Bain Strain Research Articles

Anisotropic cleavage fracture caused by transformation-induced internal stress in an as-quenched martensite

The effect of microscopic internal stresses (Type-II) generated via martensitic transformation from austenite (A) to martensite (M) on {001} M cleavage fracture was investigated in an as-quenched 0.1C–5.0Mn steel (mass%). Crystallographic orientation analysis using the electron backscatter diffraction technique revealed that cryogenic {001} M cleavage fracture was promoted predominantly in mode I fracture by Charpy impact testing, and that the Bain group, where martensite variants belong to the same Bain variants, acted as an effective unit to prevent fracture. It was also discovered that the cleavage crack preferentially propagates on (001) M rather than on (100) M in the Bain group, where (001) M was nearly parallel to (001) A in the Bain lattice correspondence ([−110] A // [100] M , [110] A // [010] M , (001) A // (001) M ). In addition, by using a combination of a micro-scale focused ion beam and high-precision digital image correlation techniques, it was found that microscopic internal stresses were anisotropically developed in each Bain group. The principal axes of the internal stresses corresponded to the <001> M coordinate axes in the Bain lattice correspondence, and the principal stress parallel to [001] M is much higher than that of the other two. After the measurement of the internal stresses, it was proved that the cleavage fracture behavior obeyed the effective normal stress in the normal direction of {001} M consisting of the resolved bending stress in the impact test and the anisotropic internal stress generated via martensitic transformation. This suggests that the transformation-induced internal stress originating from the Bain strain leads to the anisotropy of the cleavage fracture in lath martensite. • The effect of microscopic Type-II internal stress on the macroscopic cleavage fracture was investigated in lath martensite. • FIB-DIC technique revealed that martensitic transformation induces the anisotropic elastic strain in each Bain group while maintaining <001> as the principal axes. • EBSD analysis proved that mode-I cleavage crack preferentially propagates on (001) rather than on (100) in a Bain group regardless of carbon contents. • Transformation-induced internal stress originating from Bain strain leads to the anisotropy of the cleavage fracture in lath martensite.

Orientation relationships between precipitates and matrix and their crystallographic transformation in a Cu–Cr–Zr alloy

The orientation relationships between Cr precipitates and matrix in a Cu–Cr–Zr alloy with various aged states were investigated by transmission electron microscopy and High-resolution transmission electron microscopy, and the crystallographic transformations of orientation relationships were also analyzed by stereographic projection and discussed. Four kinds of orientation relationships were detected in the precipitation process of Cu–Cr–Zr alloy, and coexistence of Cr precipitates with Nishiyama-Wassermann relationship and Pitsch relationship was found in the peak-aged Cu–Cr–Zr alloy. The occurrence for cube-on-cube and Pitsch relationship in Cu–Cr–Zr alloy was thought to be caused by the retardation of additions and heterogeneous nucleation of Cr precipitates on dislocations respectively. Transformations of orientation relationships were observed during precipitation and the crystallographic rotation pathways of the transformations were represented by stereographic projection. The interrelationships of various orientation relationships were established by Bain strain and crystal rotation in the Cu–Cr–Zr alloy of this study.

Computational Simulation by Phase Field: Martensite Transformation Kinetics and Variant Selection under External Fields

Tailoring martensite transformation is critical for improving the mechanical properties of advanced steels. To provide preliminary guidance for the control of martensite transformation behaviour using external fields by computational simulation method, the phase-field method was used to calculate the morphology evolution, kinetics, and variant selection of the martensite transformation under different loading modes and magnetic field intensities. The incubation, transformation, and stable stages of the three variants based on the Bain strain group were investigated using different kinetic curves. These results clearly indicate that both uniaxial tension and compression can greatly promote the formation of martensite during the transformation stage and cause an obvious preferred variant selection. In contrast, the different variants have relatively balanced forms under shearing conditions. In addition, the magnetic field is a gentler way to form a state with balanced variants than other techniques such as shearing. Additionally, all these simulation results are consistent with classical martensitic transformation theory and thermodynamic mechanism, which proves the rationality of this research. The aim of the present study was to provide qualitative guidance for the selection of external fields for microstructural improvement in advanced steels.

Dynamic precipitation and the resultant magnetostriction enhancement in [001]-oriented Fe-Ga alloys

Precipitation of dispersive nanoparticles has recently been found to yield superfunctional properties, such as the large and sensitive magnetostriction in body-centered-cubic (bcc) Fe-Ga alloys with face-centered-tetragonal (fct) nanoprecipitates, and applying this strategy to grain-aligned alloys may allow one to obtain better performance. However, the internal stress generated during directional solidification may alter the precipitation behaviors by accelerating atomic clustering, therefore, a careful analysis of the morphology of precipitates and solute partitioning is needed. Herein, we investigated the dynamic precipitation behavior in a directionally solidified Fe73Ga27 alloy with [001] orientation. Through comparisons with random polycrystalline sample subjected to the same aging treatment, we find that the [001]-oriented sample produces sparser fct nanoprecipitates and extra interfacial omega nanoprecipitates. The internal stress accelerates Ga partitioning between the fct nanoprecipitates and the matrix, hence reducing their nucleation sites. The internal stress also alters the mutual elastic interactions between matrix and precipitates, where the Bain strains of fct nanoprecipitates are mostly accommodated by forming Ga-enriched omega nanoprecipitates and {112}<111> stacking faults at the phase front, unlike that for random polycrystalline sample, where the Bain strains are accommodated by local tetragonal distortion of the matrix. As a result, the magnetostriction enhancement ratio is 40% for the grain-aligned sample, weaker than ~165 % for the random polycrystalline sample. Our results not only shed lights on the precipitation difference between stress-containing and stress-free aging conditions but also help to guide the microstructure design of superfunctional alloys in which the type, number density and size of nanoprecipitates should be carefully controlled.

Predicting the available work from deformation-induced α′′ martensite formation in metastable β Ti alloys

Deformation-induced α′′ martensite formation is essential to the mechanical properties of a variety of metastable β Ti alloys by extending elasticity or contributing to work-hardening during plastic deformation. Nevertheless, to date, a comprehensive analysis of the effect of β texture and applied stress state on the martensitic transformation to α′′ is still lacking. The present study therefore provides a detailed analysis of the work which is made available from the shape strain of the martensitic transformation under a variety of in-plane stress states and as a function of β crystal orientation. The available work was found to strongly depend on the applied stress state and the parent grain orientation. The shape strain of the martensitic transformation was obtained from applying the phenomenological theory of martensite crystallography. In cases where this theory was not applicable, an approximation of the shape strain by the Bain strain was found to provide a good approximation of the available work. Analysis of three different metastable β Ti alloys showed no strong effect of the alloy composition on the available work. Martensite formation from typical cold- and warm-rolling β texture components under different stress states is discussed. Cases are highlighted to show how the cold- and warm-rolling β textures can be tailored to hinder martensite formation upon subsequent industrial forming operations.

Internal residual stress originated from Bain strain and its effect on hardness in Fe–Ni martensite

To further understand the internal residual stress that is microscopically generated via martensitic transformation in steels, the origin of internal strain attributed to Bain correspondence between face-centered cubic (fcc) and body-centered cubic (bcc) was evaluated from macro- and micro-viewpoints and its effect on hardness was investigated in an interstitial free Fe-16%Ni martensite. Neutron diffractometry and electron backscatter diffraction analysis showed that body-centered cubic (bcc) crystal structure of as-quenched martensite contained elastic distortions leading to small tetragonality, even in martensitic steels without solute carbon, and that the extended [001]bcc of martensite tended to be parallel to <001>fcc of prior fcc austenite. In addition, the combination of micro-scale focused ion beam (FIB) and high-precision digital image correlation techniques revealed that a micropillar fabricated by FIB processing within a martensite block was anisotropically deformed by the release of the residual strain distributed in as-quenched martensite in correspondence with the tetragonal distortions of the bcc crystal structure. These results prove that a small part of the Bain strain remained as an internal elastic residual strain and was microscopically distributed among Bain groups in lath martensite after martensitic transformation. Furthermore, the residual strain generated a hydrostatic internal stress, and therefore, the nanohardness decreased considerably by the micropillar fabrication accompanied by the release of the internal stress. This means that the internal residual stress in martensite among Bain groups influences the mechanical properties of martensitic steel.

Internal Residual Stress Originated from Bain Strain and its Effect on Hardness in Fe-Ni Martensite

To further understand the internal residual stress that is microscopically generated via martensitic transformation in steels, the origin of internal strain attributed to Bain correspondence between face-centered cubic (fcc) and body-centered cubic (bcc) was evaluated from macro- and micro-viewpoints and its effect on hardness was investigated in an interstitial free Fe-16%Ni martensite. Neutron diffractometry and electron backscatter diffraction analysis showed that the as-quenched martensite had a body-centered tetragonal (bct) crystal structure with small tetragonality, even in martensitic steels without solute carbon, and that the [001]bct of bct martensite tended to be parallel to fcc of prior fcc austenite. In addition, the combination of micro-scale focused ion beam (FIB) and high-precision digital image correlation techniques revealed that a micropillar fabricated by FIB processing within a martensite block was anisotropically deformed by the release of the residual strain distributed in as-quenched martensite in correspondence with the orientation of the bct crystal structure. These results prove that a small part of the Bain strain remained as an internal elastic residual strain and was microscopically distributed among Bain groups in lath martensite after martensitic transformation. Furthermore, the residual strain generated a hydrostatic internal stress, and therefore, the nanohardness decreased considerably by the micropillar fabrication accompanied by the release of the internal stress. This means that the internal residual stress in martensite among Bain groups influences the mechanical properties of martensitic steel.

Prediction of the Bain spin memory materials (BSMM) revealed by Kaneyoshi theory

ABSTRACT In this work, we investigate the spin transformation from ferromagnetic austenite BCT lattice to antiferromagnetic martensite BCC lattice (ji = +J → ji = -J or ↑↑→↑↓) in Bain transformation (or Bain strain) by using effective field theory which is developed by Kaneyoshi. We find that the spin orientation changes the magnetic properties in the Bain BCT→BCC transformation. Therefore, we predict that material can memory their spin orientations in the austenite-martensite transformation similar to the shape memory effect in the shape memory materials. Since the austenite-martensite transformation mechanism is first modelled by Bain, we call this spin memory effect as 'Bain spin memory materials (BSMM)’.

Small Thermal Magnetization Loop Revealed by Bain Strain

In this work, we investigate the effects of the FCC-BCC Bain transformation on the magnetic properties. We focus on the Bain corresponding that of BCC martensite phase which emerges via a contraction of the z-axis by about 20% and an expansion of the x- and y-axis by about 12% in the FCC austenite phase. To obtain Bain strain, we consider the BCT lattice (from the FCC with a = 2a) and we apply the Bain strain to BCT lattice as aBCT = bBCT = a$$ \sqrt{2} $$ and cBCT = 2a. Then, with the contraction of the z-axis by 20% and an expansion of the x- and y-axis by 13.137% of BCT lattice, we obtain a new BCC martensite lattice with aBCC = 1.6a. We find that the differences in the magnetization of austenite BCT lattice and martensite BCC lattice are very small. Therefore, we obtain very small thermal magnetization loop area versus temperature and we suggest that the prediction of Edgar Collins Bain on FCC-BCC transformations (or Bain strain) is remarkable and very successful.

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.

Phase-field simulations of thermomechanical behavior of MnNi shape memory alloys using finite element method

The thermomechanical behavior and associated microstructure evolution of MnNi shape memory alloys (SMAs) are studied via two-dimensional phase-field simulations. Simulations with complex geometries and boundary conditions are realized by using finite element method. Shear-related surface relief, determined by the combination of Bain strain and crystal rotation, was observed. In the process of pseudoelastic bending, large bending degree was realized by formation of triangular martensitic domains, and the elastic strain energy did not apparently increase. The coupling strength of a SMA pipe coupling was greatly influenced by the proceeding of the reverse transformation upon heating. It was found that large shape change of SMAs was realized by the transition between different crystal structures, this transition was driven by the free energy difference between the structures, and the stress plateau during a pseudoelastic cycle was related to the thermodynamic equilibrium state of austenite–martensite interface.

Tailoring the Bain strain of martensitic transformations in Ti[sbnd]Nb alloys by controlling the Nb content

The lattice (Bain) strain and corresponding volume change of a martensitic phase transformation are key parameters that determine the formation of a self-accommodated martensitic microstructure and related functional properties. Based on experimentally determined lattice parameters of the cubic austenite β and of the hexagonal and orthorhombic martensites α′ and α″, the lattice strain and the volume change related to the β → α′/α″ martensitic transformations in TiNb alloys are analyzed in dependence of composition. The lattice strains of the transformation β → α″ increase with decreasing Nb content but those of β → α′ are not affected by the amount of Nb. Depending on the composition, both a volume dilatation and contraction is encountered. It is proposed that the volume change plays a decisive role in determining the lattice structure of the martensitic phase that evolves when the transformation is thermally induced.

Experimental and theoretical evidence of displacive martensite in an intermetallic Mo-containing γ-TiAl based alloy

In this study the martensitic transformation behavior of a Mo-bearing γ-TiAl based alloy was investigated. Therefore, a homogenization treatment within the single β-phase field region followed by water quenching has been carried out, whereby the majority of the disordered β-phase transforms into hexagonal α2′-martensite during cooling. Since the β to α transformation in the intermetallic β-solidifying Ti–44Al–3Mo–0.1B alloy (at%) occurs at very high temperatures causing enhanced diffusional processes, a very locally diffusion-controlled transformation together with a displacive, hence purely martensitic transformation take place. This work investigates the displacive martensite formation in the high-temperature regime using state-of-the-art experimental methods as well as modelling concepts from the phenomenological theory of martensite crystallography. The high temperature at which the transformation takes place suggests the preference of plastic slip over twinning. This fact has also been verified by transmission electron microscopy, as no twinning has been observed after generation of single martensite variants forming an invariant interface plane with the initial β-lattice. Such invariant interfaces are formally possible according to the phenomenological theory of martensite crystallography, if the Bain strains of the martensite variants are superimposed by additional simple shear.

Optimality of general lattice transformations with applications to the Bain strain in steel

This article provides a rigorous proof of a conjecture by E. C. Bain in 1924 on the optimality of the so-called Bain strain based on a criterion of least atomic movement. A general framework that explores several such optimality criteria is introduced and employed to show the existence of optimal transformations between any two Bravais lattices. A precise algorithm and a graphical user interface to determine this optimal transformation is provided. Apart from the Bain conjecture concerning the transformation from face-centred cubic to body-centred cubic, applications include the face-centred cubic to body-centred tetragonal transition as well as the transformation between two triclinic phases of terephthalic acid.

Orientation relationship between austenite and non-modulated martensite in Ni–Mn–Ga single crystals

In-situ electron back scatter diffraction experiments were used to accurately determine the orientation relationships between austenite and martensite in non-modulated Ni–Mn–Ga single crystals. Using a heating stage device direct orientation measurements of austenite and martensite in single-, two- and self-accommodated state were performed. The initial single crystals show a typical self-accommodated microstructure composed of a mixture of variants allowing the distribution of martensitic variants with minimal macroscopic shear. The martensitic variants are observed on different length scales: starting from a few nanometers up to a few micrometers. The corresponding experimental pole figures reveal a strongly asymmetric distribution of martensitic variants with respect to the parent cubic orientation. Combining the microstructural and crystallographic orientation information it is obvious that a hierarchy in twin formation exists. At first the main martensitic variants arise by Bain strain and rigid body rotation. Subsequently, the remaining variants follow a specific crystallographic orientation relationship.Using training procedure a single- or two-variant state in martensite can be obtained. In-situ heating experiments reveal that such configurations show a different orientation relationship between the martensitic variants and austenite compared to that in a self-accommodated state. It strongly suggests that the orientation relationship between these two phases is not strictly fixed, as given by the main models describing this relation, but also depends on the number and width of martensitic variants. The results are discussed with respect to lattice parameters, number of variants and existing models in the literature.

A kinematically-enhanced relaxation scheme for the modeling of displacive phase transformations

In this contribution, a micro-mechanically motivated, energy relaxation-based constitutive model for phase transformation, martensite reorientation and twin formation in shape memory alloys is proposed. The formulation builds on an idealized parametrization of the austenite-twinned martensite microstructure through first- and second-order laminates. To estimate the effective rank-one convex energy density of the phase mixture, the concept of laminate-based energy relaxation is applied. In this context, the evolution of the energetic and dissipative internal state variables, that describe characteristic microstructural features, is computed via constrained incremental energy minimization. This work also suggests a first step towards the continuous modeling of twin formation within the framework of energy relaxation and can be viewed as a generalization of earlier models suggested by Bartel and Hackl (2009) and Bartel et al. (2011). More specifically, in the current model the orientation of martensitic variants in space is not pre-assigned. Variants are rather left free to arrange themselves relative to the martensite-martensite interface in an energy-minimizing fashion, where, however, it is assumed that they form crystallographically-twinned pairs. The formulation also eliminates the need to introduce specific expressions for the Bain strains in each of the martensitic variants, by relating them to a master variant and utilizing the information about their absolute orientation. The predictive capabilities of the proposed modeling framework are demonstrated in several representative numerical examples. In the first part of the results section, the focus is placed on purely energetic analysis, and the particular influence of the different microstructural degrees of freedom on the relaxed energy densities and the corresponding stress-strain responses is investigated in detail. In the second part, macro-homogeneous uniaxial strain and shear loading cases are analyzed for the dissipative case. It is shown, that the proposed model, which, compared to purely phenomenological macro-scale models, has the advantage of strong micro-mechanical motivation, is capable of qualitatively predicting central features of single crystal shape memory alloy behavior, such as the phase diagram in stress-temperature space, and pseudo-elastic and pseudo-plastic responses, while simultaneously providing valuable insight into the underlying micro-scale mechanisms.

Phase-field modeling of displacive phase transformations in elastically anisotropic and inhomogeneous polycrystals

We integrate the inhomogeneous elasticity model and the phase-field equations for displacive phase transformations in polycrystalline materials. The relaxation of the misfit strain between parent and transformed product phases or among different structural variants of transformed product phases near grain boundaries is taken into account. It is applied to the fcc to bcc martensitic transformation described by a Bain strain in a polycrystalline Fe-31at.%Ni metallic alloy. The focus is on the effect of grain boundaries on the displacive transformation behaviors. We first study nucleation of the bcc product phase at a grain boundary of a bicrystal. The predicted microstructures through nucleation near grain boundaries are compared to existing experimental observations in literature. The effects of grain boundary characteristics such as the degree and range of the misfit strain relaxation at the grain boundary and grain boundary curvature on the phase behaviors near a grain boundary are then examined for both a flat or a curved grain boundary. The model is also applied to polycrystals containing multiple grains. The effects of the misfit strain relaxation at grain boundaries, elastic anisotropy, and applied stress on the kinetics and the microstructures of displacive transformations are discussed.

Thermodynamic and relaxation-based modeling of the interaction between martensitic phase transformations and plasticity

This paper focuses on the issue plasticity within the framework of a micromechanical model for single-crystal shape-memory alloys. As a first step towards a complete micromechanical formulation of such models, we work with classical J 2-von Mises-type plasticity for simplicity. The modeling of martensitic phase transitions is based on the concept of energy relaxation ( quasiconvexification) in connection with evolution equations derived from inelastic potentials. Crystallographic considerations lead to the derivation of Bain strains characterizing the transformation kinematics. The model is derived for arbitrary numbers of martensite variants and thus can be applied to any shape-memory material such as CuAlNi or NiTi. The phase transition model captures effects like tension/compression asymmetry and transformation induced anisotropy. Additionally, attention is focused on the interaction between phase transformations and plasticity in terms of the inheritance of plastic strain. The effect of such interaction is demonstrated by elementary numerical studies.

A microcompression study of shape-memory deformation in U–13 at.% Nb

Microcompression specimens, 10–15 µm in diameter by 20–30 µm in height, were produced from individual parent grains in a polycrystalline U–13 at.%Nb shape-memory alloy using the focused ion beam technique. The specimens were tested in a nanoindentation instrument with a flat diamond tip to investigate stress–strain behavior as a function of crystallographic orientation. The results are in qualitative agreement with a single-crystal accommodation strain (Bain strain) model of the shape-memory effect for this alloy.

Bain strain upon thermoelastic martensitic transformation in intermetallic compounds based on titanium nickelide

Analysis of our original results and the data in the literature on the behavior of structural parameters of the austenitic and martensitic phases near phase transitions in alloys of the TiNi-TiMe (Me = Au, Pd, Pt, Rh, Cu, Co, Fe, Rh) system has been performed. It is established that the Bain strain and dilatation changes depend on the martensitic transformation “channel.”