Technical Notes - Relation Between the Volume of Martensite and the Number of Martensitic Plates per Unit Volume

RECENTLY, there has been much activity in the field of nucleation of martensitic transformations.'- One of the problems in this field is the calculation of the rate of nucleation (number of plates nucleated per unit untransformed volume per unit time) in terms of observable parameters. Two such observable parameters are the fraction of the length of a straight line which corresponds to the portion of the total length of the line that lies in the martensitic phase and the number of plates intersected by this straight line per unit length of line. Because of the necessity of a valid answer to this problem, the following investigation was undertaken. Although this problem has been treated in the past, a derivation of the relation between the volume and linear fractions of martensite will be described to illustrate the method used in the succeeding analyses. It is assumed that the martensitic plates are in the form of a right circular cylinder having a small height relative to the radius of the base. The volume fraction of martensite is then: fr = lXNl,hjAl [1] where f, is the volume fraction of martensite, and Nij is the number of plates per unit total volume having the area Ai and the height hi. The linear fraction of martensite is obtained as follows. For the plates having the particular area A, and height h,, the fraction sin 0 dB* will have their cylinder axes between the angles 0 and 0 + d0 to the straight line along which the linear fraction of mar-