Optimization Scheme of the Orientation Relationship from Crystallographic Statistics of Variants and its Application to Lath Martensite

Abstract

In crystallographic theory of martensitic transformation, a slightly change of orientation relationship between lath martensite and prior austenite may indicate a different transformation mechanism and a change of mechanical property. Nevertheless, when the retained austenite can be hardly found in specimen, it is a great challenge to establish an accurate determination method for orientation relationship from the variant orientations only. Although some methods have been proposed, a reasonable evaluation of the solution accuracy is still waiting to be performed, and two further attentions should be addressed clearly: 1) significant improvement of calculation efficiency without sacrificing any solution accuracy; 2) effective elimination of the influence of the random cross-sections on the calculation. After an in-depth analysis of these issues, a new approach was developed involving two key steps in this paper. Firstly, an accurate clustering algorithm was developed to perform a statistic of all variants, which can give the most probable orientation and area fraction for each variant. Different from previous methods, the second step is to perform an optimization scheme established in this work, which takes variant fractions into consideration, to determine the optimal orientation relationship and orientation of prior austenite. In addition, the influence of the random cross-sections can be effectively eliminated by inputting the equally-weighted variants into the optimization scheme. Furthermore, in-situ high temperature EBSD examinations were first performed to validate solution accuracy, the corresponding results clearly indicated that the orientation of austenite obtained from this approach exhibited a high accuracy (with an error less than 1°), exceeding the accuracy achieved by the previous methods in addition to avoiding the possible deviation of using distorted retained austenite at room temperature. Indeed, the solution accuracy is contributed by the robust optimization scheme which strictly satisfies the criterion of a minimum average deviation between the measured and predicted orientation of martensitic variants. Another contributor to the accuracy is the good agreement between the clustered variant orientations and the measured data. Under the high accuracy, the variant-level calculation, which can save much computational time compared with pixel/domain-level calculation, is beneficial for the efficiency promotion.