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To mimic the geometrical arrangement of AlN precipitates along austenite grain boundaries, a new model for precipitation at grain boundaries is used, which takes into account fast short-circuit diffusion along grain boundaries as well as the slower bulk diffusion of atoms from inside the grain to the grain boundaries.
Also, the number of available theoretical treatments of the precipitation process of AlN is rather limited.
To take into account the geometrical arrangement of AlN precipitates along austenite grain boundaries, a novel model for precipitation at grain boundaries is used [35].
A default grain size of 50 µm is used in all simulations unless stated otherwise.
Thus, the grain sizes used in the simulations are only estimated values.

This coarse-graining model using sub-divided region with high order interpolation function is adopted for finding the positions of atoms and for describing deformation on the curved structure.
Coarse-grained energy and equilibrium equation in system We regard the group of atoms around a specific node as the cluster.
The coarse-grained model has a total number of degrees of freedom 30360 (including inner displacement 1560), while MM model has 72000.
Fully atomistic simulation needs a total number of degree of freedom 12120 but our model has 8931 (including inner displacement 723).
We note that though inner displacement in coarse-graining model for CNTs occupies very small the number of degree of freedoms, it has a great effect on the deformation and on the strain energy curve (See Fig. 1(a) and Fig. 2(a)).

We defines the recovered fraction of aluminium grains as frc and the recrystallised fraction as frx.
Grain growth.
Also, krx points to the predominance of Al-Sn phase boundaries, while grain growth is characterised by the increase of Al-Al grain boundaries.
These results indicate that a model based on grain growth alone is not accurate.
However, even the simplest physically-based model tested here resulted more accurate than the polynomial fit, with a smaller number of adjustable parameters.

Grain refinement is directly related to the number of active nuclei in the melt.
If the melt temperature is low enough to avoid dissolution of the embryos, their life time is long enough to promote a high density of nuclei in the melt, thus leading to the development of large number of globular grains with small grain size [10].
The sample presents mainly homogeneous a-Al globular grains with average grain size around 50 mm and a few rosette like grains.
Isothermal processing at 620 and 640ºC led to the formation of more heterogeneous structures, with larger a-Al grains and higher number of rosettes.
In this case, due the high cooling rate of the melt, the number of nuclei developed by cavitation was smaller, therefore grain refinement was not so efficient.

The maximum cutting depth (agmax) of single abrasive grain is obtained by 21 max 4 � � � � � � = ep ds w g da CN a � � , (2) where �w is the feed rate, �s is tangential speed of the wheel, Nd is the number of dynamic effective cutting edge, C is the cutting constant, ap is cutting depth and de is the equivalent diameter of the wheel.
The number of the dynamic effective cutting edge (Nd) is the measured effective cutting edge on the unit area along the contract arc of the wheel and the workpiece.
In actual situation, the exponents � and � are related to exponents p and m. p reflects the relationship between the dynamic cut-in depth ads and the number of static effective cutting edges of unit length.
(9) When m=0, it means some grains are blunt and while m=1, it shows the triangle grain.
Acknowledgements Author gratefully acknowledges Heilongjiang Province Natural Science Foundation and the Harbin City Science Foundation of China Heilongjiang Province for their Support of this work: The contact number is E0218 and 2002AFXXJ046.

In grain boundary junctions of ferrite second-phase the particles are always globular.
Moreover, grain pearlite (Fig. 3, b), dominates over lamellar one (Fig. 3, c).
In grain volume and on grain boundaries the second-phase particles are observed.
In grain boundary junctions the second-phase particles are always globular.
Otherwise, a great number of pores form.

The steel sheet having the texture of the second group shows high r-value and good formability, therefore a number of studies have been focused on the texture formation and its utilization [4,5].
Journal Title and Volume Number (to be inserted by the publisher) 3 Figure 3 Recrystallisation occurred at grain boundary of {100}<011> by-crystal after 70% cold rolling and its texture.
A {h,1,1}<1/h,1,2> recrystallisation grain was found.
The pole figure shows the orientations at the interior of the grains and at the close point to the grain boundary.
Within A grain, the orientation slightly shifts at the close position to the grain boundary and its rotational direction was opposite to the orientation of B grain.

The literature reports a considerable number of research works that deal with grain coarsening problem in FSS welds.
The grain size is measured by IMAGEJ software.
It is observed the presence of large columnar ferrite grains.
It’s observed that the addition of Aluminum (Al) or Titanium (Ti) reducing the grains size and increase the equiaxed grains fraction with varying degrees.
The fracture surface morphology of sample treated by powder mixture (Al+Ti) addition displayed ductile morphology which is characterized by larger number of dimples and pores.

On the other hand, the rolling process is characterized by the reduced number of passes and the larger reductions applied in the initial stands [1-3].
For conventional grain sizes, preexisting grain boundaries are the preferential nucleation sites for the new recrystallized grains [8].
Numbers on the flow curves represent the DRX percentages measured at different strains.
Although, the recrystallized nuclei are observed only after some degree of growth, a substantial number of highly serrated austenite grain boundaries are also found at these stages in all deformation conditions.
It has been suggested that in the case of coarse austenite microstructures, due to the reduction of the specific grain boundary area, i. e. smaller number of potential nucleation sites, intragranular nucleation could play a more important role [10, 12].

For lower strains when the grain size is still small enough, the plastic flow governs by twinning and probably grain boundary sliding.
We suppose that this could be explained by the development of grain boundary sliding for the lower grain sizes which requires lower stresses than a transfer of shear from one grain to another via dislocation mechanism.
Variation the crystallite size and microstrains with increasing of numbers of HPT cycles.
Strain-induced grain growth.
Further deformation has led to strong grain growth in shear direction and to formation of elongated grains.