Lattice Invariant Shear Research Articles

Reorientation induced plasticity in full αʺ martensite Ti-9V-1Fe-4Al alloy

The microstructure and deformation mechanism of a full orthorhombic αʺ martensite Ti-9V-1Fe-4Al (wt.%) alloy were investigated by XRD, TEM, EBSD analyses and tensile tests. The results show that the quenched alloy has a twinned-martensite microstructure and {111}αʺ type I internal twins are formed as the lattice invariant shear for martensite transformation. The alloy plastically deforms by a complex reorientation of αʺ martensite variants via the movement of the inter-variant boundaries of <211>α′′ type Ⅱ twin, and deformation twinning of {111}α′′ type I internal twin and of newly generated {011}αʺ compound twin in primary twinned martensites. {130}α′′<3¯ 10>α′′ and {110}α′′<1 1‾ 0>α′′ plastic twins were not observed in the alloy. Such a kind of deformation induced martensite reorientation results in a good combination of strength and plasticity with yielding strength of 480 MPa, tensile strength of 1030 MPa and elongation of 23% in the alloy. The calculated results further show that the shears of {111}α′′ type I, <211>α′′ type II and {011}α′′ compound twins and the shuffle of {111}α′′ type I twin increase, while the shears of {130}α′′<3‾ 10>α′′ and {110}α′′<1 1‾ 0>α′′ twins and the shuffle of {130}α′′<3‾ 10>α′′ twin decrease with an increase of the lattice parameter ratio bα′′/aα′′. The shears of these activated twinning systems are larger than those of {130}α′′<3‾ 10>α′′ and {110}α′′<1 1‾ 0>α′′ twins, and the shuffle of {111}α′′ type I twin is also bigger than that of {130}α′′<3‾ 10>α′′ twin in the present alloy, which implies that the operative twining modes cannot be derived simply in terms of the shear and shuffle magnitude in full αʺ martensite Ti based alloys.

Quantized plastic deformation

In engineering crystal plasticity inelastic mechanisms correspond to tensorial zero-energy valleys in the space of macroscopic strains. The flat nature of such valleys is in contradiction with the fact that plastic slips, mimicking lattice-invariant shears, are inherently discrete. A reconciliation has recently been achieved in the mesoscopic tensorial model (MTM) of crystal plasticity, which introduces periodically modulated energy valleys while also capturing in a geometrically exact way the crystallographically-specific aspects of plastic slips. In this paper, we extend the MTM framework, which in its original form had the appearance of a discretized nonlinear elasticity theory, by explicitly introducing the concept of plastic deformation. The ensuing model contains a novel matrix-valued spin variable, representing the quantized plastic distortion, whose rate-independent evolution can be described by a discrete (quasi-)automaton. The proposed reformulation of the MTM leads to a considerable computational speedup associated with the use of a robust and efficient hybrid Gauss-Newton–Cauchy energy minimization algorithm. To illustrate the effectiveness of the new approach, we present a detailed case-study focusing on the aspects of crystal plasticity that are beyond reach for the classical continuum theory. Thus, we provide compelling evidence that the re-formulated MTM is fully adequate to deal with the intermittency of plastic response under quasi-static loading. In particular, our numerical experiments show that the statistics of dislocational avalanches, associated with plastic yield in 2D square crystals, exhibits a power-law tail with a critical exponent matching the value predicted by general theoretical considerations and also independently observed in discrete-dislocation-dynamics (DDD) simulations.

Elucidating deformation pathways and interface characteristic of self-accommodated dual γ/ε phase microstructure in Fe–Mn–Si–Al alloy

There has been an intense scientific interest in investigating the phenomenon of deformation-induced ε-ε martensite (hcp) interaction owing to the thermodynamically paradoxical reverse transformation and mechanical twinning. In this study, detailed transmission electron microscopy has been employed to examine the crystallographic orientation relationship, phase stability and boundaries between the intersection phases on the ε-ε intersections in a 10% tensile deformed Fe–30Mn–4Si–2Al alloy. The transformation/twinning scheme is systematically summarized initiating from the austenite matrix (γ) and two deformation-induced ε-martensite variants. It involves diverse intersection reactions: mechanical ε-twins, a 90°-rotating γ-phase from the γ matrix (γR), and 90°-rotate ε-phase re-transformed from the intersection γ. All these phases share a common 〈101〉γ || <21¯1¯0>ε axis that is equivalent to the intersection axis of the crossing {111}<12¯1>γ shears and interrelated with rotational angles with respect to the axis. Electron diffraction, coupled with stereographic analysis, revealed the distinct orientation relationships between γ–ε and γR–ε phases. The boundaries between the intersection γR and neighboring ε-phase are inclined from the corresponding {111}γ||{101¯1}ε planes. By means of the phenomenological theory of martensite crystallography (PTMC), the inclination of the boundary is rationalized by considering the lattice-invariant shear on the double {111}γ plane inside the intersection γ to satisfy the invariant plane condition of the boundary.

Effect of Hf on the lattice invariant shear and self-accommodation of martensite in Ti–Ni–Hf alloys

Effect of Hf on the lattice invariant shear and self-accommodation of martensite in Ti–Ni–Hf alloys

Revealing the microstructure evolution of the deformed superelastic NiTi wire by EBSD

The generation of irreversible macroscopic strains in superelastic NiTi alloys is an important issue closely related to the crystallography of the transformation from B2 austenite to B19’ martensite under stress. Although widely investigated at micro and nano scales by transmission electron microscopy (TEM), the observation of this phase transformation at the mesoscale is still lacking. In the present study, a superelastic NiTi wire was maintained in bending condition and investigated by electron backscattered diffraction (EBSD) technique. A strong variant selection and a formation of martensite texture were observed and quantified using the interaction work (IW) based on the distortion matrix of a single variant. A new habit plane between martensite and parent B2, {114}B2 || (201¯)M, was experimentally measured. It was explained by the Phenomenological Theory of Martensite Crystallography (PTMC) using dislocation slip {110}<001>B2 as lattice invariant shear (LIS). Some new B2 domains were also found in {114}B2 twinning relation with primary B2 grain. Two scenarios are proposed to explain them: a) the direct formation of {114}B2 deformation twin in B2, and b) a more complex one in which a primary B2 grain is transformed into a martensite variant, a (201¯)M deformation twin is formed inside this variant; then the (201¯)M twinned martensite reversely transforms into a new {114}B2 twinned B2 domain. The scenario b) permits to explain some uncommon (130)M, (201)M, and (101¯)M twins observed by EBSD between the martensite variants of the two {114}B2 twin-related B2 phases.

Effect of Hf on the microstructure and martensitic transformation behavior in Ti–Pd–Hf alloy

We investigated the microstructure and the crystallography of martensite variants in Ti–Pd–Hf alloy using electron microscopy. The martensitic transformation temperature decreased with increasing amount of Hf substituted into the Ti50−xPd50Hfx alloy. No indication of a martensitic transformation was observed in the as-quenched Ti25Pd50Hf25 and Ti10Pd50Hf40 alloys, even when the samples were cooled to 150 K. The Ti40Pd50Hf10, Ti35Pd50Hf15, and Ti30Pd50Hf20 alloys were composed of a B19 orthorhombic phase having plate-like habit-plane variants consisting of both major and minor correspondence variants several hundred nanometers in width and several tens of micrometers in length at room temperature. Lattice-invariant shear of these alloys was a {111}B19 Type I twin. A solution-treated sample of the Ti25Pd50Hf25 alloy consisted of a B2 cubic matrix with local atomic displacement and lattice distortions, and rounded H-phase particles several tens of nanometers in diameter were precipitated inside the B2 matrix upon aging of the specimen at 823 K for 10.8 ks. The as-quenched Ti10Pd50Hf40 alloy contained rounded H-phase particles several tens of nanometers in diameter embedded in a B2 matrix at room temperature. The martensitic transformation temperature in the Ti50−xPd50Hfx alloy was drastically decreased by both the fully coherent nanosized H-phase particles and the short-range order originating from clustering of solute atoms.

Crystallography of γ′-Fe4N formation on bulk polycrystalline α-Fe substrates

The crystallographic features of a range of diffusional-displacive phase transformations was described by the phenomenological theory of martensite crystallography (PTMC). While the PTMC accounts for the crystallography of γ'-Fe4N formation in bulk-aged N-supersaturated α-Fe or nitrided α-Fe whiskers, there is still a lack of understanding of the morphological and crystallographic features of γ'-Fe4N directly formed on bulk polycrystalline α-Fe substrates, in spite of its importance to the microstructure development during nitriding.In this study, the morphology and crystallography of γ'-Fe4N, formed directly by gaseous nitriding of pure polycrystalline α-Fe substrates at 823 K, were investigated by means of EBSD and serial sectioning. The α-Fe grains partly transform into γ'-Fe4N, whereby γ' grows in several morphologies consisting of different variants. Characteristic features of the thus formed γ' phase are pronounced orientation gradients accompanied by different α-γ' orientation relationships (OR) and consequently deviations from the near Pitsch OR and habit plane predicted by PTMC with a lattice invariant shear (LIS) according to {101}α〈101¯〉α in the case of bulk-aged samples. Another feature of the γ' grains are twin boundaries and it is made likely that the incompatibility of the twin boundaries with the near Pitsch OR predicted by PTMC is one of the main factors leading to the formation of an OR close to Nishiyama-Wassermann or Kurdjumov-Sachs. It is shown that the orientation gradients and the change of the habit plane are mostly compatible with modified PTMC predictions involving a change of the LIS by variation of the LIS direction while maintaining the {1¯01¯}α LIS plane.

Martensite formation in titanium alloys: Crystallographic and compositional effects

An explanation is proposed to martensite inhibition beyond characteristic concentration thresholds in titanium binary alloys. The method combines the phenomenological theory of martensite crystallography (PTMC) and thermodynamic calculations (TCs) to describe the conditions under which martensite formation is favourable. It is shown that martensite can be crystallographically prevented while being thermodynamically favourable. The PTMC is implemented by taking into account the influence of composition. After a comprehensive comparison to experiments, two twinning systems and two glide systems are inferred to be able to produce the lattice invariant shear. The critical concentrations above which martensite cannot form are computed and compared to experimental results on binary and ternary systems, showing good agreement. The proposed method may be used as a guide to design titanium alloys for controlled martensitic behaviour.

Self-accommodation and morphological characteristics of the B33 martensite in Zr–Co–Pd alloys

Thermoelastic martensitic transformation (MT) plays a vital role in shape memory effects and superelasticity of various alloys. To understand the self-accommodation mechanism of the MT of Zr–Co–Pd alloys, which demonstrate typical MT from B2 to B33 structure, the configuration of the alloy’s martensite variants and their crystallographic relationship were investigated by electron backscatter diffraction, transmission electron microscopy, and high-angle annular dark-field scanning transmission electron microscopy. Results suggest that two habit plane variants (HPVs) bounded by {021}B33 compound twinning are formed around each B2 axes of the B2 parent phase. It is determined that the minimum self-accommodation unit, to relax the strain energy accompanying MT, is a pair of trapezoid- or triangle-shaped HPVs. No lattice invariant shear exists in the martensite variants with a trapezoid- or triangle-shape. In the latter stage of MT, each HPV pair may contact and impinge on {110}B2 plane of B2 parent phase, which is shear and shuffling plane on MT. The combination of the four variants forms the roof-type morphology.

Omega Transition Accompanied by Mechanical Induced Twinned Martensite in Medium Manganese Steels

The omega transition process was firstly analyzed combined with martensitic transformation in this investigation. In order to avoid the influence of auto-tempering on metastable omega phase, martensitic transformation process was inspired by deformation at room temperature. Omega phase was found only exist within twinned martensite with single variant, and the results indicate that omega phase formed by the lattice invariant twin shear during the dynamic transformation of twinned martensite. Besides, the nature poor ductility of twinned martensite was discussed.

Self-Accommodated Dual Γ/Ε Phase Deformation Microstructure Accompanying a Reverse Transformation of Deformation-Induced Ε-Martensite

We previously reported on crossing {111} γ shears at the intersection of deformation-induced hexagonal close packed e-martensite causing an abnormal (thermodynamically paradoxical) reverse transformation and mechanical twinning. In the present study, detailed transmission electron microscopy on the e-e intersections in a 10% tensile deformed Fe-30Mn-4Si-2Al alloy has been employed to examine the crystallographic orientation relationship, phase stability and boundaries between the intersection phases. The transformation/twinning scheme is systematically summarized in a tree diagram initiating from the γ matrix and two deformation-induced e-martensite variants, diversifying into mechanical e twins, γ-phase at the intersection which is 90o-rotated from the γ matrix, and 90o-rotated e-phase re-transformed from the intersection γ. All these phases share a common γ || e axis that is equivalent to the intersection axis of the crossing {111} γ shears and interrelated with rotational angles with respect to the axis. The boundaries between the intersection γ and neighboring e are inclined from the corresponding {111}γ || {10-10}e planes. By means of the phenomenological theory of martensite crystallography (PTMC), the inclination of the boundary is rationalized considering the lattice-invariant shear on the double {111}γ plane inside the intersection γ to satisfy the invariant plane condition of the boundary.

Crystal plasticity modeling of 3rd generation multi-phase AHSS with martensitic transformation

A systematic constitutive modeling and calibration methodology were developed based on rate-independent crystal plasticity to predict the quasi static macroscopic behavior of 3rd generation multiphase advanced high strength steels (3GAHSS) prepared with a quenching and partitioning (Q&P) process. In the constitutive law, martensitic phase transformation induced by the elastic-plastic deformation of the retained austenite is represented by considering the Bain strain, the lattice invariant shear deformation, and the orientation relationship between parent austenite and transformed martensite. The amount that each martensite variant evolves is obtained through an optimization scheme that constrains the plastic deformation of the retained austenite to have minimum-energy during phase transformation. In-situ high energy X-ray diffraction (HEXRD) tensile test data was utilized for the characterization and calibration of the material model. Dislocation density based hardening parameters were separately obtained for each phase by iteratively performing crystal plasticity finite element (CPFE) simulations until the simulated stress-strain curves matched the experimentally measured curves from in-situ HEXRD. The 3D representative volume element (RVE) for the 3GAHSS was generated by utilizing Dream.3D and the MTEX Matlab toolbox software. The distributions of grain size and crystal orientation were analyzed based on the measured EBSD data and accounted for in the generation of the 3D RVE. For verification and validation of the constitutive model, crystal plasticity finite element simulations of a uniaxial tensile test were performed using the developed material model and the generated 3D RVE. Additional hypothetical RVEs were also generated by manipulating phase volume fractions, phase transformation speed, and phase properties to determine if these virtual 3GAHSS steels have improved mechanical properties. Also, forming limit curves (FLC) for the multiphase 3GAHSS were predicted from the CPFE simulation results.

Role of Crystal Symmetry in the Reversibility of Stacking-Sequence Changes in Layered Intercalation Electrodes.

The performance of many technologies, such as Li- and Na-ion batteries as well as some two-dimensional (2D) electronics, is dependent upon the reversibility of stacking-sequence-change phase transformations. However, the mechanisms by which such transformations lead to degradation are not well understood. This study explores lattice-invariant shear as a source of irreversibility in stacking-sequence changes, and through an analysis of crystal symmetry shows that common electrode materials (graphitic carbon, layered oxides, and layered sulfides) are generally susceptible to lattice-invariant shear. The resulting irreversible changes to microstructure upon cycling ("electrochemical creep") could contribute to the degradation of the electrode and capacity fade.

Crystal Plasticity Constitutive Model for Multiphase Advanced High Strength Steels to Account for Phase Transformation and Yield Point Elongation

A constitutive law was developed based on a rate-independent crystal plasticity to account for the mechanical behavior of multiphase advanced high strength steels. Martensitic phase transformation induced by the plastic deformation of the retained austenite was represented by considering the lattice invariant shear deformation and the orientation relationship between parent austenite and transformed martensite. The stress dependent transformation kinetics were represented by adopting the stress state dependent volume fraction evolution law. The plastic deformation of the austenite was determined to have the minimum- energy associated with the work during the phase transformation. In addition to the martensitic phase transformation, yield point elongation and subsequent hardening along with inhomogeneous plastic deformation were also represented by developing a hardening stagnation model induced by the delayed dislocation density evolution.

Self-stabilization of untransformed austenite by hydrostatic pressure via martensitic transformation

For improving the understanding of austenite stability in steel, hydrostatic pressure in untransformed austenite that is generated via martensitic transformation was evaluated from macro- and micro-viewpoints, and its effect on austenite stability was investigated in a Fe-27%Ni austenitic alloy. X-ray diffractometry revealed that the lattice parameter of untransformed austenite is continuously decreased via martensitic transformation only when martensite becomes the dominant phase in the microstructure. This suggests that the untransformed austenite is isotropically compressed by the surrounding martensite grains, i.e., hydrostatic pressure is generated in untransformed austenite dynamically at a later stage of martensitic transformation. On the other hand, microscopic strain mapping using the electron backscatter diffraction technique indicated that a finer untransformed austenite grain has a higher hydrostatic pressure, while a high density of dislocations is also introduced in untransformed austenite near the austenite/martensite interface because of lattice-invariant shear characterized by non-thermoelastic martensitic transformation. Furthermore, it was experimentally demonstrated that the hydrostatic pressure stabilizes the untransformed austenite; however, the austenite stabilization effect alone is not large enough to fully explain a large gap between martensite start and finish temperatures in steel.

The Role of Twinned and Detwinned Structures on Memory Behaviour of Shape Memory Alloys

Shape memory alloys have a peculiar property to return to a previously defined shape or dimension when they are subjected to variation of temperature. Shape memory effect is facilitated by martensitic transformation governed by changes in the crystalline structure of the material. Martensitic transformations are first order lattice-distorting phase transformations and occur with the cooperative movement of atoms by means of lattice invariant shears in the materials on cooling from high temperature parent phase region. The material cycles between the deformed and original shapes on cooling and heating in reversible shape memory effect. Thermal induced martensite occurs as twinned martensite, and the twinned martensite structures turn into detwinned structures by deforming the material in the martensitic condition. Deformation of shape memory alloys in martensitic state proceeds through a martensite variant reorientation. The deformed material recovers the original shape on first heating over the austenite finish temperature in reversible and irreversible shape memory cases. Meanwhile, the parent phase structure returns to the twinned structure in irreversible shape memory effect on cooling below to martensite finish temperature and to the detwinned structure in reversible shape memory effect. Therefore, the twinning and detwinning processes have great importance in the shape memory behaviour of the materials. Copper based alloys exhibit this property in metastable β-phase region, which has bcc-based structures at high temperature parent phase field, and these structures martensitically turn into layered complex structures with lattice twinning following two ordered reactions on cooling.

Phase Transitions and Elementary Processes in Shape Memory Alloys

Shape memory effect is a peculiar property exhibited by certain alloy systems, and shape memory alloys are recognized to be smart materials. These alloys have important ability to recover the original shape of material after deformation, and they are used as shape memory elements in devices due to this property. The shape memory effect is facilitated by a displacive transformation known as martensitic transformation. Shape memory effect refers to the shape recovery of materials resulting from martensite to austenite transformation when heated above reverse transformation temperature after deforming in the martensitic phase. These alloys also cycle between two certain shapes with changing temperature.Martensitic transformations occur with cooperative movement of atoms by means of lattice invariant shears on a {110} - type plane of austenite matrix which is basal plane of martensite.Copper based alloys exhibit this property in metastable β-phase field. High temperature β-phase bcc-structures martensiticaly undergo the non-conventional structures following two ordered reactions on cooling, and structural changes in nanoscale level govern this transition cooling. Atomic movements are also confined to interatomic lengths due to the diffusionless character of martensitic transformation.

Special cases of martensite compatibility: A near single-variant habit-plane and the martensite of nanocrystalline NiTi

Lattice parameters measured near the high temperature (~1000°C) bcc α to hcp β transformation in an intermetallic Mo-containing γ -TiAl based alloy indicate a middle valued eigenvalue of the corresponding deformation gradient near 1. Habit-planes calculated under the assumption of a simple slip as lattice invariant shear, agree with experimentally determined orientations of the lens like plates recorded via electron backscattering. By contrast, twinning as invariant lattice shear has been investigated in nanocrystalline NiTi. Here the grain size causes the formation mechanism of the martensite to change from a “herring-bone” morphology faciliting a habit-plane between two twinned laminates and the austenite to a single laminate, which in the nonlinear theory formally cannot form a habit-plane with the austenite. Since this might cause high accommodation strains, the effectiveness of stress accommodation of martensite formed in neighboring grains of a polycrystal is investigated. Subsequent numerical microstructural modeling is outlined. The resulting energetically most favorable transformation sequence yields the transformation kinetics.

鉄鋼のマルテンサイト/ベイナイト変態における結晶学的拘束

Attention to lath martensite and bainite in steels has been increasing due to their good mechanimcal properties. Various boundaries bewteen K-S variants contained in those microstructures contribute to their high strength and toughness so that deeper understand of nature of those boundaries is required. EBSD analyses have revealed that different variant grouping tendencies appear depending on composition and transformation temperature, such as variants belonging to the same Bain group, variants sharing the same close-packed plane parallel relationship. Kinematical compatibility (KC) condition can explain variant pairs coupled preferentially in lenticular and thin plate martensite satisfactory. In addition, it is revealed that some of the variant pairs observed in lath martensite and bainite are favorable for the KC condition when double shears are assuemd for lattice invariant shear.

Micromechanical Modelling of Microtexture Formation in Low Alloy Steel Bainite

A micromechanical model was developed to account for the particular microtexture of upper bainite in low alloy steels, i.e. the non-random spatial distribution of variants within a given former austenite grain. A self-consistent scheme and an Eshelby approach, considering both transformation shape strain and viscoplastic strain as eigenstrains, was applied to estimate coupling between parent austenite and two or more bainite variants without any applied stress. Model predictions concerning self-accommodation between variants are sensitive to the plane of the first “lattice invariant shear” in the crystallographic model used to determine the shape strain. No obvious effect of the constitutive equations of phases and of the other model parameters was found.