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In addition, by increasing the diffusion active energy of carbon in austenite, carbides hinder the motion of interface and thus refine austenite grain.
In general, the formation of austenite proceed by nucleation and growth of austenite grain [8-10].
Nucleation and growth stages involve the calculation of the volume of all growing particles, assuming that all grains never stop growing and that new grains hypothetically nucleate also in the transformed material: the extended transformed volume, i.e., at this stage, (‘hard’) impingement is ignored.
Meanwhile, the active energy for growth, QD, are also decreasing with the increase of heating rate, which may also be ascribed to the increase of austenitization temperature and the number of vacancies.
Thus, we can assume that the velocity of austenite grain growth is mainly controlled by the diffusion of carbon in austenite, and it is increasing with austenitization temperature.

It can be observed that black nanocrystalline grains embedded in the amorphous phase in the TEM image.
With the increasing in amount of Si, the Fe2Si is detected in the coating and the number of Fe2B peaks increases.
There are dendrite grains in Fig. 2 (a), ligulate flower grains in Fig. 2 (b) and equiaxed grains in Fig. 2 (c) appeared in the coatings of three alloys, respectively.
The dendrite grains in cladding layer were broken by the laser remelting.
The crystalline grains such as Fe2B and γ-(Fe,Ni) in the coating does not change obviously owing to the same reason.

It requires no processing equipment outside of the casting machine, no grain refinement procedure and no additional cycling time except for cooling down to the desired casting temperature.
Ltd. described possibility to create the appropriate slurry by simple grain refinement and employing a low pouring temperature and high cooling rate without any agitation.
In fact, Hitachi's simple grain refinement and temperature control methodology is now at the heart of several slurry-on-demand methods [5].
The reduction of 2� SL would allow grain boundaries to melt thus leading to isolated solid particles in the liquid.
The main factors for equiaxed grain growth are number of nucleuses, temperature gradient and solidification rate.

An extensive grain fracture followed by some flattening and grain capping was identified to be the important wear modes with coarser grits and the deterioration rate of coated abrasive performance was very less [7].
Although abrasive grains are also used in a grinding wheel to effect surface finishing, the important difference between a bonded grinding wheel and a coated abrasive grain is that the latter can flex and bend.
With lesser depth of cut, there will be a gradual abrasive grain wear thus the constant force profile (Figure 5b).
With the size of the abrasive grain and number of abrasive grits in a given area known, the average grinding force acting on each individual active grain at a certain time increment can then be estimated.
Force per unit grain can be computed from the finite element model Fig. 11.

In the model the microstructure evolution is described by the volume fraction of recrystallization X, un-recrystallized grain size D1, recrystallized grain size D2, the average grain size D and the maximum difference of grain size Ddis , where the subscript 1 and 2 denotes the variable in the unrecrystallized region and in the recrystallized region, respectively.
In above equations, * F represents measured loads at different time points, *X , *D , *disD represent the measured values of the recrystallized volume fractions, the average grain sizes and the maximum grain size differences.
The experimental results include the load-displacement curve, distribution of average grain size, volume fraction of dynamic recrystallization, and maximum difference of grain size.
Here a real number vector (parameter vector) is regarded as a representation of problem.
Recrystallization volume fraction Average grain size Maximum difference of grain size Fig.3 Simulated results on microstructure distribution of formed AZ31D part.

The evolution of the threshold stress is described as a function of accumulated shear strain in the grain, i.e
Furthermore, a 3D polycrystal generator, Neper [10], is used to describe the grain morphology.
In so doing, each individual grain in the polycrystal aggregate is made up of a number of elements with the same crystallographic orientation.
By contrast, the basal poles of grains in the extruded sheet only fall inside a narrow range near the ND.
Acknowledgement This research was sponsored by the Key Project of National Education Ministry with grant number 311017.

It can be seen that the original grains were elongated along the deformation direction in the low strain area.
In the high strain area however, new DRX grains were nucleated with the high stored dislocations energy.
When increasing the deformation temperature to 1100℃, a large number of new fine DRX grains emerged resulting in the high volume fraction of DRX grains in Fig.
The original grains were replaced entirely by the new DRX grains and the size of the DRX grains increased.
The DRX grains are finer correspondingly at the high strain rate condition.

First, it provides a new way to enhance the thermal stability of nanostructured materials produced by SPD because the new fine precipitated phases can be effective in inhibiting the slippage and migration of grain boundaries, thus impeding grain growth.
Fig. 1 Tensile data of Al-4.11% Cu alloys in undeformed, MAC-deformed, and post-deformation annealed conditions: (a) Ultimate tensile strength: the number of MAC passes curves; (b) Elongation to failure: the number of MAC passes curves Number of MAC passes HB 0 4 8 12 16 20 60 80 100 120 ST θ″ θ θ′ Fig. 2 The hardness-MAC passes curves of MAC-processed samples as a function of MAC passes Fig. 2 shows the hardness of samples in four conditions during MAC.
There was an obvious increase in the number and size of θ′ precipitates in 473 K annealing at the same time (Fig. 4 d).
When these two competing effects strike a balance, the number of dislocations is close to saturation.
Additionally, SPD also gave rise to great grain refinement.

At this point the grain size limit.
A class size of grains in the general wrought magnesium alloy grain size range, the average grain diameter of about 50 ~ 70μm, and the other is fine equiaxed grain diameter size of about 2 ~ 10μm.
In the small grain size, the deformation, the left large grain interior obvious deformation zone, and the right of small grains almost no distortion deformation twinning and other organizations, small grains are elongated or equiaxed .
Since the crystal grains fine, increases the surface area of ​​the grain boundary sliding and thereby deformed easily, deformation mechanism of grain boundary sliding by the plastic deformation.
But in the fine grains, the grain boundary sliding play a useful role in the deformation.

The developed models for these purposes traditionally rely on semi-empirical approaches [1] which bring about a number of inherent restrictions, e.g. the predictions are valid for the limited range of experimental conditions of laboratory simulations.
The material had been exposed to various reheating conditions resulting in austenite grain sizes of 24, 34 and 52µm.
Thus, the subsequent bainite/martensite phase is encompassed by the ferrite grains that had formed at austenite boundaries.
This length, over which the hard impingement of ferrite grains occurs, is the prior austenite grain size, dγ, however for a (a) εεεε=0 (b) εεεε=0.3 (c) εεεε=0.6 25µµµµm deformed austenite it can be expressed as an effective value which represents the minor axis of an ellipsoidal austenite grain; this axis shrinks as the amount of strain, ε, increases, i.e. [4]: )exp( ε−= γddeff (1) It had been shown that accounting for this correction in the JMAK approach, one could effectively describe the kinetics of ferrite reaction from work-hardened austenite [5].
Similarly, it is proposed here to consider the effective grain size for a non-recrystallized austenite to describe the kinetics of ferrite formation in the framework of a mixed-mode model [6] that has already been applied to describe the austenite decomposition from recrystallized austenite in a number of advanced high strength steels [2-3,5].