Abstract One typically characterizes the transformation kinetics of a parent phase, α, into a single phase, β, by measuring the volume fraction transformed, V V β, against time. Sometimes one also reports the interfacial area density between the new and the parent phase, S V α β, against the volume fraction transformed. S V α β is a dynamic interface. It migrates as the growth of the new phase takes place. Interfaces between transformed phases might be called static interfaces. These may be present before transformation starts, for example, grain boundaries of a polycrystalline parent phase. Alternatively, static interfaces, S V β β , may appear during the transformation because of impingement. Therefore, one may better understand the microstructural evolution following the behavior of the volume fraction, dynamic and static interfaces. A more complicated situation occurs if the parent phase transforms into two or more product phases, for example, α→β,γ. In this work, we apply parameters to describe the transformation of a parent phase into a single phase, the contiguity and the dispersion, to the situation in which the parent phase transforms into two or more phases. We tested these parameters against computer simulations and concluded that they combine a good description of the behavior of the simulated transformations and simplicity.

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.

A considerable number of engineering materials is polycrystalline. Cahn proposed analytical expressions for transformations nucleated at the grain faces, triple junctions, and quadruple junctions. Those places are usually the places in which a new phase takes place. Cahn assumed that the new grain boundary nucleated phase grew as spheres. Nonetheless, the austenite grain boundary nucleated ferrite does not always grow as spheres. Bradley et al. demonstrated in a series of papers that a grain boundary nucleated ferrite allotriomorph is best described by an oblate ellipsoid. The reason for ellipsoidal growth is that the growth along the grain boundary plane is faster than the thickening into the austenite. Because of this, it is of interest to have analytical solutions and computer simulations of grain boundary nucleated transformations not only for spherical growth but also for ellipsoidal growth. In this work, we present a computer simulation of grain boundary nucleated transformations that grow as ellipsoids. The computer simulation results were compared with a new exact analytical expression obtained by Villa and Rios.

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 paper generalizes previous work of Rios and Villa on spherical growth. The generalized equation applies to nucleation of ellipsoids according to an inhomogeneous Poisson point process. Microstructural evolution in three dimensions of nucleation and growth transformations of ellipsoids is simulated using the causal cone method. In the simulation, nuclei are located in space according to an inhomogeneous Poisson point process. The transformed regions grow with prolate and oblate ellipsoidal shapes. The ellipsoids have their corresponding axes parallel. The simulation and the exact analytical solution are in excellent agreement. Microstructures generated by the computer simulation are displayed. From these generated microstructures one can obtain the contiguity. In the contiguity against volume fraction plot, data from the sphere and all ellipsoids fall on the same curve. The contiguity curve for nucleation according to an inhomogeneous Poisson point process falls above the contiguity curve for nucleation according to a homogeneous Poisson point process. This behavior indicates that nucleation according to an inhomogeneous Poisson point process introduced a nucleus clustering effect.

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.

AbstractThe main goal this work is to evaluate the occurrence of the constituents and microphases observed in as-received API X80 pipe through the microstructures transformed from rich-carbon remaining austenite obtained via heat treatments. These heat treatments comprised austenitization at 1000 °C for 30 minutes, followed by annealing at 700 °C, 623 °C, 542 °C and 462 °C for 15, 60 and 300 minutes and then cooling in water or still air. The effects of the increase in annealing parameters were: 1) the increase of microhardness values of the MA constituents and martensite islands, 2) the grain size of both ferritic phase and the martensite islands were increased, 3) the rise in the mean free path of ferrite and 4) the microstrains of samples were decreased. The cooling rates influenced significantly the transformation of carbon-rich remaining austenite to hard constituents and several microphases. After annealing at 700 °C during 60 min followed by quenching, the morphology of the MA constituents and its microhardness values were compatible for both heat-treated and as-received conditions.

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.

Computer simulation of simultaneous evolution of individual texture components during recrystallization of an IF steel is carried out. A new methodology has been developed that takes as its starting point experimental data of each texture component evolving during recrystallization. In particular, Magnusson et al. data on IF steel was analyzed in a previous work with the help of the exact analytical tools developed by Rios and Villa for simultaneous transformations. From this analysis parameters such as number of nuclei of each texture component per unit of volume could be obtained and were employed as input for the present computer simulation. From this input 3-d microstructures could then be generated. The methodology proposed here combines experimental data, exact analytical methods and computer simulation and may be employed to extract the maximum information from the experimental data.

The direct three-dimensional characterization of opaque materials through serial sectioning makes possible to visualize and better quantify a material microstructure, using classical metallographic techniques coupled with computer-aided reconstruction. Titanium alloys are used as biomaterials for bone implants because of its excellent mechanical properties, biocompatibility and enhanced corrosion resistance. The Ti-6Al-4V alloy (in wt. (%)) with porous microstructure permits the ingrowths of new-bone tissues improving the fixation bone/implant. This is important to understand connectivity, morphology and spatial distribution of pores in microstructure. The Ti-6Al-4V alloy compacts were produced by powder metallurgy and sintered at three distinct temperatures (1250, 1400 and 1500 °C) to obtain distinct microstructures in terms of residual porosity. The visualization of the reconstructed 3D microstructure provides a qualitative and quantitative analysis of the porosity of Ti6Al4V alloy (volume fraction and pore morphology).

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.

Microstructural evolution in three dimensions of nucleation and growth transformations is simulated by means of cellular automata (CA). In the simulation, nuclei are located in space according to a heterogeneous Poisson point processes. The simulation is compared with exact analytical solution recently obtained by Rios and Villa supposing that the intensity is a harmonic function of the spatial coordinate. The simulated data gives very good agreement with the analytical solution provided that the correct shape factor for the growing CA grains is used. This good agreement is auspicious because the analytical expressions were derived and thus are exact only if the shape of the growing regions is spherical.