Phase Transformation Accommodated Plasticity In Nanocrystalline Nickel

Based on detailed x-ray diffraction and transmission electron microscopy we have found body-centered-cubic (bcc) Ni upon room-temperature rolling of nanocrystalline (nc) face-centered-cubic (fcc) Ni. The bcc phase forms via the Kurdjumov-Sachs (KS) martensitic transformation mechanism when the von Mises equivalent strain exceeds similar to 0.3, much higher than accessible in tensile testing. The fcc and bcc phases keep either the KS or the Nishiyama-Wasserman orientation relationship. Our results provide insights into the deformation physics in nc Ni, namely, the fcc-to-bcc phase transformation can also accommodate plasticity at large plastic strains. (C) 2008 American Institute of Physics.

Theory Of Phase Transformation And Reorientation In Single Crystalline Shape Memory Alloys

A constitutive model, based on an (n + 1)-phase mixture of the Mori-Tanaka average theory, has been developed for stress-induced martensitic transformation and reorientation in single crystalline shape memory alloys. Volume fractions of different martensite lattice correspondence variants are chosen as internal variables to describe microstructural evolution. Macroscopic Gibbs free energy for the phase transformation is derived with thermodynamics principles and the ensemble average method of micro-mechanics. The critical condition and the evolution equation are proposed for both the phase transition and reorientation. This model can also simulate interior hysteresis loops during loading/unloading by switching the critical driving forces when an opposite transition takes place.

Effect of transformation volume contraction on the toughness of superelastic shape memory alloys

Shape memory alloys (SMAs) exhibit two very important properties: shape memory phenomenon and superelastic deformation due to intrinsic thermoelastic martensitic transformation. To fully exploit the potential of SMAs in developing functional structures or smart structures in mechanical and biomechanical engineering, it is important to understand and quantify the failure mechanisms of SMAs. This paper presents a theoretical study of the effect of phase-transformation-induced volume contraction on the fracture properties of superelastic SMAs. A simple model is employed to account for the forward and reverse phase transformation with pure volume change, which is then applied to numerically study the transformation field near the tip of a tensile crack. The results reveal that during steady-state crack propagation, the transformation zone extends ahead of the crack tip due to forward transformation while partial reverse transformation occurs in the wake. Furthermore, as a result of the volume contraction associated with the austenite-to-martensite transformation, the induced stress-intensity factor is positive. This is in stark contrast with the negative stress-intensity factor achieved in zirconia ceramics, which undergoes volume expansion during phase transformation. The reverse transformation has been found to have a negligible effect on the induced stress-intensity factor. An important implication of the present results is that the phase transformation with volume contraction in SMAs tends to reduce their fracture resistance and increase the brittleness.

Coupled Nonlinear Ginzburg-Landau and Mechanics Model for Martensitic Transformations in Polycrystals

Las transformaciones martensíticas (MT) se definen como un cambio en la estructura del cristal para formar una fase coherente o estructuras de dominio multivariante, a partir de la fase inicial con la misma composición, debido a pequeños intercambios o movimientos atómicos cooperativos. En el siglo pasado se han descubierto MT en diferentes materiales partiendo desde los aceros hasta las aleaciones con memoria de forma, materiales cerámicos y materiales inteligentes. Todos muestran propiedades destacables como alta resistencia mecánica, memoria de forma, efectos de superelasticidad o funcionalidades ferroicas como la piezoelectricidad, electro y magneto-estricción etc. Varios modelos/teorías se han desarrollado en sinergia con el desarrollo de la física del estado sólido para entender por qué las MT generan microstructuras muy variadas y ricas que muestran propiedades muy interesantes. Entre las teorías mejor aceptadas se encuentra la Teoría Fenomenológica de la Cristalografía Martensítica (PTMC, por sus siglas en inglés) que predice el plano de hábito y las relaciones de orientación entre la austenita y la martensita. La reinterpretación de la teoría PTMC en un entorno de mecánica del continuo (CM-PTMC) explica la formación de los dominios de estructuras multivariantes, mientras que la teoría de Landau con dinámica de inercia desentraña los mecanismos físicos de los precursores y otros comportamientos dinámicos. La dinámica de red cristalina desvela la reducción de la dureza acústica de las ondas de tensión de red que da lugar a transformaciones débiles de primer orden en el desplazamiento. A pesar de las diferencias entre las teorías estáticas y dinámicas dado su origen en diversas ramas de la física (por ejemplo mecánica continua o dinámica de la red cristalina), estas teorías deben estar inherentemente conectadas entre sí y mostrar ciertos elementos en común en una perspectiva unificada de la física. No obstante las conexiones físicas y diferencias entre las teorías/modelos no se han tratado hasta la fecha, aun siendo de importancia crítica para la mejora de modelos de MT y para el desarrollo integrado de modelos de transformaciones acopladas de desplazamiento-difusión. Por lo tanto, esta tesis comenzó con dos objetivos claros. El primero fue encontrar las conexiones físicas y las diferencias entre los modelos de MT mediante un análisis teórico detallado y simulaciones numéricas. El segundo objetivo fue expandir el modelo de Landau para ser capaz de estudiar MT en policristales, en el caso de transformaciones acopladas de desplazamiento-difusión, y en presencia de dislocaciones. Comenzando con un resumen de los antecedente, en este trabajo se presentan las bases físicas de los modelos actuales de MT. Su capacidad para predecir MT se clarifica mediante el ansis teórico y las simulaciones de la evolución microstructural de MT de cúbicoatetragonal y cúbicoatrigonal en 3D. Este análisis revela que el modelo de Landau con representación irreducible de la deformación transformada es equivalente a la teoría CM-PTMC y al modelo de microelasticidad para predecir los rasgos estáticos durante la MT, pero proporciona una mejor interpretación de los comportamientos dinámicos. Sin embargo, las aplicaciones del modelo de Landau en materiales estructurales están limitadas por su complejidad. Por tanto, el primer resultado de esta tesis es el desarrollo del modelo de Landau nolineal con representación irreducible de deformaciones y de la dinámica de inercia para policristales. La simulación demuestra que el modelo propuesto es consistente fcamente con el CM-PTMC en la descripción estática, y también permite una predicción del diagrama de fases con la clásica forma ’en C’ de los modos de nucleación martensítica activados por la combinación de temperaturas de enfriamiento y las condiciones de tensión aplicada correlacionadas con la transformación de energía de Landau. Posteriomente, el modelo de Landau de MT es integrado con un modelo de transformación de difusión cuantitativa para elucidar la relajación atómica y la difusión de corto alcance de los elementos durante la MT en acero. El modelo de transformaciones de desplazamiento y difusión incluye los efectos de la relajación en borde de grano para la nucleación heterogenea y la evolución espacio-temporal de potenciales de difusión y movilidades químicas mediante el acoplamiento de herramientas de cálculo y bases de datos termo-cinéticos de tipo CALPHAD. El modelo se aplica para estudiar la evolución microstructural de aceros al carbono policristalinos procesados por enfriamiento y partición (Q&P) en 2D. La microstructura y la composición obtenida mediante la simulación se comparan con los datos experimentales disponibles. Los resultados muestran el importante papel jugado por las diferencias en movilidad de difusión entre la fase austenita y martensita en la distibución de carbono en las aceros. Finalmente, un modelo multi-campo es propuesto mediante la incorporación del modelo de dislocación en grano-grueso al modelo desarrollado de Landau para incluir las diferencias morfológicas entre aceros y aleaciones con memoria de forma con la misma ruptura de simetría. La nucleación de dislocaciones, la formación de la martensita ’butterfly’, y la redistribución del carbono después del revenido son bien representadas en las simulaciones 2D del estudio de la evolución de la microstructura en aceros representativos. Con dicha simulación demostramos que incluyendo las dislocaciones obtenemos para dichos aceros, una buena comparación frente a los datos experimentales de la morfología de los bordes de macla, la existencia de austenita retenida dentro de la martensita, etc. Por tanto, basado en un modelo integral y en el desarrollo de códigos durante esta tesis, se ha creado una herramienta de modelización multiescala y multi-campo. Dicha herramienta acopla la termodinámica y la mecánica del continuo en la macroescala con la cinética de difusión y los modelos de campo de fase/Landau en la mesoescala, y también incluye los principios de la cristalografía y de la dinámica de red cristalina en la microescala. ABSTRACT Martensitic transformation (MT), in a narrow sense, is defined as the change of the crystal structure to form a coherent phase, or multi-variant domain structures out from a parent phase with the same composition, by small shuffles or co-operative movements of atoms. Over the past century, MTs have been discovered in different materials from steels to shape memory alloys, ceramics, and smart materials. They lead to remarkable properties such as high strength, shape memory/superelasticity effects or ferroic functionalities including piezoelectricity, electro- and magneto-striction, etc. Various theories/models have been developed, in synergy with development of solid state physics, to understand why MT can generate these rich microstructures and give rise to intriguing properties. Among the well-established theories, the Phenomenological Theory of Martensitic Crystallography (PTMC) is able to predict the habit plane and the orientation relationship between austenite and martensite. The re-interpretation of the PTMC theory within a continuum mechanics framework (CM-PTMC) explains the formation of the multivariant domain structures, while the Landau theory with inertial dynamics unravels the physical origins of precursors and other dynamic behaviors. The crystal lattice dynamics unveils the acoustic softening of the lattice strain waves leading to the weak first-order displacive transformation, etc. Though differing in statics or dynamics due to their origins in different branches of physics (e.g. continuum mechanics or crystal lattice dynamics), these theories should be inherently connected with each other and show certain elements in common within a unified perspective of physics. However, the physical connections and distinctions among the theories/models have not been addressed yet, although they are critical to further improving the models of MTs and to develop integrated models for more complex displacivediffusive coupled transformations. Therefore, this thesis started with two objectives. The first one was to reveal the physical connections and distinctions among the models of MT by means of detailed theoretical analyses and numerical simulations. The second objective was to expand the Landau model to be able to study MTs in polycrystals, in the case of displacive-diffusive coupled transformations, and in the presence of the dislocations. Starting with a comprehensive review, the physical kernels of the current models of MTs are presented. Their ability to predict MTs is clarified by means of theoretical analyses and simulations of the microstructure evolution of cubic-to-tetragonal and cubic-to-trigonal MTs in 3D. This analysis reveals that the Landau model with irreducible representation of the transformed strain is equivalent to the CM-PTMC theory and microelasticity model to predict the static features during MTs but provides better interpretation of the dynamic behaviors. However, the applications of the Landau model in structural materials are limited due its the complexity. Thus, the first result of this thesis is the development of a nonlinear Landau model with irreducible representation of strains and the inertial dynamics for polycrystals. The simulation demonstrates that the updated model is physically consistent with the CM-PTMC in statics, and also permits a prediction of a classical ’C shaped’ phase diagram of martensitic nucleation modes activated by the combination of quenching temperature and applied stress conditions interplaying with Landau transformation energy. Next, the Landau model of MT is further integrated with a quantitative diffusional transformation model to elucidate atomic relaxation and short range diffusion of elements during the MT in steel. The model for displacive-diffusive transformations includes the effects of grain boundary relaxation for heterogeneous nucleation and the spatio-temporal evolution of diffusion potentials and chemical mobility by means of coupling with a CALPHAD-type thermo-kinetic calculation engine and database. The model is applied to study for the microstructure evolution of polycrystalline carbon steels processed by the Quenching and Partitioning (Q&P) process in 2D. The simulated mixed microstructure and composition distribution are compared with available experimental data. The results show that the important role played by the differences in diffusion mobility between austenite and martensite to the partitioning in carbon steels. Finally, a multi-field model is proposed by incorporating the coarse-grained dislocation model to the developed Landau model to account for the morphological difference between steels and shape memory alloys with same symmetry breaking. The dislocation nucleation, the formation of the ’butterfly’ martensite, and the redistribution of carbon after tempering are well represented in the 2D simulations for the microstructure evolution of the representative steels. With the simulation, we demonstrate that the dislocations account for the experimental observation of rough twin boundaries, retained austenite within martensite, etc. in steels. Thus, based on the integrated model and the in-house codes developed in thesis, a preliminary multi-field, multiscale modeling tool is built up. The new tool couples thermodynamics and continuum mechanics at the macroscale with diffusion kinetics and phase field/Landau model at the mesoscale, and also includes the essentials of crystallography and crystal lattice dynamics at microscale.

Martensite Crystallography - the apparent controversy between the infinitesimal deformation approach and the phenomenological theory of martensitic transformations

The aim of this article is to demonstrate that the apparent controversy between the infinitesimal deformation (ID) approach and the phenomenological theory of martensitic transformations (PTMTs) in predicting the crystallographic characteristics of a martensitic transformation is entirely based on unjustified approximations associated with the way in which the ID calculations are performed. When applied correctly, the ID approach is shown to be absolutely identical to the PTMT. Nevertheless, there may be some advantages in using the ID approach. In particular, it is somewhat simpler than the PTMT; it is based on a physical concept that is easier to understand and, most important, it may provide a tool for investigating some of the features of martensitic transformations that have eluded explanation via the PTMT.

In situ synchrotron X-ray diffraction studies of the effect of microstructure on tensile behavior and retained austenite stability of thermo-mechanically processed transformation induced plasticity steel

Transmission electron microscopy and in situ synchrotron high-energy X-ray diffraction were used to investigate the martensitic transformation and lattice strains under uniaxial tensile loading of Fe-Mn-Si-C-Nb-Mo-Al Transformation Induced Plasticity (TRIP) steel subjected to different thermo-mechanical processing schedules. In contrast with most of the diffraction analysis of TRIP steels reported previously, the diffraction peaks from the martensite phase were separated from the peaks of the ferrite-bainite α-matrix. The volume fraction of retained γ-austenite, as well as the lattice strain, were determined from the diffraction patterns recorded during tensile deformation. Although significant austenite to martensite transformation starts around the macroscopic yield stress, some austenite grains had already experienced martensitic transformation. Hooke's Law was used to calculate the phase stress of each phase from their lattice strain. The ferrite-bainite α-matrix was observed to yield earlier than austenite and martensite. The discrepancy between integrated phase stresses and experimental macroscopic stress is about 300 MPa. A small increase in carbon concentration in retained austenite at the early stage of deformation was detected, but with further straining a continuous slight decrease in carbon content occurred, indicating that mechanical stability factors, such as grain size, morphology and orientation of the retained austenite, played an important role during the retained austenite to martensite transformation.

Competing tetragonal and monoclinic phases in Ni2.2Mn0.80Ga

Temperature dependent synchrotron x-ray powder diffraction, differential scanning calorimetry, and magnetic measurements were performed on Ni2+xMn1-xGa (x=0.20 and 0.35) magnetic shape memory alloys. For x=0.20, though the monoclinic phase is thermodynamically stable, a trace of residual stress can stabilize a tetragonal phase. The residual-stress-induced tetragonal phase transforms to the cubic austenite phase over an unusually large temperature range (348 K < T < 693 K), suggesting extremely slow kinetics of transformation. In contrast to x=0.20, the thermodynamically stable phase of x=0.35 is tetragonal and this composition exhibits the usual features of a reversible martensitic transformation. The results suggest that for x=0.20 the monoclinic and tetragonal phases are nearly degenerate.

The effect of ageing on microstructure and nanoindentation behaviour of dc magnetron sputter deposited nickel rich NiTi films

Nickel rich NiTi films were sputter deposited on p-doped Si left angle bracket1 0 0right-pointing angle bracket substrates maintained at 300 °C. The films were subsequently solution treated at 700 °C for 30 min followed by ageing at 400 and 500 °C for 5 h. The microstructure of the films was examined by TEM and these studies revealed that the NiTi films were mostly amorphous in the as-deposited condition. The subsequent solution treatment and ageing resulted in crystallization of the films with the film aged at 400 °C exhibiting nanocrystalline grains and three phases viz. B2 (austenite), R and Ni3Ti2 whereas the film aged at 500 °C shows micron sized grains and two phases viz. R and Ni3Ti2. Nanoindentation studies revealed that the nature of the load versus indentation depth response for the films aged at 400 and 500 °C was different. For the same load, the indenter penetrated to a much greater depth for the film aged at 400 °C as compared to the film aged at 500 °C. Also the ratio of the residual indentation depth (hf) to maximum indentation depth (hmax) is lower for the film aged at 400 °C as compared to the film aged at 500 °C. This was attributed to the occurrence of stress induced martensitic transformation of the B2 phase present in the film aged at 400 °C during indentation loading which results in a transformation strain in addition to the normal elastic and plastic strains and its subsequent recovery on unloading. The hardness and elastic modulus measured using the Oliver and Pharr analysis was also found to be lower for the film aged at 400 °C as compared to the film aged at 500 °C which was also primarily attributed to the same effect.

Crystallization Studies of ZrO2-SiO2 Composite Gels

Composite ZrO2-SiO2 powders were prepared using a gel route. Morphological and crystallographic features of ZrO2 particles formed during the heat treatment, and the particle sizes of the composites have been investigated. The following polymorphic changes have been observed during the heat treatment: amorphous -> metastable-cubic/tetragonal ZrO2 -> tetragonal ZrO2 -> monoclinic ZrO2. SiO2 crystallizes above 1273 K. The martensitic transformation of ZrO2 (t -> m) was observant in situ, when exposed to a high-energy electron beam. These results are important in the production of ZrO2-toughened ceramics of controlled microstructure.

Microstructural evolution and giant magnetoresistance in melt spun and annealed Cu-85(FeCo)(15) alloy

Granular alloys of Cu with FeCo were prepared by the melt-spinning technique. The alloy was characterized by x-ray, transmission electron microscopy, vibrating sample magnetometer, and magnetoresistance measurements. The alloys were heat treated for different temperatures to optimize the magnetoresistance properties. Structural characterization reveals that the FeCo phase initially precipitates out as fcc and later transforms to the bcc structure by martensitic transformation. It is seen that the trend in the magnetoresistance properties is different for the measurements carried out at room temperature and 4.2 K. This has been attributed to the transformation of fine fcc precipitates to the bcc structure during the low temperature measurements. It is seen that the presence of fine particles causes an increase in the field for saturation and is not suitable for applications where moderate field giant magnetoresistance is required. (C) 1999 American Institute of Physics. [S0021-8979(99)08317-6].

Effect of thermal and thermo-mechanical cycling on the microstructure of Ni-rich NiTi shape memory alloys

Microstructural changes of Ni-rich NiTi shape memory alloy during thermal and thermo-mechanical cycling have been investigated using Electron Back Scattered Diffraction. A strong dependence of the orientation of the prior austenite grain on the misorientation development has been observed during thermal cycling and thermo-mechanical cycling. This effect is more pronounced at the grain boundaries compared to grain interior. At a larger applied strain, the volume fraction of stabilized martensite phase increases with increase in the number of cycling. Deformation within the martensite leads to stabilization of martensitic phase even at temperatures slightly above the austenite finish temperature. Modulus variation with respect to temperature has been explained on the basis of martensitic transformation.

Strain-Induced Grain Refinement of Cobalt During Surface Mechanical Attrition Treatment

The microstructural evolution during surface mechanical attrition treatment of cobalt (a mixture of hexagonal close packed (hep) and face-centered cubic (fcc) phases) was investigated. In order to reveal the mechanism of grain refinement and strain accommodation. The microstructure was systematically characterized by both cross-sectional and planar-view transmission electron microscopy. In the hcp phase, the process of grain refinement. Accompanied by an increase in strain imposed in the surface layer. Involved: (1) the onset of 110 111 deformation twinning, (2) the operation of (1 120) 110 1 0} prismatic and (1 120) (000 1) basal slip, leading to the formation of low-angle dislocation boundaries, and (3) the successive subdivision of grains to a finer and finer scale. Ressulting in the formation of highly misoriented nanocrystalline grains. Moreover. The formation of nanocrystalliies at the grain boundary and triple junction was also observed to occur concurrently with straining. By contrast. The fec phase accommodated strain in a sequence as follows: (1) slip of dislocations by forming intersecting planar arrays of dislocations, (2) {1 1 1} deformation twinning, and (3) the gamma(fcc) --> epsilon(hcp) martensitic phase transformation. The mechanism of grain refinement was interpreted in terms of the structural subdivision of grains together with dynamic recrystallization occurring in the hep phase and the gamma --> E: martensitic transformation in the fcc phase as well.

Nanocrystalline Formation During Mechanical Attrition of Cobalt

The nanocrystalline (nc) formation was studied in cobalt (a mixture of c (hexagonal close packed) and gamma (face-centered cubic) phases) subjected to surface mechanical attrition treatment. Electron microscopy revealed the operation of {10(1) over bar 0}< 11(2) over bar 0 > prismatic and {0001}< 11(2) over bar 0 > basal slip in the E phase, leading to the successive subdivision of grains to nanoscale. In particular, the dislocation splitting into the stacking faults was observed to occur in ultrafine and nc grains. By contrast, the planar dislocation arrays, twins and martensites were evidenced in the gamma phase. The strain-induced gamma ->epsilon martensitic transformation was found to progress continuously in ultrafine and nc grains as the strain increased. The nc formation in the gamma phase was interpreted in terms of the martensitic transformation and twinning.

Nanocrystalline Formation during Mechanical Attrition of Cobalt

The nanocrystalline (nc) formation was studied in cobalt (a mixture of c (hexagonal close packed) and gamma (face-centered cubic) phases) subjected to surface mechanical attrition treatment. Electron microscopy revealed the operation of {10(1) over bar 0}< 11(2) over bar 0 > prismatic and {0001}< 11(2) over bar 0 > basal slip in the E phase, leading to the successive subdivision of grains to nanoscale. In particular, the dislocation splitting into the stacking faults was observed to occur in ultrafine and nc grains. By contrast, the planar dislocation arrays, twins and martensites were evidenced in the gamma phase. The strain-induced gamma ->epsilon martensitic transformation was found to progress continuously in ultrafine and nc grains as the strain increased. The nc formation in the gamma phase was interpreted in terms of the martensitic transformation and twinning.