Crystalline damage growth during martensitic phase transformations

A thermomechanical model is developed within a large deformation setting in order to simulate the interactions between martensitic phase transformations and crystalline damage growth at the austenitic grain level. Subgrain information is included in the model via the crystallographic theory of martensitic transformations. The damage and transformation characteristics are dependent of the specific martensitic transformation systems activated during a loading process, which makes the model strongly anisotropic. The state of transformation for the individual transformation systems is represented by the corresponding volume fractions. The state of damage in the austenite and in the martensitic transformation systems is reflected by the corresponding damaged volume fractions. The thermodynamical forces energetically conjugated to the rate of volume fraction and the rate of damaged volume fraction are the driving forces for transformation and crystalline damage, respectively. The expressions for these driving forces follow after constructing the specific form of the Helmholtz energy for a phase-changing, damaging material. The model is used to analyze several three-dimensional boundary value problems that are representative of microstructures appearing in multiphase carbon steels containing retained austenite. The analyses show that the incorporation of damage in the model effectively limits the elastic stresses developing in the martensitic product phase, where the maximum value of the stress strongly depends on the toughness of the martensite. Furthermore, in an aggregate of randomly oriented grains of retained austenite embedded in a ferritic matrix the generation of crystalline damage delays the phase transformation process, and may arrest it if the martensitic product phase is sufficiently brittle. The response characteristics computed with the phase-changing damage model are confirmed by experimental results.     

Crystallographic variant selection of martensite at high stress/strain

The phenomenological theory of martensitic transformation is well understood that the displacive phase transformations are mainly influenced by the externally applied stress. Martensitic transformation occurs with 24 possible Kurdjomov-Sachs (K-S) variants, where each variant shows a distinct lattice orientation. The elegant transformation texture model of Kundu and Bhadeshia for crystallographic variant selection of martensite in metastable austenite at various stress/strain levels has been assessed in this present research. The corresponding interaction energies have also been evaluated. Encouraging correlation between model prediction and experimental data generation for martensite pole figures at many deformed austenite grains has been observed at different stress/strain levels. It has been investigated that the mechanical driving force alone is able to explain the observed martensite microtextures at all stress/strain levels under uniaxial tensile deformation of metastable austenite under low temperature at a slow strain rate. The present investigation also proves that the Patel and Cohen’s classical theory can be utilized to predict the crystallographic variant selection, if it is correctly used along with the phenomenological theory of martensite crystallography.     

γ-α相变中不同晶界特征下铁素体生长形貌的相场模拟

利用多相场模型模拟了奥氏体(γ)-铁素体(α)相变过程中不同晶界特征下铁素体晶粒的形貌与生长动力学.模型中通过能量梯度系数和耦合项系数的协同变化定量表达晶界能与晶界迁移率的各向异性,同时固定相场界面宽度来保证计算精度.模拟结果显示:随着原奥氏体晶界能与铁素体-奥氏体晶界能比值σ_(γ,γ)/σ_(α,γ)的增加,三叉相界面处的平衡角β减小,铁素体晶粒沿原奥氏体晶界与垂直于奥氏体晶界方向的生长速率差变大.铁素体与奥氏体晶粒间的晶粒取向越接近,铁素体生长越缓慢.模拟结果可描述铁素体晶粒生长形貌的多样性,与实验结果符合.     

Effects of Cu on the martensitic transformation and magnetic properties of Mn_(50)Ni_(40)In_(10) alloy

The structures, the martensitic transformations, and the magnetic properties are studied systematically in Mn50Ni40-xCuxIn10, Mn50-xCuxNi40In10, and Mn50Ni40In10-xCux alloys. The partial substitution of Ni by Cu reduces the martensitic transformation temperature, but has little influence on the Curie temperature of austenite. Comparatively, the martensitic transformation temperature increases and the Curie temperature of austenite decreases with the partial replacement of Mn or In by Cu. The magnetization difference between the austenite phase and the martensite phase reaches 70 emu/g in Mn50Ni39Cu1In10; a field-induced martensite-to-austenite transition is observed in this alloy.     

Ni53.2Mn22.6Ga24.2单晶的两步热弹性马氏体相变及其应力应变特性

对具有两步完全热弹性的Ni_53.2Mn_22.6Ga_24.2单晶的物性采用多种测量手段进行了表征,特别研究了不同温度下的应力-应变特性.研究表明,热诱发的中间马氏体相变应变远大于马氏体相变应变.在较低的形变温度下,沿单晶母相［001］方向的压应力诱发的是两步马氏体相变,材料表现出赝弹性;在较高的形变温度下,只能观察到一步马氏体相变,材料展现出完全超弹性特性.此外,利用热力学理论分别计算了诱发马氏体相变和中间马氏体相变的临界应力与形变温度的关系,与实验测量得到的结果相符. 关键词： 马氏体相变 形状记忆效应 应变 超弹性     

Crystallographic variant selection of martensite during fatigue deformation

Metastable austenitic stainless steels are prone to form deformation-induced martensite under the influence of externally applied stress. Crystallographic variant selection during martensitic transformation of metastable austenite has been investigated thoroughly with respect to the interaction between the applied uniaxial cyclic stress and the resulting accumulated plastic strain during cyclic plastic deformation. The orientation of all the Kurdjomov–Sachs (K-S) variants has been evaluated extensively and compared with the measured orientation of martensite with their corresponding interaction energies by applying the elegant transformation texture model recently developed by Kundu and Bhadeshia. Encouraging correlation between model prediction and experimental data generation for martensite pole figures at many deformed austenite grains has been observed. It has been found that both the applied uniaxial cyclic stress and the accumulated plastic strain are having strong influence on crystallographic variant selection during cyclic plastic deformation. Patel and Cohen’s classical theory can be utilized to predict the crystallographic variant selection, if it is correctly used along with the phenomenological theory of martensite crystallography.     

Determination of the normal and anomalous hall effect coefficients in ferromagnetic Ni50Mn35In15 − x Si x Heusler alloys at the martensitic transformation

The magnetization, the electrical resistivity, the magnetoresistance, and the Hall resistivity of Ni₅₀Mn₃₅In_{15 ? x} Si _x (x = 1.0, 3.0, 4.0) Heusler alloys are studied at T = 80-320 K. The martensitic transformation in these alloys occurs at T = 220?C280 K from the high-temperature ferromagnetic austenite phase into the low-temperature martensite phase having a substantially lower magnetization. A method is proposed to determine the normal and anomalous Hall effect coefficients in the presence of magnetoresistance and a possible magnetization dependence of these coefficients. The resistivity of the alloys increases jumpwise during the martensitic transformation, reaches 150?C200 ??? cm, and is almost temperature-independent. The normal Hall effect coefficient is negative, is higher than that of nickel by an order of magnitude at T = 80 K, decreases monotonically with increasing temperature, approaches zero in austenite, and does not undergo sharp changes in the vicinity of the martensitic transformation. At x = 3, a normal Hall effect nonlinear in magnetization is detected in the immediate vicinity of the martensitic transformation. The temperature dependences of the anomalous Hall effect coefficient in both martensite and austenite and, especially, in the vicinity of the martensitic transformation cannot be described in terms of the skew scattering, the side jump, and the Karplus-Lutinger mechanisms from the anomalous Hall effect theory. The possible causes of this behavior of the magnetotransport properties in Heusler alloys are discussed.     

Ultrasonic characterization of Cu-Al-Ni single crystals lattice stability in the vicinity of the phase transition

Measurements of elastic constants of the austenite phase when approaching the phase transformation either upon cooling or stressing is of the crucial interest for the shape memory alloy field. Acoustic properties (wave velocity and also attenuation changes) of the Cu-Al-Ni single crystal were investigated in situ during stress-induced martensitic transformation at constant (room) temperature. The parent austenite cubic lattice of the Cu-Al-Ni exhibits very high elastic anisotropy (anisotropy factor A approximately 12). The measurements were made using nine combinations of (i) applied uniaxial compression in a given crystal direction, (ii) the wave propagation and (iii) polarization vectors. The chosen configurations are sufficient for evaluation of all independent third order elastic constants (TOEC). The longitudinal modes were also measured by the immersion technique, using the transducer pair in a water tank installed on the testing machine. The device works as "a ultrasonic extensometer" measuring a transverse strain of the specimen. The dependencies of both natural and initial wave velocities on the applied stress may be evaluated. Three elastic constants of the stress-induced martensite were determined. The elastic properties were found to vary with the increasing stress above the Ms transformation temperature, which is interpreted as a precursor for the martensitic transformation. The onset of the transformation was additionally identified from the acoustic emission measurement.     

On the cryogenic magnetic transition and martensitic transformation of the austenite phase of 7MoPLUS duplex stainless steel

The magnetic behaviour and martensitic transformation at cryogenic temperatures (down to 4 K) of the austenite phase of the duplex stainless steel (DSS), 7MoPLUS, were studied. As regards the prediction of Neel temperature, the empirical expressions for austenitic stainless steels are not applicable to the austenite phase of 7MoPLUS, although the composition of the austenite phase falls within the composition ranges within which the expressions were developed. Regarding the prediction of martensitic point Ms, the applicability of ‘old’ and recently developed expressions has been examined. The recently developed expressions, which take into account more alloying elements and their interactions, are not suitable for the austenite phase of 7MoPLUS. But for the ‘old’, simpler expressions, they seem to be valid in the sense that they all predict high stability of the austenite phase. Results obtained from 7MoPLUS were qualitatively the same as those obtained from another DSS, designated as 2205. Reasons for the applicability and inapplicability of these empirical expressions are suggested.     

18 MeV质子辐照对TiNi形状记忆合金R相变的影响

 研究了用HZ-B串列加速器的18MeV质子辐照对TiNi形状记忆合金R相变的影响，辐照在奥氏体母相状态下进行。示差扫描量热法（DSC）表明，辐照后R相变开始温度T^s_R和逆马氏体相变结束温度T^f_A随辐照注量的增加而降低。当注量为1.53×10¹⁴/cm²时，T^sR和T^f_A分别下降6K和13K，辐照未引起R相变结束温度T^s_R和逆马氏体相变开始温度T^f_A的变化。表明辐照后母相(奥氏体相)稳定。透射电镜（TEM）分析表明辐照后没有引起合金可观察的微观组织变化。辐照对R相变开始温度T^s_{R和逆马氏体相变结束温度Af的影响可能是由于质子辐照后产生了孤立的缺陷团，形成了局部应力场，引起晶格有序度的下降所造成的。}     

Hall effect in a martensitic transformation in Ni-Co-Mn-In Heusler alloys

The Hall effect, transverse magnetoresistance, and magnetization of Ni₄₈Co₂Mn₃₅In₁₅ Heusler alloys have been studied at T = 77–300 K in magnetic fields up to 15 kOe. It has been shown that a martensitic transformation is accompanied by a change in the sign of the constant of the ordinary Hall effect, which means a strong change in the electronic spectrum in the martensitic transformation, while the anomalous Hall effect (AHE) constant is positive in both the austenite and martensite phases. In both phases, there are no correlations between the AHE constant and the square of the resistivity, which are characteristic of the side jump mechanism in the AHE theory. In the near vicinity of the martensitic transformation, the field dependences of the Hall resistance are complex and nonmonotonic, indicating a change in the relative concentrations of the austenite and martensite phases in strong fields.     

Damage evolution and multi-scale analysis of carbon fiber-reinforced cross-ply laminate with thermal residual stress

In order to study the mechanical and thermal properties of carbon fiber-reinforced cross-ply laminate, a macroscopic [90/0]_8S cross-ply laminate model and a unit cell of fiber regular distribution near the [90/0]_8S laminate interlaminar zone with plastic matrix and interface were created. Then the damage initiation discipline details of [90/0]_8S cross-ply laminate are researched, and the effects of interfacial coefficient of thermal expansion on thermal residual stress distribution and damage initiation are researched in detail both based on the macroscopic and microscopic models. It shows that the initial damage of interlaminar interface occurs in macroscopic model and the initial damage in microscopic model occurs both at intralaminar interface and interlaminar cohesive zone. No matter in macroscopic or microscopic model, the residual stress of 6.27 × 10^?6/°C interfacial coefficient of thermal expansion is larger than that of 6.27 × 10^?7/°C interfacial coefficient of thermal expansion. And the initial damage expands more widely in the first one.     

合金元素对TiC/奥氏体界面稳定性影响的第一性原理计算

界面结合强度与材料的强度、硬度、耐磨损、耐腐蚀等性能息息相关,TiC是钢中常见的析出相,研究它与铁基体的界面结合状态,探寻合理的界面强度提升方案,对提升钢的性能具有十分重要的理论意义和应用价值.本文以TiC/奥氏体基体界面为研究对象,采用基于密度泛函理论的第一性原理计算方法从原子尺度上研究TiC/奥氏体基体界面的结合状态.首先本文对界面结合强度以及电子结构进行了计算分析,之后进行高通量计算,研究过渡族金属元素(Mn、Tc、Re、Ru、Os、Co、Rh和Ir)在TiC/奥氏体基体界面的偏析行为及其对界面结合强度的影响,最后通过差分电荷密度分析并解释过渡族金属元素的作用机理.计算研究表明,掺杂Re元素可显著提升界面的强度,为实验上设计高性能钢铁材料提供了新的思路.     

Electronic structures and magnetisms of the Co_2TiSb_(1-x)Sn_x(x= 0, 0.25, 0.5) Heusler alloys: A theoretical study of the shape-memory behavior

The total energy, electronic structures, and magnetisms of the Al Cu2Mn-type Co2TiSb1-xSnx(x = 0, 0.25, 0.5) with the different lattice parameter ratios of c/a are studied by using the first-principles calculations. It is found that the phase transformation from the cubic to the tetragonal structure lowers the total energy, indicating that the martensitic phase is more stable and that a phase transition from austenite to martensite may happen at a lower temperature. Thus, a ferromagnetic shape memory effect can be expected to occur in these alloys. The Al Cu2Mn-type Co2TiSb1-xSnx(x = 0, 0.25, 0.5) alloys are weak ferrimagnets in the austenitic phase and martensitic phase.     

Multi-phase transformation kinetics of HSLA steels during continuous cooling: experiments and cellular automaton (CA) simulation

ABSTRACT

Kinetics of multiply ferrite/bainite phase transformation of HSLA steels is investigated by experiments and cellular automaton (CA) simulation. Peak-differentiation method to elucidate the sequential ferrite and bainite phase transformation individually, which is verified by the CA simulation. Such CA modelling executed using classic JMAK theory, but also gives an insight of microstructure evolution of the multi-phase transformation routine on different cooling rate. From that, it enables classic JMAK modelling to capture the detached phase transformation with different growth models and interface-migration mechanisms. Also, we find that the final phase constitution is sensitive to the cooling rate. With increasing the cooling rate, bainite sheaves nucleated at prior austenite boundaries and ferrite/austenite interfaces are significantly facilitated, which seriously inhibits the growth of prior ferrites. The scenario can be interpreted by the CA simulation and the influence of the cooling rate on sequential multi-phase transformation can be also obtained.     

The effect of Si content on the martensitic transfor-mation temperature of Ni55.5e18Ga26.5-xSix alloys

This paper investigates the effects of substitution of Si for Ga on the martensitic transformation behaviours in Ni-Fe-Ga alloys by using optical metallographic microscope and differential scanning calorimetry (DSC) methods. The structure type of Ni_55.5Fe₁₈Ga_26.5-xSi_x alloys is determined by x-ray diffraction (XRD), and the XRD patterns show the microstructure of Ni-Fe-Ga-Si alloys transformed from body-centred tetragonal martensite (with Si content x = 0) to body-centred cubic austenite (with x = 2) at room temperature. The martensitic transformation temperatures of the Ni_55.5Fe₁₈Ga_26.5-xSi_x alloys decrease almost linearly with increasing Si content in the Si content range of x ≤ 3. Thermal treatment also plays an important role on martensitic transformation temperatures in the Ni-Fe-Ga-Si alloy. The valence electronic concentrations, size factor, L2₁ degree of order and strength of parent phase influence the martensitic transformation temperatures of the Ni-Fe-Ga-Si alloys. An understanding of the relationship between martensitic transformation temperatures and Si content will be significant for designing an appropriate Ni-Fe-Ga-Si alloy for a specific application at a given temperature.     

Atomic force microscopy study on microstructural changes by 'training' in Fe-Mn-Si-based shape memory alloys

Microstructural changes after several cycles of the thermomechanical treatment consisting of a small deformation by stress-induced martensitic transformation (fcc to hcp) and subsequent reversion to austenite by heating (referred to as 'training') have been studied by atomic force microscopy in Fe-Mn-Si based shape memory alloys. Well-trained samples contain a uniform distribution of thin martensite plates of the same variant, the widths of which decrease with increasing number of the training cycles, and their distribution becomes more uniform. Such microstructural development by training originates mainly from extremely thin plates (about 1 nm thick) of hcp phase that are still retained together with stacking faults in the austenite even after heating far above the reverse transformation temperature. In the reverse transformation on heating, a martensite plate that looks as though it is apparently one plate is, in fact, split into very thin plates, which indicates that the plate actually consists of extremely thin martensite plates and these thin plates are reverse-transformed one after another by reverse movement of the Shockley partial dislocations at their tips. This mode of reverse transformation ensures a perfect shape memory effect.     

Exploring the origin of variant selection through martensite-austenite reconstruction

An approach of near neighbour correlation, with manual intervention, was developed for reconstructing parent austenite microstructure in a martensitic stainless steel. This was validated in a ferrite-austenite dual structure. Two-hundred and twenty randomly selected austenite grains were reconstructed from the experimental EBSD (electron backscattered diffraction) measurements. From these reconstructions, martensite variant selection was quantified as the number of variants (n_V) and the variant selection index (VSI: a statistical index for the relative area fractions of the variants). For each prior austenite grain, both n_V and VSI appeared to depend on the associated transformation (austenite-martensite) strain. Selection of common variants between two neighbouring austenite grains was related to the presence of 60°<111?>?or Σ3 boundary in the austenite phase and corresponding minimisation of the transformation strain.