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On the genesis of secondary recrystallization nuclei
Scripta Mattialia,
Vol. 34, No. 5, pp. 685-687,1996 Elswier Science Ltd Copyright 0 1996 Acta Metallurgica Inc. Printed in the USA. All rights reserved 1359-6462/96 $12.00 + .OO
Pergamon 0956-716X(95)00561-7
ON THE GENESIS OF SECONDARY RECRYSTALLIZATION NUCLEI V. Yu. Novikov* Department of Metallography Moscow Institute of Steel and Alloys (Received May 24, 1995) Introduction
The conditions necessary for the development of secondary recrystallization (SR) are, first, the stagnation of normal grain growth in a fine-grained matrix and, second, the presence of crystallites which can overcome factors responsible for the growth inhibition. During SR, these crystallites usually attain a linear dimension of ablout 100 times greater than the mean grain size in the matrix. At the same time, the maximum grain size before SR commencement is 3-5 times as large as the mean grain size. Thus the question arises, how can grains of initially “normal” size become abnormally large SR grains? The assumption (1) that such grains, appear as a result of coalescence of several grains of nearly the same orientation seems to the present author rather artificial. It appears more reasonable to assume that grains which attain an abnormally large size grow very fast. However, there are no experimental data relating to the transient period from the microstructure of normal grain-size non-homogeneity to that of the abnormal one. This can be apparently explained by a very low number fraction of crystallites which are able to grow during SR. Thus a computer simulation appears the only means to approach the problem of nucleation during SR. This report presents the data on large grain behaviour at the incubation period of SR obtained by computer simulation. Model
In a statistical model of grain growth (2) grains of any size class were believed to be in the mean field of the nearest neighbours i.e. the number of adjacent grains of a given size class was assumed proportional to the total number of grains of the class at a given instant of time. However, the concept of the mean field is incorrect in respect to the neighbours of large crystallites because the latter are surrounded by grains the mean size of which is not greater than the most probable grain size, D, (3). Hence, we used here the model (2) in a slightly modified form. It was assumed that any crystallite the size of which is 5 or more times greater than D, is in a “random field” of the nearest neighbours. According to this concept, a random part
*Address for correspondence: Treptower Str. 74 d, D-22147 Hamburg, Germany.
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of the neighbours is described by the mean field approximation whereas the rest are the grains whose size is not greater than D,, their number fractions in different size classes being random. For SR to develop it is necessary to inhibit the grain growth. Hence a drag force was introduced whose magnitude is independent of both time and the size of grains. The value of the drag force was taken equal to 0,7/D,,,,,which provides simultaneously both the invariability of D, with time and the growth of several large grains (4). A model polycrystal was assumed to consist of two groups of grains, C 1 and C2, each group being characterised by certain properties of boundaries between the grains of this group as well as between the grains of different groups. Such an approach corresponds to the description of the array of grains by a disorientation distribution function. Initial size distributions of Cl- and C2-grains were supposed identical. The energy of all the grain boundaries and the mobility of boundaries Cl/Cl and C2/C2 were assumed to be identical whereas the mobility of the boundary Cl/C2 was supposed to be x times greater than the mobility of other boundaries i.e. y,,=~~~=y,~,M,,=M,,, M,,=x M, ,. These assumptions mean that a polycrystal with a scattered multi-component texture is considered. Since in the initial microstructure the sizes of the largest grains in both of the groups are identical, these grains have the same driving force for growth. However, the growth rate of C2-grains was assigned to be greater due to an increased magnitude of the average mobility of their boundaries (5) which was achieved by an appropriate decision upon the relative number of the grains. If the number of the C2-grains is small they should be surrounded preferably by C 1-grains and hence the average mobility of the boundaries of the C2-grains should approach M,,. The data given below refer to the case when the initial relative number of the C2grains is equal to 0.1. Results and Discussion
Fig. 1 shows the evolution of grain-size non-homogeneity at the incubation period of SR, the ratio D,,,JDm being a measure of the non-homogeneity and D,, the maximum grain size. It is seen that the enhancement of the average boundary mobility of the C2-grains due to an increase in x leads to a significant increase of the ratio D,JD,, It is worth noting that since the time elapsed from the start of the growth process the relative volume of the C2 group increases only slightly. The latter testifies that the data of Fig. 1 do relate to an incubation period of SR. A comparison of curves 1 and 3 in Fig. 1 demonstrates the effect of the average boundary mobility on alterations in D,,/D,. Whereas at x=1 (i.e. at equal mobility of all the
Figure 1. Effect of the average mobility of the boundaries of CZ-grains on grain size non-homogeneity: (1) F 2; (2) F 1.5; (3) x=1. See text.
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ON THE GENESIS OF SECONDARY
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Time. al-b. units
Figure 2. Effect of the average mobility of boundaries of CZ-grains on D&I,,:
(1) x=2; (2) x=1.5. See text.
boundaries) D,,&,, reaches by time ~20 arb. units the value of approximately 9, at x=2 the ratio by the same time is equal to -16. It should be mentioned that the latter is the result of the joint effect of both the driving force and the mobility. In fact, a large crystallite growing faster due to a greater mobility only reaches a greater size which leads to an increase of its driving force and to a subsequent increase of its growth rate. Thus, an increased average mobility of boundaries of some large grains could cause an abnormal increase of their size. It is necessary to note that a proper value of the drag force is also responsible for such a behaviour of large grains. As follows from the simulation data obtained the size distribution of C2-grains during grain growth moves to the right-hand part of the overall distribution provided the mobility of their boundaries is increased. Rather than to compare the size distributions of Cl- and CZgrains it is more suitable to focus our attention on the size of large grains which could become SR nuclei. Consider grains in decreasing order of their sizes beginning from D,,. The grains of size D,, are almost exclusively C2grains. Among the grains of a smaller size, the fraction of C2grains reduces gradually with a decrease in grain size. Then, the appropriate measure of population of C2-grains among the largest ones could be the D,,/D,, ratio where D,, is the maximum grain size at which >95% of grams belong to C2 group, and D,, the grain size at which the number fractions of Cl- and C2-grains are equal. As can be seen from Fig. 2 the magnitude of the ratio at x=:2by time f=20 arb. units is twice as large as that at x=1.5. It can be concluded from these data that an increased average boundary mobility affects also the SR texture because most of the SR nuclei are crystallites with such a boundary mobility. References 1. V.V.Gubematorov, N.A.Bryshko, B.K.Sokolov and B.N.Balandin, Phys.Met.Metallogr.(SSR), 2. V.Yu.Novikov, Acta Met, 26, 1739 (1978) 3. V.Yu.Novikov, E.A.Zalem and Yu.A.Smimova, Acta Met.Mater., 40, 3457 (1992) 4. V.Yu.Novikov, l~hys.Met.Metallogr.(USSR), 66, No 2, 125 (1988) 5. V.Yu.Novikov, Texture, 2,35 (1975)
57,No 2, 124 (1984).
Vol. 34, No. 5, pp. 685-687,1996 Elswier Science Ltd Copyright 0 1996 Acta Metallurgica Inc. Printed in the USA. All rights reserved 1359-6462/96 $12.00 + .OO
Pergamon 0956-716X(95)00561-7
ON THE GENESIS OF SECONDARY RECRYSTALLIZATION NUCLEI V. Yu. Novikov* Department of Metallography Moscow Institute of Steel and Alloys (Received May 24, 1995) Introduction
The conditions necessary for the development of secondary recrystallization (SR) are, first, the stagnation of normal grain growth in a fine-grained matrix and, second, the presence of crystallites which can overcome factors responsible for the growth inhibition. During SR, these crystallites usually attain a linear dimension of ablout 100 times greater than the mean grain size in the matrix. At the same time, the maximum grain size before SR commencement is 3-5 times as large as the mean grain size. Thus the question arises, how can grains of initially “normal” size become abnormally large SR grains? The assumption (1) that such grains, appear as a result of coalescence of several grains of nearly the same orientation seems to the present author rather artificial. It appears more reasonable to assume that grains which attain an abnormally large size grow very fast. However, there are no experimental data relating to the transient period from the microstructure of normal grain-size non-homogeneity to that of the abnormal one. This can be apparently explained by a very low number fraction of crystallites which are able to grow during SR. Thus a computer simulation appears the only means to approach the problem of nucleation during SR. This report presents the data on large grain behaviour at the incubation period of SR obtained by computer simulation. Model
In a statistical model of grain growth (2) grains of any size class were believed to be in the mean field of the nearest neighbours i.e. the number of adjacent grains of a given size class was assumed proportional to the total number of grains of the class at a given instant of time. However, the concept of the mean field is incorrect in respect to the neighbours of large crystallites because the latter are surrounded by grains the mean size of which is not greater than the most probable grain size, D, (3). Hence, we used here the model (2) in a slightly modified form. It was assumed that any crystallite the size of which is 5 or more times greater than D, is in a “random field” of the nearest neighbours. According to this concept, a random part
*Address for correspondence: Treptower Str. 74 d, D-22147 Hamburg, Germany.
685
686
ON THE GENESISOF SECONDARY
Vol. 34, No. 5
of the neighbours is described by the mean field approximation whereas the rest are the grains whose size is not greater than D,, their number fractions in different size classes being random. For SR to develop it is necessary to inhibit the grain growth. Hence a drag force was introduced whose magnitude is independent of both time and the size of grains. The value of the drag force was taken equal to 0,7/D,,,,,which provides simultaneously both the invariability of D, with time and the growth of several large grains (4). A model polycrystal was assumed to consist of two groups of grains, C 1 and C2, each group being characterised by certain properties of boundaries between the grains of this group as well as between the grains of different groups. Such an approach corresponds to the description of the array of grains by a disorientation distribution function. Initial size distributions of Cl- and C2-grains were supposed identical. The energy of all the grain boundaries and the mobility of boundaries Cl/Cl and C2/C2 were assumed to be identical whereas the mobility of the boundary Cl/C2 was supposed to be x times greater than the mobility of other boundaries i.e. y,,=~~~=y,~,M,,=M,,, M,,=x M, ,. These assumptions mean that a polycrystal with a scattered multi-component texture is considered. Since in the initial microstructure the sizes of the largest grains in both of the groups are identical, these grains have the same driving force for growth. However, the growth rate of C2-grains was assigned to be greater due to an increased magnitude of the average mobility of their boundaries (5) which was achieved by an appropriate decision upon the relative number of the grains. If the number of the C2-grains is small they should be surrounded preferably by C 1-grains and hence the average mobility of the boundaries of the C2-grains should approach M,,. The data given below refer to the case when the initial relative number of the C2grains is equal to 0.1. Results and Discussion
Fig. 1 shows the evolution of grain-size non-homogeneity at the incubation period of SR, the ratio D,,,JDm being a measure of the non-homogeneity and D,, the maximum grain size. It is seen that the enhancement of the average boundary mobility of the C2-grains due to an increase in x leads to a significant increase of the ratio D,JD,, It is worth noting that since the time elapsed from the start of the growth process the relative volume of the C2 group increases only slightly. The latter testifies that the data of Fig. 1 do relate to an incubation period of SR. A comparison of curves 1 and 3 in Fig. 1 demonstrates the effect of the average boundary mobility on alterations in D,,/D,. Whereas at x=1 (i.e. at equal mobility of all the
Figure 1. Effect of the average mobility of the boundaries of CZ-grains on grain size non-homogeneity: (1) F 2; (2) F 1.5; (3) x=1. See text.
Vol. 34, No. 5
ON THE GENESIS OF SECONDARY
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5
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687
20
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Time. al-b. units
Figure 2. Effect of the average mobility of boundaries of CZ-grains on D&I,,:
(1) x=2; (2) x=1.5. See text.
boundaries) D,,&,, reaches by time ~20 arb. units the value of approximately 9, at x=2 the ratio by the same time is equal to -16. It should be mentioned that the latter is the result of the joint effect of both the driving force and the mobility. In fact, a large crystallite growing faster due to a greater mobility only reaches a greater size which leads to an increase of its driving force and to a subsequent increase of its growth rate. Thus, an increased average mobility of boundaries of some large grains could cause an abnormal increase of their size. It is necessary to note that a proper value of the drag force is also responsible for such a behaviour of large grains. As follows from the simulation data obtained the size distribution of C2-grains during grain growth moves to the right-hand part of the overall distribution provided the mobility of their boundaries is increased. Rather than to compare the size distributions of Cl- and CZgrains it is more suitable to focus our attention on the size of large grains which could become SR nuclei. Consider grains in decreasing order of their sizes beginning from D,,. The grains of size D,, are almost exclusively C2grains. Among the grains of a smaller size, the fraction of C2grains reduces gradually with a decrease in grain size. Then, the appropriate measure of population of C2-grains among the largest ones could be the D,,/D,, ratio where D,, is the maximum grain size at which >95% of grams belong to C2 group, and D,, the grain size at which the number fractions of Cl- and C2-grains are equal. As can be seen from Fig. 2 the magnitude of the ratio at x=:2by time f=20 arb. units is twice as large as that at x=1.5. It can be concluded from these data that an increased average boundary mobility affects also the SR texture because most of the SR nuclei are crystallites with such a boundary mobility. References 1. V.V.Gubematorov, N.A.Bryshko, B.K.Sokolov and B.N.Balandin, Phys.Met.Metallogr.(SSR), 2. V.Yu.Novikov, Acta Met, 26, 1739 (1978) 3. V.Yu.Novikov, E.A.Zalem and Yu.A.Smimova, Acta Met.Mater., 40, 3457 (1992) 4. V.Yu.Novikov, l~hys.Met.Metallogr.(USSR), 66, No 2, 125 (1988) 5. V.Yu.Novikov, Texture, 2,35 (1975)
57,No 2, 124 (1984).