Strain–temperature behavior of NiTiCu shape memory single crystals

Single crystal specimens of NiTi10Cu alloys were subjected to temperature cycling conditions under constant tensile and compressive stresses and the transformation strains were monitored. The [111] orientation exhibited the highest experimental transformation strains (6.64%) in tension while the [001] provides the highest transformation strains in compression (5.34%). These transformation strain levels are significantly higher than previously reported values on NiTiCu alloys. The theoretical treatment includes both the calculation of the CVP (correspondent variant pair) formation strain incorporating the growth of monoclinic phase from the most favorably oriented orthorhombic variant, and the concomitant detwinning of the monoclinic martensite. The experimental transformation strain values are consistently below the theoretical levels due to two main reasons: the slip deformation in the austenite domains as confirmed with TEM studies, and the incomplete transformation resulting in a mixture of orthorhombic and monoclinic phases as determined from diffraction patterns. The experimental transformation strains are higher in tension compared to compression for most single crystal orientations due to two factors: the additional strain associated with the detwinning of the B19′phase in the final microstructure (such as in [111] case), and the partial completion of the second step of the transformation limiting the compression strains.     

Phase transformation yield surface determination for some shape memory alloys

Like in the “plasticity” theory, the prediction of phase transformation yield surfaces constitutes an essential issue in the modelling of polycrystalline shape memory alloys thermomechanical behaviour. Usually for “micro–macro” integration, the nature of the interface between austenite and twinned or untwinned martensite under stress free state and the choice of correspondence variants (CV) or habit plane variant (HPV) are predominant toward the explicit shape of the phase transformation surface. If the predictions for Cu–Al–Be, Cu–Al–Zn (interface between austenite and one single variant of martensite for cubic to monoclinic phase transformation) and Cu–Al–Ni (interface between austenite and twinned martensite for cubic to orthorhombic phase transformation) are fairly good; the prediction is not efficient in the important case of Ti–Ni (interface between austenite and twinned martensite with stress free state for cubic to monoclinic phase transformation). The usual hypothesis consisting in neglecting the effect of stress on the interface geometrical configuration must be revised.     

Effects of transformation temperature on variant pairing of bainitic ferrite in low carbon steel

The effects of transformation temperature on the variant pairing tendency of bainitic ferrite (BF) and the orientation relationship (OR) between BF and austenite matrix are investigated quantitatively in low-carbon, low-alloy steel by means of electron backscatter diffraction analysis. By numerical reconstruction of the austenite orientation it was found that BF holds a near Kurdjumov-Sachs OR with respect to the austenite matrix. The angular deviation of the close-packed planes (CPPs) becomes smaller with decreasing transformation temperature, while the small misorientation angle between the close-packed directions (CPDs) remains nearly the same. BF variants with small misorientations are formed side by side at high transformation temperatures by sharing the same Bain correspondence. In contrast, BF variants are formed adjacently at lower transformation temperatures by sharing the same parallel relations for CPP. In particular, pairing of twin-related variants is dominant in this case. Such a variant pairing tendency with respect to transformation temperature is discussed from the viewpoint of self-accommodation of transformation strain and inter-variant boundary energy.     

A three-dimensional phase-field model for computer simulation of lamellar structure formation in γTiAl intermetallic alloys

A three dimensional phase-field model of α^′₂→α₂+γ transformation is developed to simulate the formation of coherent multi-domain lamellar structures in γTiAl intermetallic alloys. The model takes into account the effect of coherency strain associated with the lattice rearrangement accompanying the phase transformation, and the anisotropy in interfacial energy. Simulation studies based on the model successfully predicted the essential features associated with the multi-domain lamellar structures observed experimentally. It is shown that the coherency strain accommodation is the dominating factor responsible for the formation of the lamellar structure. The neighboring lamellae of γ phase are found to have either a twin or a pseudo-twin relationship, with the former being dominant. It is found that strain-induced correlated nucleation plays an important role in the formation of the twined lamellae. The lamellar thickness is determined by the interplay among the elastic strain energy, interfacial energy and bulk chemical free energy. Domains within individual lamellae are isotropic and domain boundaries are smoothly curved. No special self-accommodating morphological patterns are observed on the (0001)_α2 plane, which is very different from the pattern formation predicted for the coherent hexagonal → O-phase transformations.     

Determination of the habit plane characteristics in the β–α′ phase transformation induced by stress in Ti–5Al–2Sn–4Zr–4Mo–2Cr–1Fe

The characteristics of the habit planes of the α″ orthorhombic martensite plates, induced by stress within a commercial sheet of Ti–5Al–2Sn–4Zr–4Mo–2Cr–1Fe have been investigated. First, the orientations of several grains in BCC phase which presented at least one α″ orthorhombic martensite plate, were determined by EBSD. The Miller indexes of habit planes within a parent grain were deduced from the intersection lines of the martensite plates on two perpendicular sides of the sample and from the orientation of the parent grain. These data are compared to the characteristics of the habit planes, calculated from the phenomenological theory of the martensitic transformation proposed by Wechsler, Liebermann and Read. The different results and their dispersions are analysed in this contribution.     

Geometrical Model of Polymorphous Transformations in Titanium and Zirconium

A geometrical model of transformation of a body-centered cubic lattice of α-phase into a hexagonal close-packed lattice of α-phase is developed with the aim of explaining the special features of the crystal geometry of formation of martensite phases in titanium and zirconium and in alloys based on them. The transformation is described as mutual reconstruction of coordination polyhedra of the cubic and hexagonal lattices through an intermediate configuration of the crystal structure of ω-phase. In the language of algebraic geometry the transition is implemented as reconstruction of an 11-atom cluster that represents a union of three octahedra around a common edge into an 11-atom cluster composed of 11 tetrahedra united over faces. Experimentally observed orientation relations and habit planes at α → ω and β → α transformations are describable by elements of the structure of the mentioned clusters.     

Austenite to bainite phase transformation in the heat-affected zone of a high strength low alloy steel

The austenite to bainite phase transformation was investigated in a low alloy structural steel after simulated welding heat treatment, by means of light microscopy, electron backscatter diffraction and transmission electron microscopy. Upper bainite packets result from the growth of groups of laths having close crystallographic orientations but highly misoriented habit planes. Self-accommodation of the transformation eigenstrain was evaluated for various bainite configurations using a micromechanical model. The observed pairs of variants seem to help limiting plastic strain in the austenite phase, thus enhancing growth of the bainite phase during cooling.     

In situ TEM observation of stress-induced martensitic transformations and twinning processes in CuAlNi single crystals

Stress-induced martensitic transformations and twinning processes were studied in thin foils of CuAlNi single crystals strained in situ in a transmission electron microscope. The nucleation and growth of the martensite plates were monitored for three transformation processes known from bulk experiments: (i) the transformation of austenite into 2H martensite at low-stress levels; (ii) the twinning/detwinning processes in 2H martensite; and (iii) the transformation between austenite and 18R martensite at higher stress levels. The morphology of the austenite/martensite habit planes was examined, and the existence of planar interfaces between a single variant of 2H martensite and austenite on the microscopic level was proven.     

马氏体相变的晶体学特征—不变平面应变

自20世纪20年代以来,基于马氏体相变产生的浮凸和在母相中预先刻制的直线变成在相界面上连续的折线,提出了以切变为基础的马氏体相变的晶体学特征—"不变平面应变"的概念。随后,以该概念为基础建立了马氏体相变晶体学表象理论(PTMC)。然而,刘宗昌等基于相同的实验,即马氏体相变后的直线刻痕仍为直线和浮凸形态为帐篷形,分别在2010年和2013年《热处理》杂志上发表文章,否定马氏体相变的"切变"机制进而否定马氏体相变的"不变平面应变"。如所周知,否定马氏体相变的"切变机制"就是否定"不变平面应变",因此刘宗昌等于2013年发表的文章彰显出他们的轻率。本文作者已在3篇文章中列举用原子力显微镜和透射电镜观察的结果驳斥了他们的错误观点,至少可以说,他们没有理解我们文章中的实验和理论。为此,本文再次引用Yang和Wayman的透射电镜实验结果,即单变体马氏体使预存在的层错迹线(直线)变成折线,而自协调的多个马氏体可使迹线仍为直线;单变体马氏体的浮凸为N形,但多变体马氏体的浮凸可以是帐篷形或更为复杂的形态,由此可以说明刘宗昌等错误观点的原因。最近,本文作者及其合作者基于PTMC计算了Mn80Fe15Cu5热弹性合金马氏体相变的惯习面,并与实验结果相符,由此确认了"不变平面应变"是马氏体相变晶体学特征的正确性。     

Crystallographic analysis of the FCC → BCC martensitic transformation in high-carbon steel

Based on the phenomenological crystallographic theory of martensitic transformations, the following crystallographic characteristics of the tetragonal martensite in high-carbon steel have been calculated: orientation relationships between the crystal lattices of the bct martensite and fcc austenite; the magnitude and direction of the macroscopic shear; the habit plane; the angle and the axis of rotation of the crystal lattice of the martensite. The calculation was performed for three variants of lattice deformation: Bain deformation; two-shear Kurdjumov-Sachs deformation; and the deformation we suggested upon the analysis of the fcc-bcc transformation. In the last variant, a minimum rotation of the crystal lattice of martensite is required; consequently, this variant is closest to the real mechanism of the martensitic transformation. An expression has been derived that describes the interrelation between the degree of tetragonality of the crystal lattice of martensite and the magnitude of the shear deformation of the lattice. It has been shown that the 12 crystal-lographically equivalent variants of shear upon the formation of the lattice of the tetragonal martensite form three groups in each of which the martensite has the same tetragonality axis. For each variant of the shear, we have two equivalent variants of deformation of the martensite with invariant lattice. This results in 24 variants of orientation relationships.     

Metallographic study of thermoelastic martensite transformation in a Cu-Zn-Al alloy

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THE LIMITATION OF MATANSITIC INVARIANT HABIT PLANE AND MARTENSITE MORPHOLOGY

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Effect of grain boundary character on the martensitic transformation in Fe–32at.%Ni bicrystals

The effect of grain boundary character on the martensitic transformation was examined in two types of Fe–32at.%Ni bicrystals containing a 90°<211> tilt or a 90°{211} twist boundary focusing on the martensite-start temperature (Ms) during cooling, the morphology of the martensite and the variant selection. The Ms of bicrystals with a tilt boundary was higher than that of single crystals, while bicrystals with a twist boundary showed no significant difference from that of single crystals. Coarse lenticular martensites formed symmetrically in neighbouring grains around the tilt boundary. In contrast, tiny martensites were uniformly distributed in bicrystals with a twist boundary, and in single crystals. In the vicinity of the tilt and twist boundaries, some variants with the habit plane almost parallel to the boundaries were preferentially selected among 24 variants. Moreover, since the equivalent variants in neighbouring grains at the tilt boundary are selected, strain compatibility of the shape strain of martensite across the tilt boundary is satisfied, resulting in an increased Ms. The effect of pre-strain on the heterogeneous nucleation of martensite at the boundaries was also investigated.     

Fe-C-Mn-Si钢中奥氏体共格孪晶界对贝氏体铁素体变体选择的影响

将C含量(质量分数)分别为0.05%和0.4%的Fe-C-Mn-Si钢进行等温处理得到贝氏体组织,采用EBSD技术对奥氏体共格孪晶界上形成的贝氏体铁素体变体进行分析.结果表明,2种钢中的贝氏体铁素体与母相奥氏体均成近似K-S取向关系.奥氏体孪晶界两侧形成取向相同的变体对.此变体对形成后,孪晶界基本不再显现.晶体学分析表明,共格孪晶界两侧可能出现的变体对最多不超过3组,且这3组变体对的惯习面均与孪晶界平行,因此,贝氏体铁素体变体都将沿孪晶界生长.含C量为0.05%的Fe-C-Mn-Si钢中奥氏体孪晶界上只观察到一组贝氏体铁素体变体对的形成,这是因为C含量较低,贝氏体铁素体生长速度较快,消除了其它变体对的形核机会,先形核的变体对一旦形核就迅速覆盖整个孪晶面.而在含C量为0.4%的Fe C Mn-Si钢中,由于C含量较高,贝氏体铁素体生长速度较慢,3组变体对均有机会形核,因此,在孪晶界上可以观察到这3组变体对同时出现.     

Fe-C-Mn-Si钢中奥氏体共格孪晶界对贝氏体铁素体变体选择的影响

将C含量(质量分数)分别为0.05%和0.4%的Fe-C-Mn-Si钢进行等温处理得到贝氏体组织,采用EBSD技术对奥氏体共格孪晶界上形成的贝氏体铁素体变体进行分析.结果表明,2种钢中的贝氏体铁素体与母相奥氏体均成近似K-S取向关系.奥氏体孪晶界两侧形成取向相同的变体对.此变体对形成后,孪晶界基本不再显现.晶体学分析表明,共格孪晶界两侧可能出现的变体对最多不超过3组,且这3组变体对的惯习面均与孪晶界平行,因此,贝氏体铁素体变体都将沿孪晶界生长.含C量为0.05%的Fe-C-Mn-Si钢中奥氏体孪晶界上只观察到一组贝氏体铁素体变体对的形成,这是因为C含量较低,贝氏体铁素体生长速度较快,消除了其它变体对的形核机会,先形核的变体对一旦形核就迅速覆盖整个孪晶面.而在含C量为0.4%的Fe-C-Mn-Si钢中,由于C含量较高,贝氏体铁素体生长速度较慢,3组变体对均有机会形核,因此,在孪晶界上可以观察到这3组变体对同时出现.     

Evolution of crystallographic texture and microstructure in the orthorhombic phase of a two-phase alloy Ti–22Al–25Nb

Evolution of crystallographic texture in the orthorhombic phase of a two-phase alloy Ti–22Al–25Nb (at%), consisting of orthorhombic (O) and bcc (β/B2) phases, was studied. The material was subjected to deformation in two-phase field as well as in the single β phase field. The resulting evolution of microstructure and crystallographic texture were recorded using scanning electron microscopy and X-ray diffraction. The orthorhombic phase underwent change in morphology (from platelets to equiaxed) on rolling in the two-phase field with the texture getting sharper with the amount of deformation. Rolling above β transus temperature led to hot deformation of single β phase microstructure and its subsequent cooling produced transformed coarse platelets of orthorhombic phase with texture in orientation relation with the high temperature deformed β phase.     

Controlling factor for nucleation of martensite at grain boundary in Fe-Ni bicrystals

A favourable nucleation of martensites at a grain boundary was investigated using Fe-Ni bicrystals containing a <211> symmetric tilt boundary with various tilt angles, focusing on the martensite-start temperature (Ms), the morphology of martensites and the variant selection. Near the grain boundaries, some variants with the habit plane almost parallel to the boundaries were preferentially selected and their variants changed depending on the tilt angle. In addition, the equivalent variants were symmetrically adjoined at the boundary to maintain the compatibility of shape strain of martensites across the boundary. Such characteristic nucleation can be regarded as a self-accommodation across the boundary, which is called cooperative nucleation (CN). The CN effectively reduces the strain energy due to the formation of martensites compared with the independent nucleation within a grain resulting in an increase in Ms. The characteristic variant selection of martensites can also be explained from the minimisation of strain energy.     

Phase transitions in crystals with a BCC structure

A theory of bcc-hcp and bcc-fcc structural phase transformations in metals with a high-temperature bcc lattice has been constructed on the basis of a pseudo-spin Ising Hamiltonian, which describes cooperative oscillations of atomic planes in a two-well potential with allowance for interactions between nearest neighbors. The picture of diffuse scattering and of the combined rearrangement of original Bragg reflections and diffuse scattering into Bragg reflections upon transitions into low-temperature phases has been calculated at all temperatures. It is shown that the bcc-hcp and bcc-fcc phase transformations occur in a temperature interval rather than at a point. In the case of the bcc-hcp transformation, as the temperature decreases, the bcc structure first transforms jumpwise into an orthorhombic structure close to the hcp structure and then, with a further decrease in temperature, this structure smoothly changes into the strictly close-packed hexagonal structure at T → 0. In the case of the bcc-fcc transition, there occurs an analogous transformation into a strictly close-packed face-centered cubic structure at T → 0, but now through a monoclinic structure.     

A direct method for the crystallography of martensitic transformation and its application to TiNi and AuCd

A simple and straightforward method to obtain a complete set of twining planes and habit planes of martensitic crystals by using the crystallographic data is proposed under the bulk strain energy minimization hypothesis. This method can also be used to obtain the diffraction pattern corresponding to martensitic transformation forming the invariant planes. Applications to the cubic→trigonal and cubic→monoclinic martensitic transformation are presented. The results well explain the morphological differences between R-phase in TiNi and ζ′₂ martensite in AuCd.     

Effect of external stress and bias magnetic field on transformation strain of heusler alloy Ni-Mn-Ga

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