THE SHAPE, CONFIGURATION AND STRESS-FIELD OF TWINS AND MARTENSITE PLATES

It is shown that the equilibrium shape of a twin or martensite plate can be calculated by treating the interface as a distributed array of dislocations and by calculating their equilibrium distribution. The shape of an isolated twin is an ellipse to first approximation. Second approximation treatments show that the tip of the twin sharpens with increasing stress for the screw dislocation case while it becomes blunter with increasing stress for the edge dislocation case. A colony of twins is treated in much the same way as a stacked array of piled-up dislocations for the screw dislocation case. It is found that the twins flatten out with decreasing separation. Expressions are derived for the stress-field and for the strain energy of such stacked twins. It is shown that the twin spacing should be proportional to the square root of the twin length, from which the twin boundary energy can be calculated.