(235), Martensite: An Inclusion-Theory Explanation
H M. Ledbetter, Martin Dunn
We consider what is, perhaps, martensite's greatest crystallographic problem: ferrous martensites with a habit plane p near (225)f, or viewed more recently as nearer (449)f or even (112)f. We predict p within 2.6 degrees of observation and on the (hhl)f line 1.15 degrees from (112)f toward (111)f. Exact agreement with observation can be achieved by decreasing slightly the twin ratio from x = 0.5 and increasing slightly the aspect ratio from c/a = 0. Considering the shape-change direction d, we explain its unusual wide variation along a curve on a Wulff net. We suggest also why d scatters above and below this Wulff-net curve. Our approach uses mainly inclusion theory, where the principal input is the eigenstrain, the strain that would result if the phase transformation occurred in stress-free surroundings. Inclusion theory offers possibilities to calculate strain, stress, and elastic-strain energy. We point out why the 1953-1954 crystallographic theories of Wechsler-Lieberman-Read and Bowles-Mackensie can not (despite many modifications)explain (225)f martensite habit planes. Also, we suggest a simple test of our inclusion-theory calculations. As a specific example material, we consider the Fe-Cr-C alloy studied thoroughly by Muddle and colleagues, both for p and d. Our solution is an invariant-plane-strain deformation with a twinning raction x = 0.5. The elastic-strain energy, 0.026 GJ/m3, is about 15% of the estimated chemical free-energy difference G(fcc) - G(bcc). This alloy shows much larger departures from the Kurdjomov-Sachs orientation relationships than does a (3 10 15) f ferrous martensite.