entropy and the averaging procedure proposed by Voigt are used. In this way, it is shown that on the basis of the measurements of four respectively chosen ultrasonic velocities it is possible to find simultaneously the maximum-entropy distribution function of the crystallite orientation and the crystallite stiffness moduli.
Keywords:Ultrasonic velocities  Crystallite orientation  Stiffness moduli
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