FTMP-based Simulation and Evaluation of Apparent Reduction in Elastic Modulus

Authors

  • S Ihara
  • M Uematsu
  • T Hasebe

DOI:

https://doi.org/10.21152/1750-9548.14.4.373

Abstract

This study attempts to quantitatively evaluate the apparent reduction in elastic moduli, generally observed in metallic materials during unloading and/or cyclic elasto-plastic deformation, based on Field Theory of Multiscale Plasticity (FTMP). Two typical arrangements of bowing-out dislocation segments that yield mutually-distinct trends are examined by utilizing the FTMP-based duality diagram representation scheme. It is demonstrated that not only the scheme allows us to visualize the associated energy flow but also to correlate the resultant apparent shear modulus reduction rate in a unified manner by the duality coefficient measured on the duality diagrams. The scheme is demonstrated to be effective also for more complex cases accompanied by pinning/unpinning and the following relaxation processes.

References

L. P. Kubin, "Dislocation Patterns: Experiment, Theory and Simulation," in Stability of Materials, A. Gonis, P. E. A. Turchi and J. Kudrnovský, Eds., Plenum Press, New York, 1996, pp. 99-135. DOI: https://doi.org/10.1007/978-1-4613-0385-5_4

S. Raj and G. M. Pharr, "A compilation and analysis of data for the stress dependence of the subgrain size," Mater. Sci. Eng., vol. 81, pp. 217-237, 1986. DOI: https://doi.org/10.1016/0025-5416(86)90265-x

E. Kröner, "Initial Studies of a Plasticity Theoy Based upon Statistical Mechanics in Inelastic Behavior of Solids," in Inelastic Behavior of Solids, M. F. Kanninen, W. F. Adler, W. F. Rosenfield and R. I. Jaffee, Eds., McGraw-Hill, New York, 1970, pp. 137-147. DOI: https://doi.org/10.1126/science.167.3926.1761-a

T. Hasebe, "Continuum Description of Inhomogeniously Deforming Polycrustalline Aggeregate ased on Field Theory," IUTAM Symposium on Mesoscopic Dynamics of Fracture Pricess and Materials Strength. Edited by kitagawa, H. and Shibutani, Y., Kluwer Academic Publishers,, pp. 381-390, 2004. DOI: https://doi.org/10.1007/978-1-4020-2111-4_36

T. Hasebe, "Interaction Fields Based on Incompatibility Tensor in Field Theory of Plasticity -Part I: Theory-," IMMIJ, vol. 2, no. 1, pp. 1-14, 2009. DOI: https://doi.org/10.12989/imm.2009.2.1.001

T. Hasebe, "Interaction Fields Based on Incompatibility Tensor in Field Theory of Plasticity -Part II: Application-," IMMIJ, vol. 2, no. 1, pp. 15-30, 2009. DOI: https://doi.org/10.12989/imm.2009.2.1.015

T. Hasebe, M. Sugiyama, H. Adachi, S. Fukutani and M. Iida, "Modeling and Simulations of Experimentally-Observed Dislocation Substructures Based on Field Theory of Multiscale Plasticity (FTMP) Combined with TEM and EBSD-Wilkinson Method for FCC and BCC poly/Single Crystals," Mater. Trans., vol. 55, no. 5, pp. 779-787, 2014. DOI: https://doi.org/10.2320/matertrans.m2013226

T. Hasebe and T. Naito, "FTMP-based 4D Evaluations of Discrete Dislocation Systems," in New Frontiers of Nanometals (Proc. 35th RisØ int. Symp. on Maters. Sci.), S. Faester, Ed., 2014, pp. 305-312. DOI: https://doi.org/10.13140/2.1.4287.9368

S. Ihara and T. Hasebe, "FTMP-based Simulations and Evaluations of Geometrically-Necessary Boundaries (GNBs) of Dislocation," Int. Jnl. of Multiphysics, vol. 13, no. 3, pp. 253-268, 2019. DOI: https://doi.org/10.21152/1750-9548.13.3.253

L. Kubin, G. Canova, B. Devincre, V. Pontikis and Y. Brechet, "Dislocation Microstructure and Plastic Flow: 3D Simulation," Solid State Phenomena, vol. 23&24, pp. 455-472, 1992. DOI: https://doi.org/10.4028/www.scientific.net/ssp.23-24.455

H. M. Zbib, M. Rhee and J. P. Hirth, "3D Simulation of Curved Dislocations: Discretization and Long range Interactions," in Advances in Engineering Plasticity and its Applications, T. Abe and T. Tsuruta, Eds., Pergamon, 1996, pp. 15-20. DOI: https://doi.org/10.1016/b978-0-08-042824-6.50009-x

F. Yoshida, T. Uemori and K. Fujiwara, "Elastic–Plastic Behavior of Steel Sheets under in-plane Cyclic Tension–Compression at Large Strain," Int. J. Plast., pp. 633-659, 2002. DOI: https://doi.org/10.1016/s0749-6419(01)00049-3

M. Yang, Y. Akiyama and T. Sasaki, "Evaluation of Change in Material Properties due to Plastic Deformation," J. Mater. Process. Technol., pp. 232-236, 2004. DOI: https://doi.org/10.1016/j.jmatprotec.2004.04.114

R. H. Wagoner, "Sheet Springback," in Continuum Scale Simulation of Engineering Materials: Fundamentals – Microstructures – Process Applications, D. Raabe, F. Roters, F. Barlat and L. Chen, Eds., Wiley-VCH, 2004, pp. 757-774. DOI: https://doi.org/10.1002/3527603786

N. Brown, "Observations of Microplasicity," in Microplasticity, C. J. McMahon, Jr., Ed., John Wiley and Sons Inc., New York, 1968, pp. 45-73.

A. Granato and K. Lucke, "Theory of Mechanical Damping Due to Dislocations," J. Appl. Phys., vol. 27, pp. 583-593, 1956. DOI: https://doi.org/10.1063/1.1722436

J. F. Nye, "Some Geometrical Relations in Dislocated Crystals," Acta Metall., vol. 1, pp. 153-162, 1953. DOI : https://doi.org/10.1016/0001-6160(53)90054-6

K. Kondo and M. Yuki, "On the Current Viewpoints of Non-Riemannian Plasticity Theory," in RAAG Memoirs of Unifying Study of Basic Problems in Engineering and Physical Science by Means of Geometry, vol. 2, K. Kondo, Ed., Gakujutsu Bunken Fukyu-kai, 1958, pp. 202-226.

I. Yoon, "FTMP based Development of Continuous Field Evaluation Method for Three-Dimensional Discrete Dislocation System," Undergraduate Thesis, Kobe University, 2012.

M. Yamada, T. Hasebe, Y. Tomita and T. Onizawa, "Dislocation Dynamics Simulation on Stability of High Dense Dislocation Structure Interacting with Coarsening Defects," IMMIJ, vol. 1, no. 4, pp. 437-448, 2008. DOI: https://doi.org/10.12989/imm.2008.1.4.437

Published

2020-11-15

How to Cite

Ihara, S., Uematsu, M. and Hasebe, T. (2020) “FTMP-based Simulation and Evaluation of Apparent Reduction in Elastic Modulus”, The International Journal of Multiphysics, 14(4), pp. 373-388. doi: 10.21152/1750-9548.14.4.373.

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Articles