Iterative Determination of the Orientation Relationship Between Austenite and Martensite from a Large Amount of Grain Pa
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The crystallographic study of martensite and lower bainite by electron backscatter diffraction has been under considerable interest in recent years[1–6]. Miyamoto et al.[2] studied the variant selection of individual martensitic or bainitic laths, which required the complete reconstruction of the parent austenite microstructure[3] from martensitic or bainitic EBSD orientation maps. The variant pairing tendencies between martensitic laths in iron–carbon alloys were studied by Stormvinter et al.,[4] and a similar study was also conducted for a bainitic low carbon steel by Takayama et al.[5] In all of these studies,[1–6] it was noted that a previously observed orientation relationship (such as Kurdyumov–Sachs or Nishiyama– Wasserman) was not accurate enough for reliable parent austenite reconstruction or variant pair indexation, necessitating the use of an experimentally determined orientation relationship (hereafter referred to as OR).
Suikkanen et al.[6] studied the variant pairing of a 0.2C-2Mn-1.5Si-0.6Cr steel using the Nishiyama– Wasserman orientation relationship; however, the selection of this predetermined OR was based on a visual observation of pole figures rather than a rigorous statistical analysis. The determination of a sufficiently accurate experimental orientation relationship is clearly of vital importance in the crystallographic study of martensite or bainite. It has been demonstrated that a satisfactorily accurate experimentally determined orientation relationship can be obtained from EBSD data by manual selection of a single parent austenite grain[3] or by comparing a large number of potential orientation relationships to grain boundary misorientation data.[7] The first method, while effective, involves a tedious and in certain cases impractical manual selection process of parent austenite grains. The second method is completely automatic, but the calculation time required is dependent on the size of the orientation relationship dataset, which at high desired accuracies may become significant. A fast, reliable method for the determination of the orientation relationship would facilitate faster automatic handling and analysis of large EBSD datasets of martensitic and bainitic steels. The orientation relationship between austenite and martensite can be expressed in the following manner: Oc Ci Tc!a ¼ Oa;i
½1
In Eq. [1], Oc and Oa;i are orientation matrices representing the crystallographic orientations of austenite and martensite. Tc!a is a misorientation matrix representing the orientation relationship between the phases and Ci is a symmetry operator for one of the 24 mutually equivalent crystallographic solutions present in cubic symmetry. The use of different symmetry operations results in a different Oa variant orientation for the same Oc . Assuming that two different martensitic variants have been formed from the same austenitic parent grain, the misorientation matrix M between the two would be: ðOa;i Þ1 Oa;j ¼ M
½2
or, replacing Oa;i and Oa;j with the left side of Eq. [1]: ðOc Ci Tc!a Þ1 Oc Cj Tc!a
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