Abstract
A plastic strain gradient theory incorporating the geometrically necessary dislocation density based on the low order displacement finite element method is proposed for calculation of the hardness value by Berkovich indentation. The obtained analysis results by this work are found to be in good agreement with the experimental data. Three-dimensional modeling technique of Berkovich indentation is also suggested. An empirical coefficient that includes the strain gradient effect into the yield stress formula is introduced and determined by reviewing area factors and hardness curves generated from the analyses. As pile-up occurs, classical plasticity theory gives a higher area factor and lower hardness value than those from experiment. However the strain gradient plasticity theory used in this work gives corrected area factor and hardness values. Dislocation density plots are generated that can explain the size effect during indentation and the availability of the three-dimensional modeling of Berkovich indentation.
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Recommended by Associate Editor Dae-Cheol Ko
Moon Shik Park received his B.S. degree (1987) from Hanyang University, and his M.S. (1989) and Ph.D. (1994) from Korea Advanced Institute of Science and Technology. He worked for Daewoo Heavy Industries and Boeing Commercial Airplane Group as an airplane structural engineer and designer. He was also the Dean of Academic Information Affairs Office and is currently a professor in the Department of Mechanical Engineering at Hannam University, Korea. His research interests include computational structural mechanics for design and analysis.
Yeong Sung Suh received his B.S. degree (1981) from Seoul National University, and his M.S. (1987) and Ph.D. (1990) from Rensselaer Polytechnic Institute (RPI), U.S.A. He was a postdoctoral researcher at both RPI and the Ohio State University. Currently he is the department chair in the department of mechanical engineering at Hannam University, Korea. His research interests include modeling and analysis of nonlinear material behavior in metal matrix composites and metal forming processes.
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Park, M.S., Suh, Y.S. Hardness estimation for pile-up materials by strain gradient plasticity incorporating the geometrically necessary dislocation density. J Mech Sci Technol 27, 525–531 (2013). https://doi.org/10.1007/s12206-012-1243-4
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DOI: https://doi.org/10.1007/s12206-012-1243-4