Institute of Metals Division - Discussion of Plastic Deformation Modes in Fe-Ni-C Martensites

A. G. Crocker and M. Bevis (Battersea College of Technology)— Richman and Richman and conard17 have recently published the very interesting results of their studies on the plastic deformation of Fe-Ni-C martensites and of an Fe-5 wt pct Be alloy. Other work on the range of Fe-Be alloys containing between 16 and 27 at. pct Be has also been reported by Richman." One of the fascinating features of this work is that the materials investigated deform primarily by means of twinning and that several twinning modes are operative in addition to the well-established (112 ) mode of bcc materials The composition planes of these unusual twins were determined using a single-surface analysis and reported as (0131, "{045)" or "{089)", and It is now thought1' that the "{0,1,13)" habit reported for the Fe-Ni-C alloys'' is more likely to be near "{127)". Although the full twinning elements of these unusual twinning modes could not be determined directly from the experimental results, the authors attempt to deduce the elements by considering twin intersectionslQ and by using the projection technique of Jaswon and Dove. The basic assumption of their approach is that the (013) habits are truly rational planes but that the other habits are irrational and merely approximated to by the indices quoted above. They thus deduce that the twinning mode describing the (013) habit is either Type I or compound and that the modes describing the other habits are Type 11. This deduction must however be false as all twinning modes in cubic structures obeying the classical orientation relationships of deformation twinning must be compound. Type-I and Type-I1 modes can occur in all of the other crystal systems (indeed in the triclinic system compound modes are not allowed), but in the cubic system only compound modes can arise. This fact, which does not appear to be well-known, fol- lows immediately from the relations between the four twinning elements defining a twinning mode. Thus for a Type-I mode which is uniquely defined by the rational twinning elements K1 = hi and given by: where the summation convention of the tensor calculus has been adopted. For cubic materials the metrics and reduce to the unit tensors and j so that we have It is clear from these equations that both ki and ui must take on integral values; i.e., Kz, and ql must be rational, if hi and vi are integers, i.e., if K1 and are rational. Thus for cubic materials a Type-I mode must degenerate into a compound mode and the same result also arises for Type-II modes. The apparently irrational habits observed by the authors can thus not be explained in terms of Type-I1 twinning if the classical laws of deformation twinning are to be obeyed. An alternative explanation of the irrational habits is that they may arise from twinning modes with four irrational twinning elements. These modes, which do not obey the classical orientation relationships associated with deformation twinning, have been shown to arise as the result of double twinning processes in magnesium,22 but may also describe a simple shear on an irrational plane in an irrational direction. Indeed double twinning processes in bcc