The kinetics of pressure-induced α→ω transformation in Ti

Singh, Anil K.; Mohan, Murali; Divakar, C

doi:10.1063/1.330530

Cited by 27 publications

(12 citation statements)

References 4 publications

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“…Time evolution under the master equation leads to k i approaching zero or one asymptotically. This is more consistent with experimental data [18,26] from static compression experiments, and leads to better agreement with dynamic data [9,13,24].…”

Section: Introductionsupporting

confidence: 88%

A Model for Phase Transitions Under Dynamic Compression

Greeff

2016

J. dynamic behavior mater.

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An approach is described for simulating phase transitions among an arbitrary number of phases under dynamic compression. The time evolution of the phase fractions k i is governed by the master equation, which naturally incorporates the constraints P i k i ¼ 1 and 0 k i 1. The rates are taken to be strongly nonlinear functions of the thermodynamic driving forces. The implementation of the method is described, and illustrative applications to phase transitions in Zr are shown. The relation of the model to irreversible thermodynamics is discussed. A modification for the case where domain growth limits the transformation rate is described. This variant gives sigmoidal transformation-time curves, with the second phase fraction proportional to t 3 at early time.

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Section: Introductionsupporting

confidence: 88%

A Model for Phase Transitions Under Dynamic Compression

Greeff

2016

J. dynamic behavior mater.

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“…x transformation occurs via a nucleation and growth mechanism, when stress-assisted nucleation controls the overall transformation rate. It is interesting to compare our results with previous investigations of [13,15] where the fraction of x-phase was measured during isochronal pressure exposure in the pressure range between 4 and 10 GPa. These authors had determined two parameters: ance of the first nuclei of the omega phase under certain pressure, and (ii) the time necessary to transform more than 50 % of the a-phase to x-phase.…”

Section: Discussionmentioning

confidence: 70%

“…Indeed, we observe *25 % of x-phase in samples deformed for c = 785 (N = 5, which corresponds to 5 min) under a pressure of 4 GPa, whereas without shear deformation it would take 27 h to obtain the first nuclei! It should be noted that the results presented in [13,15] were obtained in in-situ measurements, whereas ours are estimated by the amount of phase remaining after unloading which had inevitably led to an underestimation of the x-phase fraction. In Table 1 the portions of HPT-induced omega phase are presented together with corresponding applied pressures, shear strains and time of deformation (duration of pressure exposure).…”

Section: Discussionmentioning

confidence: 89%

Evidence of α → ω phase transition in titanium after high pressure torsion

Ivanisenko¹,

Kilmametov

Rösner³

et al. 2008

International Journal of Materials Research

104

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Evidence of a ? x phase transition in titanium after high pressure torsion It is well known that a high pressure x-phase is formed in Ti at high pressures in the range between 2 and 8 GPa. This martensitic-type transformation demonstrates very large hysteresis, and hence the x-phase can be retained in the material after release of pressure. Additionally, applied shear stresses are known to facilitate the a ? x transformation. This paper describes an investigation on the x-phase formation after high pressure torsion under a wide range of pressures and shear strains by means of X-ray diffraction and transmission electron microscopy. We show that the x-phase forms in Ti upon high pressure torsion deformation after 300 s under a pressure of 3 GPa. This suggests that the transformation kinetics are notably increased as compared with the kinetics of pressure-induced transformation.

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“…Data on the kinetics are, however, sparse, and we can make only some general observations. Singh et al 33 have made quantitative observations of the transition kinetics under static pressure. They find a continuously varying relaxation time that depends exponentially on pressure in the range from 5 to 9 GPa.…”

Section: Resultsmentioning

confidence: 99%

Shock-induced α–ω transition in titanium

Greeff

Trinkle

Albers

2001

Journal of Applied Physics

121

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Equilibrium free energies for the ␣ and phases of Ti are constructed. The result is a consistent picture of the ambient pressure, static high pressure, and shock data, as well as first-principles electronic structure calculations. The Hugoniot consists of three segments: a metastable ␣-phase region, a transition region, and an-phase branch. All the Hugoniot data are consistent with a transition occurring at ϳ12 GPa. An early identification ͓R. G. McQueen et al., in High Velocity Impact Phenomena, edited by R. Kinslow ͑Academic, New York, 1970͔͒ of a phase transition at 17.5 GPa appears to have been an artifact. The shock Hugoniot extends further into the metastable region than static data, indicating the existence of a relaxation process occurring on a time scale intermediate between those of the static and dynamic measurements.

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The kinetics of pressure-induced α→ω transformation in Ti

Abstract: Shock-induced α-ω phase transition and mechanisms of spallation in shock loaded titanium alloys AIP Conf.

Cited by 27 publications

References 4 publications

A Model for Phase Transitions Under Dynamic Compression

A Model for Phase Transitions Under Dynamic Compression

Evidence of α → ω phase transition in titanium after high pressure torsion

Shock-induced α–ω transition in titanium

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