×

A model for plasticity kinetics and its role in simulating the dynamic behavior of Fe at high strain rates. (English) Zbl 1419.74004

Summary: The recent diagnostic capability of the Omega laser to study solid-solid phase transitions at pressures greater than 10 GPa and at strain rates exceeding \(10^{7} \)s\(^{ - 1}\) has also provided valuable information on the dynamic elastic-plastic behavior of materials. We have found, for example, that plasticity kinetics modifies the effective loading and thermodynamic paths of the material. In this paper we derive a kinetics equation for the time-dependent plastic response of the material to dynamic loading, and describe the model’s implementation in a radiation-hydrodynamics computer code. This model for plasticity kinetics incorporates the Gilman model for dislocation multiplication and saturation. We discuss the application of this model to the simulation of experimental velocity interferometry data for experiments on Omega in which Fe was shock compressed to pressures beyond the \(\alpha \)-to-\(\varepsilon \) phase transition pressure. The kinetics model is shown to fit the data reasonably well in this high strain rate regime and further allows quantification of the relative contributions of dislocation multiplication and drag. The sensitivity of the observed signatures to the kinetics model parameters is presented.

MSC:

74-05 Experimental work for problems pertaining to mechanics of deformable solids
74C20 Large-strain, rate-dependent theories of plasticity
74J40 Shocks and related discontinuities in solid mechanics
74E15 Crystalline structure
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Barker, L. M.; Hollenbach, R. E.: Laser interferometer for measuring high velocities of any reflecting surface, J. appl. Phys. 43, 4669-4675 (1972)
[2] Boehly, T. H.; Craxton, R. S.; Hinterman, T. H.; Kelly, J. H.; Kessler, T. J.; Kumpan, S. A.; Letzring, S. A.; Mccrory, R. L.; Morse, S. F. B.; Seka, W.; Skupsky, S.; Soures, J. M.; Verdon, C. P.: The upgrade to the OMEGA laser system, Rev. sci. Instrum. 66, 508-510 (1995)
[3] Colvin, J. D.; Legrand, M.; Remington, B. A.; Schurtz, G.; Weber, S. V.: A model for instability growth in accelerated solid metals, J. appl. Phys. 93, 5287-5301 (2003)
[4] Colvin, J.D., Kalantar, D.H., 2006. Scaling of pressure with intensity in laser-driven shocks and effects of hot X-ray preheat. In: Furnish, M.D., Elert, M., Russell, T.P., White, C.T. (Eds.), Proc. APS Conf. Shock Compression of Condensed Matter, Amer. Inst. Phys. CP845, pp. 1413 – 1416.
[5] Gilman, J. J.: Microdynamics of plastic flow at constant stress, J. appl. Phys. 36, 2772-2777 (1965)
[6] Hawreliak, J.: Analysis of the X-ray diffraction signal for the \(\alpha \) - &z.epsiv; transition in shock-compressed iron: simulation and experiment, Phys. rev. B 74, 184107 (2006)
[7] Kalantar, D. H.: Multiple film-plane diagnostic for shocked lattice measurements, Rev. sci. Instrum. 74, 1929-1934 (2003)
[8] Kalantar, D. H.: Direct observation of the \(\alpha \) - &z.epsiv; transition in shock-compressed iron via nanosecond X-ray diffraction, Phys. rev. Lett. 95, 075502 (2005)
[9] Magnenet, V.; Rahouadj, R.; Ganghoffer, J. -F.; Cunat, C.: Continuous symmetries and constitutive laws of dissipative materials within a thermodynamic framework of relaxation, Int. J. Plasticity 23, 87-113 (2007) · Zbl 1331.74134
[10] More, R. M.; Warren, K. H.; Young, D. A.; Zimmerman, G. B.: A new quotidian equation of state (QEOS) for hot dense matter, Phys. fluids 31, 3059-3078 (1988) · Zbl 0654.76042 · doi:10.1063/1.866963
[11] Remington, B. A.: Materials science under extreme conditions of pressure and strain rate, Metall. mater. Trans. A 35A, 2587-2607 (2004)
[12] Smith, R. F.; Eggert, J. H.; Jankowski, A.; Celliers, P. M.; Edwards, J.; Gupta, Y. M.; Asay, J. R.; Collins, G. W.: Stiff response of aluminum under ultrafast shockless compression to 110GPa, Phys. rev. Lett. 98, 065701 (2006)
[13] Steinberg, D. J.; Lund, C. M.: A constitutive model for strain rates from 10 - 4 to 106s - 1, J. appl. Phys. 65, 1528-1533 (1989)
[14] Taylor, J. W.; Rice, M. H.: Elastic – plastic properties of iron, J. appl. Phys. 34, 364-371 (1963)
[15] Zel’dovich, Y.B., Raizer, Y.P., 2002. In: Hayes, W.D., Probstein, R.F. (Eds.), Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Dover, Mineola, NY.
[16] Zimmerman, G. B.; Kruer, W. L.: Numerical simulation of laser-initiated fusion, Comments plasma phys. Control. fusion 2, 51-61 (1975)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.