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.     

Fine tuning straightening process using genetic algorithms and finite element methods

Abstract

The process of straightening steel sections is used not only to actually straighten the product but also to reduce its internal residual stresses. Fine tuning this process within an industrial plant is complicated because of the time needed for conducting the tests and the difficulties in measuring the final residual stresses. This paper presents a methodology based on genetic algorithms and finite element analysis that seeks the best position of the rollers to produce a straightened product with the minimum amount of residual stresses. The process consists of simulating multiple roller positions using a previously validated finite element model and analysing the resulting residual stresses. Genetic programming is used to choose the best solutions that will give rise to the next generation of individuals. For several generations, the system combines a series of optimum solutions in which residual solutions are minimised. The best solutions obtained enable the rollers to be positioned in a way that guarantees a good end quality for the product.     

百米U75V钢轨矫直前冷却过程弯曲变形的有限元分析

通过研究百米钢轨冷却的边界条件,采用三维瞬态非线性有限元法计算分析了百米U75V平直钢轨矫直前冷却过程中的弯曲变形变化规律。结果表明,平直钢轨在冷却过程中的弯曲变形是一个循环反复的过程,但钢轨最终是弯向轨头的;在考虑钢轨与冷床摩擦作用的情况下,平直钢轨终冷后,其变形特点是中间平直、两端弯曲,端部弯曲范围约为18 m。     

Applications of Computational Fluid Dynamics (CFD) in iron- and steelmaking: Part 2

Abstract

After presenting a review of some applications of computational fluid mechanics (CFD) to ironmaking processes in Part 1, the authors now explore the use and extent of CFD in steelmaking and steel casting processes. Steelmaking processes generally include the basic oxygen furnace, electric arc furnace or equivalent, the ladle and continuous casting and incorporating a tundish and moulds. All these steelmaking processing steps involve highly coupled complex transport phenomena. The use of CFD to model such processes has been an active area of research for the last three decades. Many models have been developed to predict mixing behaviour, slag foaming, gas–liquid interactions, multiphase flows, as well as heat and mass transfer aspects. In the present review, the role of CFD in modelling steelmaking operations is reviewed, discussed and critiqued.     

Consequences of transformation plasticity on the development of residual stresses and distortions during martensitic hardening of SAE 4140 steel cylinders

Residual stresses and distortions developing during martensitic hardening of steel can be quantitatively determined by finite element calculations, if the underlying processes are adequately modelled and the materials and process data necessary are known. In this context also transformation plasticity effects have to be taken into account. Model calculations for SAE 4140 steel cylinders demonstrate the influence of these effects on the developing residual stresses. Using a special device which allows martensitic transformation under constant external loads, for SAE 4140 the transformation plasticity constant K = 4.2 · 10^?5mm²/N is determined. With this constant and assuming realistic heat transfer conditions, the development of residual stresses and distortions of SAE 4140 cylinders with a diameter of 30 mm and a length of 90 mm is modelled. The calculated results are in good agreement with experimental findings.     

Optimising tension levelling process by means of genetic algorithms and finite element method

Abstract

This paper presents a method based on genetic algorithms and the finite element method which is useful for automatically adjusting the parameters of a tension levelling process. First, the optimum parameters of the steel to be used in the simulation programme are sought. The process consists of simulating controlled cyclical deformation tests on finite element (FE) models of standard steel test pieces with different laws of cyclical behaviour. Genetic algorithms are used to optimise the parameters of the simulation model so that the behaviour of the material is as close as possible to the results obtained in real experimental tests. This ensures that the behaviour of the material in the FE model is as realistic as possible. The model of behaviour of the material selected is used to design and check out a second tension levelling FE model. Based on this second model, the roll penetration, the lengthwise tension and the strip feedrate are adjusted. There is also optimisation with genetic algorithms so that the final residual tensions in the product are below a specified threshold and as even as possible. For a solution to be considered as valid, it must be confirmed that the steel plate is subject to the tensions envisaged at various process control points. From the best solutions found, the one with the fastest feedrate is selected so as to maximise output.     

热轧中碳宽带钢冷却过程横向弯曲变化规律的数值模拟

 针对目前困扰热轧中碳高强度宽带钢生产的横向弯曲缺陷,使用有限元软件ABAQUS结合FORTRAN语言编写子程序,建立热轧带钢轧后冷却有限元模型。通过模型计算,分析带钢轧后冷却过程中上下表面的冷却不均以及带钢厚度对带钢横向弯曲的影响。研究结果表明,相同厚度情况下,带钢上下表面冷却不均程度越大,带钢横向弯曲程度越严重,上下表面相同冷却效率比的情况下,带钢越厚,带钢横向弯曲越严重。冷却过程中,受温度变化和相变的综合影响,带钢弯曲方向和大小会发生较大变化,且冷却过程中带钢弯曲量最大值远远大于冷却结束后横向弯曲量。     

Applications of Computational Fluid Dynamics (CFD) in iron- and steelmaking: Part 1

Abstract

All operations in process metallurgy involve complex phenomena comprising momentum, heat, and/or mass transport; iron- and steelmaking is not an exception. Transport phenomena, i.e. fluid flows, heat transfer and mass transfer, play a dominant role in process metallurgy since their respective laws govern the kinetics of the various physical phenomena occurring in ironmaking and in steelmaking. These phenomena include such events as three-phase reactions, entrainment of slag and gas in liquid steel, vacuum degassing, alloy melting and mixing, the movements and flotation of inclusions, melt temperature losses, residence times in a metallurgical reactor, erosion of refractory linings, etc. In all these aspects, the evolution in our techniques and abilities to model single and multiphase flows and their attendant heat and mass transfer processes has contributed significantly to our understanding and effectively operating these processes, to designing improvements, and to developing new processes. To be ignorant of these matters can doom a processing operation to the scrap heap of metallurgical failures. Computational fluid dynamics (CFD) and computational heat and mass transfer has been a very effective tool over the last three decades, for modelling iron- and steelmaking processes, starting from the blast furnace up to continuous casting and beyond. With the advent of commercial CFD packages and ever increasing computational power through parallel processing, CFD has now become the dominant approach for predicting various aspects in iron- and steelmaking processes. In Part 1 of this review paper, the applications of CFD in ironmaking processes are thoroughly reviewed, discussed and critiqued. In Part 2, fluid flows and CFD in steelmaking and steel casting processes are similarly reviewed and critiqued.     

Modelling Transformation Induced Plasticity – an Application to Heavy Steel Plates

The time‐dependent inhomogeneous temperature distribution during the cooling of steel plates gives rise to thermal strains which, in turn, generate plastification and thus residual stresses. Moreover, transformation from the parent austenite phase into a product phase typically entails not only metallurgical strains but also accounts for transformation induced plasticity (TRIP), which again generates transformation related residual stresses. It is the goal of this paper to build a unified model that takes into account all relevant contributions to the total strain rate, i.e., elastic, plastic, thermal, metallurgical and TRIP strain contributions. The material parameters relevant for TRIP are determined by means of dilatometric tests as well as by purely numerical means. For the evolution of the product phase a kinetic relationship will be presented that allows differentiating between different local cooling rates. It is set up with an Avrami‐like approach, specially designed for complex cooling histories. The material model is implemented into the commercial finite element package ABAQUS, which allows to simulate the evolution of the residual stresses in heavy steel plates after complete cool‐down to room temperature.     

热轧槽钢轧后冷却过程模拟

利用有限元软件对热轧20#槽钢轧后冷却过程进行模拟,获得了轧后冷却过程温度场变化规律及典型部位的温度变化.通过实际测量值进行验证,模拟结果与实际冷却过程吻合较好.为研究槽钢轧后冷却规律提供了一种方法,对设置终轧温度及改善冷却条件提供了理论依据,进而有利于保证产品性能和减小冷却变形.对生产过程中轧制工艺制定、残余应力研究具有指导意义.     

Residual stress-affected diffusion during plasma nitriding of tool steels

Plasma nitriding of tool materials is common practice to improve the wear resistance and lifetime of tools. Machining-induced compressive residual stresses in shallow layers of some tenths of microns are observed accompanied by other characteristic properties of machined surfaces in these high-strength materials. After plasma nitriding of M2 high-speed steel, previously induced compressive residual stresses remain stable and the depth of diffusion layers decreases with increasing compressive residual stresses. This article reports investigations of plasma nitrided samples with different levels of residual stresses induced prior to the nitriding process. For comparison, experiments with bending load stresses during plasma nitriding have also been carried out. The plasma nitriding treatment was performed at constant temperature of 500 °C with a gas mixture of 5 vol pct N₂ in hydrogen. Nitriding time was varied from 30 to 120 minutes. All samples were characterized before and after plasma nitriding concerning microstructure, roughness, microhardness, chemical composition, and residual stress states. Experimental results are compared with analytical calculations on (residual) stress effects in diffusion and show a clear effect of residual and load stresses in the diffusion of nitrogen in a high-strength M2 tool steel.     

热处理对典型低合金钢棒材力学性能影响的机理

棒材在线淬回火热处理不仅可显著降低成本,而且有利于改善材料性能.通过实验室试验、组织性能检测、有限元模拟等就典型45#钢和40Cr钢进行研究,结果表明:45#钢和40Cr钢淬硬层深度分别约为4.8,18 mm,临界冷速约72,16℃/s;600℃高温回火保温20 min后,钢中碳化物分布弥散均匀,强塑性和沿横截面均匀性...     

热轧带钢的冷却参数与翘曲关系

针对卷取温度为500℃的12 mm厚X70管线钢热轧带钢,利用MARC有限元软件建立层流冷却过程中的热-力-相变耦合的数学模型,计算两种下上冷却水比时层流冷却过程中温度场、应力、应变、相变体积分数和翘曲度随时间的变化.结果表明:1.25水比的冷却过程中,厚度方向上各面的冷却速度不一致,导致水冷前期带钢上下表面应变不同,带钢会产生向上的翘曲,冷却过程中边部最大的翘曲量达到21.84 mm;水冷后期带钢板形会逐渐恢复平直,但由于水冷过程中发生塑性变形,终冷时厚度方向上贝氏体含量的差异,卷取时带钢边部依然有-9 mm的翘曲量.上下表面的不均匀冷却是引起翘曲的根本原因.在保证X70管线钢性能条件下,采用1.58的下上水比工艺,卷取时边部翘曲量仅为-0.58 mm,合适的下上水比能大幅度减小层流冷却过程中带钢的横向翘曲.      

A Simple Model of the Mold Boundary Condition in Direct-Chill (DC) Casting of Aluminum Alloys

An accurate thermofluids model of aluminum direct-chill (DC) casting must solve the heat-transfer equations in the ingot with realistic external boundary conditions. These boundary conditions are typically separated into two zones: primary cooling, which occurs inside the water-cooled mold, and secondary cooling, where a film of water contacts the ingot surface directly. Here, a simple model for the primary cooling boundary condition of the steady-state DC casting process was developed. First, the water-cooled mold was modeled using a commercial computational fluid dynamics (CFD) package, and its effective heat-transfer coefficient was determined. To predict the air-gap formation between the ingot and mold and to predict its effect on the primary cooling, a simple density-based shrinkage model of the solidifying shell was developed and compared with a more complex three-dimensional (3-D) thermoelastic model. DC casting simulations using these two models were performed for AA3003 and AA4045 aluminum alloys at two different casting speeds. A series of experiments was also performed using a laboratory-scale rectangular DC caster to measure the thermal history and sump shape of the DC cast ingots. Comparisons between the simulations and experimental results suggested that both models provide good agreement for the liquid sump profiles and the temperature distributions within the ingot. The density-based shrinkage model, however, is significantly easier to implement in a CFD code and is more computationally efficient.     

H型钢连铸质量缺陷和浸入式水口结构优化的数值模拟

研究的H型钢Q235(/%:0.06c,0.30si,1.60Mn,0.010P,0.003S,0.025Mo,0.40Ni,0.017Ti,0.15Cu)由80 t LD-LF-喂硅钙线-28 t中间包-430 mm×300 mm×85 mm H型连铸一热轧工艺生产。由于H型铸坯易产生纵裂纹缺陷,根据H型连铸坯采用直通型浸入式双水口浇铸的实际工艺参数建立数学模型,采用流体有限元软件CFD进行结晶器流场和温度场分布汁算,得出直通型双水口浇铸时,熔池冲击深度大,不利夹杂上浮;液面得不到足够热量补充,导致坯壳过早凝固,不利于化渣。数值模拟结果表明,改用三侧孔水口进行浇铸,避免了直通型水口的不利因素,流场和温度场分布合理,可降低漏钢事故和裂纹发生的机率。     

Elastoplastic finite element analysis of short-fiber-reinforced SiC/Al composites: effects of thermal treatment

Elastoplastic finite element analyses of realistic models of short-fiber-reinforced composites were extended to include the effects of prior thermal treatments on predictions of subsequent mechanical properties. Two three-dimensional models were used, one in which the fiber ends were transversely aligned and another in which they were staggered. Both models were found to be necessary for accurate predictions of the behavior of higher volume fraction composites. The temperature dependence of the yield stress of the matrix material was explicitly included in the analysis. The spatial and temporal history of calculated. The room temperature residual stresses were also predicted. Both the plastic deformation and the residual stresses in the matrix were spatially non-uniform and varied rapidly from the regions near the ends of the fiber to those near the midpoint. Predictions of subsequent tensile stress-strain properties were in good quantitative agreement with experiments. The presence of residual stresses and locally deformed regions caused the tensile behavior to differ from the compressive behavior. These differences were complex and depended on the volume fraction and aspect ratio of the reinforcement. The analyses provide detailed insight into the deformation mechanisms of these composites.     

成形工艺对冷弯方管残余应力及焊接微观组织的影响简

 冷弯方管成形有“直接成方”和“圆成方”两种方式。为了研究成形工艺对于产品的不同影响,以规格为100mm×100mm×6mm,材料为Q235的两种成形工艺的方管为研究对象,采用钻孔法对方管各个部位的残余应力进行了测量,并观测了焊缝处的显微组织。研究结果表明,不同成形工艺对纵向残余应力的分布影响较大,焊缝处的残余应力最大。“圆成方”过程中施加较大的焊接压力使得其焊接热影响区宽度小于“直接成方”工艺条件下焊接热影响区的宽度,且抑制了奥氏体晶粒长大,冷却后获得较为细小均匀的晶粒。     

Three-dimensional modelling of thermal residual stresses and mechanical behavior of cast SiC/A1 particulate composites

Thermal residual stresses developed during casting of SiC/aluminum particulate-reinforced composites were investigated as a function of cooling rate and volume fraction of particles using thermo-elastoplastic finite element analysis. The phase change of the matrix during solidification and the temperature-dependent material properties as the composite is cooled from the liquidus temperature to room temperature were taken into account in the model. Further, the effect of thermal residual stresses on the mechanical behavior of the composites was also studied. Based on the study, it was found that the matrix undergoes significant plastic deformation during cool down and has higher residual stress distribution as the cooling rate increases. The model which does not include the solidification of the matrix tends to overestimate the residual stresses in the matrix and underestimate the tensile modulus of elasticity of the composites. In addition, the presence of thermally induced residual stresses tends to decrease the apparent modulus of elasticity and increase the yield strength of the composites compared to those without residual stresses.     

Spray Cooling Heat Transfer and Calculation of Water Impact Density for Cooling of Steel Sheet Materials by Inverse Process Modelling

Modern steel grades require accurate temperature control during processing. The cooling section technology has to deliver prescribed cooling rates while fulfilling specific constraints, e.g. on the minimum surface temperature. For all material thicknesses, numerical cooling system set value prediction is advantageous and above 10 mm, the possible cooling rates and the experimental parameter determination are limited by physical constraints. Laboratory measurements provide quantitative experimental data on the heat transfer coefficient (HTC) depending on the cooling system parameter water impact density and the temperature difference. The desired final material properties determine temperature control and cooling rate. This information is used to predict the optimum cooling section set values for a specific cooling task. The inverse modelling calculations use a simple cooling section process model. Illustrative examples for optimum cooling of strip or sheet material using water spray cooling demonstrate the approach. Additionally, the physical limitations due to the finite heat conductivity of the strip are calculated and discussed.