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.

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.