Computer simulation of martensitic microstructures

Scripta METALLURGICA et MATERIALIA

Vol. 24, pp. 533-536, 1990 Printed in the U.S.A.

Pergamon Press plc All rights reserved

COMPUTER SIMULATION OF MARTENSITIC MICROSTRUCTURES

Rakesh Gupta, V. Sarin and V. Raghavan Indian Institute of Technology Delhi New Delhi - ii0 016, India (Received November 8, 1989) (Revised January 2, 1990) Introduction In a recent paper (I), simulated microstructures of martensite for the three habit planes of 13,10,15~, {259}, and {225} have been reported. These microstructures are based on a two-dimensional model, which assumes that martensitic plates of different generations intersect an equatorial plane of observation (view plane) of a spherical grain at right angles. In spite of this limitation, the model yielded microstructures, which are quite similar to the experimental structures. In this paper, we have extended the simulation to three dimensions. A computer program has been developed which is capable of generating simulated microstructures for any combination of a habit plane and aview plane. The Simulation Procedure For efficient utilization of space within the spherical grain, the angle 0 between two neighbouring plates of a generation is set equal to the smallest angle between any two variants of the habit plane (I). The first primary plate passes through the centre of the grain. The centre-to-centre distance between the first primary plate and the second plates, i.e., the immediate neighbour on either side, is R sin 8, where R is the radius of the grain. The distance between the first plate and the third plate on either side is 2R sino. sin f~/2 - 0) and so on. The number of primary plates on either side of a central plate is obtained by using Eqn. (i) of Ref. (I). The variants chosen for the primary plates in the simulation are : First, third, etc. plates Second, fourth, etc. plates

(225) (125)

(259) (159)

(3,10,15) (3,10,15)

In the secondary generation, the first plate is located by finding a variant, which bears the minimum angle with the (i00) plane that passes through the midpoint of the line joining the centres of the two bounding plates of the primary pocket. The other secondary plates form with the minimum angle 8 between one another. The variants chosen for the secondary plates in the simulation are : First, third, etc. plates Second, fourth, etc. plates

(522) (522)

(952) (952)

(15,10,3) (15,10,3)

The plates, in general, intersect the view plane at different angles and thus have different apparent thicknesses, which are larger than the true thicknesses. The apparent semithickness c' of a plate that makes an angle a with the view plane is given by c

,

c

~2

= (~ - ~ c ) sin e +

~r

2

2~ -

)2

sine + r 2

where r and c are the radius and the semithickness of the plate.

553 0036-9748/90 $5.00 + .00 Copyright (c) 1990 Pergamon Press plc

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MARTENSITIC MICROSTRUCTURES

Using the common criterion that a growing martensitic plate is stopped by the grain boundaryand the neighbouring plates, it is seen in the simulation that the secondary plates in a primary pocket grow to a final elongated shape. The energetics of the growth process (2) appear to favour this possibility. The numerical data on all the plates that form on a given view plane are stored in a data file, in a form compatible with AutoCAD. Printed copies of the microstructures are then obtained. Results and Discussion About i00 mierostructures were simulated for the three habit planes {3,10,15}, {259}, and {225}, using a c/r ratio of 0.05. Typical microstructures for some selected view planes are given in Figs. I to 3. The simulated microstructures are in good qualitative agreement with the experimental microstructures found in the literature. A few observations pertinent to the illustrated microstructures can be made. Figs. l(a), 2 (a) and 3 (a) are on view planes perpendicular to the primary plates. A comparison of the microstructures of Figs. 2(a) and 3 (a) and of Figs. 2(c) and 3(c) shows that, for a given view plane, the microstructures of the {3,10,151 and {259} habits look very similar. This arises from the fact that the angle ® for the two cases, 18.90 ° and 21.99 °, are close to each other. By virtue of the minimum angle e for the {225} habit (40.75 ° ) being twice as large as for the other two habits, the plates are not so well packed here, Fig. l(a). However, when viewed on a (i01) plane, Fig. l(b), the plates appear to be better packed. The zig-zag nature of the primary generation is not always evident. For example, the primary plates in Fig. 3(b) appear parallel to one another on a (i00) view plane. References i. Pratyush Kumar and V. Raghavan, Scripta Metall., 22, 975 (1988). 2. V. Raghavan and M. Cohen, Acta Metall., 20, 779 (1972).

(a) Fig. I : Simulated Microstructures for the {225} Habit. View Planes : (a)(052), and (b) (I01)

(b)

gol.

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MARTENSITIC

(a)

MICROSTRUCTURES

535

(b)

\

(c)

.(d)

Fig. 2 : Simulated Microstruc_tures for the { 259 } Habit. View Planes : (a) (095), (b) (121), (c) (I01), and (d) (121).

,

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MARTENSITIC MICROSTRUCTURES

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!

Ii

Ca)

(c)

/

~b)

(d)

Fig. 3 : Simulated Microstructu_zes for the {3,10,15} Habit. View Planes : (a) (0,15,10), (b) (i00), (c) (I01), and (d) (II0).