We analyse features of the patterns formed from a simple model for a martensitic phase transition that fragments the unit square into rectangles. This is a fragmentation model that can be encoded by a general branching random walk. An important quantity is the distribution of the lengths of the interfaces in the pattern, and we establish limit theorems for some of the asymptotics of the interface profile. In particular, we are able to use a general branching process to show almost sure power law decay of the number of interfaces of at least a certain size and a general branching random walk to examine the numbers of rectangles of a certain aspect ratio. In doing so we extend a theorem on the growth of the general branching random walk as well as developing results on the tail behaviour of the limiting random variable in our general branching process.

The fine microstructure resulting from the martensitic transformation drives many of the desired mechanical properties for quench-and-temper steels. The scale of martensite features correlates with austenite grain size, such that finer austenite grains produce finer martensitic structures. Measuring prior austenite grain (PAG) size from observations of the hierarchical martensitic structure using etch-based techniques remains challenging, especially for fine-grained specimens with low C and P content. This has driven an interest in our field in reconstructing prior austenite microstructure from electron backscatter diffraction (EBSD) data collected on tempered martensite. However, reliably reconstructing the data is not straightforward because (1) up to 24 variants can theoretically be observed from a single PAG; (2) the shear-induced plasticity that arises from martensite formation produces significant scatter in the pole figure; (3) there is inherent noise in Hough-indexed EBSD data; (4) annealing twins exist within many PAGs, producing martensite variants of similar orientations when compared with the parent grains; and (5) variation in austenite orientation can occur across a single PAG. To the author's knowledge, the majority of reconstruction algorithms published to date utilize either point-to-point or flood-fill approaches, which can produce artifacts due to the relatively high probability of adjacent EBSD observations falling within any reasonable tolerance angle with 24 variants in a parent and four annealing twin orientations. Therefore, we propose a probabilistic austenite reconstruction technique based on a clustering algorithm known as graph cutting. We demonstrate its application to steels and a binary ferrous alloy, then validate the results against chemical etching and retained austenite orientations. The graph cutting technique utilizes the misorientation distribution of martensitic variants and the potential austenite orientations for each observation, as estimated via Bayesian inference of the experimental orientation relationship and its scatter. It is found that this technique produces accurate reconstructions with identification of annealing twins in the PAGs, even in the presence of a large fraction of poorly indexed data points.

The shape memory properties of Ni–Al alloy are investigated using molecular dynamics simulation. The phase transformation behaviors for various Ni composition ratios are studied under quasistatic cooling and heating process. Various loadings, i.e., uniaxial, shear, and biaxial, are applied on a 68% Ni–Al alloy till plasticity takes place. The atomic configurations are inspected and analyzed using a common neighbor parameter. The shape recovery capability of the plastically deformed alloy is examined after heating above the phase transformation temperature. It is found that there would be shape recovery if the twinning plane reorientation or moving was the major yielding mechanism. For those loadings in which stacking faults or dislocations nucleate, the deformed model would not restore to its original shape after heating and the corresponding maximum shear stress is noticeably higher. There is no direct dependence between the yield strain and the shape recovery capability. Our findings could provide a possible explanation for the functional fatigue of the polycrystalline shape memory alloy.

In the present work, the effect of cooling rate on the evolution of the microstructure and mechanical properties of an α + β titanium alloy has been systematically investigated. Titanium alloy samples were heated to 1066 °C (above the β transus), 930 °C (just below the β transus), and 850 °C (well below the β transus) followed by oil quenching, air cooling, and furnace cooling, respectively. Primary alpha (αp), lamellar alpha (αL), and martensite (α′) were the dominant features of the microstructures for all the samples heated below the β transus. Furnace-cooled samples showed variation in the size and shape of the αp and fraction of αL according to the heating temperature. At slower cooling rates, the thickness of the αL increased with the increase in temperature. Transmission electron microscopy and X-ray diffraction confirmed the presence of α′ in all the quenched samples. The volume fraction and size of the αp decreased with the increase in temperature but was independent of the cooling rate. The microhardness was relatively unaffected by the cooling rate for heating just below the β transus, i.e., 930 °C. The modulus of elasticity was found to be extremely sensitive to the microstructure.

Titanium–tantalum based alloys can demonstrate a martensitic transformation well above 100 °C, which makes them attractive for shape memory applications at elevated temperatures. In addition, they provide for good workability and contain only reasonably priced constituents. The current study presents results from functional fatigue experiments on a binary Ti–25Ta high-temperature shape memory alloy. This material shows a martensitic transformation at about 350 °C along with a transformation strain of 2 pct at a bias stress of 100 MPa. The success of most of the envisaged applications will, however, hinge on the microstructural stability under thermomechanical loading. Thus, light and electron optical microscopy as well X-ray diffraction were used to uncover the mechanisms that dominate functional degradation in different temperature regimes. It is demonstrated the maximum test temperature is the key parameter that governs functional degradation in the thermomechanical fatigue tests. Specifically, ω-phase formation and local decomposition in Ti-rich and Ta-rich areas dominate when T max does not exceed ≈430 °C. As T max is increased, the detrimental phases start to dissolve and functional fatigue can be suppressed. However, when T max reaches ≈620 °C, structural fatigue sets in, and fatigue life is again deteriorated by oxygen-induced crack formation.

Improved understanding of the interactions between solutes and the austenite/ferrite interface can benefit modeling of ferrite growth during austenite decomposition, as the transformation kinetic is significantly affected by solutes that influence interface mobility. Solute-interface interactions dominate solute segregation at the interface in binary systems, but in multi-component alloys, solute–solute interactions may also affect segregation. In this study, interface segregation in Fe–Mn–N is examined and compared with Fe–Mn–C, to reveal the extent to which C affects the segregation of Mn. Atom probe tomography (APT) is well-suited to analyze solute concentrations across the interface, as this technique combines high spatial resolution and compositional sensitivity. Measurements of Mn show that segregation is only observed for Fe–Mn–C. This demonstrates that Mn segregation is primarily driven by an affinity for C, which also segregates to the interface. However, the measurement of N in steels by APT may be affected by a variety of experimental factors. Therefore, in verifying the Fe–Mn–N result, systematic examination is conducted on the influence of pulsing method (voltage versus laser), sample preparation (ion milling versus electropolishing), and vacuum storage on the measured N concentration. Both laser pulsing and focused ion beam sample preparation are observed to decrease the apparent N concentration.

A quantitative and automated phase analysis of dual-phase (DP) steel using electron backscatter diffraction (EBSD) was attempted. A ferrite–martensite DP microstructure was produced by intercritical annealing and quenching. An EBSD map of the microstructure was obtained and post-processed for phase discrimination. Band slope (BS), which was a measure of pattern quality, exhibited much stronger phase contrast than another conventional one, band contrast. Owing to high sensitivity to lattice defect and little orientation dependence, BS provided handiness in finding a threshold for phase discrimination. Its grain average gave a superior result on the discrimination and volume fraction measurement of the constituent phases in the DP steel.

The martensitic transformation behavior of the meta-stable austenite phase in low alloyed TRIP steels has been studied in situ using high-energy X-ray diffraction during deformation. The stability of austenite has been studied at different length scales during tensile tests and at variable temperatures down to 153 K. A powder diffraction analysis has been performed to correlate the macroscopic behavior of the material to the observed changes in the volume fraction of the phases. Our results show that at lower temperatures the deformation induced austenite transformation is significantly enhanced and extends over a wider deformation range, resulting in a higher elongation at fracture. To monitor the austenite behavior at the level of an individual grain a high-resolution far-field detector was used. Sub-grains have been observed in austenite prior to transformation.

Retained austenite is an important characteristic of properly heat-treated steel components, particularly gears and shafts, that will be subjected to long-term use and wear. Normally, either X-ray diffraction or optical microscopy techniques are used to determine the volume percent of retained austenite present in steel components subjected to specific heat-treatment regimes. As described in the literature, a number of phenomenological, experimental, and calculation factors can influence the volume fraction of retained austenite determined from X-ray diffraction measurements. However, recent disagreement between metallurgical properties, microscopy, and service laboratory values for retained austenite led to a re-evaluation of possible reasons for the apparent discrepancies. Broad, distorted X-ray peaks from un-tempered martensite were found to yield unreliable integrated intensities whereas diffraction peaks from tempered samples were more amenable to profile fitting with standard shape functions, yielding reliable integrated intensities. Retained austenite values calculated from reliable integrated intensities were found to be consistent with values obtained by Rietveld refinement of the diffraction patterns. The experimental conditions used by service laboratories combined with a poor choice of diffraction peaks were found to be sources of retained austenite values containing significant bias.

Electron backscatter diffraction (EBSD) techniques were used to characterize “hot-rolled” quenched and partitioned microstructures produced via Gleeble thermal simulations representing a hot-strip cooling practice for steel. In particular, EBSD was utilized to positively identify the morphology and location of retained austenite, to qualitatively distinguish martensite from ferrite, and in an attempt to identify transition carbides. Large pools of retained austenite and some thin films were accurately indexed; however, there was some disparity between austenite volume fractions measured by EBSD and those measured by X-ray diffraction. Due to similarities between the crystal structures of martensite and ferrite (body centered tetragonal versus body centered cubic, respectively), martensite could not be distinguished from ferrite by indexing of diffraction patterns; however, martensite could qualitatively be distinguished from ferrite by regions of low image quality based on the very high dislocation density of martensite.

Une « nouvelle » théorie est introduite comme alternative à la théorie phénoménologique des transformations martensitiques. Cette théorie est basée sur des cartographies EBSD expérimentales traitées par un nouveau logiciel de reconstruction automatique des grains parents.

Les aciers TRIP présentent une ductilité élevée et une forte résistance. Cette propriété remarquable trouve son origine dans la transformation martensitique de l'austénite. Ce comportement est modélisé avec une approche par transition d'échelle en utilisant le cadre de la thermomicromécanique pour déterminer les forces motrices ainsi que les lois de germination et de croissance qui contrôlent l'évolution de la microstructure. La présence de frontières mobiles et la discontinuité du champ de déformation au passage de ces interfaces sont prises en compte dans l'écriture des équations de champs. On montre que le champ de contrainte interne associé à la transformation se compose d'une contribution à longue distance responsable de la sélection des variantes et d'une contribution locale liée à la morphologie des microdomaines et au mode de croissance. On utilise une approche cristallographique à variables internes pour déterminer ces contributions. L'utilisation d'un modèle auto-cohérent classique permet ensuite de décrire le comportement global. Les résultats numériques obtenus sont comparés avec les données expérimentales pour un alliage FeNi et un acier TRIP 0,2C-1,5Si-1,5Mn élaboré par l'IRSID.

This work concerns the use of parallel electron energy loss spectroscopy (PEELS) to investigate the detection, distribution, and quantification of carbon in various steel microstructures generated by rapid cooling rates or by isothermal transformation. The feasibility of detecting C in steels containing very small amounts of carbon was first examined by calculating the minimum detectable mass fraction for a variety of binary Fe-C alloy specimen thicknesses and microscope conditions. These theoretical studies indicated that the detection of carbon in steel microconstituents containing about 0.01 wt.% (or even less) was easily possible with an analytical transmission electron microscope equipped with a LaB6 emitter and a PEEL spectrometer. These theoretical calculations seemed to be reasonable, as it proved possible to make a quantitative PEELS study of the partitioning between the microconstituents ferrite, retained austenite, and martensite found in an ultralow carbon (0.03 wt.%) steel weld metal provided care was taken to avoid hydrocarbon contamination. Studies of both carbon and molybdenum segregation to ferrite/martensite interfaces in an isothermally transformed Fe-C-Mo alloy were also carried out in order to investigate the nature of the “solute drag” effect in this alloy system.