Grain Boundary Nucleation of Proeutectoid Ferrite in an Fe-C-Ni Alloy.

Enomoto, Masato; Kobayashi, Yusaku

doi:10.2355/isijinternational.39.600

Cited by 4 publications

(2 citation statements)

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“…These are considered to be relevant in ferrite transformation in iron alloys. [13][14][15][16] For simplicity, the growth is assumed to occur at a constant rate, i.e. proportional to holding time.…”

Section: Calculation Of the Size Of Sections On The Test Plane 221mentioning

confidence: 99%

Estimation of Number of Precipitate Particles per Unit Volume from Measurements on Polished Specimen Surfaces. Computer Simulation.

Umezaki

Enomoto²

2000

ISIJ International

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* The figure indicates that if the average of b s /a s values is less than 0.5, the particles are an oblate ellipsoid. Figure 9 shows the variation of N V with time in a system in which DNϭ100 particles are nucleated successively per unit time and grow at the same rate as in Fig. 8. The rate of increase in the particle number was determined to be J V ϭ 102.8 by least square method, close to the increasing rate of actual particle numbers. These figures show that the procedures described above can correctly estimate the particle density in the case of both constant and varying particle numbers. Figure 10 shows the variation of N V with time calculated with the same nucleation and the growth rate as in Figs. 8 and 9, incorporating particle impingement. The N V first increases with time, but turns to decrease at tϳ8. If nucleation stops at tϭ8, the amount of decrease becomes greater. Figure 11 shows the variation with time of the number of clusters of impinging particles, where n is the number of sections contained in one cluster. Solid triangles are the sum of the clusters of various sizes to be observed on the test plane. Thus, the influence of particle impingement on the estimation of particle density is very large. The simulat- ed temporal variation of N V is similar to that of the number of ferrite allotriomorphs in Fe-C(-X) alloys reported previously, 15,16) which indicates that impingement of ferrite particles already occurred within austenite grain boundaries, although the fraction transformed was small at the time of measurement. Simulation Incorporating Particle ImpingementThe omission of undetectably small particles can have a large influence on the estimation of the total number of particles since the weight factor a i is large for small i ( Table 1). The amount of error may depend on the growth kinetics, that is, if the initial growth rate of particles is large the proportion of small particles is small. Determination of the Number of Non-sphericalParticles The N V of Nϭ500 oblate particles of qϭ0.4 nucleated under the site saturation mode was calculated and results are shown in Fig. 12a. Solid symbols were calculated from Eq. (13). They indicate that N V is correctly evaluated by measuring oblate particles along the major axis of elliptical sections if the shape factor (ϭ0.832, Fig. 3) is included. If these particles are approximated as spheres, N V is underestimated as shown by open symbols. The amount of error is consistent with the omission of the shape factor.On the other hand, prolate particles are classified by measuring the length along the minor axes of elliptical sections.Simulation results for prolate particles of qϭ3 are shown in Fig. 12b. The N V is again correctly evaluated by incorporating the shape factor (ϭ1.81) as shown by solid symbols. A slightly smaller N V value at the earliest time (tϭ0) is probably because D max (ϭ20) was too large compared to the particle size at that time (2rϭ1). If these particles were treated as spheres and the particle size was measured along the major ...

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Section: Calculation Of the Size Of Sections On The Test Plane 221mentioning

confidence: 99%

Estimation of Number of Precipitate Particles per Unit Volume from Measurements on Polished Specimen Surfaces. Computer Simulation.

Umezaki

Enomoto²

2000

ISIJ International

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“…13,14) The SS method has been applied to various systems. Enomoto and Kobayashi 16) analyzed the number and size of ferrite particles in a Fe-C-Ni alloy per unit volume and compared the results with measured values. Susan et al 17) performed a stereological analysis of pores in a metal, the results of which were highly dependent on the similarity of these pores to a sphere.…”

Section: Introductionmentioning

confidence: 99%

Reliability of Inclusion Statistics in Steel by Stereological Methods

Shimasaki

Shoji

et al. 2016

ISIJ Int.

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In this paper, we investigate the reliability of estimating of inclusion size distribution and number density in steel by using stereological methods. The magnitude of the inclusion concentration in steel is evaluated by the total oxygen and the assumed average inclusion sizes. The principles of Schwartz-Saltykov (SS) and modified SS (MSS) methods are introduced. A simulation model is developed to disperse particles with a predefined particle size distribution (PSD) randomly into a three dimensional (3D) space. A series of test planes are generate to measure the two dimensional (2D) PSD and particle number density (PND) on the cross-sections (CS). The SS and MSS methods are applied to investigate the reliability of the translation between the 3D and 2D information of the system, such as the 2D and 3D PSD and PND. The influence of predefined 3D PSD on the reliability of the stereological methods are studied, such as mono sized, lognormal and normal distributions. The effect of the representative group diameters in the discretized groups for SS and MSS methods is investigated as well.

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Evaluation of the accuracy of the three-dimensional size distribution estimated from the schwartz-saltykov method

Takahashi

Suito

2003

Metall Mater Trans A

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The validity of estimation of the three-dimensional size distribution (3-DSD) using the SchwartzSaltykov (SS) method has been evaluated by applying the discrete two-dimensional size-distribution (2-DSD) model. The coefficient for the SS method has been generalized, and the verification of this method has been studied by focusing on the measured number of sectioned particles on the cross section of the specimen, the step width of the histogram for the SS method, and the oversight of small sectioned particles. The total number of particles per unit volume (total N V (T.N V )) and the number of particles in each size class, estimated by the SS method, are found to be always underestimated compared with the true N V value, without regard to the oversight of small sections. The T.N V value can be reasonably estimated by an extrapolation method, in which the step width of the histogram approaches zero. The relative frequency in a distribution function is correctly determined independent of the step width when the oversight involves a sectioned particle size equal to or less than one-tenth of the true mean diameter of the particles. The quantitative 3-DSD can be obtained from the reasonably estimated value of T.N V and the correctly determined relative frequency.

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Grain Boundary Nucleation of Proeutectoid Ferrite in an Fe-C-Ni Alloy.

Cited by 4 publications

References 0 publications

Estimation of Number of Precipitate Particles per Unit Volume from Measurements on Polished Specimen Surfaces. Computer Simulation.

Estimation of Number of Precipitate Particles per Unit Volume from Measurements on Polished Specimen Surfaces. Computer Simulation.

Reliability of Inclusion Statistics in Steel by Stereological Methods

Evaluation of the accuracy of the three-dimensional size distribution estimated from the schwartz-saltykov method

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