Heterogeneous Nucleation Of Martensite Research Articles

Stabilization of Martensite on Nanoprecipitates and Kinetics of Explosive Martensite Transition

Based on the theory of diffuse martensitic transitions (DMT), the physical mechanism of the influence of dispersed precipitate nanoparticles on the appearance of such features of the deformation behavior of alloys with the shape memory effect (SME) as the stabilization of martensite at temperatures significantly higher than the As and Af temperatures characteristic of an alloy in the absence of nanoparticles c-oherent with the matrix is analyzed. The reason for the stabilization of martensite is the internal elastic stress fields associated with the particles, which serve as sites for the heterogeneous nucleation of martensite. It has been shown theoretically that, with an increase in the volume concentration of nanoparticles, the recovery of shape memory deformation occupies an increasingly narrow temperature range and occurs at an ever higher temperature. After reaching a certain critical value of the particle concentration, the return of the deformation of SM loses its stability and becomes explosive.

Computational thermodynamics and kinetics of displacive transformations in titanium-based alloys

The thermodynamics of Ti-based systems are described for β–α′/α″ martensitic transformation and athermal ω formation at low temperatures. The new descriptions can better represent the relationship between the partitionless equilibrium temperature and the measured martensite-formation/reversion temperatures. The anomalous β-stabilizing effects of Al, Sn, and Zr in ternary Ti–V/Nb-based alloys are well modeled for the first time. The Gibbs energy function of ω–Ti at ambient pressure is assessed. The formation temperature of athermal ω phase is assessed in some binary systems and estimated in some ternary systems based on electrical resistivity and first-principles calculations. The critical driving force for heterogeneous martensitic nucleation is modeled by solution-hardening interfacial friction using the present thermodynamic descriptions. The competition between martensite and athermal ω phase can be understood based on their transformation thermodynamic and kinetic factors.

Phase transformation in δ Pu alloys at low temperature: In situ dilatometric study

The purpose of this work is to precisely study the martensitic transformation in a plutonium-gallium alloy. Thus, the thermodynamics and kinetics of the δ→α'+δ phase transformation in a Pu-Ga alloy were studied under isochronal and isothermal conditions. The activation energy of the δ→α'+δ phase transformation at a constant cooling rate (0.5 K.min−1) was determined by using Kissinger and Ozawa models. The average value of the activation energy was found to be at −56 kJ.mol−1. Dilatometry measurement was also used to trace 'in situ' the entire transformation for several temperatures. The kinetics of the δ→α'+δ transformation were modelled under isothermal conditions in the theoretical frame of the Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory. It is proposed that the transformation consists of three stages. The α' transformation begins with a nucleation of pre-existing embryos. Then, both nucleation and rapid growth of α' occurs simultaneously and finally, the plates width expend. Apparent activation energies for nucleation and growth transformation were determined from the temperature dependence of the constant K at respectively −34 kJ.mol−1 and −60 kJ.mol−1. Adler et al. [1] investigated also the thermodynamics and the kinetics of the martensitic transformation in Pu alloys. These nucleation energies were found by modelling of heterogeneous martensitic nucleation via strain interaction with observed superdislocation-like nucleation sites in PuGa alloys. The values obtain by this model was very close to those we find. Investigations in steels alloys indicate that these energies are of the same order for nucleation near dislocation. Then, it could be indicating a strong relationship between these dislocations and martensitic nucleation sites.

Mechanisms of martensite nucleation at grain boundaries

Martensitic transformation is a nondiffusive phase transition, in which strain plays the role of the order parameter [1, 2]. In many materials such as steels and iron-based alloys, martensitic transformations are phase transitions of the first order, which are characterized by a small activation barrier and, in the limiting case, can even be athermal. In some alloy systems, the martensitic transformation is a phase transition of the first order that is close to the second-order process, and is accompanied by a decrease in the elastic modulus [2, 3]. It was suggested that certain precursor states (significantly reducing the barrier for nucleation) in the lattice could play the role of subcritical nuclei for such transformations, while defects could be the centers for the local loss of stability of the lattice [3]. The question concerning the character of nucleation of martensite crystals has not yet been given a final answer. Most researchers believe that the martensite phase nucleates via a heterogeneous mechanism. It was suggested that dislocations, stacking faults, grain boundaries, and other structural defects are preferential sites for the nucleation of martensite. Elastic stresses related to the structural defects favor the nucleation process. In addition, dislocations can serve as boundaries of the growing crystalline phase. Numerous investigations were devoted to the nucleation of martensite on separate dislocations, stacking faults, dislocation loops, and various dislocation ensembles [4‐9]. However, experiments [10] did not reveal any influence of dislocations on the nucleation of martensite, while showing evidence for a facilitated nucleation at grain boundaries of certain types. Ueda et al. [11] studied the martensitic transformation in Fe‐Ni bicrystals, established that twinned martensite crystals could nucleate via a self-accommodation mechanism at the tilt boundaries, and calculated the elastic energy of such crystals with accommodated transformation strains. A molecular-dynamics simulation of the bcc-to-hcp martensite transformation in zirconium [12] also showed the possibility of martensite nucleation at the grain boundary, which was accompanied by the appearance of anomalies in the phonon spectrum. This paper is devoted to an analysis of the two possible mechanisms of martensite nucleation at grain boundaries in the alloy systems (such as iron-based alloys) without a decrease in the elastic moduli. Thermodynamics of the martensite nucleation via selfaccommodation across grain boundaries and the nucleation at nonequilibrium boundaries and their contacts with disclination stress fields are considered. Homogeneous and heterogeneous nucleation of martensite. It is assumed that a martensite nucleus has the same platelike shape as a macroscopic crystal, with a small ratio of thickness h to the lateral dimensions l and L , and is typically oriented along the transformation invariant plane with the unit normal vector n . In the absence of strain sources, the free energy of such a martensite plate is described by the following expression

The kinetics of lath martensitic transformation

The multicomponent solution thermodynamics, a model for barrierless heterogeneous martensitic nucleation, a model for the composition and temperature dependence of the shear modulus, and a set of unique interfacial kinetic parameters are integrated to model the kinetics of lath martensitic transformation. It is shown that Ms in multicomponent alloys can be predicted within ±40K. The geometric partitioning of austenite grain and the dependence of average lath volume on the fraction transformed is established by a careful analysis of lath microstructure. The main contribution of lath martensitic transformation is due to autocatalytically generated defects.

Heterogeneous nucleation of martensite on precipitates and the martensitic-transformation kinetics in shape memory alloys

Heterogeneous nucleation of martensite on precipitates and the martensitic-transformation kinetics in shape memory alloys

Heterogeneous nucleation of martensite at dislocations and the martensitic-transformation kinetics in shape memory alloys

The martensite phase formation in elastic fields of isolated screw and edge dislocations, as well as in planar clusters of like-sign dislocations and in a two-dimensional network of opposite-sign edge dislocations, is quantitatively analyzed within the theory of smeared martensitic transitions. The heterogeneous nucleation of martensite at dislocations is shown to increase the characteristic temperature of the martensitic transition and its temperature smearing.

Heterogeneous nucleation of martensite near free surface

A theoretical model is proposed which describes heterogeneous nucleation of an embryo of hcp-martensite near a free surface at a tilt grain boundary segment containing some extrinsic dislocations. The total energy gain due to the hcp-embryo nucleation is analysed in detail depending on internal (the distance from free surface and orientation of the grain boundary plane) and external (the temperature and shear stress) conditions. It is shown that the main characteristics of the hcp-embryo nucleation (the energy barrier and critical size) depend strongly on the distance from the free surface.

Effect of grain boundary character on the martensitic transformation in Fe–32at.%Ni bicrystals

The effect of grain boundary character on the martensitic transformation was examined in two types of Fe–32at.%Ni bicrystals containing a 90°<211> tilt or a 90°{211} twist boundary focusing on the martensite-start temperature (Ms) during cooling, the morphology of the martensite and the variant selection. The Ms of bicrystals with a tilt boundary was higher than that of single crystals, while bicrystals with a twist boundary showed no significant difference from that of single crystals. Coarse lenticular martensites formed symmetrically in neighbouring grains around the tilt boundary. In contrast, tiny martensites were uniformly distributed in bicrystals with a twist boundary, and in single crystals. In the vicinity of the tilt and twist boundaries, some variants with the habit plane almost parallel to the boundaries were preferentially selected among 24 variants. Moreover, since the equivalent variants in neighbouring grains at the tilt boundary are selected, strain compatibility of the shape strain of martensite across the tilt boundary is satisfied, resulting in an increased Ms. The effect of pre-strain on the heterogeneous nucleation of martensite at the boundaries was also investigated.

A continuum description of dislocations in elastically nonlinear media: martensitic embryo formation

Candidate sites for heterogeneous nucleation of martensite are constructed from two dislocation structures placed in a nonlinear, nonlocal elastic continuum. The resulting static strain fields of the dislocation arrays give rise to mesoscopic embryos of the product phase, which exhibit athermal behavior as the effective temperature of the system is changed. A high-potency dislocation array gives rise to a strained classical (sharp boundary) martensitic embryo at high temperatures, corresponding to the limit of metastability for the martensitic phase. This embryo grows rapidly with decreasing temperature, interacting with the system boundary before the transformation can occur. A low-potency dislocation gives rise to a more diffuse, nonclassical structure, which increases in strain amplitude and size with decreasing effective temperature, becoming metastable before finally triggering the transformation of the full system. Transformation occurs in the low-potency case when force is 61% of the driving force at the lattice instability, and the strain embryo achieves 80% of the transformation strain.

Computational thermodynamics and the kinetics of martensitic transformation

To assist the science-based design of alloys with martensitic microstructure, a multicomponent database kMART (kinetics of MARtensitic Transformation) encompassing the components Al, C, Co, Cr, Cu, Fe, Mn, Mo, N, Nb, Ni, Pd, Re, Si, Ti, V, and W has been developed to calculate the driving force for martensitic transformation. Built upon the SSOL database of the Thermo-Calc software system, a large number of interaction parameters of the SSOL database have been modified, and many new interaction parameters, both binary and ternary, have been introduced to account for the heat of transformation, T0 temperatures, and the composition dependence of magnetic properties. The critical driving force for face-centered cubic (fcc) → body-centered cubic (bcc) heterogeneous martensitic nucleation in multicomponent alloys is modeled as the sum of a strain energy term, a defect-size-dependent interfacial energy term, and a composition-dependent interfacial work term. Using our multicomponent thermodynamic database, a model for barrierless heterogeneous martensitic nucleation, a model for the composition and temperature dependence of the shear modulus, and a set of unique interfacial kinetic parameters, we have demonstrated the efficacy of predicting the fcc → bcc martensitic start temperature (Ms) in multicomponent alloys with an accuracy of ± 40 K over a very wide composition range.

Martensitic embryo formation at dislocations near surfaces

Abstract A two-dimensional continuum model for heterogeneous nucleation of martensite is studied. This nonlinear, nonlocal Landau-type model incorporates slip dislocations into the continuum picture. The elastic strain field of the dislocations occurs in the context of a strongly nonlinear host matrix which models a structural phase transformation. This matrix has more than one stress-free strain. Martensitic embryo structures are observed at temperatures which are much higher than the equilibrium temperature between the parent and product phases. The structure of the embryo as a function of temperature, and the interaction with a nearby free surface which allows for the abrupt appearance of surface relief, are examined.

Thermodynamic Calculation of Stacking Fault Energy and its Effect on Fcc→Hcp Phase Transformation in Nitrogen Alloyed Stainless Steels

The observed fcc→hcp phase transformation in some iron-based alloys, such as Fe-Mn-based shape memory alloys, is due to the formation of stacking faults, expansion of the faults by the movement of Shockley partial dislocations followed by ordered overlapping of the faults. Therefore, alloy systems with low stacking fault energy (SFE) are naturally more prone to the fcc→hcp martensitic phase transformation. Nitrogen (N) is known as an austenite stabilizing element; however, some existing experimental data in the literature have shown that it decreases the stacking fault energy of austenitic steels. Therefore, one would expect that N alloying should promote the fcc(γ)→hcp(e) martensitic transformation and thus have a destabilizing effect on austenite. To resolve the above discrepancies we have considered the effect of N on the stacking fault energy of fcc iron-based alloys. Our calculations have shown that by increasing N in solid solution, the stacking fault energy of the system initially increases to a maximum and then decreases. Using a phenomenological description for fcc(γ)→hcp(e) heterogeneous martensitic nucleation kinetics, we have demonstrated that increasing nitrogen concentration decreases the driving force for the fcc(γ)→hcp(e) martensitic transformation and increases the friction work due to both nitrogen solid solution strengthening and segregation of nitrogen to stacking faults for fcc iron-based alloys.

Dislocations in nonlinear nonlocal media: Martensitic embryo formation

A model is developed for determining the stress and strain fields of an array of slip dislocation defects in a two-dimensional elastic medium with a highly nonlinear and nonlocal energy functional. The medium serves as a model for an elastic system in the vicinity of a martensitic structural phase transformation, in the high-temperature regime where the metastable product phase first acquires local stability. The dislocation array is a model of a candidate site for heterogeneous nucleation of martensite. The slip dislocation defects are included in the continuum by means of a static, external “topological” field superimposed on the conventional elastic displacement field. The results indicate that a fully transformed martensitic region of mesoscopic size is stabilized by the nonlinear elastic field of the dislocations at temperatures substantially higher than the equilibrium temperature T 0, consistent with the Kaufman-Cohen “preexisting embryo” hypothesis.

Modelling of austenite stability in low-alloy triple-phase steels

A model for the stability of dispersed austenite in low alloy triple-phase steels has been developed. The model was based on the dislocation dissociation model for classical heterogeneous martensitic nucleation by considering stress effects on the nucleation site potency distribution. The driving force for martensitic transformation has been calculated with the aid of computational thermodynamics. The model allows for the effects of chemical composition of austenite, mean austenite particle size, yield strength of the steel and stress state on austenite stability. Chemical enrichment in C and Mn, as well as size refinement of the austenite particles lead to stabilization. On the contrary, the increase in the yield strength of the steel and triaxiality of the stress state lead to destabilization. The model can be used to determine the microstructural characteristics of the austenite dispersion, i.e. chemical composition and size, for optimum transformation plasticity interactions at the particular stress state of interest and can then be useful in the design of low-alloy triple-phase steels.

An atomistic simulation study of the effect of crystal defects on the martensitic transformation in Ti - V bcc alloys

An atomic level analysis of the effect of crystal defects such as free surfaces, dislocations and grain boundaries on the martensitic transformation in bcc Ti, Ti - 15V (atom %) and Ti - 25V (atom %) has been carried out using the embedded atom method (EAM) interatomic potentials to quantify the atomic interactions and molecular dynamics to study the evolution of atomic positions with time. The presence of crystal defects has been found to have a profound effect on the martensitic transformation in these alloys. The defects can either facilitate the bcchcp martensitic transformation, the transformation which is typically observed in these alloys, or promote formation of the martensitic phase with a face centred orthorhombic (fco) structure. In the case of free surfaces, the atomistic simulation results revealed the role these defects and their crystallographic characters play in the heterogeneous nucleation of martensite and their effect on the progress of martensitic transformation and the crystal structure of the martensitic phase. In Ti and Ti - 15V, where the hcp phase is thermodynamically more stable than the bcc phase, the presence of dissociate a/2 [111] edge dislocations was found to facilitate the bcchcp transformation. In Ti - 25V where the bcc phase is more stable, these dislocations give rise to the formation of dormant hcp martensitic embryos. These embryos are likely to be activated under stress or during cooling giving rise to the bcchcp transformation. The grain boundaries were found to promote formation of the fco martensite accompanied by significant reduction of the mismatch stresses in the grain boundary region.

On the heterogeneous nucleation of martensite

Martensitic nucleation near inhomogeneities is modeled using linear elasticity. The coherent strain energy due to the formation of a martensite embryo decreases when the inhomogeneity is elastically stiffer than the matrix and vice versa. A maximum reduction of 20% in strain energy is calculated for the case when the embryo is formed near a free surface. The results are consistent with the experimental observations of preferential nucleation of martensite at a free surface. A possible explanation for the nature of the “preexisting martensite embryo” in the Kaufman and Cohen model of a nucleation site is also proposed: the dislocation loop in the parent phase is itself the site for the embryo such that it will transform into martensite during transformation. The calculated critical characteristics of this embryo are in good agreement with the model of Chen and Chiao and their experimental results.

Kinetics of F.C.C. → B.C.C. heterogeneous martensitic nucleation—I. The critical driving force for athermal nucleation

Employing available experimental data for athermal f.c.c. → b.c.c. martensitic transformation in binary, ternary and multicomponent Fe-base alloys, a model is developed and tested for the critical driving force at the M s temperature. Incorporating the theory of solid solution hardening, we describe the composition dependence of the athermal frictional work for martensitic interface motion governing the kinetics of barrierless heterogeneous nucleation. The available data suggests that the composition dependence of the athermal frictional work is of the same form as that for slip deformation. We have evaluated the athermal strengths of 14 alloying elements Al, C, Co, Cr, Cu, Mn, Mo, N, Nb, Ni, Si, Ti, V and W from the experimental data. Except for Al, Ni and Co, the athermal strengths of the common substitutional alloying elements are similar in magnitude, while the interstitial solutes C and N exert a stronger influence. Previously proposed superposition laws are used to account for the presence of multiple solutes having different athermal strengths. With an improved assessment of the magnetic parameters of alloy systems, the model predicts M s temperatures within ±40 K for M s > 300 K where thermal contributions to the frictional work can be neglected.

Distributed-activation kinetics of Heterogeneous Martensitic Nucleation

Martensitic nucleation under normal circumstances is a heterogeneous process, and the heterogeneity can be explained by the potency distribution of defects that provide the nucleation sites, including both preexisting and autocatalytically generated defects. The potency distribu- tion of the preexisting defects has been shown earlier by small-particle studies to follow an exponential function, whereas that of the autocatalytic defects is found in the present work to obey a Gaussian function. A major distinction between these two distributions is that the number density of thepreexisting defects increases monotonically with decreasing defect potency, while the number density of theautocatalytic defects is distributed about a mode, giving a saturation level of its cumulative distribution. As a result of these potency distributions, the nucleating sites of both origins exhibit distributions in their activation energies for nucleation, and a distributed- activation kinetic model is now proposed to take these variations into account for martensitic transformations. The features of this model are tested with considerable success in experiments on an Fe-32.3Ni alloy, leading to calculations of the entire course of martensitic transformation curves (including the athermal, anisothermal, and isothermal contributions), the changing shapes of time-temperature-transformation (TTT) diagrams for a range of Fe-Ni compositions, and the grain-size dependence of “bursting” behavior.

Martensitic Nucleation&amp;mdash;Revisited

Some recent findings concerning heterogeneous martensitic nucleation are highlighted in this memorial tribute to Professor Zenji Nishiyama. It is now possible, with appropriate experimental observations, to express the distributions of nucleation-defect potencies (or equivalently, the activation energies) of both preexisting and autocatalytically-generated defects. Based on this treatment, the full course of a martensitic transformation on cooling or on isothermal holding can be derived