Calculation of coupled problem between temperature and phase transformation during gas quenching in high pressure

The gas quenching is a modern, effective processing technology. On the basis of nonlinear surface heat-transfer coefficient obtained by Cheng during the gas quenching, the coupled problem between temperature and phase transformation during gas quenching in high pressure was simulated by means of finite element method. In the numerical calculation, the thermal physical properties were treated as the functions of temperature and the volume fraction of phase constituents. In order to avoid effectual "oscillation" of the numerical solutions under smaller time step, the Norsette rational approximate method was used.     

Residual-stress measurements in time-controlled quenched austenitic stainless steel

This paper presents experiments to determine the residual stresses generated during the low-speed quenching of austenitic stainless steel. Austenitic stainless steel was chosen because it does not undergo any phase transformation during quenching. As a result, the resultant residual-stress pattern depends only on plastic deformation taking place during the quench. Different quenching rates were used in the experiment to quantify their effect on the generation of residual stresses. These stresses were measured along the surface of the specimen in a direction parallel to the quench direction and in depth below the surface.     

具有非线性表面换热系数半圆柱薄壳在快速冷却过程中的热分析

用实验和数值计算相结合的方法，得到半圆柱壳体快速冷却过程中内外表面的非线性表面换热系数。在此基础上，用有限单元法对半圆柱壳体的热应力和变形进行了分析。在数值计算中，模拟钢的CCT图，计算了奥氏体、珠光体、贝氏体和马氏体的体积百分比，并将热物理性质和力学性能处理为相变体积百分比和温度的函数。所得结果表明，在半圆柱壳体快速冷却过程中的热应力和变形计算中，有必要考虑非线性表面换热系数、相变等非线性效应。     

A New Approach in Modeling Phase Distribution in Fully Developed Bubbly Pipe Flow

Turbulent two-phase flow equations are derived and solved for fully developed pipe flow using a composite eddy-viscosity model and a new void-fraction equation. The void fraction profile is first specified from experiments and the velocity field is calculated to validate the eddy-viscosity model. Consequently, a new equation is presented for calculation of the void fraction. This void-fraction equation incorporates the gradient of turbulent normal stresses in the radial direction, the conventional lift force, and a contribution from the unsteady drag force. The implications of this new equation, for the bubbly flow regime, are investigated by calculating the void-fraction distribution for a given velocity field. Inclusion of the normal turbulent stresses in the radial direction is shown to simulate correctly the experimentally observed trends of the phase distribution, both for upward and downward bubbly flow, without the need for a fictitious term such as the so called ``lubrication force'. This revised version was published online in July 2006 with corrections to the Cover Date.     

Size effects in martensitic microstructures: Finite-strain phase field model versus sharp-interface approach

A finite-strain phase field model for martensitic phase transformation and twinning in shape memory alloys is developed and confronted with the corresponding sharp-interface approach extended to interfacial energy effects. The model is set in the energy framework so that the kinetic equations and conditions of mechanical equilibrium are fully defined by specifying the free energy and dissipation potentials. The free energy density involves the bulk and interfacial energy contributions, the latter describing the energy of diffuse interfaces in a manner typical for phase-field approaches. To ensure volume preservation during martensite reorientation at finite deformation within a diffuse interface, it is proposed to apply linear mixing of the logarithmic transformation strains. The physically different nature of phase interfaces and twin boundaries in the martensitic phase is reflected by introducing two order-parameters in a hierarchical manner, one as the reference volume fraction of austenite, and thus of the whole martensite, and the second as the volume fraction of one variant of martensite in the martensitic phase only. The microstructure evolution problem is given a variational formulation in terms of incremental fields of displacement and order parameters, with unilateral constraints on volume fractions explicitly enforced by applying the augmented Lagrangian method. As an application, size-dependent microstructures with diffuse interfaces are calculated for the cubic-to-orthorhombic transformation in a CuAlNi shape memory alloy and compared with the sharp-interface microstructures with interfacial energy effects.     

高温条件下材料与结构力学行为的研究进展

本文回顾了最近10年来材料与结构高温力学行为若干热点问题的研究进展,包括高温下材料力学行为的多尺度特性、多组元材料的蠕变力学性能、拘束条件下的高温断裂理论、高温下的结构安全评定理论等。指出：为了保障重大高温装备的安全运行,并为高技术工艺装备的实现提供理论支撑,必须实现时间尺度与空间尺度上的事件的转换与关联,解决高温材料老化的物理化学动力学问题,理清应力应变场与化学动力学过程的相互作用;应强化材料界面缺陷及高温结合强度的微观测量方法与理论分析的研究;需要进一步研究损伤影响下的实际蠕变裂尖应力场,精确描述拘束效应的蠕变裂纹扩展速率模型,以进一步建立拘束下的高温断裂理论;在高温结构的安全评定方面,在目前的失效评定图基础上引入与材料、结构同时关联的损伤维度（时间相关）,可望实现较为复杂损伤机制下的失效评定。     

Prediction of 42CrMo steel flow stress at high temperature and strain rate

The compressive deformation behavior of 42CrMo steel was investigated at temperatures ranging from 850 to 1150 °C and strain rates from 0.01 to 50 s⁻¹ on Gleeble-1500 thermo-simulation machine. Based on the classical stress–dislocation relation and the kinematics of the dynamic recrystallization, the flow stress constitutive equations of the work hardening-dynamical recovery period and dynamical recrystallization period were established for 42CrMo steel, respectively. The stress–strain curves of 42CrMo steel predicted by the established models are in good agreement with experimental results when the strain rate is relatively low. So, the proposed deformation constitutive equations can be used to establish the hot formation processing parameters for 42CrMo steel.     

Modelling of laminated microstructures in stress-induced martensitic transformations

This paper is concerned with micromechanical modelling of stress-induced martensitic transformations in crystalline solids, with the focus on distinct elastic anisotropy of the phases and the associated redistribution of internal stresses. Micro-macro transition in stresses and strains is analysed for a laminated microstructure of austenite and martensite phases. Propagation of a phase transformation front is governed by a time-independent thermodynamic criterion. Plasticity-like macroscopic constitutive rate equations are derived in which the transformed volume fraction is incrementally related to the overall strain or stress. As an application, numerical simulations are performed for cubic β₁ (austenite) to orthorhombic γ₁′ (martensite) phase transformation in a single crystal of Cu-Al-Ni shape memory alloy. The pseudoelasticity effect in tension and compression is investigated along with the corresponding evolution of internal stresses and microstructure.     

Hydrodynamics and heat transfer characteristics of G–S magnetically stabilized beds consisting of admixtures of shale oil and magnetic particles

The hydrodynamic and heat transfer behavior of a bed consisting of magnetic and shale oil particle admixtures under the effect of a transverse magnetic field is investigated. The phase diagram, bed void fraction are studied under wide range of the operating conditions i.e., gas velocity, magnetic field intensity and fraction of the magnetic particles. It is found that the range of the stabilized regime is reduced as the magnetic fraction decreases. In addition, the bed voidage at the onset of fluidization decreases as the magnetic fraction decreases. On the other hand, Nusselt number and consequently the heat transfer coefficient is found to increase as the magnetic fraction decreases. An empirical equation is investigated to relate the effect of the gas velocity, magnetic field intensity and fraction of the magnetic particles on the heat transfer behavior in the bed.     

机械载荷作用下单边裂纹载流薄板的应力场

采用坐标变换的方式,将单边裂纹载流薄板通电瞬间由温度产生的应力场表达式中的各应力分量分离,并用极坐标进行表示．给出了Ⅰ型穿透裂纹尖端附近的应力场的表达式．最后将温度产生的应力场与单向拉伸载荷作用产生的应力场相叠加,推导出用极坐标表示的机械载荷作用下单边裂纹载流薄板的应力场的表达式,并给出算例．     

有限长厚壁管在过冷沸腾状态下的热应力响应

在求得有限长厚壁管水淬时瞬态温度分布的基础上［１］，引入了包含相变的热弹塑性本构方程的增量形式．用有限元法求得了瞬态热应力和残余应力．对影响热应力和残余应力的各种因素进行了分析和讨论．     

A 3-D constitutive model for shape memory alloys incorporating pseudoelasticity and detwinning of self-accommodated martensite

A 3-D constitutive model for polycrystalline shape memory alloys (SMAs), based on a modified phase transformation diagram, is presented. The model takes into account both direct conversion of austenite into detwinned martensite as well as the detwinning of self-accommodated martensite. This model is suitable for performing numerical simulations on SMA materials undergoing complex thermomechanical loading paths in stress–temperature space. The model is based on thermodynamic potentials and utilizes three internal variables to predict the phase transformation and detwinning of martensite in polycrystalline SMAs. Complementing the theoretical developments, experimental data are presented showing that the phase transformation temperatures for the self-accommodated martensite to austenite and detwinned martensite to austenite transformations are different. Determination of some of the SMA material parameters from such experimental data is also discussed. The paper concludes with several numerical examples of boundary value problems with complex thermomechanical loading paths which demonstrate the capabilities of the model.     

汽轮机轮盘热处理残余应力分析

百万核电汽轮机红套低压转子工作环境的蒸汽参数较低,各级轮盘均处于湿度较大的工作区域,易产生应力腐蚀,引起裂纹萌生和扩展．为提高轮盘的抗腐蚀能力,降低工作应力是一个有效的方法．通过热处理方法,在轮盘表面形成预压应力以抵消部分旋转拉应力是可行的方法,而产生适当深度和大小的预压应力则需对热处理过程进行谨慎的设计．本文以汽轮机轮盘为研究对象,建立轴对称有限元模型,通过对ABAQUS软件的二次开发,实现对轮盘热处理过程的温度场及应力场进行数值模拟．计算综合考虑了非线性的材料热物性参数、力学性能参数、表面换热系数及不同材料组织转变的相变潜热、热物性参数和力学参数,通过对不同热处理方法得到的残余应力场的比较,获得了较合理的水冷方式,为热处理工艺确定提供参考．     

Quench characteristics and mechanical responses during quench propagation in rare earth barium copper oxide pancake coils

Quench and mechanical behaviors are critical issues in high temperature superconducting(HTS)coils.In this paper,the quench characteristics in the rare earth barium copper oxide(REBCO)pancake coil at 4.2K are analyzed,and a two-dimensional(2D)axisymmetric electro-magneto-thermal model is presented.The effects of the constituent materials,background field,and coil size are analyzed.An elastoplastic mechanical model is used to study the corresponding mechanical responses during the quench propagation.The variations of the temperature and strain in superconducting layers are compared.The results indicate that the radial strain evolutions can reflect the transverse quench propagation and the tensile hoop and radial stresses in superconducting layers increase with the quench propagation.The possible damages are discussed with the consideration of the effects of the background field and coil size.It is concluded that the high background field significantly increases the maximum tensile hoop and radial stresses in quenching coils and local damage may be caused.     

Analysis of Plane Phase Strains of Rods and Plates

The problem of a rod and a plate subjected to plane strain in the interval of the direct phase transformation is formulated as a nonlinear boundary-value thermoelastic problem with an implicit dependence on temperature (through a phase parameter simulating the volume fraction of new-phase crystals). An analytical solution of the problem of a rod bent into a ring and a plate bent into a tube as a result of phase strains under the action of a small end bending moment is given. A numerical analysis of the buckling problem of a titanium nickelide (alloy) rod (plate) under longitudinal compression in the interval of the direct phase transformation shows that buckling becomes possible if the compressive load is much lower than the Euler critical load calculated before the transformation. Branches of buckled equilibrium states corresponding to loads lower than the Euler load are plotted as functions of the phase parameter. In all cases considered, the deflections increase abruptly in the neighborhood of the critical points. The evolution of buckling modes is studied, and the phase-strain distributions along the rod (plate) are shown. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 156–164, March–April, 2006.     

Coupling effects in bending problems for beams of a shape memory alloy

Coupling effects of boundary-value problems that arise for shape-memory alloys whose phase compositions depend on the acting stresses and whose elastic moduli change with variation in the fraction of martensite are studied. Algorithms and results of solution of a number of beam bending problems are given. It is established that in coupled problems, the changes in the stress-strain state upon cooling proceed more smoothly than in uncoupled problems. This is due to the propagation of the front of the beginning of the transformation over the cross section. Overload of the outer layers of the beam and unloading of the inner layers of the beam are found to be related to the propagation of the front of completion of the transformation. Moscow State Aviation Institute, Moscow 125871. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 164–173, January–February, 1998.     

TiNi合金冲击相变过程中温度变化规律的实验研究

针对初始SME(shape memory effect)和PE(pseudo-elastic)状态TiNi合金试样,采用带有红外测温系统的SHPB冲击压缩装置,实时测量了冲击相变过程中两种材料试样表面瞬态温度,并根据实验结果计算了相应的温度变化。实验结果表明,冲击加载相变过程中,温度随相变应变的增大而升高,当应变最大时,温度最高;卸载过程中,对初始PE状态试样,温度降低,对初始SME状态试样,温度保持最高温度不变或降低,这同加载最高温度有关;卸载完成后,两种试样温度均高于其初始温度。计算温度结果表明,相变耗散功对加、卸载相变过程中温度变化的作用不可忽略。     

LATTICE DEFORMATION AND PHASE TRANSFORMATION FROM NANO-SCALE ANATASE TO NANO-SCALE RUTILE TiO_2 PREPARED BY A SOL-GEL TECHNIQUE

1. Introduction Titania TiO2 is a polymorphic oxide, inclusive of two common polymorphs: anatase (space group I41/amd, a0=0.37852 nm, c0=0.95139 nm) and rutile (space group P42/mnm, a0=0.45933 nm, c0=0.29592 nm) , both with octahedrally coordinated tetragonal structures. Anatase is a metastable structure and readily transforms to the stable morphic rutile upon heating (Gribb & Banfield, 1997). Because of their wide application in ceramics, catalysis, electronics, sensors and electrodes, they…     

NiTi形状记忆合金裂纹尖端热力耦合行为研究

本文对NiTi形状记忆合金I型裂纹尖端热力耦合行为进行了数值仿真分析和实验验证。建立了包含相变和热力耦合的本构模型,通过有限元计算得到了裂纹尖端附近的纵向应变、马氏体体积分数和温度场分布,依据马氏体相变情况对裂纹尖端有效应力强度因子进行了修正,揭示了加载速率对形状记忆合金裂纹尖端有效应力强度影子的影响规律。参数研究表明,随着加载频率的增加,裂纹尖端附近温度逐渐升高,马氏体相变区域逐渐缩小,有效应力强度因子呈下降趋势,形状记忆合金表现出增韧效应,有助于减缓裂纹扩展。本研究结果对于揭示热力耦合作用下超弹性形状记忆合金疲劳裂纹扩展规律具有重要参考意义。     

Stochastic thermal stresses in an FGM annular disc of variable thickness with spatially random heat transfer coefficients

The second-order statistics (i.e. mean and standard deviation) of the temperature and thermal stresses are evaluated in an axisymmetrically heated functionally graded annular disc of variable thickness with spatially random heat transfer coefficients (HTCs) on the major surfaces of the disc. This annular disc is assumed to have arbitrary variations in the HTCs and material composition along the radial direction only. The randomness in the HTCs is considered to be a random field. The stochastic temperature field is analysed by considering the annular disc to be a multilayered one with stepwise thickness variation, where each layer is assumed to have constant deterministic material properties and random HTCs. In order to evaluate the statistics, the Monte Carlo simulation method is applied to analytical solutions for the deterministic temperature and thermal stresses. The analytical solution for the thermal stresses is obtained through the use of a piecewise power function approximation for Young’s modulus. Numerical results demonstrate the effects of the magnitude of the HTC means, volume fraction distributions of the constitutive materials and thickness variation on the statistics of the temperature and thermal stresses.