On the theory of the effect of precipitate particles on grain growth in metals

1966 ◽  
Vol 294 (1438) ◽  
pp. 298-309 ◽  
Keyword(s):  
Particle Size ◽  
Grain Size ◽  
Grain Boundary ◽  
Grain Growth ◽  
Boundary Energy ◽  
Second Phase ◽  
Pinning Force ◽  
Essential Difference ◽  
The Matrix ◽  
Critical Particle Size

A theoretical model of the energy changes accompanying grain boundary movement has been developed. It has been shown that small boundary movements will reduce the energy of a polycrystalline metal only when there is a heterogeneous grain size. The pinning force exerted by precipitate particles of a second phase on the grain boundary has also been considered. The release of grain boundary energy which accompanies grain growth has been considered as a source of energy for the unpinning process. The theory predicts a critical particle size which is dependent on the volume fraction of second phase, the matrix grain size, and the degree of heterogeneity of the matrix. Coalescence of the precipitate to a size in excess of the critical radius will permit grain growth to occur. Theoretical predictions of the critical particle size are in good agreement with values determined experimentally. The essential difference between grain growth and secondary recrystallization is indicated by the theory.

Phase Field Simulation of Grain Growth with Particle Pinning

2016 ◽  
Vol 724 ◽  
pp. 8-11
Author(s):  
Chun Yu Teng ◽  
Yun Fu ◽  
Zhan Yong Ren ◽  
Yong Hong Li ◽  
Yun Wang ◽  
...  
Keyword(s):  
Particle Size ◽  
Grain Size ◽  
Grain Boundary ◽  
Grain Growth ◽  
Phase Field ◽  
Particle Number ◽  
Boundary Energy ◽  
Service Condition ◽  
Second Phase ◽  
Pinning Effect

The properties of alloys depend on its microstructure, such as the size of grains. In general, the balanced mechanical properties of alloys can be obtained with small grain size. While the grain size of alloys may increases under heat treatment, thermal mechanical processing and service condition of high temperature, i.e., the grain growth is inevitable. The effort of most research is to control the rate of grain growth and avoid abnormal grain growth. For example, pinning the grain boundary and reduce its mobility with the second phase particles in order to prevent grain growth. Therefore, the properties of the alloys will not decreases dramatically and the structure retains a high degree of integrity. The details of grain growth with particle pinning were investigated by phase field simulations in the present paper. It is found that, with the same size of pinning particles, the pinning effect increases with the increases of the pinning particle number. With the same pinning particle number, the pinning effect increases with the increases of pinning particle size. Under the same total volume of pinning particles while different particle size and number, the pinning effect is complicated and it will be discussed in details. The pinning effect decreases with the increases of grain boundary energy. These findings could shed light on the understanding of the grain growth kinetics with particle pinning.

Effect of Ca on Grain Size and Toughness in CGHAZ of C-Mn Steel

2011 ◽  
Vol 291-294 ◽  
pp. 886-889
Author(s):  
Kun Ning Jia
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Grain Growth ◽  
Second Phase ◽  
Pinning Force ◽  
Second Phase Particles ◽  
Impact Experiment ◽  
Strong Pinning ◽  
Mn Steel

Through adding enough calcium to C-Mn steel, the second phase particles of CaO can be found in C-Mn steel. The microstructure, the grain size and the toughness of CGHAZ in micro-calcium steel and no micro-calcium steel were studied by TEM, SEM and series impact experiment. The research shows that: the second phase particles CaO in micro-calcium steel have strong pinning force to grain boundary of CGHAZ; the second phase particles can retard grain growth in the course of welding in micro-calcium steel, fining grain at CGHAZ and improving the toughness of CGHAZ in micro-calcium steel.

Orientation Selectivity of Secondary Recrystallization in Grain-Oriented Silicon Steel

2013 ◽  
Vol 753 ◽  
pp. 337-340 ◽  
Author(s):  
Yoshiyuki Ushigami ◽  
Yoshihiro Arita ◽  
Kohsaku Ushioda
Keyword(s):  
Grain Size ◽  
Boundary Energy ◽  
Secondary Recrystallization ◽  
Silicon Steel ◽  
Orientation Selectivity ◽  
Pinning Force ◽  
Grain Boundary Energy ◽  
Deviation Angle ◽  
The Matrix ◽  
Goss Orientation

It has been observed that grain size of Goss secondary grain has a strong correlation with deviation angle from the exact Goss orientation and sharper Goss grain has larger grain diameter. This orientation selectivity of secondary recrystallization has been investigated with the statistical model of grain growth in which inhibitor and texture are taken into account. The model assumes that sharper Goss grain has a higher frequency of CSL boundaries to the matrix grains and thus has lower statistical grain boundary energy and suffers lower pinning force from the inhibitor. The analysis showed that this model successfully explains orientation selectivity and depicts the effect of inhibitor and texture.

Secondary Recrystallization in Grain-Oriented Silicon Steel

2004 ◽  
Vol 467-470 ◽  
pp. 853-862 ◽  
Author(s):  
Yoshiyuki Ushigami ◽  
Tomoji Kumano ◽  
Tsutomu Haratani ◽  
Shuichi Nakamura ◽  
Shigeto Takebayashi ◽  
...  
Keyword(s):  
Boundary Energy ◽  
Secondary Recrystallization ◽  
Silicon Steel ◽  
Second Phase ◽  
In Situ Observation ◽  
Pinning Force ◽  
Goss Texture ◽  
Second Phase Particles ◽  
The Matrix ◽  
Grain Growth Behavior

Mechanism of Goss secondary recrystallization in grain-oriented silicon steel has been investigated by temperature gradient annealing and by in situ observation utilizing synchrotron x-ray topography. The results support the selective growth theory. Migration of Goss grains is controlled by second phase particles (inhibitor) and sharper Goss grains, which have higher frequency of CSL boundaries to the matrix, start to grow preferentially while the other matrix grains are stagnated by inhibitor. CSL boundaries are supposed to have lower grain boundary energy, thus suffer lower pinning force from the inhibitor and start to migrate at higher inhibition level. Based on this model, we have made a computer simulation and have found that this model successfully depicts the important features of secondary recrystallization; grain growth behavior of secondary grains, secondary grain size and sharpness of Goss texture.

Effect of Grain Boundary Energy in Recrystallization Simulation by Phase Field Method

2020 ◽  
Vol 993 ◽  
pp. 953-958
Author(s):  
Yan Wu ◽  
Ren Chuang Yan ◽  
Er Wei Qin ◽  
Wei Dong Chen
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Grain Growth ◽  
Phase Field ◽  
Boundary Energy ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Grain Boundary Energy ◽  
Average Grain Size

In this paper, the effect of grain boundary energy in AZ31 Mg alloy with multi-order parameters phenomenological phase field model has been discussed during the progress of recrystallization. The average grain size of the recrystallization grain at a certain temperature and a certain restored energy but various grain boundary energies have been studied, and the simulated results show that the larger the grain boundary energy is, the larger the average grain size will be, and the speed of grain growth will increase with the increase of grain boundary energy. Additionally, temperature will also increase the grain growth rate.

scholarly journals Grain Boundary Properties and Grain Growth: Al Foils, Al Films

2004 ◽  
Vol 819 ◽  
Author(s):  
Katayun Barmak ◽  
Wayne E. Archibald ◽  
Anthony D. Rollett ◽  
Shlomo Ta'asan ◽  
David Kinderlehrer
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Grain Growth ◽  
Misorientation Angle ◽  
Driving Forces ◽  
Boundary Energy ◽  
Orientation Imaging Microscopy ◽  
Solute Drag ◽  
Grain Structure ◽  
Two Dimensional

AbstractRelative grain boundary energy as a function of misorientation angle has been measured in cube-oriented, i.e., <100> fiber-textured, 120 [.proportional]m-thick Al foil using orientation imaging microscopy and a statistical multiscale method. The energies of low-angle boundaries increase with misorientation angle, in good agreement with the Read-Shockley model. The relative energies of high-angle boundaries exhibit little variation with misorientation. Examination of the grain structure of <111> fiber-textured, 100 nm-thick Al films annealed at 400°C for 0.5-10 h shows 5 and 6 sided grains to be the most frequent, and the fraction of four-sided grains to be significant. The mean number of sides is slightly lower than the expected value of 6 for two- dimensional structures. Of lognormal, gamma and Rayleigh distributions, gamma gives the best fit to the grain size data in the films; however, the difference between gamma and lognormal is small. Grain growth is not self-similar and stagnates after one hour of annealing. The evolution of the grain size distribution with time indicates that the growth stagnation in the films is neither consistent with boundary pinning by grooving nor with conventional treatments of solute drag. Surface, elastic-strain and plastic-strain energy driving forces do not play a significant role in the grain growth and the subsequent stagnation since the films are strongly textured even in the as- deposited state. The steady-state distributions of reduced grain area for two-dimensional, Monte Carlo and partial differential equation based simulations show excellent agreement with each other, even when anisotropic boundary energies are used. However, comparison with experimental distributions reveals a significantly higher population of small grains in the experiments.

scholarly journals Kinetics of Austenite Grain Growth during a Continuous Heating of a Niobium Microalloyed Steel

2004 ◽  
Vol 467-470 ◽  
pp. 929-934 ◽  
Author(s):  
David San Martín ◽  
Francisca García Caballero ◽  
Carlos Capdevila ◽  
C. Carcía de Andrés
Keyword(s):  
Grain Size ◽  
Grain Boundaries ◽  
Heating Rate ◽  
Grain Growth ◽  
Continuous Heating ◽  
Second Phase ◽  
Austenite Grain Size ◽  
Austenite Grain ◽  
Average Grain Size ◽  
The Matrix

Grain growth is a thermally activated process in which the average grain size increases as temperature and time increases. The driving force for grain growth results from the decrease in the free energy associated with the reduction in total grain boundary energy. There are several known factors that influence the migration of grain boundaries such as second phase particles precipitated in the matrix and the solute elements segregated at grain boundaries. The austenite grain boundaries are revealed using the thermal etching method. Carbon extraction replicas were prepared to determine the composition and size of precipitates present in the matrix. In this work, the evolution of the average prior austenite grain size (PAGS) of a low carbon steel microalloyed with niobium is studied as a function of temperature and heating rate. Austenite grains show a two-stage growth. It has been found that as heating rate increases, the grain coarsening temperature (TGC) increases and the grain size at that temperature decreases. TGC temperature lies around 40-60°C below the temperature for complete dissolution of carbonitrides (TDISS).

scholarly journals Dome Concordia ice microstructure: impurities effect on grain growth

2002 ◽  
Vol 35 ◽  
pp. 552-558 ◽  
Author(s):  
Jérôme Weiss ◽  
Jérôme Vidot ◽  
Michel Gay ◽  
Laurent Arnaud ◽  
Paul Duval ◽  
...  
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Grain Boundaries ◽  
Grain Growth ◽  
Growth Process ◽  
Boundary Energy ◽  
Ice Core ◽  
Dust Particles ◽  
The Holocene ◽  
Average Grain Size

AbstractWe present a detailed analysis of the microstructure in the shallow part (100–580m) of the European Project for Ice Coring in Antarctica (EPICA) ice core at Dome Concordia. In the Holocene ice, the average grain-size increases with depth. This is the normal grain-growth process driven by a reduction of the total grain-boundary energy. Deeper, associated with the Holocene–Last Glacial Maximum (LGM) climatic transition, a sharp decrease of the average grain-size is observed. to explain modifications to the microstructure with climatic change, we discuss the role of soluble and insoluble (microparticles) impurities in the grain-growth process of Antarctic ice, coupled with an analysis of the pinning of grain boundaries by microparticles. Our data indicate that high soluble impurity content does not necessarily imply a slowing-down of grain-growth kinetics, whereas the pinning of grain boundaries by dust particles located along the boundaries does explain modifications to the microstructure (small grain-sizes; change in grain-size distributions, etc.) observed in volcanic ash layers or dusty LGM ice.Moreover, classical mean-field models of grain-boundary pinning are in good quantitative agreement with the evolution of grain-size along the EPICA ice core. This suggests a major role for dust in the modification of shallow polar ice microstructure.

Abnormal Grain Growth Topology and Kinetics

2007 ◽  
Vol 539-543 ◽  
pp. 2401-2406
Author(s):  
Paulo Rangel Rios ◽  
Martin E. Glicksman
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Grain Growth ◽  
Abnormal Grain Growth ◽  
Common Point ◽  
The Matrix ◽  
Boundary Curvature ◽  
Number Of Faces

One common point amongst extant theories of abnormal grain growth (AGG) is that they treat this phenomenon in terms of the relative grain size, or grain radius, of the abnormal grains. Topological and metrical quantities of abnormal grains, such as the number of their faces, or their grain boundary curvature, are taken into account only indirectly through the grain size itself. This paper, by contrast, treats AGG in terms of concepts, that include both the boundary curvature and the number of faces of the abnormal grain. Two cases are examined: 1) AGG, in which the matrix grains are fully pinned, so normal grain growth cannot occur; 2) AGG in which the matrix grains are free to evolve, so that normal grain growth ensues simultaneously in the matrix.

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