Habit Plane Variants Research Articles

Magnitude of incompatibility between habit plane variants related by 180° rotation

Magnitude of incompatibility between habit plane variants related by 180° rotation

Phase-field description of fracture in NiTi single crystals

A phase-field model for thermomechanically-induced fracture in NiTi at the single crystal level, i.e., fracture under loading paths that may take advantage of either of the functional properties of NiTi–superelasticity or shape memory effect–, is presented, formulated within the kinematically linear regime. The model accounts for reversible phase transformation from austenite to martensite habit plane variants and plastic deformation in the austenite phase. Transformation-induced plastic deformation is viewed as a mechanism for accommodation of the local deformation incompatibility at the austenite–martensite interfaces and is accounted for by introducing an interaction term in the free energy derived based on the Mori–Tanaka and Kröner micromechanical assumptions and the hypothesis of martensite instantaneous growth within austenite. Based on experimental observations suggesting that NiTi fractures in a stress-controlled manner, damage is assumed to be driven by the elastic energy, i.e., phase transformation and plastic deformation are assumed to contribute in crack formation and growth indirectly through stress redistribution. The model is restricted to quasistatic mechanical loading (no latent heat effects), thermal loading sufficiently slow with respect to the time rate of heat transfer by conduction (no thermal gradients), and a temperature range below Md, which is the temperature above which the austenite phase is stable, i.e., stress-induced martensitic transformation is suppressed. The numerical implementation of the model is based on an efficient scheme of viscous regularization in both phase transformation and plastic deformation, an explicit numerical integration via a tangent modulus method, and a staggered scheme for the coupling of the unknown fields. The model is shown able to capture transformation-induced toughening, i.e., stable crack advance attributed to the shielding effect of inelastic deformation left in the wake of the growing crack under nominal isothermal loading, actuation-induced fracture under a constant bias load, and crystallographic dependence on crack pattern.

Full-field strain investigation of twinned martensite in a thermally activated Cu–Al–Ni single crystal using Localized Spectrum Analysis

The paper presents a full-field strain analysis of the appearance/disappearance of twinned martensite in a Cu–Al–Ni single crystal subjected to thermal cycles. Localized Spectrum Analysis (LSA) was employed to process images of a checkerboard pattern preprinted on the sample’s surface, enabling us to obtain strain maps with a suitable trade-off between strain resolution (2×10−4) and spatial resolution (0.26 mm). During the cooling of the initially austenitic sample, habit plane variants (HPVs) were identified from the in-plane components of their mean right strain tensor. The match between measured data and theoretical expectations enabled us to measure the stretch parameters associated with the cubic-to-orthorhombic transformation occurring in the material. Various deformation mechanisms were revealed by an analysis in the strain space. In particular, the process of martensite appearance during cooling appeared to be based on the coordinated activation of HPVs pairs whose strain levels globally compensate each other. Elastic strain gradients were also evidenced, highlighting the need for additional deformation to achieve kinematic compatibility at microstructure interfaces. Lastly, several thermal cycles were applied to the previously-trained sample, enabling us to quantify the level of spatio-temporal repeatability of the phase transformation.

Solving the puzzle of hierarchical martensitic microstructures in NiTi by (111)-oriented epitaxial films

The martensitic microstructure decides on the functional properties of shape memory alloys. However, for the most commonly used alloy, NiTi, it is still unclear how its microstructure is built up because the analysis is hampered by grain boundaries of polycrystalline samples. Here, we eliminate grain boundaries by using epitaxially grown films in (111)B2 orientation. By combining scale-bridging microscopy with integral inverse pole figures, we solve the puzzle of the hierarchical martensitic microstructure. We identify two martensite clusters as building blocks and three kinds of twin boundaries. Nesting them at different length scales explains why habit plane variants with ⟨011⟩B19' twin boundaries and {942} habit planes are dominant; but also some incompatible interfaces occur. Though the observed hierarchical microstructure agrees with the phenomenological theory of martensite, the transformation path decides which microstructure forms. The combination of local and global measurements with theory allows solving the scale bridging 3D puzzle of the martensitic microstructure in NiTi exemplarily for epitaxial films.

An investigation on reorientation and textural evolution in a martensitic NiTi rolled sheet using EBSD

Variant reorientation is a ubiquitous phenomenon in shape memory alloys and has a great influence on their texture and mechanical response. In the present study, a martensitic NiTi rolled sheet is investigated by the electron backscattering diffraction (EBSD) technique; the variant reorientation and texture evolution are followed during bending. The initial weak texture components of martensite evolve by reorientation toward a strong texture around [1¯04]M and a weak one around [1¯12]M. The initial laths are transformed into blocks made of one or two variants. The EBSD maps were analyzed with the Interaction Work (IW) criterion associated with (a) the individual variant and (b) habit plane variants (a combination of two distortion variants). Compared with the experimental results, the prediction given with individual variant fits better than with the habit plane variants. An empirical quantification of the threshold on interaction work (IW) permits to rationalize and predict the variant pairs formed by the reorientation and their numbers in the blocks. A critical influence of the pre-texture of the parent B2 grains on the final texture and on the number of variants per block was revealed. This study could give insights into the mechanical response of the NiTi alloys with various textures during tensile and fatigue tests.

A finite strain thermomechanically-coupled constitutive model for phase transformation and (transformation-induced) plastic deformation in NiTi single crystals

A 3D finite-strain constitutive model for the deformation response of NiTi at the single crystal level is proposed. The model accounts for reversible phase transformation from austenite to martensite habit plane variants, plastic deformation in the austenite phase, and rate effects induced from latent heat. It is developed within the formalism of irreversible thermodynamics with internal state variables based on the Eulerian logarithmic strain and its corrotational objective rate. The inelastic deformation is defined as an average over a representative volume element as classical in the micromechanics-based modeling approach. Transformation-induced plastic deformation is viewed as a mechanism for accommodation of the local deformation incompatibility at the austenite–martensite interface. It is accounted for by introducing an interaction term in the free energy, which is described through the Eshelby tensor by regarding the habit plane variants as ellipsoidal inclusions embedded in the austenite matrix, in order to accurately reflect the internal stress states that contribute to dislocation slipping. The numerical implementation of the model in an efficient scheme and its calibration are described in detail. The proposed model is validated by comparing simulations with available experimental data in single NiTi crystals. Numerical simulations of polycrystals are performed to obtain an insight into the interaction between phase transformation and plastic deformation induced by intergrannular constraints. The efficiency of the numerical implementation of the model is verified by simulations of indentation tests.

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.

Geometry and energy barrier of martensite in the initial stage martensitic transformation in B19’ TiNi shape memory alloy

This study addresses the selectivity of self-accommodation microstructures in the initial stage of martensitic transformation in B19’ TiNi. It is known that specific habit plane variant (HPV) pairs, including {111¯}mtype I twin planes that are called initial stage microstructure (ISM) in this study, are preferentially formed in the initial stage of martensitic transformations. To elucidate on the selectivity of the ISM, the energy barrier at the formation of the twin plane, which is the candidate for the starting point of HPV pair formation, and the geometry of the HPV pair are theoretically analyzed in this paper. Using geometrical non-linear theory analysis, the compatible twin plane which has exact twin orientation relationship can be formed in the specific five groups of HPV pair. Using ab-initio simulations and Eshelby theory analysis results, {111¯}mtype I twin is determined to have a relatively small energy barrier among the twins in TiNi. Therefore, this paper shows that the HPV pair having a twin plane with a small energy barrier of formation and a structure that can effectively reduce the elastic strain is preferentially formed as the ISM.

Statistical variations in predicted martensite variant volume fractions in superelastically deformed NiTi modeled using habit plane variants versus correspondence variants

Habit plane variants (HPVs) are traditionally used as the fundamental microstructure unit in micromechanical models of shape memory alloys. Recently, an approach using Correspondence Variants (CVs) has emerged. Previous research has shown that HPVs cannot completely explain superelastic deformation of Nitinol, especially beyond initiation of the martensitic phase transformation that gives rise to superelasticity. In this work, a statistical comparison of both modeling approaches is presented for the case of superelastic Nitinol subjected to uniaxial tension and uniaxial compression. Specifically, volume fractions of variants that contribute to deformation were calculated using the two models and then compared. The relative differences were found to be about 30% in tension and 10% in compression at high strains. Allowing detwinning to occur in the HPV model reduced the relative differences in CV volume fractions to about 20% in tension.

Deformation mechanisms in a superelastic NiTi alloy: An in-situ high resolution digital image correlation study

An in-situ high resolution digital image correlation investigation during uniaxial tensile deformation reveals the recoverable and the non-recoverable strain mechanisms in a Ni51Ti49 alloy with a mean grain size of 35 μm. Recoverable strain is due to the martensitic transformation, for which more than one variant per grain can be activated. The majority of the activated variants exhibit high Schmid factor. The variant selection can be influenced by shear transmission across grain boundaries, when the geometrical compatibility between the neighboring habit plane variants is favourable; in these cases variants that do not have the highest Schmid factor, with respect to the macroscopically applied load, are activated. The experimentally determined transformation strains agree well with theoretical calculations for single crystals. The non-recoverable strain is due to deformation slip in austenite, twinning in martensite and residual martensite. The results are discussed in view of possible twinning modes that can occur in austenite resulting in significant non-recoverable strain.

Micromechanical response analysis of Ti-Ni shape memory alloy undergoing martensitic reorientation and detwinning

The micromechanical deformation behavior of Ti-Ni shape memory alloy in the fully martensitic state is studied using a previously developed constitutive model for martensitic reorientation and detwinning. Considering a microscale two-variant material particle, the interaction between different martensitic habit plane variants in a variant pair is investigated by numerical simulations. It is shown that the variant pairs can be compatible or incompatible while interacting with each other. Furthermore, our numerical analysis shows that the predicted loading response of Ti-Ni shape memory alloy under simple tension depends on the number of existing martensitic variants in a material particle under consideration.

In situ, 3D characterization of the deformation mechanics of a superelastic NiTi shape memory alloy single crystal under multiscale constraint

Microstructural elements in NiTi shape memory alloys (SMAs) – precipitates, phase boundaries, inclusions, grain boundaries – can be viewed as sources of multiscale constraint that influence their deformation response. We characterized in situ, and in 3D, the deformation and the evolution of microstructure during a tension test in a superelastic NiTi specimen containing some of these sources of constraint. The method used was far-field high-energy X-ray diffraction microscopy (ff-HEDM), complemented by electron microscopy. We simulated the local stress state in the specimen using a microstructural model informed by the experimental data. Using these combined microstructure, deformation, and stress data, we report three phenomena, and relate them to specific sources of constraint. During initial elastic loading, axial lattice strain in austenite increased monotonically. On partial stress-induced phase transformation to martensite, the stress redistributed to both phases leading to a stress relaxation in austenite. The specimen contained a dense distribution of inclusions, which led to the activation of martensite habit plane variants that produce less than theoretical maximum transformation strain. Large Ni4Ti3 precipitates potentially contributed to the poor transformation response. Under load, proportional gradients in local rotation and elastic stretch developed in the martensite phase, because of the constraint at phase interfaces. This combined ff-HEDM, electron microscopy, microstructural simulation toolbox provides a versatile method to understand the effect of constraint on inelastic deformation in other alloys with hierarchical microstructure.

Twinning of deformation-induced ε-martensite in Fe-30Mn-6Si shape memory alloy

The ε-martensite, which is induced by tensile plastic deformation, twins under further plastic deformation due to the collision of different habit plane variants. Crystallographic characteristics of the mechanical ε twins were examined in this study by electron backscattering diffraction in a Fe-30Mn-6Si shape memory alloy, which was subjected to tensile deformation of up to 10% at room temperature. ε twins of {1 0 1¯ 2} and {1 0 1¯ 1} types were observed at the intersections of two different habit plane variants. Non-basal shearing forces on the pre-existing ε-martensite in the directions perpendicular to or 30°-inclined from the intersection axis (Type I and II) are responsible for the {1 0 1¯ 2} and {1 0 1¯ 1} ε twins, respectively. The former twins at Type I intersections exhibited a self-accommodating microstructure consisted of different twinning-plane variants. The occurrence of the {1 0 1¯ 1} twinning at Type II intersections suggests an inclined twinning shear mechanism.

Formation process of the incompatible martensite microstructure in a beta-titanium shape memory alloy

The formation modes of habit plane variant (HV) clusters (HVCs) in a Ti-23Nb-3Al (mol%) shape memory alloy were investigated by in situ optical microscopy with high-speed digital video camera. In addition to the kinematic compatibility condition, the nucleation mode and the interfacial energy between martensites were clearly shown to have critical roles. The VI cluster, which is formed by two HVs connected by a {111} type I twin, predominated in the early stage of the martensitic transformation, and had a lower energy barrier to nucleation and growth than did the VII cluster, which is formed by two HVs connected by a <211> type II twin. Eighty percent of the VI clusters were observed to form by paired nucleation or branching, in which the junction plane corresponds to the nucleation site of the relevant HV(s). In contrast, VII clusters formed as a result of collisions of HVs. Neither paired nucleation nor branching was observed for VII. VI nuclei rather than VII nuclei had a strong tendency to form, and this difference was not fully explained by the kinematic compatibility (KC) conditions. The junction planes formed by the collision of growing HVs should have larger deviation from the KC condition. The compatibility of the junction plane between HVs depends on the formation modes.

The effect of microstructure on stress-induced martensitic transformation under cyclic loading in the SMA Nickel-Titanium

A combined experimental and analytical study to determine the configurations of transforming martensite during ambient temperature cyclic deformation of superelastic Nickel-Titanium has been conducted. Full-field, sub-grain-size microscale strain measurements were made in situ during cycling using distortion-corrected Digital Image Correlation combined with Scanning Electron Microscopy (SEM-DIC). Using grain orientation maps from Electron Backscatter Diffraction analysis, possible configurations of martensite formed during cyclic deformation were identified by matching the calculated and measured strain fields. This analysis showed that the inclusion of Correspondence Variants (CVs) in addition to Habit Plane Variants (HPVs) of transformed martensite was necessary to provide a robust fit between calculated and measured strain fields. The approach also provided evidence that there was a more rapid accumulation of residual strain in CV regions and that a correlation existed between residual strain accumulation and the loss of actively transforming martensite in later cycles. It was also found that regions of CVs could coexist with untransformed austenite and Habit Plane Variants (HPVs) in individual grains throughout the microstructure, and that these regions of CVs formed before the end of the macroscopic stress plateau. The CV structure that forms during the initial superelastic deformation of Nickel-Titanium plays a critical role in shaping and stabilizing subsequent martensite recovery during cyclic loading.

Compatibility at Junction Planes between Habit Plane Variants with Internal Twin in Ti-Ni-Pd Shape Memory Alloy

Compatibility at Junction Planes between Habit Plane Variants with Internal Twin in Ti-Ni-Pd Shape Memory Alloy

In situ scanning electron microscopy study of the thermoelastic martensitic transformation in Ti–Ni shape memory alloy

The thermoelastic martensitic transformation from the B2 to B19′ structures in the Ti–Ni shape memory alloy was observed by in situ scanning electron microscopy in order to investigate the self-accommodation microstructure. Nucleation of the V-shaped habit plane variant cluster (2HPVC) triggers the formation of the hexangular HPVC (6HPVC) that is formed by six habit plane variants in the grain interior. The triangular morphology (3HPVC) is a derivative of 2HPVC. The autocatalytic transformation spreads from the 6HPVCs to the grain boundary and the reverse transformation proceeds like a rewind of the forward transformation. 2HPVC and 6HPVC are the most favorable morphologies for nucleation and growth, respectively, as explained by the analysis of the kinematic compatibility at junction planes.

In Situ Neutron Diffraction Studies of Large Monotonic Deformations of Superelastic Nitinol

Superelastic Nitinol micromechanics are studied well into plastic deformation regimes using neutron diffraction. Insights are made into the nature of initial transformation, bulk transformation, plastic deformation, and unloading. Schmid factor predictions based on habit plane variants are found to best describe the very first grains that transform, prior to the transformation plateaus. However, the bulk transformation behavior that gives rise to transformation plateaus violates single crystal Schmid factor analyses, indicating that in bulk polycrystals, it is the effect of grain neighborhoods, not the orientations of individual grains, that drives transformation behaviors. Beyond the plateaus, a sudden shift in micromechanical deformation mechanisms is observed at ~8.50 %/4.75 % tension/compression engineering strain. This mechanism results in reverse-phase transformation in both cases, indicating a strong relaxation in internal stresses of the samples. It is inferred that this mechanism is most likely initial bulk plastic flow, and postulated that it is the reason for a transition from fatigue life enhancement to detriment when pre-straining superelastic Nitinol. The data presented in this work provide critical datasets for development and verification of both phenomenological internal variable-driven and micromechanical theories of transformation-plasticity coupling in shape memory alloys.

Formation Process of Triangular Morphology of Self-Accommodation Martensite in Ti-Nb-Al Shape Memory Alloy

The formation process of a habit plane variant (HPV) cluster with triangular morphology (T-cluster) in Ti- Nb-Al shape memory alloy was investigated by in-situ optical microscopy. Upon cooling the specimen, martensitic transformation occurred and two types of V-shaped clusters and the T-clusters were observed. Two types of V-shaped cluster were the cluster connected by the {111} type I twin (VI) and the cluster connected by the type II twin (VII). The T-cluster is formed by the connection of three HPVs by {111} type I twin. The T-cluster is formed by the growth of the third HPV that is nucleated at the tip of a HPV in a VI-cluster and exhibits inward growth. It is suggested that the T-cluster is a derivative of the VI-cluster. This growth behaviour is discussed based on the incompatibility of the clusters.

Preferential Morphology of Self-accommodation Microstructure in Ti-Ni-Pd Shape Memory Alloy

The formation frequency of junction planes (JPs) and orientation relationships across the JPs in self-accommodation microstructure in Ti-25Ni-25Pd was investigated by TEM and SEM-EBSD. Each martensite plates followed the invariant plane condition and identified as habit plane variants (HPV). The self-accommodation microstructure consisted of four kinds of HPV and contained three kinds of JPs. The formation frequency of each JP was 14% for {011}B19 compound twin, 36% for <111>B19type I twin and 50% for <211>B19type II twin. The formation frequency was explained by the magnitude of the incompatibility at the JPs.