CRITICAL ASSESSMENT 1: Outstanding issues in crystallographic variant selection in displacive transformations

Abstract

Variant selection has been a well researched subject in metallurgy and materials science in recent decades. The emergence of experimental techniques capable of determining crystallographic orientation at the grain level has provided insight into the fundamental processes underlying variant selection. The theory, however, is far from complete. Fundamental questions, such as the specific roles of stress and strain in variant selection, have yet to be fully resolved. It remains unclear whether variant selection is a nucleation controlled phenomenon or growth controlled. The possibility of using unconventional forces such as magnetic or electrical fields to influence variant selection is of interest, but needs further research. Any phenomenon related to phase transformation gains importance only when it can be controlled to improve material properties, and it is still unclear how variant selection can be applied to this end. The literature is critically assessed and an attempt is made to identify areas for future research with potential to allow effective application of variant selection.

Keywords:

• Variant selection
• Displacive phase transformations
• Martensite
• Crystallographic orientation
• Grain orientation
• Materials design
• Reviews
• Critical assessment

Introduction

In steels, the number of possible crystallographic variants of martensite within any given grain of austenite is determined by symmetry to be 24. This is so for any other displacive transformation product, such as bainite or Widmanstätten ferrite. It is important to note that the 24 variants arise because the habit plane and orientation relationships are irrational;^1–3 the frequently quoted Nishiyama–Wasserman orientation relation that implies just 12 variants is an approximation to the irrational form. The Kurdjumov–Sachs or KS orientation relationship does involve 24 variants but these are also nothing but the average orientation derived from experiments done on many steels.⁴

Variant selection is said to occur when the interaction of an external field, such as a stress,⁵ strain,⁶ or magnetic field,⁷ with the displacements due to transformation favours the formation of one or more orientations relative to those others possible in principle. The influence of electrical fields, with or without electrical current flow, on martensitic transformations is a rich area that is yet to be explored; work on other transformations indicates that there could be discoveries to be made.⁸

Variant selection is a feature of both single and polycrystalline austenite. In the latter case, the overall crystallographic texture of the material is influenced by the selection. Mechanical twinning is not a phase transformation but it too involves displacements and hence can occur selectively, thereby altering texture⁹ – indeed, the relationship between twinning and texture has been identified as a phenomenon requiring in depth analysis in twinning-induced plasticity steels.¹⁰

The purpose of this critical assessment is to outline the outstanding difficulties and open questions associated with work on crystallographic variant selection, a phenomenon that has seen a major resurgence in interest since the routine availability of techniques such as electron back-scattered diffraction (ESBD). Coverage is confined to displacive transformations because here the problem is simplified by the fact that transformation products are confined to individual grains of the parent phase.

Effect of stress and plastic strain on variant selection

The interaction of applied stress alone with the shape deformation of a displacive transformation may be expressed as⁵(1) where s and δ represent the shear and dilatational terms of the shape strain, τ is the shear stress resolved appropriately on to the habit plane, and σ_n is the stress resolved normal to that plane. A greater interaction energy U favours the formation of that variant. Although the theory predicts only the ranking of the variants, attempts have been made to estimate the volume fractions of every one of the 24 variants.^11,12

Much more difficult is an understanding of how plastic strain influences variant selection, partly because the vast majority of experiments in this field apply stress and strain simultaneously, making it difficult to distinguish cause and effect.^13–18

A few studies exist where plastic strain has been applied to austenite prior to its transformation.^6,19 But understanding the mechanism by which variant selection occurs is more convoluted. The interaction with plastic strain may be based on the relationship of the habit plane or Bain strain with slip activity via dislocations.^6,20–22 But there are in some cases fitting parameters involved²⁰ and justification is needed to select the Bain strain as the only component of the total transformation strain that matters. It has been argued²³ that plastic strain is a stronger driver for variant selection than stress alone.

The difficulty in dealing with plastic strain is compounded when the mechanical stabilisation associated with large plastic strains sets in, because such stabilisation can actually suppress transformation.^24–26 Large plastic strains will lead to type II residual stresses²⁷ and will also influence the intergranular stresses that might have considerable effect on selection of variants in poly-crystalline material. So it is not obvious that it is the defects associated with the deformation that lead to the nucleation of favoured variants, or the interaction between the glissile transformation interfaces and the defect structure that causes selection via favoured growth. It has also been argued²⁸ that the variant selection in the plastically deformed austenite could be the result of the interaction of residual stress with the volume and shear strain associated with martensite plates and hence could be predicted using the shape deformation theory proposed by Patel and Cohen.⁵

It is considered here that the most important outstanding issue is to clarify the mechanism by which plastic deformation influences variant selection in subsequent transformation. Some possibilities might be listed as follows, although a distinction should really be made between small and large plastic strains, where the adjectives are in the context of the strain required to cause mechanical stabilisation:²⁶

(i)	Dislocations provide additional nucleation sites for martensite, but the prior deformation biases the nature of the defects, and hence of the variants that can be induced. It is assumed that the stress field of the defect is seminal in inducing nucleation although the core may also play an unknown role. In such a case the theory may be similar to that of stress-induced transformation.
(ii)	The substructure caused by deformation may not be isotropic, thus favouring the development of martensite that can grow at a prominent angle to the slip plane debris.6
(iii)	In materials that deform heterogeneously, shear band intersections promote martensite nucleation.29,30 The process may involve, as an intermediate step, the formation of ϵ-martensite, but it has been argued that this is not necessary in high stacking fault energy materials.31 It is noteworthy that in predicting the stress-induced α′ texture, it is not necessary to consider intermediate steps but rather the shape deformation of α′ as a whole.32,33
(iv)	During deformation, flow of dislocations takes place on the active slip systems determined by the orientation of the austenite crystal and the direction of applied stress. This might cause residual stress to develop, which might be different in different crystals. This stress might interact with shear and dilatational strain component associated with specific α′ variants and thus cause variant selection. The similarity in alignment of active slip planes and the favoured variants clearly indicates the role of the former in variant selection.23
(v)	The competition between stress and strain in variant selection is another important aspect to consider. Since the mechanisms of variant selection for these two fields could be entirely different, the nature of variant selection under the influence of both is a matter for further investigation. It has been shown34 that the texture of austenitic stainless steel is altered due to variant selection and that the texture can be predicted by assuming that variant selection is taking place under the influence of stress alone. However, further work at the level of individual grains is required to improve understanding of these phenomena.

Variant selection during nucleation and growth

Another issue often debated is whether variant selection occurs at the nucleation or growth stage. It is quite possible that the transformation strains at the nucleation stage are different from those associated with the macroscopic shape deformation.³⁵ However, in all cases where pure stress-induced transformation takes place (stress below yield), it is the growth interaction that is found to predict the favoured variants.^20,36 On the other hand, when the parent microstructure is two-phased, it is possible that the presence of the non-transforming phase influences the nucleation of martensite. Thus, in hexagonal titanium alloys, variant selection can take place due to preferential nucleation on the β grains.³⁷

Evolution of transformation strain during variant selection

The evolution of transformation strain during variant selection appears to have been little researched but is likely to be highly significant in the practical use of the phenomenon to improve mechanical properties. Bhadeshia et al. indicated for the first time that variant selection is influenced by the applied stress, resulting in anisotropic transformation strains during displacive transformation.³⁸ Subsequent work³⁹ clearly showed transformation plasticity to increase with increasing stress (below the yield stress), which was attributed to higher variant selection at higher stress levels. The changing nature of transformation strain with changing nature of external stress has been described with the help of mathematical models,⁴⁰ supported by experimental evidence.²³ However, no report has been found on the nature and amount of transformation strain due to variant selection caused by plastic deformation.

Effect of variant selection on microstructure and properties

Before addressing the potential use of variant selection to improve steel properties, it is appropriate to consider an important morphological characteristic of bainite or martensite microstructures. As described by many researchers,^41–43 martensite or bainite has a tendency to form in ‘packets’ with typical cystallographic features that are capable of playing a critical role in variant selection^23,44 or cleavage fracture.^42,45,46 However, a clear definition of the ‘packets’ is vital. It has been shown that the packets are crystallographically closely spaced^23,42,46 with respect to the (100) plane of the martensite/bainite phase. Mangal et al.²³ have shown that because of the reduced orientation differences, the variants belonging to one Bain group can form in the shape of ‘packets’, where individual plates or sheaves are nearly parallel. This gives less hard impingement and as a result these variants are preferred for growth. The findings of Suikkanen et al.⁴⁷ support this assertion. Thus, where there is variant selection due to application of external stress and/or strain there is a tendency for more variants to form from one Bain group. This suggests that a higher level of variant selection will lead to large regions in the microstructure having parallel plates or sheaves that have low angle phase boundaries with respect to (100) cleavage planes. This might increase the possibility of cleavage cracking. More research is required on the extent to which variant selection could promote the chance of cleavage failure. It is already known from the work of Albery and Jones⁴⁸ and Ohta et al.⁴⁹ that variant selection can reduce the harmful residual stress in welded joints, which improves the fatigue properties. Although Ohta et al. have not shown evidence of variant selection, it is a compelling explanation of the good properties that were achieved. It is understood that Ohta et al. used a ‘low temperature electrode’, which may have led to higher transformation strain. Higher strain can develop only if, during solidification of the weldment, martensite forms with a higher degree of variant selection. It must be remembered that when the assembly is cooled after welding, phase transformation takes place under constraint. Strains arise due to the contraction of the weld material, which is constrained by the solid base metal. External influences in the form of tensile stress and strain will both therefore have been present in the weldment used by Ohta et al., which could have influenced variant selection. It would be of interest to study the apparent improvement of fatigue strength with more variant selection in conjunction with the possibility of creating more low angle boundaries, which has not to date been done systematically.

Problems in identifying variants using EBSD technique

The large amount of strain naturally associated with displacive transformations perforce involves plastic accommodation that creats dislocation debris. Considerable spread in the austenite/martensite pole figure is thus expected. The inherent dislocations in martensite/bainite would also contribute to this spread in orientation distribution. For example, in low carbon martensite, where the plastic accommodation is more severe, a high degree of spread has been found³³ in the pole figures. A lack of sharpness in pole figures can also be a result of movement of boundaries or tempering, as has been found in meteorites.⁵⁰

Such spreading in pole figures may prevent the EBSD technique from determining the precise position or orientation relationship between parent and product phases. For this reason, caution must always be exercised in drawing conclusions relating to variant selection from ESBD observations. Cayron et al.⁵¹ recently attributed the spread or ‘rings’ observed in their pole figure to two-stage transformation of the martensite, a conclusion subsequently shown³³ probably to be incorrect.

Conclusion

Assessment of the recent literature suggests considerable interest in the subject of variant selection. The theoretical framework available to describe the phenomenon has become stronger as better experimental and modelling techniques have been used to explore it. The present status of the theory has been critically discussed. As well as describing the progress made, an attempt has been made to identify shortcomings of present approaches and areas in which further research should be encouraged. In particular, relatively little effort has been directed towards the use of variant selection to improve material properties. The need to explore the effect of ‘unconventional’ fields (e.g. electrical and magnetic) on variant selection has also been emphasised.