Kinematic theory for scale-invariant patterns in acicular martensitas

Madan Rao and Surajit Sengupta

Physica A: Statistical Mechanics and its Applications, 1996, vol. 224, issue 1, 403-411

Abstract: We present a kinematic theory which explains the emergence of scale-invariant patterns in acicular martensites which occur, for example, in Fe C and Fe Ni alloys. Scale-invariant structures emerge naturally as a consequence of competition between the average tip-velocity, ν, and the rate of nucleation, I, of the martensite grains. Martensite growth is analyzed in terms of fixed points of a well-defined renormalization group. It is shown that the stationary probability distribution of the martensite grain size P(l), is governed by two fixed points - an unstable (noncritical) fixed point at ν/I = 0, characterized by a Gamma distribution and a stable (critical) fixed point at ν/I = ∞, characterized by a Lévy distribution, P(l) ∼ l−α. A universal crossover function describes the SPD at intermediate values of ν/I. The analysis may also be used to compute the tip-velocity from optical micrograph pictures of martensite grains.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:224:y:1996:i:1:p:403-411

DOI: 10.1016/0378-4371(95)00349-5

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