Coupled temperature,stress, phase transformation calculation

The quenching of steels involves thermal, mechanical, and structural phenomena and their couplings. In this paper, a coupled thermal, phase transformation, internal stresses calculation model is presented. Especially, the stress-phase transformation interactions (transformation plasticity and kinetics modifications through internal stresses) are taken into account in this model, not only for martensitic transformation but also for diffusion dependent transformation. Using a specific case, the cooling of a cylinder made of eutectoid carbon steel, an analysis of how the stress phase transformation interactions affect the internal stresses, and plastic strain evolutions during cooling are performed. The calculated results show that internal stresses have an important effect on the kinetics of pearlitic transformation. These changes in transformation kinetics modify the levels of the internal stresses themselves and the residual stresses.     

Mathematical model of phase transformations and elastoplastic stress in the water spray quenching of steel bars

A mathematical model, based on the finite-element technique and incorporating thermo-elasto-plastic behavior during the water spray quenching of steel, has been developed. In the model, the kinetics of diffusion-dependent phase transformation and martensitic transformation have been coupled with the transient heat flow to predict the microstructural evolution of the steel. Furthermore, an elasto-plastic constitutive relation has been applied to calculate internal stresses resulting from phase changes as well as temperature variation. The computer code has been verified for internal consistency with previously published results for pure iron bars. The model has been applied to the water spray quenching of two grades of steel bars, 1035 carbon and nickel-chromium alloyed steel; the calculated temperature, hardness, distortion, and residual stresses in the bars agreed well with experimental measurements. The results show that the phase changes occurring during this process affect the internal stresses significantly and must be included in the thermomechanical model. Y. NAGASAKA, formerly Visiting Research Engineer with the University of British Columbia. S.E. CHIDIAC, formerly Research Associate with the University of British Columbia.     

In-Situ Synchrotron Diffraction Studies on Transformation Strain Development in a High Strength Quenched and Tempered Structural Steel—Part I. Bainitic Transformation

In-situ phase transformation behavior of a high strength (830 MPa yield stress) quenched and tempered S690QL1 (Fe-0.16C-0.2Si-0.87Mn-0.33Cr-0.21Mo (wt pct)) structural steel during continuous cooling under different mechanical loading conditions has been studied. Time-temperature-load resolved 2D synchrotron diffraction patterns were recorded and used to calculate the phase fractions and lattice parameters of the phases during heating and cooling cycles under different loading conditions. In addition to the thermal expansion behavior, the effects of the applied stress on the elastic strains during the formation of bainite from austenite and the effect of carbon on the lattice parameter of bainitic ferrite were calculated. The results show that small tensile stresses applied at the transformation temperature do not change the kinetics of the phase transformation. The start temperature for the bainitic transformation decreases upon increasing the applied tensile stress. The elastic strains increase with increase in the applied tensile stress.     

Plasticite de transformation durant la transformation perlitique d'un acier eutectoïde

The transformation plasticity of an eutectoid steel has been studied during the isothermal pearlitic transformation. The variations of the deformation due to transformation plasticity have been measured in function of the applied tensile stresses and of the progress of the transformation. We take into account the modification of the transformation kinetics by the applied tensile stress. In the range of transformation temperature and applied stresses studied, we observe that the deformation due to transformation plasticity increases linearly with the applied stress and the progress of the transformation. These results are compared to the models of Greenwood-Johnson and Poirier. The comparison to these models and a further analysis lead us to propose that the transformation plasticity does not only depend on mechanical properties of the phases or on the volume variation during transformation. The relative velocity of the growth interface in regard of the mean velocity of the propagation of defects due to transformation strain accommodation, must intervene and conditions the magnitude of the deformation due to transformation plasticity.     

In-Situ Synchrotron Diffraction Studies on Transformation Strain Development in a High-Strength Quenched and Tempered Structural Steel—Part II. Martensitic Transformation

In-situ synchrotron diffraction studies on the kinetics of phase transformation and transformation strain development during bainitic transformation were presented in part I of the current article. In the current article, in-situ phase transformation behavior of a high-strength (830 MPa yield stress) quenched and tempered S690QL1 [Fe-0.16C-0.2Si-0.87Mn-0.33Cr-0.21Mo (wt. pct)] structural steel, during continuous cooling and under different mechanical loading conditions to promote martensitic transformation, has been studied. Time–temperature–load resolved 2D synchrotron diffraction patterns were recorded and used to calculate the phase fractions and lattice parameters of the phases during heating and cooling cycles under different loading conditions. In addition to the thermal expansion behavior, the effects of the applied stress on the elastic strains during the martensitic transformation were calculated. The results show that small tensile stresses applied at the transformation temperature do not change the kinetics of the phase transformation. The start temperature for the martensitic transformation increases with the increasing applied tensile stress. The elastic strains are not affected significantly with the increasing tensile stress. The variant selection during martensitic transformation under small applied loads (in the elastic region) is weak.     

Dilatothermy - a new quantitative research method for allotropic transformation

The authors have developed a mathematical heat treatment model which allows to take into account the exothermal effect of allotropic transformation and to predict the microstructure of heated products. In this model, the cooling law of the product is calculated by a numerical integration of the “Fourier” equation taking into account the internal heat production due to the allotropie transformation. The process of this transformation has to be known as kinetics equations. To reach this aim, the authors have developed a new method of studying the allotropie transformation and have it applied to different recrystallised carbon steels. The method consists of two steps: experimental and numerical. From the experimental point of view, a new technique, dilatothermy, has been developed. It consists of realising simultaneously a thermal analysis and a dilatometrie one on the same specimen and of benefitting from the advantages of both methods. From the numerical point of view, the results of dilatothermy tests are treated in order to find a complete mathematical model of transformation comprising, for each microstructure, and equation describing transformation kinetics, the value of transformation heat and the mean transformation temperature of each constituent. The validity of the heat treatment model has been checked by both computation and laboratory tests. Some application cases have been considered. It is shown that the models are applicable to all types of thermal treatment carried out industrially. They allow the calculation of the steel temperature, the amount of each microstructural constituent and the temperature range in which they were formed.     

GCr15轴承钢大方坯凝固过程微观偏析模型及应用研究

建立了考虑δ/γ相变的GCr15轴承钢大方坯连铸凝固两相区溶质微观偏析模型,并应用于220 mm ×260 mm铸坯的凝固传热。结果表明:通过模型可以获得高碳钢精确的固液相线温度,以及温度与固相率的关系;GCr15轴承钢大方坯凝固过程仅析出γ相,凝固末期S、P和C元素的偏析严重;固相率越大,冷却速率对偏析度的影响更明显;S和P元素含量以及冷却速率对零塑性温度（ZDT）影响较大;采用基于凝固传热模型优化的连铸工艺后,铸坯中心碳偏析指数控制在0.961.05,且铸坯未产生内裂纹。     

CCSE船板钢连续冷却转变行为及动力学研究

 热轧在线组织性能预报系统的准确性很大程度上取决于钢的相变动力学模型,因此需要合理的模型来描述钢的相变动力学行为。采用热膨胀仪对CCSE船板钢的静态连续冷却转变曲线进行测定,并结合室温金相组织及硬度得出CCT曲线。采用Matlab编程拟合相变开始及结束温度与冷却速率之间的关系曲线,并对相变动力学模型参数进行优化,最后对比试验钢连续转变过程中的试验数据和回归模型的动力学行为曲线。结果表明,模拟计算值与试验值拟合程度很高,进一步说明该模型的合理性。     

Mathematical model of heat flow and austenite-pearlite transformation in eutectoid carbon steel rods for wire

A mathematical model incorporating both heat transfer and the transformation of austenite to pearlite in eutectoid carbon steel rods has been developed. A computer program based on the implicit finite-difference technique has been written which permits the temperature distribution and fraction of austenite transformed to be predicted as a function of cooling conditions, rod diameter and the transformation characteristics of the steel. The program takes into account the temperature-dependent heat transfer and thermophysical properties; and stresses the importance of the enthalpy of transformation. The model has been checked for internal consistency with theoretical equations, and model predictions have been compared to published industrial data for rod cooling in water at 100 °. The effect on the temperature distribution and fraction of austenite transformed of several variables,viz., rod diameter, starting temperature, heat transfer conditions, transformation characteristics and quenchant temperature, has been predicted using the model. The range of variables studied are typical of those found in industrial processes such as patenting and controlled cooling. Use of the model in the design of controlled cooling processes and in coping with problems such as segregation in wire rods is currently under study. PRAKASH K. AGARWAL, formerly Graduate Student in the Department of Metallurgical Engineering, University of British Columbia.     

Nb微合金钢连续冷却过程中铁素体晶粒尺寸的预测

基于相变动力学和热力学原理,讨论了合金元素Nb对铁素体相变的影响,建立了连续冷却过程中Nb微合金钢铁素体晶粒尺寸预测模型,模拟了应变量、轧制温度、冷却速度和固溶Nb含量对铁素体晶粒尺寸的影响,并将模型计算结果和试验结果进行比较,两者吻合良好,表明该模型能够用来预测Nb微合金钢连续冷却过程中铁素体晶粒尺寸。     

The Influence of Vanadium on Ferrite and Bainite Formation in a Medium Carbon Steel

The influence of vanadium additions on transformation kinetics has been investigated in a medium carbon forging steel. Using dilatometry to track transformation during continuous cooling or isothermal transformation, the impact of vanadium on both ferrite-pearlite and bainite has been quantified. Transmission electron microscopy and atom probe tomography have been used to establish whether vanadium was present in solid solution, or as clusters and precipitates. The results show that vanadium in solid solution has a pronounced retarding influence on ferrite-pearlite formation and that, unlike in the case of niobium, this effect can be exploited even during relatively slow cooling. The influence on bainite transformation was found to depend on temperature; an explanation in terms of the effect of vanadium on heterogeneous nucleation is tentatively proposed.     

形变对Cr-Mo低合金钢相变的影响

 Cr-Mo低合金钢在工业生产中有着重要的应用。CCT曲线是研究过冷奥氏体相转变的重要依据。通过Gleeble-3500热模拟试验机及DIL805A淬火变形膨胀仪模拟了Cr-Mo低合金钢的变形及冷却工艺,并利用超组元模型进行热力学计算分析。理论计算结果表明,形变通过提高了Cr-Mo低合金钢相变过程中的自由能进而影响了碳在奥氏体中的活度及相界面碳平衡摩尔分数,相界面碳平衡摩尔分数的变化带来了相变驱动力与形核驱动力的不同,进而影响相变的孕育期与过冷度。结果表明,相变孕育期与过冷度的变化与理论计算结果一致,热力学计算很好地解释了形变对相变的影响。同时表明形变可以提高铁素体相变临界冷速,当冷速为0.3 ℃/s时,Cr-Mo低合金钢可获得最为均匀细小的铁素体晶粒。适当的变形与冷却工艺对改善Cr-Mo低合金钢组织与性能有着重要的作用。     

Continuous Cooling Transformation Behavior and Kinetic Models of Transformations for an Ultra-Low Carbon Bainitic Steel

 The aim was to investigate transformation behavior and transformation kinetics of an ultra-low carbon bainitic steel during continuous cooling. Continuous cooling transformation (CCT) curves of tested steel were measured by thermal dilatometer and metallographic structures at room temperature were observed by optical microscope. Then transformation kinetic equation of austenite to ferrite as well as austenite to bainite was established by analyzing the relationship of lnln［1/(1-f)］ and lnt in the kinetic equation on the basis of processed experimental data. Finally, the measured and calculated kinetic behaviors of the steel during continuous cooling were compared and growth patterns of transformed ferrite and bainite were analyzed. Results showed that calculated result was in reasonable agreement with the experimental data. It could be concluded that the growth modes of transformed ferrite and bainite were mainly one dimension as the Avrami exponents were between 1 and 2.     

Evaluation of the fatigue behavior of ductile irons with various matrix microstructures

The stress-failure (S-N) curves for ferritic irons, pearlitic irons, and austempered ductile irons (ADIs) have been determined under tension-tension loading with a stress ratio of 0.1. The effects of Ti contents of up to 0.10 wt pct (resulting from the deliberate use of Ti-containing steel scrap) on fatigue behavior were investigated. It was found that ferritic and pearlitic ductile irons can contain up to 0.10 wt pct Ti without any adverse effect on fatigue behavior. In ADIs, fatigue properties deteriorate at such high Ti contents. Tests were also conducted to investigate the effects of microstructural features on fatigue properties. It was found that the effect of the graphite nodule count (the number of graphite particles on a unit area of a polished surface) on the fatigue limit is significant only in ADIs. Scanning electron microscope (SEM) analysis has shown that cracks usually initiate from surface dross-type defects. However, in ADIs, fatigue cracks can also initiate at shrinkage cavities and at surface or subsurface locations. An offset bilinear S-N curve behavior (the linear S-N curve at higher stress levels is separated from the linear S-N curve at lower stress levels) has been observed in ADIs. This is attributed to surface residual compressive stresses, which prohibit fatigue crack initiation from surface positions at lower applied stress levels. In ferritic and pearlitic ductile irons, the offset bilinear S-N curve behavior is not observed because of the rapid relaxation of the residual compressive stresses.     

铬和铝元素对低碳贝氏体钢组织和性能影响

 低碳贝氏体钢通常需要添加一定量合金元素来提升性能,为了研究合金元素铬和铝在低碳贝氏体钢中的作用,以Fe-C-Si-Mn-Mo系贝氏体钢为基础,设计了单独添加铬元素和复合添加Cr+Al元素的3种低碳贝氏体钢,研究了铬和铝的添加对连续冷却处理低碳贝氏体钢显微组织、力学性能及贝氏体相变的影响规律。结果表明,连续冷却条件下,铬可以促进低碳贝氏体钢相变趋向于更低的温度区间进行,细化贝氏体组织,从而提高强度;铝可以促进贝氏体相变动力学,但对低碳贝氏体钢意义不大。同时,添加铝会使低碳贝氏体钢组织粗化,导致强度和伸长率同时下降。综合来看,复合添加铬和铝的优化效果不如单独添加铬,单独添加铬的低碳贝氏体钢强度达到1 623 MPa,伸长率为10.5%,结果可以为低碳贝氏体钢成分设计提供依据。     

New bainite kinetics of high strength low alloy steel in fast cooling process

Based on Kolmgorov-Johnson-Mehl-Avrami analysis, a new bainite kinetics of high strength low alloy steel in fast cooling process was developed by utilizing different experimental methods.Upper bainite transformation morphological evolutions at a cooling rate of 8.3 K/s were directly observed by laser scan-ning confocal microscopy.This qualitative analysis suggests that bainite packet is more suitable to give a one-dimensional growth model if it is considered as a transformation unit.The nucleation rate of bainite packets in fast cooling process is assumed to give an a priori item.One-dimensional growth model with constant growth rate which is assumed as a function of cooling rate is adopted as well.Thus, the devel-oped new bainite kinetics is simple in expression and contains an adjustable parameter and an empirical pa-rameter.Experimental results show upper bainite and lower bainite transformations in fast cooling proces-ses.Their referential phase volume fractions are calculated by the expanded lever rule on the first deriva-tive dilatometer curves.For the similar transformation mechanisms, upper bainite and lower bainite are considered to give the same kinetics.With considering the Nakamura′s equation, the bainite kinetics is fit-ted with experimental data.Results show that bainite volume fractions and bainite transformation rates can be expressed precisely by the newly developed bainite kinetics.     

Nb对高碳钢珠光体球化的影响

摘要：设计了2种不同Nb含量的高碳珠光体钢（0.025Nb和Free -Nb），采用光学显微镜、扫描显微镜、透射电镜和硬度测试仪对两种试验钢珠光体球化前后的显微组织进行了观察和球化后的硬度进行了测量。结果表明：Nb元素可以细化高碳珠光体钢的片层间距，相同条件下具有更多的铁素体 渗碳体界面，在球化退火的第一阶段提供大量的位错和亚晶界使片状珠光体快速熔断，同时也给第二阶段碳的扩散提供高速扩散通道；细小的片层间距缩短了碳和合金元素的扩散距离，使球化转变速度加快，促进了高碳珠光体的球化。Nb元素的添加获得了细小片层间距以及更多的合金碳化物使试验钢的初始硬度偏高，球化退火前4h硬度值下降幅度较大，球化退火4h后对试验钢硬度的影响不大。     

A model of internal stress superplasticity based on continuum micromechanics

A new theoretical model is proposed to explain internal stress superplasticity under a simultaneous applied stress during thermal cycling. The analyzed material is an elasticity uniform body containing an elastic spherical inclusion, surrounded by a plastic matrix obeying a power law creep. It is assumed that only relaxation by interface diffusion is significant. At first it is shown that an inclusion dilatation can be counterbalanced by a certain matrix plastic flow. Assuming a certain stress distribution for this condition, a stationary flow on heating or cooling results. Typical behavior of this stationary flow is analyzed for the specific cases of high or low applied stresses. Under a low applied stress, the internal stress by an inclusion dilatation strongly accelerates the flow in the direction of the applied stress, which is in proportion to the applied stress, to the heating or cooling rate and to the inclusion volume fraction.     

FEM technique to study residual stresses developed in continuously cast steel during solid–solid phase transformation

Abstract

Solid–solid phase transformation of as cast steel may generate stress concentration zones in the microstructure due to the accumulation of thermodynamic (cooling and phase transformation processes) stresses in the microstructure at the interface between phases. These stress concentration zones are vulnerable regions to the formation of microcracks or the growth of flaws in these regions. In the present investigation, a finite element model was created to simulate the cooling of ASTM-SAE grade 1010 steel with different cooling rates. The phase transformation simulations were based on the continuous cooling transformation diagram. Therefore, they were quasi-real models. The models predict analytically the generation of stress concentration regions due to thermodynamic strains during the cooling of a sample from the austenite temperature range with different cooling rates.