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Statistical Modeling of a Dislocation Phase-Field in Ductile Single Crystals

Published online by Cambridge University Press:  17 March 2011

M. Koslowski ,
M. Ortiz  and
A.M. Cuitino
M. Koslowski
Affiliation:
Graduate Aeronautical Laboratories California Institutie of Technology Pasadena, CA 91125, USA
M. Ortiz
Affiliation:
Graduate Aeronautical Laboratories California Institutie of Technology Pasadena, CA 91125, USA
A.M. Cuitino
Affiliation:
Department of Mechanical and Aerospace Engineering Rutgers University Piscataway, NJ 08854, USA
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Abstract

A model for the description of strain hardening and hysteresis at different temperatures and strain rates in ductile single crystals is introduced. The theory accounts for: and arbitrary number and arrangement of dislocation lines over a slip plane; the long-range elastic interactions between dislocation lines; the core structure of the dislocations; the interaction between the dislocations and applied resolved shear stress field; and the dissipative in teractions with short-range obstacles and lattice friction, resulting in hardening, path dependency and hysteresis. We introduce a variational formulation for the statistical mechanics of dissipative systems. The influence of finite temperature as well as the mechanics are modeled with Metropolis Monte Carlo simulations and a mean field approximation. The theory predicts a range of behaviors which are in qualitative agreement with observation, including: hardening and dislocation multiplication under monotonic loading and hysteresis loops under under cyclic loading. The flow stress was found to be dependent on the temperature and on the strain rate only at finite temperature.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 701: Symposium T – Statistical Mechanical Modeling in Materials Research , 2001 , T4.5.1
Copyright
Copyright © Materials Research Society 2002

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References

REFERENCES

[1] Lachenmann, R. and Schultz, H. Scirpta Metallurgic a 4:709–714(1970).Google Scholar
[2] Nagasaka, M.. Japanese Journal of Applied Physics, 38:171–175 (1999).Google Scholar
[3] Morrow, J.. Unpublished test results (1975).Google Scholar
[4] Ortiz, M.. Journal of Applied Mechanics-Transactions of the ASME, 66(2):289–298 (1999)Google Scholar
[5] Koslowski, M., Cuitino, A.M. and Ortiz, M.. cond-mat/01109447, Los Alamos National Laboratory; http://xxx.lal.gov/abs/cond-mat/0109447Google Scholar
[6] Baskes, M.I., Hoagland, R.G., and Tsuji, T.. Modeling and Simulation in Materials Science and Engineering, 6(1):9–18(1998).Google Scholar
[7] Rodney, D. and Phillips, R.. Physical Review Letters, 82(8):1704–1707(1999).Google Scholar
[8] Shenoy, V.B., Kukta, R.V., and Phillips, R.. Physical Review Letters 84(7):1491–1494(2000).Google Scholar
[9] Ortiz, M. and Phillips, R.. Advances in Applied Mechanics, 36:1–79(1999).Google Scholar
[10] Nowak, U.. IEEE Transactionson Magnetics, 31:4169–4171 (1995).Google Scholar
[11] Lyberatos, A.. Journal of physiscs D-Applied Physics, 33:R117–R133(2000).Google Scholar
[12] Binder, K. (editor). Monte Carlo Methods in Statistical Physics. Springer-Verlag (1986)Google Scholar
[13] Sethna, J.P., Dahmen, K., Kartha, S., Krumhansl, J.A., Roberts, B. W., and Shore, J.D.. Physical Review Letters 70:3347–3350 (1993).Google Scholar