马氏体相变的分形描述

FRACTAL DESCRIPTION OF THEMARTENSITIC TRANSFORMATION

概述了理论计算和Ｒｉｃｈａｒｄｓｏｎ作图两种测量谢宾斯基地毯分维的方法。用作图法测量了Ｆｅ－２９％Ｎｉ－０．１６％Ｃ合金冷至－１２５℃所得马氏体和残余奥氏体构成的显微组织的谢宾斯基分维。从作图法可知：（１）描述马氏体相变的谢宾斯基分维的物理意义是，分维值越大，残余奥氏体随马氏体尺寸减小而减少的比率越低；（２）由同一形态的马氏体和残余奥氏体构成的显微组织是否有谢宾斯基分维，决定于残余奥氏体面积和马氏体尺寸之间的关系是否满足 Ａ（ε）＝Ａ＿０ε￣（２－Ｄ）式。

The method of measuring the fractal dimension of a Sierpiriski carpet aresummarized. One is theoretical, the other is the Ricliardson plotting. The Sierpinski fractaldimension of a metallograph consisting of martensite and retained austenite, taken from anFe-29%Ni-0. 16%C alloy treated by cooling to -125℃, has been measured by theplotting method. From the plotting method, two important ideas can be realized : (1) thephysical significance of the Sierpinski fractal dimension in describing the martensitictransformation is that the larger the Sierpinski fractal dimension, the more siowly theretained austenite disappors as the size of the martensite crystais decreases; (2) whether ametallograph, consisting of martensite crystals having the same morphology and retainedaustenite, has the character of a Sierpinski fractal deponds on whether the relation betweenthe area of the retained austenite and the size of the martensite crystais obeysA (ε)= A_0 ε ￣(2- D) .