Stress-induced martensitic phase transformations in polycrystalline CuZnAl shape memory alloys under different stress states

The effect of different uniaxial and triaxial stress states on the stress-induced martensitic transformation in CuZnAl was investigated. Under uniaxial loading, it was found that the compressive stress level required to macroscopically trigger the transformation was 34 pct larger than the required tensile stress. The triaxial tests produced effective stress-strain curves with critical transformation stress levels in between the tensile and compressive results. It was found that pure hydrostatic pressure was unable to experimentally trigger a stress-induced martensitic transformation due to the large pressures required. Traditional continuum-based transformation theories, with transformation criteria and Clausius-Clapeyron equations modified to depend on the volume change during transformation, could not properly predict stress-state effects in CuZnAl. Considering a combination of hydrostatic (volume change) effects and crystallographic effects (number of transforming variants), a micromechanical model is used to estimate the dependence of the critical macroscopic transformation stress on the stress state.     

Effect of stress state on the stress-induced martensitic transformation in polycrystalline Ni-Ti alloy

The effect of stress state on the character and extent of the stress-induced martensitic transformation in polycrystalline Ni-Ti shape memory alloy has been investigated. Utilizing unique experimental equipment, uniaxial and triaxial stress states have been imposed on Ni-Ti specimens and the pseudoelastic transformation strains have been monitored. Comparisons between tests of differing stress states have been performed using effective stress and effective strain quantities; a strain offset method has been utilized to determine the effective stress required for transformation under a given stress state. Results of the tests under different stress states indicate that (1) despite the negative volumetric strain associated with the austenite-to-martensite transformation in Ni-Ti, effective stress for the onset of transformation decreases with increasing hydrostatic stress; (2) effective stressvs effective strain behavior differs greatly under different applied stress states; and (3) austenite in Ni-Ti is fully stable under large values of compressive hydrostatic stress.     

Study of Thermoelastic Martensitic Transformations Using a Phase-Field Model

The mechanisms of face-centered cubic (fcc)\( \Leftrightarrow \)face-centered tetragonal (fct) thermoelastic martensitic transformations (MTs) in Mn-rich Mn-Cu alloys were studied using a phase-field model. In this article, a phase-field model describing the martensitic transformation was developed with the capability of treating continuously varying temperatures under two boundary conditions. The analysis of various energies during the microstructural evolution reveals that the elastic strain energy is a resistant force in the forward MT, but it becomes a driving force in the reverse MT. The feature of self-accommodation in forward MT is revealed by comparing the elastic strain energy of two martensitic variants with three martensitic variants. The simulated microstructural evolution demonstrates that the plate of polytwinned martensite shrinks with increasing temperature, and during the sequent cooling, the plate of polytwinned martensite grows and almost retraces to its original state. This reversibility of MTs is in good agreement with the reported experimental observation of thermoelastic MTs.     

Stress-state effects on the stress-induced martensitic transformation of carburized 4320 steels

The effect of different stress states on the stress-induced martensitic transformation of retained austenite was investigated in carburized 4320 steels with an initial retained austenite content of 15 pct. Experiments were conducted utilizing a specialized pressure rig and comparison between stress-strain behaviors of specimens with different austenitization and tempering histories was performed under these stress states. Experimental results indicated considerable asymmetry between tension and compression, with triaxial stress states resulting in the highest strength levels for the untempered material. Fine carbide precipitates due to low-temperature tempering increased the strength and ductility of the specimens and also changed the austenite-to-martensite transformation behavior. Numerical simulations of stress-strain behaviors under different stress states were obtained, with an existing micromechanical self-consistent framework utilizing the crystallographic theory of austenite/martensite transformation and the minimum complementary free-energy principle. The model was modified for carburized steels upon microstructural investigation and predicted the same trends in effective stress-effective strain behavior as observed experimentally.     

Effect of internal stress on autocatalytic nucleation of martensitic transformation

On the basis of classical nucleation theory of martensitic transformation (MT), the effect of internal stress on autocatalytic nucleation of MT is quantitatively described. The complex stress field pictures outside a formed martensitic plate are first calculated through Eshelby’s theory, and then the interaction energies between the martensitic plate and embryos with 24 possible variants can be further obtained. Based on the calculation of interaction energy, the effect of internal stress on autocatalytic nucleation of MT and morphological characteristics of martensite are explained. In this investigation, two kinds of alloys—non-thermoelastic materials (e.g., Fe-30Ni) and thermoelastic materials (e.g., Cu-46.6Zn)—are studied, and their difference in autocatalytic nucleation and morphological characteristics of martensite are indicated.     

Three-dimensional computational-cell modeling of the micromechanics of the martensitic transformation in transformation-induced-plasticity-assisted multiphase steels

A three-dimensional finite-element microstructural cell model involving an inclusion of retained austenite embedded within a ferrite grain, which is surrounded by a homogeneous matrix representing the behavior of a transformation-induced-plasticity (TRIP)-assisted multiphase steel, was developed in order to address the micromechanics of the martensitic transformation in small isolated austenite grains. The transformation of a single martensite plate is simulated after various amounts of prior plastic deformation under different in-plane loading conditions. The values of the mechanical driving force and of the elastic and plastic accommodation energies associated with the transformation are calculated as a function of the externally applied loading conditions. The mechanical driving force and the total accommodation energy are of the same order of magnitude. The mechanical driving force depends upon the stress state and is the highest for plane-strain conditions. The total accommodation energy is almost independent of the stress state. It is affected by the amount of plastic straining prior to transformation and is very much dependent on the level of the shear component of the transformation strain. The results of this study provide guidelines for the development of realistic stress-state-dependent transformation evolution laws for TRIP-assisted multiphase steels.     

Analysis of the Effect of Nonhydrostatic Compression Conditions on Direct Phase Transformations in Carbon

We have analyzed the effect of deviations from hydrostatic compression conditions on the driving force for transformations of graphite to dense phases. We consider transformations of the hexagonal (2H) and rhombohedral (3R) modifications of graphite to lonsdaleite and diamond by martensitic mechanisms, and also a direct diffusional transformation. Comparative estimates of the driving forces were made for hydrostatic and uniaxial compression schemes, and also for shear loading. We show that a loading scheme combining hydrostatic compression with uniaxial compression is more favorable for the martensitic transformation of 2H-graphite to lonsdaleite, while shear loading and uniaxial loading are more favorable for the transformations of 3R-graphite; and lonsdaleite is formed in the first case, while diamond is formed in the second case.     

Modeling the effects of stress state and crystal orientation on the stress-induced transformation of NiTi single crystals

A model that combines the phenomenological theory of martensite with a generalized Schmid’s law has been used to predict the principal stress combinations required to induce the martensitic transformation in unconstrained NiTi shape memory alloy (SMA) single crystals. The transformation surfaces prescribed by the model are anisotropic and asymmetric, reflecting the unidirectional character of shear on individual martensite habit planes. Model predictions of the transformation strain as a function of stress axis orientation for a uniaxial applied stress further demonstrate the anisotropy of the stress-induced transformation in NiTi single crystals. Model results for the uniaxial stress case compare favorably with previously published experimental observations for aged NiTi single crystals.     

Martensitic Phase Transformation from Non-isothermally Deformed Austenite in High Strength Steel 22SiMn2TiB

Non-isothermal compressive deformation was performed on high strength steel 22SiMn2TiB for the study of martensitic phase transformation from deformed austenite. The transformation start temperature M _s decreased with the increase of deformation from 0 to 50 pct, and the variation of deformation rate (0.1 and 10 s^?1) and the appearance of deformation-induced ferrite and bainite showed no influence on the change of M _s temperature. The deformation at both the rates increased the volume fraction of retained austenite; however, the carbon content of retained austenite decreased at 10 s^?1 and remained basically unchanged at 0.1 s^?1. The yield strength of austenite at M _s temperature and the stored energy in deformed austenite were experimentally obtained, with which the relationships between the change of M _s temperature and the thermodynamic driving force for martensitic phase transformation from deformed austenite were established by the use of the Fisher-ADP–Hsu model. And finally, the transformation kinetics was analyzed by the Magee–Koistinen–Marhurger equation.     

Micromechanical Modelling of TRIP Steels

The combined thermodynamic‐micromechanical model of Fischer [1] is applied to a low‐alloyed TRIP steel with a volume fraction of 16% of retained austenite. The model is implemented in a finite element code. The mesh consists of 9 by 9 by 9 cubical elements, each representing a single grain with a random crystallographic orientation. The retained austenite grains are randomly dispersed through the entire mesh. The extent of the martensitic transformation in all austenite grains is calculated. A large spread in transformation rate is observed. The most favourably oriented grains reach a full martensitic structure, while the martensite volume fraction of less favourably oriented grains is less than 50%. When the chemical driving force is more negative, the onset of the transformation is delayed and the increase of the martensite volume fraction is slower. The calculated results are compared with experimentally obtained values. Although in general a reasonable agreement is found, Fischer's approach leads to some discrepancies with experimental observations.     

Effects of Strain Rate and Plastic Work on Martensitic Transformation Kinetics of Austenitic Stainless Steel 304

The martensitic transformation behavior and mechanical properties of austenitic stainless steel 304 were studied by both experiments and numerical simulation.Room temperature tensile tests were carried out at various strain rates to investigate the effect on volume fraction of martensite,temperature increase and flow stress.The results show that with increasing strain rate,the local temperature increases,which suppresses the transformation of martensite.To take into account the dependence on strain level,strain rate sensitivity and thermal effects,a kinetic model of martensitic transformation was proposed and constitutive modeling on stress-strain response was conducted.The validity of the proposed model has been proved by comparisons between simulation results and experimental ones.     

A relaxed-constraint model for the tensile behavior of polycrystal shape-memory alloy wires

This article provides a micromechanics-based theory to elucidate that the thermomechanical behavior of a polycrystal shape-memory alloy (SMA) wire is different from that of a bulk material. The study is based on the observation that a polycrystal wire cannot retain any significant amount of internal stress in the transverse direction; thus, the internal stress of its constituent grains is predominantly tensile and the transverse components can be relaxed to zero. The heterogeneous tensile internal stress is then calculated from a self-consistent relation. By this internal stress and an irreversible thermodynamic principle, the decrease of Gibbs free energy and the thermodynamic driving force for martensitic transformation in the grain is established. This leads to a kinetic equation for the evolution of the martensite phase in each constituent grain and then, by an orientational average process, the evolution of the overall phase-transformation strain of the polycrystal SMA wire. Applications of the theory to a Ti-Ni wire under a thermal cycle and under a stress cycle have led to results that are consistent with experimental data. As compared to the bulk behavior, the range of transformation temperatures for the wire is substantially narrower, and the tangent modulus of its stress-strain curves is much lower. These characteristics point to the superiority of an SMA wire over the bulk in smart-material applications and are both attributable to its reduced geometrical constraint in the transverse direction.     

Experimental study on the thermoelastic martensitic transformation in shape memory alloy polycrystal induced by combined external forces

Combined tension and torsion experiments with thin wall specimens of Cu-Al-Zn-Mn polycrystalline shape memory alloy (SMA) were performed at temperatureT =A _f + 25 K. The general stress-strain behaviors due to the thermoelastic martensitic transformation, induced by a combination of external forces of axial load and torque, were studied. It is shown that the progress of martensitic transformation (MT) at general stress conditions can be well considered as triggered and controlled by the supplied mechanical work (a kind of equivalent stress) in the first approximation. Pseudoelastic strains in proportional as well as nonproportional combined tension-torsion loadings were found fully reversible, provided that uniaxial strains were reversible. The axial strain can be controlled by the change of torque andvice versa due to the coupling among tension and torsion under stress, not only in forward transformation, but also in reverse transformation on unloading. The pseudoelastic strains of SMA polycrystal are path dependent but well reproducible along the same stress path. The evolution of macroscopic strain response of SMA polycrystal, subjected to the nonproportional pseudoelastic loading cycles with imposed stress path, was systematically investigated. The results bring qualitatively new information about the progress of the MT in SMA polycrystal, subjected to the general variations of external stress. PETR SITTNER, Research Associate, formerly with the Faculty of Engineering, Mie University     

Kinetics of strain-induced martensitic nucleation

Intersections of shear bands in metastable austenites have been shown to be effective sites for strain-induced martensitic nucleation. The shear bands may be in the form of ε’ (hcp) martensite, mechanical twins, or dense bundles of stacking faults. Assuming that shear-band intersection is the dominant mechanism of strain-induced nucleation, an expression for the volume fraction of martensite vs plastic strain is derived by considering the course of shear-band formation, the probability of shear-band intersections, and the probability of an intersection generating a martensitic embryo. The resulting transformation curve has a sigmoidal shape and, in general, approaches saturation below 100 pct. The saturation value and rate of approach to saturation are determined by two temperature-dependent parameters related to the fee-bee chemical driving force and austenite stacking-fault energy. Fitting the expression to available data on 304 stainless steels gives good agreement for the shape of individual transformation curves as well as the temperature dependence of the derived parameters. It is concluded that the temperature dependence of the transformation kinetics (an important problem in the development of TRIP steels) may be minimized by decreasing the fee, bec, and hep entropy differences through proper compositional control.     

Kinetics of strain-induced martensitic nucleation

Intersections of shear bands in metastable austenites have been shown to be effective sites for strain-induced martensitic nucleation. The shear bands may be in the form of ε’ (hcp) martensite, mechanical twins, or dense bundles of stacking faults. Assuming that shear-band intersection is the dominant mechanism of strain-induced nucleation, an expression for the volume fraction of martensite vs plastic strain is derived by considering the course of shear-band formation, the probability of shear-band intersections, and the probability of an intersection generating a martensitic embryo. The resulting transformation curve has a sigmoidal shape and, in general, approaches saturation below 100 pct. The saturation value and rate of approach to saturation are determined by two temperature-dependent parameters related to the fee-bee chemical driving force and austenite stacking-fault energy. Fitting the expression to available data on 304 stainless steels gives good agreement for the shape of individual transformation curves as well as the temperature dependence of the derived parameters. It is concluded that the temperature dependence of the transformation kinetics (an important problem in the development of TRIP steels) may be minimized by decreasing the fee, bec, and hep entropy differences through proper compositional control.     

Martensitic Transformation during Simultaneous High Temperature Forming and Cooling Experiments

The main target of hot stamping is to combine accurate forming, low forming forces and high material strength in complex steel components. In the present study, the hot stamping process is simulated by means of simultaneous forming and quenching experiments. This is performed by uniaxial compression tests at high temperatures using a dilatometer. The effects of process parameters like strain, strain rate, initial deformation temperature, austenization time and applied forces on the martensitic transformation of the boron steel 27MnCrB5 are investigated. It is concluded that with increasing strain rate and initial deformation temperature, martensite content, hardness and martensite start temperature (Ms) are increased. On the contrary, when applying larger deformations, the above mentioned properties are decreased. It is also concluded that, regardless of the process parameters, higher applied forces retard the successful martensitic transformation during hot stamping.     

Niti and NiTi-TiC composites: Part II. compressive mechanical properties

The deformation behavior under uniaxial compression of NiTi containing 0, 10, and 20 vol pct TiC participates is investigated both below and above the matrix martensitic transformation temperature: (1) at room temperature, where the martensitic matrix deforms plastically by slip and/or twinning; and (2) at elevated temperature, where plastic deformation of the austenitic matrix takes place by slip and/or formation of stress-induced martensite. The effect of TiC particles on the stress-strain curves of the composites depends upon which of these deformation mechanisms is dominant. First, in the low-strain elastic region, the mismatch between the stiff, elastic particles and the elastic-plastic matrix is relaxed in the composites: (1) by twinning of the martensitic matrix, resulting in a macroscopic twinning yield stress and apparent elastic modulus lower than those predicted by the Eshelby elastic load-transfer theory; and (2) by dislocation slip of the austenitic matrix, thus increasing the transformation yield stress, as compared to a simple load-transfer prediction, because the austenite phase is stabilized by dislocations. Second, in the moderate-strain plastic region where nonslip deformation mechanisms are dominant, mismatch dislocations stabilize the matrix for all samples, thus (1) reducing the extent of twinning in the martensitic samples or (2) reducing the formation of stressinduced martensite in the austenitic samples. This leads to a strengthening of the composites, similar to the strain-hardening effect observed in metal matrix composites deforming solely by slip. Third, in the high-strain region controlled by dislocation slip, weakening of the NiTi composites results, because the matrix contains (1) untwinned martensite or (2) retained austenite, which exhibit lower slip yield stress than twinned or stress-induced martensite, respectively. K.L. FUKAMI-USHIRO, formerly Graduate Student, Department of Materials Science and Engineering, Massachusetts Institute of Technology D. MARI, formerly Postdoctoral Fellow, Department of Materials Science and Engineering, Massachusetts Institute of Technology     

Martensite Transformation in Ni-Mn-Ga Ferromagnetic Shape-Memory Alloys

The crystal structure of Ni-Mn-Ga ferromagnetic shape-memory alloys is extremely sensitive to composition. Several martensitic structures including tetragonal (five-layered), orthorhombic (seven-layered), and nonmodulated tetragonal have been observed. Temperature-dependent X-ray diffraction measurements and calorimetry have revealed markedly different transformation behavior in the tetragonal and orthorhombic materials. The orthorhombic material shows a much larger difference between the martensite start and finish temperatures as compared to tetragonal martensite. The difference in transformation character can be explained from a thermodynamic standpoint by including the difference in the strain energy contribution for the two different martensite phases. This article is based on a presentation made in the symposium entitled “Phase Transformations in Magnetic Materials," which occurred during the TMS Annual Meeting, March 12–16, 2006, in San Antonio, Texas, under the auspices of the Joint TMS-MPMD and ASMI-MSCTS Phase Transformations Committee.     

The stabilization of martensite in Cu-Zn-AI shape memory alloys

The martensitic transformation temperature in shape memory alloys can be affected differently by aging above and below the transformation temperature. Under such circumstances the normally reversible transformation can be prevented and the martensite structure “stabilized”. This effect has been studied using electron microscopy, differential scanning calorimetry, and mechanical testing. Evidence is given of an apparently martensitic high temperature transformation, and a careful comparison is made of the stabilized and unstabilized states of the alloy. Three possible models for stabilization are considered in the light of the results obtained, and it is concluded that no single mechanism can be responsible for all the phenomena observed. Formerly with the Department of Metallurgy and Materials Science, University of Cambridge, England