Abstract This work introduces a deterministic approach to the martensite transformation curve. Martensite is a nucleation-controlled transformation that has two characteristics: autocatalysis and auto-accommodation. Only a small number of martensite units initially form owing to primary nucleation. These new units may cause the transformation of other units by autocatalysis. We call this kind of transformation chained autocatalysis. Moreover, as the transformation progresses, the auto-accommodation influences the arrangement of new units. This work assumes that the transformation-saturation relates to the exhaustion of the chained autocatalysis, which underlines the microstructure. To compare, we considered the KJMA’s extended-transformation concept that implies assuming exhaustion by impingement. Data from isothermal martensite transformations and anisothermal martensite transformations are used to validate the model. Those data comprised different grain sizes and carbon contents. The model is based upon Verhulst’s logistic concept. We propose that the model's high fitting-capability stems from its deterministic aspect combined with martensite’s self-similarity. Additionally, we suggest that chained autocatalysis controls the rate of martensite transformation. Therefore, the relaxation of transformation strains by plasticity assisted by mutual accommodation determines the transformation's martensite volume in the absence of post-propagation coarsening/coalescence.

This paper proposes an alternative to the Avrami equation capable of describing whole transformation curves with significant fitting-correlations. The model bears physically meaningful parameters which permit considering the initial transformation kinetics independently from the subsequent microstructural evolution. Data of martensite, bainite, recrystallization, and pearlite transformations validate the model. Further to the expeditious description of transformation curves, the model guides the modeling of specific mechanisms.

This work presents a consolidated view of the autocatalysis, thermal and entropic effects in martensitic transformation of polycrystalline Fe-31wt%Ni-0.02wt%C, which has been a standard material for the investigation of fundamental aspects of the martensite transformation. The present work is based on the description of classical microstructure descriptors of the transformation and on generally accepted concepts regarding the martensitic transformation in iron base alloys. Present work agrees with the view that the autocatalysis is a means by which the martensite transformation promotes further nucleation and growth. Autocatalysis induces the nucleation and growth of secondary plates in addition to the relatively small number of primary nucleation sites and their corresponding primary plates. We demonstrate that autocatalysis can be factored out into intragrain and intergrain components. The analysis of these factors establishes that intragrain autocatalysis is athermal but intergrain autocatalysis possess an Arrhenius temperature dependence. The reasons for such a behavior are discussed in detail.

This study advances a methodology that consolidates the description of time-dependent (isothermal) as well as time-independent (athermal) martensitic transformation curves. Our model is applied in an extended 3-space, thus permitting inclusion of the effects of autocatalysis on nucleation to be distinguished from the initiation of the transformation, as influenced by entropic barriers. Autocatalysis is then considered as a mechanism for circumventing the effect of the latter. The utility of this proposed mathematical formalism was validated with a database consisting of seven different steels that transform athermally or isothermally.

In a recent paper, the present authors [Materials Research. 2015. 18(3): 595-601] demonstrated that the thickness of athermal martensite plates had a thermally activated component. The reason for this was probably the interaction of the athermal glissile martensite-austenite interface with dislocations located within the surrounding austenite. Based on this result, here we derive a new expression for the volume fraction against temperature for athermal martensite transformation. This new expression includes a thermal activated term. The expression obtained here gives good agreement with athermal martensite transformation in Fe-Ni-C and Fe-C alloys.

The properties of steels that undergo martensite transformation after or during processing depend on characteristics and arrangement of martensite units within the microstructure. In this work, the global microstructure descriptors of martensite transformation are related to the individual dimensions of the martensite units, the "intrinsic dimensions", – radius, thickness and aspect ratio – compensated for interactions among those units. In other words, the dimensions a martensite unit would have if it grew without impingement. This is accomplished by means of the microstructural path method. The methodology was applied to experimental data of martensite transformation in FeNiC and FeC alloys. The analysis of martensite dimensions permitted observing that the microstructural path of martensite includes a thermally activated step. We conclude that this thermally activated step does not mean that martensite itself has thermally activated growth step but that arrest of the martensite thickening process, owing to dislocation interaction with the interface motion may be thermally activated.

This work reviews issues and advances a formalism for quantitative interpretation of martensite microstructure, heeding the influence of transformation uniformity and the interaction of martensite with its surroundings. The relationship of volume fraction and number density of martensite units required for kinetics analysis is derived. Additionally we apply the new model to obtain the microstructural path function (MPF) of martensite, and to analyze the autocatalytic spread of the transformation during the martensite burst in Fe-31 wt. (%) Ni-0.02 wt. (%) C. The growth of an autocatalytic spread event relates to the chemical driving force, whereas the number of such events relates to the probability of finding a nucleation site to initiate the reaction.

Modeling the martensite reaction requires reckoning with spatial aspects of the reaction. For that, we used formal kinetics, more specifically, the microstructural path method (MPM) to analyze the microstructure observed in a burst. The microstructural path analysis revealed that the size of the spread cluster in extended space, characterized by the Vandermeer and Juul-Jensen's impingement compensated mean intercept length, λG, remained constant, independently of the parent austenite grain size. Moreover, current analysis introduced a purely formal description of the reaction progress by taking the parent austenite grain size as the progress variable. This description worked very well and resulted in a relationship between the volume fraction of partially transformed austenite, V VG, and austenite grain size, λG. The significance of these findings in the light of the advantages and disadvantages of formal kinetics is discussed.

A formal kinetic approach was applied to the spread of isothermal martensite over the neighboring austenite grains in a Fe-23.2 wt. (%) Ni-2.8 wt. (%) Mn alloy. The number of grains in a spread event changed with parent austenite grain size. However, isothermal martensite spread formed from fine-grained parent austenite and athermal martensite from a Fe-31 wt. (%) Ni-0.02 wt. (%) C alloy studied in a previous work followed the same microstructural path. The number of grains per spread- event found in the present study was shown to be consistent with the number of neighbors of the grain originating the spread event by means of a simple geometrical model of the parent austenite grain network. The study of the kinetics of isothermal martensite spread showed that the nucleation rate of the spread-event in isothermal martensite remained constant during the transformation. This result parallels the constant nucleation rate of the spread-event also found using the same methodology in athermal martensite formed in a Fe-31 wt. (%) Ni-0.02 wt. (%) C alloy studied in a previous work.