Variant Selection Rule Research Articles

Orientation dependence of variant selection and intersection reactions of ϵ martensite in a high-manganese austenitic steel

The orientation dependence of ϵ martensite during loading of a polycrystalline austenitic Fe-30Mn-4Si-2Al steel has been investigated by electron backscatter diffraction, emphasising the variant selection rule and plate–plate intersection reactions. Two types of plate–plate intersection reactions, which are characterised by incident shear direction of either 30° or 90° with respect to the intersection axis, were found in the grains along the [001]–[111] directions and [001]–[101] directions, respectively. In the intersecting volume of the latter type reaction, a γ phase rotated 90° from the austenite matrix along the ⟨011⟩ zone axis of the intersecting ϵ plates, which was theoretically predicted by Sleeswyk [A.W. Sleeswyk, Philos. Mag. 7 (1962) p.1597], has been experimentally observed for the first time.

Transformation Texture in Hot-rolled Steel Sheets and Its Prediction

Crystallographic textures of hot-rolled steel sheets are thought to be inherited from the textures of austenite, which develop during hot rolling, due to the orientation relationship between austenite and product phases and the therein-involved variant selection rules. However, despite numerous investigations, there is still difficulty in the prediction of textures of ferrite or martensite in the hot-rolled steels. In this article are described the present state of such prediction of transformation textures in hot-rolled steel sheets. In particular, the way to calculate the transformation textures based on the so-called MODF method and a variant selection rule that has been recently proposed are described in detail. Combined with the proposed variant selection rule, the MODF method may be capable of quantitatively predicting the transformation texture in hot-rolled steel sheets.

A Variant Selection Rule in Transformation in Steel and Prediction of Transformation Texture

Quantitative prediction of transformation textures in steel becomes possible if a variant selection rule is taken into account, in which ferrite nucleating on austenite grain boundaries prefers to have orientation relationship with two neighboring austenite grains at the same time. The mathematical model of the variant selection rule is described and some examples of simulation in transformation textures in hot-rolled steel sheets are presented using the textures of retrained austenite and the misorientation distribution function method. An excellent agreement is attained between the predicted and experimental ferrite textures.

Modeling of Texture Evolution during Hot Forging of Alpha/Beta Titanium Alloys

Texture development during the subtransus hot forging of alpha/beta titanium alloys with an equiaxed-alpha microstructure was modeled using the Los Alamos polycrystalline plasticity (LApp) code and a \( {\left\langle {111} \right\rangle } \)pencil-glide polycrystalline plasticity code coupled with the finite-element-method (FEM) program DEFORM. The methodology treated the partitioning of the imposed strain between the alpha and beta phases, and thus enabled the prediction of the distinct deformation textures developed in the primary alpha and beta matrix during hot working. Two variant selection rules in conjunction with the beta deformation texture were also examined to establish a method for predicting the transformation texture of secondary alpha developed as a result of beta decomposition during cooldown following forging or heat treatment. The approach was validated via an industrial-scale trial comprising hot pancake forging of Ti-6Al-4V.

Variant Selection of Plate Martensite in Fe-28.5at.%Ni Alloy

Variant selection rule of plate martensite in a coarse-grained Fe-28.5at.%Ni alloy was investigated. Crystallographic analysis of martensite plates was carried out by electron back scattering diffraction (EBSD) analysis in a scanning electron microscope with a field emission type gun (FE-SEM). Certain variant selections were recognized for martensite plates in the Fe-28.5at.%Ni alloy. Equivalent strain, which was calculated from the shape strain of each variant, was used to evaluate the accommodation of the shear strain induced by martensite transformation. Variant selection was ruled not only by the shear strain accommodation but also by the ngle between habit planes of adjacent martensite plates.

A Dislocation Reaction Model for Variant Selection During theAustenite‐to‐Martensite Transformation

Variant selection rules are described that predict the austenite‐to‐martensite transformation textures of an Fe‐30%Ni alloy. The occurrence of variant selection is explained in detail using the crystal plasticity model of Bishop and Hill and the Kurdjumov‐Sachs transformation relationship. A correlation is established between the slip systems of the former and the rotation axes of the latter. The selection criteria are based on a combination of slip activity, that is, active slip systems, and permissible dislocation reactions. Thus some of the variants selected are associated with slip systems that are active while the remainder are accounted for by the in‐plane reaction of active dislocations to form inactive or unstressed dislocations. The variant selection criteria are tested against the experimental findings of Liu and Bunge (Materials Letters, 10(7,8), 336–343, 1991) and found to be in good agreement.

Variant Selection during the γ-to-α' Transformation of a Fe-30%Ni Alloy

dislA variant selection model is described that predicts the crystal orientations that result when austenite undergoes the transformation to martensite in an Fe-30%Ni alloy. The Kurdjumov-Sachs relationship was employed in conjunction with the crystal plasticity theory of Bishop and Hill to analyse the experimental findings of Liu and Bunge. The proposed variant selection rule is based on a slip activity criterion that encompasses the 'inactive' or unstressed dislocations produced by the in-plane reaction of active dislocations.

A Variant Selection Model for the Prediction of Fcc-To-Bcc Transformation Textures

In the present work, a simple model is described for the prediction of fcc-to-bcc transformation textures. It employs a discrete distribution of orientations and is based on the Kurdjumov-Sachs relationship for the γ -to- α transformation. An important feature of the model involves the variant selection rule, which assumes that nucleation is favoured according to a slip system based variant selection criterion. Subsequent selective growth involves a transformation work rule based on the Bain strains and the presence of an internal stress field. The transformation texture predicted from an experimental 95% cold rolled Ni-30wt%Co alloy texture is compared to experimental martensite textures for both a Nb-microalloyed steel and a Fe-30%Ni alloy. The predicted texture displays better agreement with the steel data.

Modeling texture change during the static recrystallization of interstitial free steels

A recrystallization model was developed based on the principal features of oriented nucleation and selective growth. The nucleation mechanism that is adopted assumes that nucleation takes place in deformed grains with relatively high Taylor factors. The selective growth law is based on the assumed high mobility of {110} plane matching (PM) boundaries and also includes a variant selection rule. The two submodels enable the full recrystallization process to be simulated. The theory is applied to the annealing of a Ti-Nb alloyed interstitial free (IF) steel. It is demonstrated that the nucleation and growth algorithms can successfully account for the annealing textures observed, including the presence of a strong {111} component. An important feature of the model is that it permits the role of variant selection to be assessed; it also shows the effect on the texture of the low mobility of low-angle grain boundaries (LAGBs).

Modeling Texture Change during the Recrystallization of an IF Steel.

The texture changes taking place during the recrystallization of a Ti and Nb bearing interstitial free (IF) steel were investigated. Samples taken from the hot band of a 0.08%Ti-0.01%Nb IF steel were subjected to cold rolling reductions of 70 and 85%, and annealed at 720°C to investigate the effect of cold reduction on the recrystallization texture. The main components observed after cold-rolling were the {001} and {112} , together with the ND fiber increased, especially between {111} and {111} . Higher cold reductions led to stronger intensities of the latter components. The formation of recrystallization textures in IF steels is discussed in terms of a selective growth theory in which nuclei possessing favorable axis rotation relationships with respect to the deformed matrix undergo preferential growth. By adopting a suitable axis variant selection rule and employing it in conjunction with a nucleus availability factor, it is shown that recrystallization textures can be successfully predicted from experimental rolling textures.

Orientation dependence of β1 → β1′ stress-induced martensitic transformation in a Cu-AI-Ni alloy

A systematic investigation was carried out to settle some critical issues on the orientation dependence of the stress-induced martensitic transformation. The transformation we picked up is the βl (DO3) → β1′ (18R) stress-induced transformation in a Cu-14.1 mass pct Al-3.9 mass pct Ni alloy. By utilizing tensile tests and two surface analyses coupled with X-ray diffraction, the following clear results were obtained. Concerning the variant selection rule under stress, it was found to be the shape strain which interacts with an applied stress. The critical resolved shear stress for the martensitic transformation was found to have orientation dependence, the shear stress increasing with the normal stress. The observed transformation strains were consistent with those calculated from the shape strain in all orientations. The strong orientation dependence of the Young’s modulus was consistent with that predicted by the elastic constants in the parent phase.

BAINの関係による変態集合組織の解析

The merit of use of BAIN relation in analizing the transformation texture was first described, as compared with that of NISHIYAMA (N) or KURDJUMOV-SACHS (K-S) relation. This was primarily because there were only three variants in BAIN, while 12 and 24 variants in N and K-S relations respectively, and each variant in N or K-S was oriented close to one of the three BAIN variants. Secondly, computer simulations of transformation textures were conducted on steels transformed from rolled austenite using variant selection rules. In these rules, the work done by specific stress on rolling against the lattice deformation (BAIN distortion) of martensite transformation was calculated for each <001>axis of austenite, and such BAIN variants that had the work larger than certain critical value were selected.Transformation textures simulated in this way were successful in explaining Fe-Ni textures experimentally determined by other authors. Evidence which showed the effect of the sense of the specific stress was presented; calculations based on the forward rolling stress could explain the case of transformation during rolling, whereas simulations due to reverse or internal stress of rolling were coincident with the transformation after rolling. Some explanations were given to the nature of such hypothetical internal stress and to the mechanisms of variant selection in martensite transformation.