Lattice Invariant Deformation Research Articles

On the bcc/B2 interface structure in a refractory high entropy alloy

A refined microstructure consisting of bcc precipitates embedded in an ordered B2 matrix has been observed in the refractory high entropy alloy (RHEA) AlMo0.5NbTa0.5TiZr, resembling an “inverted superalloy-like” microstructure. A planar {100} bcc/B2 interface exists in this state. Coarsening of the microstructure occurs after aging at 1000 °C for 6 h, resulting in a faceted interface. In this case, the primary plane of the interface is parallel to a {100} plane, while the step associated with the facet is parallel to a {110} plane. Misfit dislocations at the interface were observed on the {110} interface plane, with Burgers vector of a/2〈111〉bcc, which extend into the bcc phase, and have an average spacing of 13.7 ± 0.6 nm. No lattice invariant deformation (LID) normal to the primary {110} planes was observed, such that the transformation between the B2 and bcc phases constitutes a pure expansion.

Elastic interaction energy analysis during twin plane formation in the martensitic transformation process of α"-martensite in Ti-Nb-Al

To understand the twin selection mechanism that occurs in the initial stage of the martensitic transformation of shape memory alloys, the stress state during twin plane formation was numerically analyzed by micromechanics. The self-accommodation microstructure of α''-martensite of the Ti-23Nb-3Al (at%) shape memory alloy, in which the lattice parameter was adjusted to eliminate the formation of internal twinning due to lattice-invariant deformation, was adopted for analysis. The two lattice correspondence variants (CVi and CVj) formed a twin plane. CVi was assumed to be spheroid, and the elastic strain energy during twin plane formation was evaluated by analyzing the elastic interaction energy when CVj formed around CVi. There are three types of twins ({011}α" compound twin, {111}α" type I twin, and <211>α" type II twin) in the self-accommodation microstructure of α"-martensite. Regardless of the CVi geometry (i.e., aspect ratio (1 to 0.01) and minor axis orientation), the {111}α" type I twin exhibited minimum elastic interaction energy, indicating that minimum elastic strain energy was generated during this twin plane formation. This result is consistent with the experimental results, which showed the selective formation of {111}α" type I twins in the initial stage of martensitic transformation.

In-situ observation of nucleation, growth and interaction of deformation-induced [formula omitted] martensite in metastable Ti–10V–2Fe–3Al

Microstructure evolution, dominated by the formation of deformation-induced α″ martensite during the 3-point bending of a metastable β Ti–10V–2Fe–3Al alloy containing 5% α, was observed in-situ using forward-scatter electron imaging and electron backscattering diffraction. α″ plates nucleated heterogeneously from {580}α″ habit planes at α-β interfaces and triggered the nucleation of additional α″ plates at the advancing interface during growth and upon impingement with high-angle boundaries. Further thickening of the impinged α″ plates led to a build-up of strain energy which induced 13031‾0α'' twinning within obstacle-forming α″ plates. Until now, this twinning system was observed in Nb and Ta alloyed Ti shape memory alloys only. This in-situ study is also the first to document the activation of 13031‾0α'' twinning by α″ impingement in a metastable β matrix. The first forming variants were {011}α″ compound twin-related variant pairs, each forming from up to two individual habit planes. These variant pairs were consistently predicted by determining the grain-average stress with finite element analysis and computing the available work from the transformation strain of the α″ variants. At higher indenter loads, grains that were unfavourably oriented to martensite formation accommodated the local stress by forming aggregates of different α″ variants, obeying either {111}α″ type I or 211α'' type II twin relationships. Scanning transmission electron microscopy revealed α″ substructures comprising columnar domains oriented perpendicular to the habit plane along with the absence of lattice invariant deformation. The growth of α″ plates involved ledge formation at α″-β interfaces.

Effect of Hydrogen on the Substructure of Lenticular Martensite in Fe-31Ni Alloy

This study investigated the effect of hydrogen on the substructure of martensite in Fe-31Ni alloy. In both the hydrogen-charged and uncharged specimens, typical lenticular martensite plates formed after subzero cooling. However, we found that the fraction of twinned region (including the area of midrib) in lenticular martensite plate increased with increasing hydrogen content. In addition, the width of individual twins in the hydrogen-charged specimen was slightly smaller than that in the uncharged specimen. These results indicated that the existence of hydrogen facilitated twinning deformation as a lattice invariant deformation. We presented a comprehensive discussion about the reason why hydrogen enhanced twinning deformation. Even though tetragonality of martensite in the hydrogen-charged specimen could not be confirmed by X-ray diffraction, the transmission electron microscopy observations and the first-principles calculations suggested that hydrogen might increase the tetragonality of martensite. We proposed that solid solution hardening and an increase in the tetragonality of martensite by the existence of hydrogen were the possible reasons for facilitating twinning deformation as a lattice invariant deformation in martensitic transformation.

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.

Determination of the structure of α-β interfaces in metastable β-Ti alloys

The crystallography and structure of the interfaces formed between refined hexagonal close packed (hcp) α precipitates and the body centered cubic (bcc) β matrix in a solution-treated and quenched metastable β titanium alloy, Ti-5Al-5Mo-5V-3Cr (wt%, Ti-5553), were investigated after heating to 600 °C and subsequently aging for 0 and 30 min, respectively. The two phases adopted the classical Burgers orientation, and the observed interfacial structures were analyzed using a topological model, i.e. they contained disconnections, as well as β crystal lattice dislocations acting as a lattice invariant deformation (LID). The structure of the α/β interface was observed along two mutually perpendicular directions, in high angle annular dark-field scanning transmission electron microscopy (HAADF-STEM). Viewed along the [0001]α:[110]β directions, an array of disconnections was observed to accommodate the misfit between the α and β crystals. While the spacing of these disconnections varied, the step height associated with them was always twice the {112}β interplanar spacing, and their Burgers vector b was [−0.0190.0190.034]β. When the interface was viewed along the [1¯1¯20]α:[1¯11]β direction, in the sample aged for 0 min at 600 °C the misfit between the two lattices along [0001]α:[110]β was so small that no misfit or lattice invariant dislocations were observed within the field of view, in contrast with the interface structure reported in other more conventional titanium alloys. After aging the sample for 30 min, however, the interfacial structure equilibrated, and crystal lattice dislocations were observed on the terrace planes, accommodating the LID, with b = 12[1¯1¯1¯]β. Growth of the α precipitates is shown to occur principally by the emission of disconnections from the tip of the existing α precipitates into the β matrix, and its resulting conversion to α. These results, combined with analysis using the topological model, show that the nucleation and growth of the hcp α phase from the bcc β matrix in this alloy can be described in terms of the motion of disconnections, accompanied by the displacive diffusion necessary to accommodate the differences in composition between the α and β phases.

Difference in thermodynamics between ferrite and martensite in the Fe-Ni system

Very fine duplex microstructure composed of recrystallized-ferrite and reversed-austenite was developed by prior cold rolling and subsequent intercritical annealing in binary Fe-Ni alloys. The equilibrium austenite fraction in the recrystallized-ferrite matrix was much smaller than that in the tempered-martensite matrix, which demonstrates that martensite is less stable than ferrite even though they have the same crystal structure of body-centered cubic. The difference in molar Gibbs energy between ferrite and martensite attributed to elastic strain energy in the martensite but not to lattice defects caused by lattice invariant deformation was evaluated to be 103J/mol at 773K.

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.

The Frank-Bilby Equation and Invariant-plane Interfaces

At equilibrium the tensor strains and rotations produced by the network of dislocations in a semi-coherent interphase interface are equal and opposite to those arising from the coherent terraces. We express this condition using the Frank-Bilby equation. All strains and rotations are partitioned between the two phases in a manner dependent on the relative compliance of the phases. Consequently, the proposition that a parent-martensite habit plane is an invariant plane of the shape transformation is only exact in the absence of rotational distortions. Rotational distortions are inevitably produced by lattice-invariant deformation (slip or twinning), and also, generally, by transformation dislocations (disconnections).

Deformation Mapping and the Role of Carbides on the Microstructure and Properties of Evolved Adiabatic Shear Bands

Impacting hardenable steel such as 4340, results in the formation of adiabatic shear bands (ASBs). Previous studies have shown that the presence of carbides/second-phase particles in the pre-deformation microstructures of 4340 steel increases their susceptibility to the formation of ASBs. The current study examines the role of carbides on the microstructure and properties within evolved ASBs in 4340 steel after impact. Geometric phase analysis was used to map local deformation fields within the evolved ASBs. It was observed that carbide fragmentation due to plastic deformation of carbides produces both residual carbides and residual carbide particles in regions away from the shear bands. Extensive carbide fragmentation produces fine residual carbide particles which are redistributed within the ASBs. This is attributed to strain localization within the ASBs which result in higher local strain and strain rates within the shear bands than in regions outside the bands. In addition, it is observed that the residual carbide particles trap and pin dislocations within the shear bands and contribute to an increase in local hardening. A more homogenous distribution of narrower and shorter rotational and shear-strain fields were revealed by the local deformation maps within the evolved ASBs. Lattice deformation mapping revealed that the ferrite matrix, prior to impact, had broader and longer rotational and shear-strain fields perpendicular to the direction of impact. This is attributed to lattice-invariant deformation and shape deformation processes that occur on specific crystallographic planes during martensitic transformation. It is concluded that strain localization during high strain rate deformations does not occur on specific crystallographic planes. This results in a more regular distribution of internal lattice rotational and strain fields within the evolved ASBs.

Intra-variant substructure in Ni–Mn–Ga martensite: Conjugation boundaries

The microstructure of a Ni–Mn–Ga alloy in the martensitic phase was investigated using transmission electron microscopy. Inter-variant twin boundaries were observed separating non-modulated tetragonal martensite variants. In addition, intra-variant boundary structures, referred to here as “conjugation boundaries”, were also observed. We propose that conjugation boundaries originate at the transformation interface between austenite and a nascent martensite variant. In the alloy studied, deformation twinning was observed, consistent with being the mode of lattice-invariant deformation, and this can occur on either of two crystallographically equivalent conjugate {101}〈101¯〉 twinning systems: conjugation boundaries separate regions within a single variant in which the active modes were distinct. The defect structure of conjugation boundaries and the low-angle of misorientation across them are revealed in detail using high-resolution microscopy. We anticipate that the mobility of such boundaries is lower than that of inter-variant boundaries, and is therefore likely to significantly affect the kinetics of deformation in the martensitic phase.

The β → α phase transformation in plutonium

The β→α transformation in plutonium is discussed in terms of the crystallography of the two phases and the resulting topological modeling of the β/α interface. There has been little microscopy work on the transformation, but it is probably martensitic. β-Pu is monoclinic I2/m, while α-Pu is monoclinic P21/m. α-Pu has been described as a hexagonal close-packed pseudostructure with AB stacking of the (020)α planes with pseudo-close-packing along [100]α and two other directions. β-Pu is less obvious, but X-ray diffraction suggests that the (103)β planes, which are selected as the terrace plane, have the highest structure factor and are therefore among the closest-packed planes. Other pseudo-close-packed planes, such as {222¯}β and {321¯}β, could also act as terrace planes for the transformation. The (103)β planes have a pseudo-hexagonal grid of Pu atoms with AB stacking and pseudo-close-packing along [301¯]β and two other directions. A selection of terrace planes as (020)α//(103)β with disconnections along [100]α//[301¯]β provides the basis for topological modeling. The model predicts a habit plane that is ∼6° from the terrace plane. The extra Pu atoms in the β structure (17 for every 16 in α) are accommodated by having 16 (103)β planes transform into 17 (020)α planes at steps in the interface. Short-range interstitial diffusion of Pu atoms from β to α is required for the transformation to proceed. Possible lattice invariant deformation systems are discussed.

Distribution of Dislocations in Nanostructured Bainite

The dislocation density in ferrite and austenite of a bainitic microstructure obtained by transformation at very low temperature (300 °C) has been determined using transmission electron microscopy. Observations revealed that bainitic ferrite plates consist of two distinctive regions with different substructures. A central region in the ferrite plate is observed with dislocations that may result from lattice-invariant deformation at the earlier stage of bainite growth. As plastic deformation occurs in the surrounding austenite to accommodate the transformation strain as growth progresses, the Ferrite/Austenite interface has also a very distinctive dislocation profile. In addition, atom-probe tomography suggested that dislocation tangles observed in the vicinity of the ferrite/austenite interface might trap higher amount of carbon than single dislocations inside the bainitic ferrite plate.

Martensite Midrib in an Fe-1C-17Cr Stainless Steel

An Fe-1.0C-17Cr (wt.%) stainless steel was subjected to subzero treatment to investigated the structure of martensite midrib. The midrib region appeared in the thin plate and lenticular martensites have been observed detailed by TEM. The TEM result reveals that the transformations of thin plate martensite and lenticular martensite are initiated at the same midrib region. The former keeps the lattice-invariant deformation mode of twinning during subsequent growth, whereas the latter combines both twinning and slip modes. Midrib region is a preferential position for carbide precipitations after tempering. M3C and M23C6carbide were found in this alloy, and related to the ferrite by Bagaryatsky OR and K-S OR, respectively.

Determination of crystallographic parameters associated with martensitic transformation in the alloy Fe-24.5 at % Pt

Considering the concrete slip system as a lattice invariant shear one, the orientation relationship between austenite and martensite and the analytical solutions for the habitus orientation, amount of lattice invariant deformation, and magnitude of the total shape deformation have been derived using rigorous version of the infinitesimal deformation (ID) approach for a description of the fcc to bcc martensitic transformation observed in an iron-platinum alloy with 24.5 at % Pt. The results of the present study are numerically compared with those obtained both in experiment and within the infinitesimal approach and a phenomenological theory of Bowles and Mackenzie (BM).

Martensitic interfaces and transformation crystallography in Pu–Ga alloys

The face-centered cubic (δ) to monoclinic (α) martensitic transformation in Pu–Ga is unusual because it produces a relative large change of volume up to 20%. Moreover, the transformation crystallography is not predicted satisfactorily by the classical phenomenological theories of martensite crystallography, which is based on the hypothesis that the habit plane is an invariant plane of the total shape change. In this study we use the recently developed topological model where the habit plane, i.e., the interface between the parent and martensite phases, is envisaged as a semi-coherent configuration with coherent terraces reticulated by a network of disconnections or transformation dislocations, and defects producing lattice-invariant deformation. The authors show explicitly that this network not only accommodates the coherency strains, so that no long-range strain field arises, but also produces diffusionless transformation by motion of the disconnections across the interface. It was show that the predicted habit plane inclination with respect to the parent and martensite phases in a Pu–Ga alloy is in good agreement with published experimental observations when the lattice-invariant deformation is \( (201)_{\alpha } /[10\overline{2} ]_{\alpha } \) twinning, as observed experimentally.

Crystallography of Martensite in TiAu Shape Memory Alloy

The twin structure, habit plane orientation, and morphology of B19 martensite in TiAu, which is a candidate shape memory alloy (SMA) for high-temperature and biomedical applications, were investigated by conventional transmission electron microscopy. Almost all internal twins were {111} type I twins as lattice-invariant deformation (LID). The type II twin was scarcely observed in TiAu, unlike in TiPd and TiPt SMAs. The habit plane roughly corresponded to the twinning plane (K1 plane) of the type II twin because of the superb lattice parameter ratio of TiAu. As a result, an energy-minimizing microstructure referred to as “twins within twins” appears as the major microstructure. The selection rules for the twinning of LID are also discussed considering the results of extensive studies on LID in SMAs.

Atomic Arrangement of Interphase Boundary between Bainite and Austenite in Fe-Si-C Alloy

Atomic arrangement of bainite/austenite interface was examined by high resolution electron microscopy in a Fe-2Si-1.4C alloy. Lattice transition region with an intermediate lattice structure between two phases, which is a characteristic feature of shear-type deformation, was not observed either between upper bainite and austenite or between lower bainite and austenite. However, high density dislocations existed inside upper and lower bainites, which may be introduced as a result of lattice invariant shear deformation. Based on these experimental facts, the shear deformation assisted-diffusional transformation model was proposed for the bainitic transformation.

Fe-Si-C 合金におけるベイナイトとオーステナイトとの相境界の原子配列

Atomic arrangement of bainite/austenite interface was examined by high resolution electron microscopy in a Fe-2Si-1.4C alloy. Lattice transition region with an intermediate lattice structure between two phases, which is a characteristic feature of shear-type deformation, was not observed either between upper bainite and austenite or between lower bainite and austenite. However, high density dislocations existed inside upper and lower bainites, which may be introduced as a result of lattice invariant shear deformation. Based on these experimental facts, the shear deformation assisted-diffusional transformation model was proposed for the bainitic transformation.

Orientation Relationship, Habit Plane, Twin Relationship, Interfacial Structure, and Plastic Deformation Resulting from the δ → α′ Isothermal Martensitic Transformation in Pu-Ga Alloys

The orientation relationship, habit plane, parent-product interface at the atomic level, twin relationship, and plastic deformation resulting from the δ→α′ isothermal martensitic transformation in Pu-Ga alloys are examined using optical microscopy, transmission electron microscopy (TEM), and finite element calculations. The δ → α′ transformation exhibits a ∼20 vol pct collapse when the fcc δ phase transforms to the monoclinic α′ phase, which results in unique and intriguing crystallography and morphology. Here, we show that the orientation relationship is very close to that previously reported by Zocco et al. (1990), but has small rotational misalignments between the two phases both parallel and perpendicular to the $$ \left[ {110} \right]_\delta ||\left[ {100} \right]_{\alpha '} $$ direction. The amount of plastic deformation is exceedingly large due to the ∼20 vol pct collapse, and TEM is used to quantify the difference in dislocation density between untransformed δ matrix and regions of δ adjacent to the transformed α′. The twins contained in α′ plates are shown to have a (205) α orientation as the lattice invariant deformation and are found to be composed of two alternating variants that share a common α′ direction, but differ by a 60 deg rotation about α′ . A combination of electron diffraction and optical microscopy has been employed to examine the macroscopic habit plane, and the analysis suggests that a large fraction of the observed habit planes are on or near {111} δ . Finally, high resolution TEM reveals that the interface is faceted on {111} δ exhibiting a series of terrace and ledges.