The mathematical modeling of phase transformation of steel during quenching

In the heat treatment of steel, uneven cooling in variably introduces residual stresses in the workpiece. These residual stresses can combine with the thermomechanical stresses encountered in operation to cause premature fatigue failure of the material. A prediction of the residual and thermoelastoplastic stresses developed during heat treatment would be beneficial for component design. In this article a numerical model is developed to predict the thermoelastoplastic and residual stresses during rapid cooling of a long solid cylinder. The total strains developed during cooling of the cylinder comprise elastic, thermal, and plastic strains and strains due to phase transformation. For plastic deformation an extension of Jiang’s constitutive equations developed by Jahanian is adopted. The properties of the material are assumed to be temperature dependent and characterized by nonlinear strain hardening. For phase transformation two parts are considered: nucleation according to Scheil’s method and phase growth according to Johnson and Mehl’s law. For martensitic transformation, a law established by Koisteinin and Marburger is used. Non-additivity of pearlitic and bainitic nucleation suggested by Manning and Lorig is taken into account by means of a correction factor to Scheil’s summation of the transition from pearlitic to bainitic. The effect of phase transformation and temperature dependence of material properties is investigated. It is shown that by neglecting the temperature dependency and phase transformation in numerical calculations, the results are underestimated. The numerical results are compared with the available experimental data in the literature, and good agreement is observed.     

双相不锈钢管道全位置焊接残余应力三维有限元数值模拟

以热弹塑理论为基础，利用ANSYS非线性分析有限元程序，对双相不锈钢管道接头环焊缝残余应力进行三维数值模拟。建立了管道全位置焊接瞬态温度场和应力场三维移动热源模型，获得了环焊缝焊接接头轴向和环向残余应力的分布规律：在管道接头内表面的焊缝及近缝区的轴向和环向残余应力均为拉应力，随着离开焊缝距离的增加，由拉应力逐渐过渡为压应力。在管道接头外表面焊缝中心处的轴向残余应力为压应力，而环向残余应力为拉应力。从环向位置上的应力变化规律可以看出正半周和负半周的应力分布具有明显的对称性。研究结果为优化生产工艺，控制残余应力提供了理论依据。     

Finite element simulation of butt welded 2·25Cr–1·6W steel pipe incorporating bainite phase transformation

Abstract

This article presents a newly developed global optimisation method for the finite element simulation of welding process considering bainite transformation. In this method, the pattern search algorithm was applied to determine kinetic parameters in Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation during a continuous cooling process. Meanwhile, the JMAK equation was modified into an explicit form as a function of welding temperature field to improve calculation efficiency in the optimisation process. This methodology improves the accuracy as calculating the temperature dependent volume fraction of bainite transformation in finite element simulation. The calculated welding residual stresses considering phase transformation effects exhibited better agreement with the measured results than those calculated without phase transformation. The influences of variable cooling rates on welding residual stresses were also investigated.     

温度和相变影响的弹塑性本构关系及应用

通过考虑温度和相变对等效物性参数的影响,建立了包含附加应力和应变的弹塑性增量本构关系,并采用该本构关系和ABAQUS软件构建了淬火过程的数值模拟平台.该本构模型引入的附加应力和应变分别由温度变化和相演化引起的.具有明确的物理意义.通过对26Cr2Ni4MoV钢的圆筒零件水淬过程的模拟表明,该模型能够正确地分析残余应力沿半径方向的分布规律.并且在截面中间部位残余应力值和靠近外表面的应力峰值与实测值更加接近,说明全面考虑温度和相变影响的弹塑性增量本构关系可改善模拟计算的精度.     

焊接顺序对薄壁八边形管-板焊接接头残余应力的影响（英文）

考虑实际焊接中热-机械的直接耦合效应,通过热-弹塑性有限元法建立三维有限元模型来研究不同焊接顺序对薄壁6061铝合金焊件焊后残余应力分布的影响,采用单道TIG焊接实验来验证模拟结果的准确性;利用九种不同的焊接顺序来研究八边形管和底板之间焊后残余应力的分布状态。结果表明,焊缝及其附近存在的初始残余应力并不影响最终残余应力的分布;选择合理的焊接顺序可以有效降低八边形管-板接头的残余应力。     

Predictive modeling and experimental results for residual stresses in laser hardening of AISI 4140 steel by a high power diode laser

A predictive model for residual stresses induced in a laser hardened workpiece of AISI 4140 steel with no melting has been developed and experimentally verified. A transient three-dimensional thermal and kinetic model is first solved to obtain the temperature and solid phase history of the workpiece, which is then sequentially coupled to a three-dimensional stress model to predict residual stresses. The phase transformation strains are added to the thermal strains at each time step during the heating and cooling cycles to obtain the resultant residual stresses in the workpiece. The importance of considering phase transformation has been explained through the comparison of the magnitudes of residual stresses with and without the inclusion of phase transformation kinetics. The model predicted strong compressive residual stresses of about 200 MPa in the heat affected zone due to austenite-to-martensite transformation. The predictions matched well with the X-ray diffraction measurements.     

低碳钢管道焊接残余应力有限元分析

利用ＡＤＩＮＡ非线性分析有限元程序,对低碳钢管道环焊缝接头焊接残余应力进行有限元分析。在热弹塑性分析中考虑了材料热物理和力学性能依赖于温度变化。结果表明：在管道接头内表面焊缝中心及近缝区轴向和环向残余应力均为拉应力,随离开焊缝距离的增加,逐渐过渡为压应力。在管道接头外表面焊缝中心处的轴向残余力为压应力,而环向残余应力为拉应力。计算预测值和实侧值基本一致,表明有限元法能够经济而有效地预测管道环焊缝接头的焊接残余应力。     

相变塑性对低温相变钢焊接接头残余应力计算精度的影响

基于JWRIAN焊接数值模拟软件,开发了考虑固态相变的热-冶金-力学耦合的数值计算方法来模拟低温相变钢的焊接残余应力.重点讨论了固态相变中的体积变化、屈服强度变化和相变塑性对焊接残余应力的影响.结果表明,相变引起的体积变化和屈服强度变化对最终的焊接残余应力分布和大小有显著影响,相变塑性与前两者相比较影响相对较小,但它对焊缝和热影响区在相变过程中的应力变化趋势有一定的减缓作用,从而适度"松弛"了残余应力.     

核电SA508-3钢厚壁圆筒纵向焊接残余应力分析

针对由某公司生产首次应用到核电设备上的SA508-3钢,为了获得焊接残余应力分布及规律,采用ANSYS有限元软件对60 mm厚圆筒纵焊的焊接接头进行温度场及残余应力数值模拟,并将模拟结果与相同工艺条件下焊接试验结果进行比较验证.结果表明,模拟结果与试验结果基本吻合;焊接时热源周围极窄区域温度高,梯度大,远离热源温度峰值急剧下降;圆筒外表面残余应力大于内表面残余应力;焊缝及近焊缝区的残余拉应力值较大,远离焊缝中心残余拉应力值逐渐减小;圆筒两端和中部的残余应力在方向上或数值大小上不同;这对控制圆筒残余应力提供了理论依据.     

基于工作温度8Cr4Mo4V钢制轴承外套圈尺寸及应力变化特征分析

测定了8Cr4Mo4V钢制直壁圆筒形轴承外套圈在不同工作温度下内外径尺寸及表面残余应力的变化特征,分析了引起轴承外套圈尺寸变化和表面残余应力变化的因素,并对轴承外套圈进行了微观组织观察。结果表明,在不同工作温度下,保温300 h后轴承外套圈的尺寸均增加1~2 μm,轴承外套圈外径的尺寸变化量大于内径尺寸变化量;工作温度下残留奥氏体转变为马氏体,马氏体深度回火,均会使轴承外套圈内径表面残余压应力增加。工作温度为150 ℃时,内、外径表面残余压应力绝对值增加幅度最大,随着工作温度的提高,表面残余压应力绝对值增加幅度降低。轴承外套圈内外径表面残余压应力的增大是由于轴承钢中残留奥氏体转变为马氏体,发生体积膨胀引起的。马氏体发生深度回火导致体积收缩,外套圈内外径收缩尺寸量不同将引起内外径表面的残余压应力值变化不同,尺寸收缩将导致内径残余压应力增大,而外径残余压应力减小。     

A composite cylinder model for the prediction of residual stresses in gamma-titanium composites

An experimental study of the residual stress formation and evolution in γ-titanium-based composite material was completed for some important processing and heat treatment conditions. A concentric cylinder model based on Norton’s creep law with the coefficients replaced by new terms related to time and temperature was developed by a combination of viscoplasticity and thermoelastic analysis of concentric cylinder domains representative for the matrix and the fiber. The x-ray diffraction (XRD) technique was used to measure average residual stresses at the neighborhood of Saphikon fibers. The composite was fabricated by hot isostatic pressing. The residual stress at the matrix decreased as the temperature of the heat treatment increased up to an optimum value, after which the residual stress started to build up despite the increase in the annealing temperature. This phenomenon was depicted through the numerical model as well as in the XRD.     

铝合金薄壁圆筒纵直缝焊接残余应力数值模拟

利用热弹塑性有限元方法对薄壁铝筒纵直焊缝TIG焊进行了数值模拟计算,建立了分析模型,定量地描述了准稳态温度场和残余应力场计算数值以及在整个圆筒上的分布情况,并进行了试验验证.结果表明,焊接时热源周围极窄区域温度高、梯度大,离开热源,温度峰值急剧下降;纵向残余应力在焊缝及热影响区为拉应力,最大值位于焊缝长度中心截面上;纵向残余应力在圆周上表现出拉压区交替变化的趋势.利用应力释放法对焊接件进行应力测量,测量结果与模拟计算结果吻合良好.     

The application of rational approximation in the calculation of a temperature field with a non-linear surface heat-transfer coefficient during quenching for 42CrMo steel cylinder

The calculation of a temperature field has a great influence upon the analysis of thermal stresses and stains during quenching. In this paper, a 42CrMo steel cylinder was used an example for investigation. From the TTT diagram of the 42CrMo steel, the CCT diagram was simulated by mathematical transformation, and the volume fraction of phase constituents was calculated. The thermal physical properties were treated as functions of temperature and the volume fraction of phase constituents. The rational approximation was applied to the finite element method. The temperature field with phase transformation and non-linear surface heat-transfer coefficients was calculated using this technique, which can effectively avoid oscillationin the numerical solution for a small time step. The experimental results of the temperature field calculation coincide with the numerical solutions.     

一种消除小直径管道焊接应力技术的数值分析

小直径管道的应力腐蚀问题一直是工程界较难解决的问题，作者针对这一难题，提出了一种新型的消除应力方法——温差形变处理技术。利用MSC．Marc大型通用非线性有限元分析软件，对小直径管道环缝焊接接头的原始残余应力及温差形变法消除残余应力进行了有限元模拟，得到了一系列关于加热位置、加热宽度和加热持续时间的数据和规律。结果表明，采用温差形变处理技术，在内外表面的焊缝处都可以得到零值左右的残余应力，从而为进一步的试验分析工作和工程应用奠定了基础。     

Applied mechanics in grinding—VI. Residual stresses and surface hardening by coupled thermo-plasticity and phase transformation

The present study aims to investigate the residual stresses and surface hardening in ground components caused by the coupled effect of thermo-plasticity and phase transformation. A feasible numerical method was developed to accommodate appropriately the phase transformation in a workpiece experiencing critical temperature variation during grinding. The change of material properties was modelled as a function of temperature history. It found that if material properties are temperature-independent, the residual stresses in both the grinding direction and that perpendicular to it are tensile. The maximum residual stress in this case does not vary with the further increment of grinding heat. When material properties are temperature-dependent, however, the rise of grinding temperature promotes surface hardening and increases the maximum residual stress. The study showed that the volume growth associated with phase change plays an important role in the formation and nature transition of residual stresses. Nevertheless, residual stresses in the no-martensite zone is nearly unaffected by surface hardening and volume change. This paper offers insight into the understanding of surface hardening mechanism introduced by grinding.     

盲孔法测量非均匀残余应力时的释放系数

盲孔法测量沿深度非均匀的残余应力时,积分法是最常用的计算方法,其释放系数矩阵[a],[b]对计算精度有很大影响.由于在标定释放系数矩阵时假定各层上的残余应力均匀分布,当应力梯度变化较大时会引起较大的计算误差.文中首先建立了标定释放系数矩阵的三维有限元模型,并通过模拟均匀残余应力场验证了其有效性.在此基础上分析了积分法标定的释放系数矩阵用于计算沿深度非均匀残余应力时的误差,并提出了二次标定的修正方法.结果表明,采用二次标定的释放系数矩阵计算得到的残余应力值更接近于真实应力.     

1Cr12Ni3Mo2VN钢高频淬火过渡区的喷丸强化和残余应力

采用不同的喷丸工艺,分析了喷丸强度对1Cr12Ni3Mo2VN钢局部高频淬火试样的表面质量与残余应力沿层深变化的影响.研究表明,喷丸一方面在试样表层形成了有益的残余压应力场,另一方面增大了试样表面的粗糙度,喷丸应综合考虑两者的影响;对于试验所用的材料和热处理状态,喷丸强度为0.5A的喷丸工艺优于喷丸强度为0.4A和0.6A的喷丸工艺.     

固态相变对P91钢激光对接接头残余应力的影响

基于SYSWELD软件,模拟了P91钢激光对接焊时的温度场和焊接残余应力,并探讨了固态相变产生的体积膨胀、屈服强度变化和相变塑性对焊接残余应力的影响. 数值模拟结果表明,体积膨胀和屈服强度变化对焊接残余应力的大小与分布有显著的影响; 相变塑性在相变过程中有"应力松弛"效应,对焊缝和热影响区的纵向和横向残余应力的值有一定程度的影响. 对比数值模拟结果与试验结果可知,采用文中建立的有限元模型计算得到的残余应力与中子法测量得到的结果基本吻合,在考虑相变塑性的情况下,计算结果与实测值吻合更好.     

冷凝罐接管与筒节焊接应力的有限元分析

通过ANSYS有限元软件,对冷凝罐接管与筒节多层焊的焊接过程进行了数值模拟。针对接头的马鞍形空间轨迹特点,编写了沿焊道移动的热源方程,并采用逐层激活与逐步激活的生死单元技术实现了接头的熔敷过程模拟,使模拟与实际施焊过程相符．通过模拟研究了焊接过程动态温度场、应力场和焊接残余应力的分布状况。结果表明：焊接残余应力主要集中在接头的焊缝区和热影响区,周向应力与径向应力均在内层焊道中较高。在焊缝外表而沿接管周向应力为拉伸应力,其余为压应力,内表面三向均为拉仲应力,筒节一侧的焊趾与焊根部位应力较高,且为三向拉伸应力,是裂纹易发部位。文中所建立的沿马鞍形轨迹移动的热源方程可用于该类接头的焊接过程研究.     

固态相变对P91钢焊接残余应力的影响

基于SYSWELD软件,首先模拟了P91的Satoh试验,得到加热、冷却过程中的温度-应力曲线. 通过Satoh试验探讨了因固态相变引起的体积变化、屈服强度的变化和相变过程中的超塑性对残余应力形成过程的影响. 随后,以平板TIG重熔模型为研究对象,系统讨论了固态相变对焊接残余应力分布和大小的影响. 结果表明,体积膨胀对焊接残余应力的形成过程和最终应力的大小与分布有显著影响,它不仅可改变焊缝及HAZ处的应力大小,甚至可能改变应力的符号. 相变引起的屈服强度变化对残余应力的形成及最终应力值的大小也有较明显的影响. 相变塑性的影响比前两者小,它在相变过程中有一定的"应力松弛"效应.