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The composite coating is a mechanical disordered composite; a large number of spheroidal ceramic grains are distributed in Ni base alloy matrix.
Because the thermal expansion coefficients and elastic modulus of Ni base alloy and spheroidal ceramic grains are different, there will be residual stresses in both ceramic grains and Ni base alloy in fabricating process.
V1 is the volume of the ceramic grain in two-phase cell.
Thermal expansion coefficients of two-phase cell For two-phase cell，Ni base alloy and ceramic grain are isotropy, the elastic constants of Ni base alloy and ceramic grain can be expressed as (8) Where, and, are Lame’s constants of Ni base alloy and ceramic grain respectively.
For the spheroidal ceramic grains, Sijkl can be determined by reference [7].

A number of models of the recrystallisation behaviour of IN718 have been developed [3-6] which are based on empirical observations of the relationships between strain, strain rate and temperature and the recrystallised volume fraction and grain size.
Set initial conditions Calculate if delta phase is present Increase grain set diameter Calculate dislocation density Recrystallising or growing Increase grain set diameter R G Set new number of dislocations Set dislocation density in new grains Nucleate new grains Calculate length of grain boundary available for nucleation Calculate partition ratios New increment Set new number of dislocations Set new dislocation density Stop Y N Set initial conditions Calculate if delta phase is present Increase grain set diameter Calculate dislocation density Recrystallising or growing Increase grain set diameter R G Set new number of dislocations Set dislocation density in new grains Nucleate new grains Calculate length of grain boundary available for nucleation Calculate partition ratios New increment Set new number of dislocations Set new dislocation density Stop Set initial conditions Calculate if delta phase is present
Increase grain set diameter Calculate dislocation density Recrystallising or growing Increase grain set diameter R G Set new number of dislocations Set dislocation density in new grains Nucleate new grains Calculate length of grain boundary available for nucleation Calculate partition ratios New increment Set new number of dislocations Set new dislocation density Stop Y N Figure 3.
At 1080 o C both models predicted the grain size to within one ASTM number however the volume fractions recrystallised were over predicted significantly.
At 1000 o C the volume fractions recrystallised were better at within 5% however the grain sizes were less reliable with some predictions being 2-3 ASTM numbers in error.

In order to evaluate whether or not the proposed misorientation condition is obeyed, the number fraction dn of the experimentally measured distribution must be compared with the number fractions dr obtained for a random misorientation distribution.
The ratio dn/dr can be interpreted as the number intensity fi of the given reference misorientation ∆gr.
Tolerance [º] Number Fraction Nuclei [%] Number Fraction Grown Grains [%] Density Nuclei Density Grown Grains 5 0.37 6.49 0.37 6.46 10 2.46 23.4 0.30 2.89 15 11.7 67.5 0.43 2.47 Table 1 : Number fractions and number densities of nuclei and grown grains observed in a growth experiment on Fe-2.8%Si, before and after growth, respectively.
In the first example it was shown that the <110>26.5º orientation relation controls the selective growth of a number of nucleus grains, which grow at the expense of a single crystal matrix of a Fe-2.8%Si steel.
Conf. on Grain Growth, ICGG-3, Ed. by H.

To solve this problem it is advisable to perform the experiments in conditions where the number of ‘free parameters’ influencing the (near)cube grains formation during annealing is strongly limited.
The numbers of correctly indexed points was always above 98%.
In homogeneously (less) deformed matrix the recrystallized areas were composed of single isolated grains or small chains of grains surrounded by deformed/recovered matrix.
Most of the grains were elongated along specific directions.
However, only one set of elongated grains shows the (near)cube orientation.

The fibrous grains are aligned close to the billets extrusion direction.
Showing; the grain sizes obtained, using the mean linear intercept λx parallel and λy perpendicular to the main direction of alignment, grain aspect ratio, equivalent circular diameter (ECD) grain size after grain reconstruction from the EBSD data, the standard deviation of the ECD grain size distributions normalised with respect to the mean diameter (σSD/dm), the percentage of HAGB area, and the mean boundary misorientations.
Overall, this leads to a slightly larger average ECD grain size than for Route A and a grain aspect ratio close to one (Table 1).
The average 'grain sizes' determined in table 1 for this alloy are therefore somewhat misleading, as they are dominated by the larger numbers of small grains present, which are particularly fine in the case of the 90° die.
Altering the die angle from 120 to 90°, changes the ideal shear strain per extrusion cycle from 1.15 to 2, but reduces the total number of cycles to obtain the same strain (from 15 to 9 in this case).

Moreover, a lower tensile strength was observed at a larger prior austenite grain size.
The prior austenite grain size was calculated from the planar mean area using Eq.1.
R = ( ( 3 A ) / ( 2 N π ) )1/2 (1) Here, R is the mean radius, A is the area of observed cross section and N is the number of grains in observed cross section. 3.
The prior austenite grain size increases with increasing solution treatment time.
These values are shown in Figs.7 to 10 in terms of the prior austenite grain size.

An average size of original grains was 17 mm.
The fraction of these grains is about 0.2.
The elongation of original grains and the development of strain-induced grain boundaries results in decreasing the transverse grain size.
In contrast to central area, the screw rolling to 63% reduction in area leads to the formation of a number of new fine grains on the sample edge (Fig. 3b).
In the present study, any bulging of original grain boundaries, leading to new grain development was not revealed in spite of frequently observed grain boundary serrations.

But grains grew up obviously after normalizing annealing at 850°C for 1h because the mobility of grain boundary is so good at elevated temperature that pinning effect of precipitates can’t prevent the migration of grain boundary.
At least 100 grains were randomly measured in each case and the average grain sizes were estimated.
(a) (c) (b) (f) (e) (d) Fig. 1 Microstructures of the coiled bands (a) 550°C/1h, (b) 550°C/2h, (c) 550°C/3h, (d) 650°C/1h, (e) 650°C/2h, (f) 650°C/3h Table 1 Average grain sizes and the dates of precipitates in the coiled bands Process Average grain size [μm] Precipitate Average size [nm] Number density* Volume fraction [%] 550°C/1h 20 124 3.9 0.047 550°C/2h 23 134 5.0 0.065 550°C/3h 24 138 4.7 0.070 650°C/1h 21 148 4.5 0.067 650°C/2h 24 118 6.6 0.070 650°C/3h 29 110 9.1 0.084 * The number density of precipitates represents the average number of precipitates in a view field.
Hence, grains coarse obviously, which suggests normalizing annealing is necessary in order to gain large grains.
After normalizing annealing at 850°C for 1h, grains grew up obviously owing to the good mobility of grain boundary at elevated temperature and the average grain sizes are more than 100μm.

The driving force for boundary motion was provided by the surface tension of a curved grain boundary: bp a= γ , where bγ is the grain boundary surface tension and a is the width of the shrinking grain [10].
Similar to the 8.4° <100> grain boundary, a 12.0°<100> grain boundary (bicrystal B) did not move in a conventional way.
Behavior of a 14.3° <100> grain boundary (bicrystal C) at 580°C.
Behavior of a 14.3° <100> grain boundary (bicrystal C) at 600°C.
The change of the shape of this boundary above 510°C can be understood as a roughening of the low energy symmetric grain boundary configuration, as observed and discussed in a number of studies on special high angle CSL grain boundaries [3,7,8].

The Effect of Copper Content on the Dynamic Grain Growth in AL-Cu-Zr systems K.
An increase in grain size occurred in both materials due to deformation, but this dynamic grain growth (DGG) was much greater in the material with the higher copper content.
An increase in grain size with strain - dynamic grain growth - during hot deformation is a common characteristic reported for a number of materials, and is characterised by a grain growth rate significantly exceeding that which occurs in the absence of plastic strain [5].
This shows that both alloys have undergone dynamic grain growth.
With 2wt% Cu, the initial banded grain structure persisted to large strains and there was relatively little dynamic grain growth.