Analytical Description of Plastic Deformation Distribution in the Neck of a Flat Tensile Specimen

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Mechanics, Materials Science & Engineering, October 2015 – ISSN 2412-5954

Analytical Description of Plastic Deformation Distribution in the Neck of a Flat Tensile Specimen Yevgeny Ye. Deryugin1a, Natalya Antipina2 1 – Institute of Strength Physics and Materials Science of the SB RAS, Tomsk, Russia 2 – National Research Tomsk Polytechnic University, Tomsk, Russia a – dee@ispms.tsc.ru

Keywords: neck of a flat specimen, plastic deformation, analytical description ABSTRACT. This work presents an analytical description of the non-uniform field distribution of plastic deformation in a flat specimen, which determines distortion of the specimen in the necking zone. The proposed method enables to be simulated the real non-uniform distributions of plastic deformation and neck distortion according to experimental measurements data. Analytical expressions are suitable for calculation of gradients and concentration of stress in the neck of a flat specimen made of real material, using well-known analytical and numerical methods: finite element methods, boundary element methods, relaxation element methods etc.

1. Introduction. Tensile test of the material is one of the basic test types that can outline the most important mechanical properties of the materials in engineering applications. The peculiarity of many structural metals and alloys is the descending segment on the conventional stress-strain diagrams associated with plastic deformation localization in the neck emerging before the material fracture. The specimen cross-sectional area at point of necking reduces suddenly followed by load decrease required for further specimen deformation before fracture. To analyze accurately the physical mechanisms of plastic deformation and material strengthening at the pre fracture stage, we need to calculate the dependence corresponding to the material response in the neck local zone, where the plastic deformation is maximum and develops at highest rate. The true load diagram in the given local volume is not reflected if to take into account only a cross section reduction in the neck, since the plastic deformation distribution in the neck is extremely non-uniform. As experience shows [1, 2], the maximum degree of plastic deformation and the critical state of the material is reached at the center of the minimum cross section of a flat specimen. There are certain difficulties in experimental measurement of the geometric shape and plastic deformation distribution in the necking zone [3]. Experimental techniques for measuring local deformation of solid bodies under different boundary loading conditions are now being developed [18]. Therefore, description of the specimen plastic distortion related to non-uniform plastic deformation distribution in the emerging neck is one of topical problems in mechanics of the deformed solid body. In this paper, we propose a universal method for the analytical setting of a smooth field with plastic deformation gradients in the local zone of a flat tensile specimen that determines the geometric shape of the neck and plastic deformation distribution in it. The proposed form of analytical description allows one to obtain distributions, which agree with experimental measurements data qualitatively and quantitatively, by variation of geometrical parameters in equations. An analytical setting of plastic deformation distribution in the neck zone allows calculating distribution and concentration of stresses in a solid body at the pre fraction stage using the methods of continuum theory of defects [911] and numerical methods for the deformed solid mechanics [12-14]. Calculation of stresses in the necking zone is an independent task and is not presented in this work. 2. Description of plastic deformation distribution in the neck of a flat tensile specimen. Experimental studies of plastic deformation distribution emerging in the neck of a flat tensile specimen show that generally, this distribution is extremely non-uniform and at the macro-scale level satisfy the following conditions [2 - 4, 15]: a) Maximum degree of plastic deformation is observed in the center of a symmetric neck; b) Plastic deformation degree decreases with distance from this center; c) In the minimum cross-section of a specimen, the material is subjected to the more severe plastic deformation; MMSE Journal. Open Access www.mmse.xyz


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