Three-dimensional finite element modeling of gas metal-arc welding

The modeling of the gas metal-arc (GMA) welding process in three dimensions for moving heat sources has been attempted using the finite element method. The occurrence of finger penetration in the weldment resulting from a streaming type of metal transfer at high contents is explained by assuming that the heat content of transferring droplets is distributed in a certain volume of the workpiece below the arc. Volumetric distribution of the heat content of transferring droplets has been considered as an internal heat-generation term, and the differences between penetration characteristics in two cases of globular and streaming conditions of metal transfer have been analyzed. It is shown that weld penetration depends on the depth at which the droplets distribute their energy inside the workpieces. Temperature dependence of thermophysical properties,i.e., thermal conductivity and specific heat, has been included. Latent heat is incorporated by a direct iteration method. Heat losses from the plate caused by convection and radiation are also considered. The model is validated by predicting the weld-bead dimensions and comparing them with experimental data.     

Computer simulation of transformation induced plasticity using finite element method

Some important aspects associated with the transformation induced plasticity in Al₂O₃ZrO₂ are analyzed using a computer simulation based on Finite Element Method (FEM). These aspects include (i) an estimation of the residual stress in the second phase, arising during post fabrication cooling, which affects the critical stress for transformation, (ii) the constitutive behavior of the material during the dilatational transformation of ZrO₂ and (iii) the crack deflection due to the transformation. This simulation study was conducted for angular as well as spherical shapes of second phase particles and also for varying volume fractions of the second phase, using a master finite element mesh. Apart from this numerical experiment, analytical expressions were derived for the residual stress and the constitutive behavior, assuming spherical shape for the second phase particles. The analysis of the constitutive behavior mainly consists of an estimation of the composite modulus and of the irreversible strain due to the transformation. The comparison of the analytical solutions with the results obtained through the simulation shows a very good agreement. Using the simulation of crack deflection, the increase in crack surface area due to the transformation was computed, to approximately estimate the improvement in fracture toughness due to the crack deflection mechanism.     

Thermomechanical analysis of direct chill casting using finite element method

The transient nature of the start-up phase is the most critical phase in the direct chill (DC) casting during which the quality of the ingot is questioned. The hot crack and cold crack are the two major problems in the DC casting which originate during and after the solidification. In this work, the thermal, metallurgical, and the mechanical fields of DC casting are modeled. The attention is focused on the mushy state of alloy where the chances are high for the hot tearing. The heat conduction and metallurgical phase-change phenomenon are modeled together in a strongly coupled manner. An isothermal staggered approach is followed to couple the thermal and mechanical parts within a time step. Finite element method is used to discretize the thermal and mechanical field equations. A temperature-based fixed grid method is followed to incorporate the latent heat. The mushy state of alloy is characterized through the Norton-Hoff viscoplastic law and the solid phase is modeled through the Garafalo law. An axisymmetric round billet is simulated. The casting material is considered as AA1201 aluminum alloy. It is found that all the components of stress and viscoplastic strain are maximum at the billet center. Further, the start-up phase stresses and strains are always higher than the steady state phase. Therefore, the chances of hot crack formation are higher during the start-up phase and specifically at the billet center. It is proved that through the ramping procedure, the vulnerability of start-up phase can be lowered.     

A new finite element model for welding heat sources

A mathematical model for weld heat sources based on a Gaussian distribution of power density in space is presented. In particular a double ellipsoidal geometry is proposed so that the size and shape of the heat source can be easily changed to model both the shallow penetration arc welding processes and the deeper penetration laser and electron beam processes. In addition, it has the versatility and flexibility to handle non-axisymmetric cases such as strip electrodes or dissimilar metal joining. Previous models assumed circular or spherical symmetry. The computations are performed with ASGARD, a nonlinear transient finite element (FEM) heat flow program developed for the thermal stress analysis of welds.* Computed temperature distributions for submerged arc welds in thick workpieces are compared to the measured values reported by Christensen¹ and the FEM calculated values (surface heat source model) of Krutz and Segerlind.² In addition the computed thermal history of deep penetration electron beam welds are compared to measured values reported by Chong.³ The agreement between the computed and measured values is shown to be excellent.     

The study of surface-active element oxygen on flow patterns and penetration in A-TIG welding

A three-dimensional mathematical model was developed to simulate the flow patterns and temperature distributions in a moving A-TIG weld pool of 304 stainless steels with different oxygen content using PHOENICS software. It is shown that the surface-active element, oxygen, is important, because it affects the weld shape by changing the flow patterns in the weld pool. The weld bead penetration and the depth/width ratio increase first sharply and then remain nearly a constant with increasing oxygen content. Depending upon the oxygen contents, three, one, or two vortexes that have different positions, strength, and directions may be found in the weld pool. Oxygen can cause significant changes in the weld shape by varying the sign of the surface tension coefficient. The situation with the maximum surface tension moves from the edge to the center with increasing oxygen content. As oxygen content exceeds a critical value, a positive surface tension coefficient dominates the flow patterns. The vortexes with opposite directions caused by positive surface tension coefficient can efficiently transfer the thermal energy from the arc, creating a deep weld pool. The critical oxygen content increases with the increase of the welding current.     

Mechanism and optimization of oxide fluxes for deep penetration in gas tungsten arc welding

Five single oxide fluxes—Cu₂O, NiO, SiO₂, CaO, and Al₂O₃—were used to investigate the effect of active flux on the depth/width ratio in SUS304 stainless steel. The flux quantity, stability, and particlesize effect on the weld-pool shape and oxygen content in the weld after welding was studied systematically. The results showed that the weld depth/width ratio initially increased, followed by a decrease with the increasing flux quantity of the Cu₂O, NiO, and SiO₂ fluxes. The depth/width ratio is not sensitive to the CaO flux when the quantity is over 80×10⁻⁵ mol on the 5×0.1×50 mm slot. The Al₂O₃ flux has no effect on the penetration. The oxygen content dissolved in the weld plays an important role in altering the liquid-pool surface-tension gradient and the weld penetration. The effective range of oxygen in the weld is between 70 and 300 ppm. A too-high or too-low oxygen content in the weld pool does not increase the depth/width ratio. The decomposition of the flux significantly depends on the flux stability and the particle size. Cu₂O has a narrow effective flux-quantity range for the deep penetration, while the Al₂O₃ flux has no effect. The SiO₂ flux with a small particle size (0.8 or 4 μm) is a highly recommended active flux for deep penetration in actual gas tungsten arc welding (GTAW) applications.     

Modelling of the cooling of a structural steel section using the finite element method

B.Tech. Rajeev Baskiyar, principal research engineer, R&D Centre for Iron and Steel, Steel Authority of India Ltd., India. The paper deals with the simulation study of the cooling of hot‐rolled angles. The heat transfer model has been developed using the finite element method. Comparative analysis has been done of alternative cooling strategies in the context of the uniformity of the temperature profile engendered by each for camber alleviation.     

面心纯铝轧制织构的晶体塑性有限元模拟

基于率相关晶体塑性本构模型,分别将Taylor模型和有限单元模型两种多晶模型嵌入大型有限元程序ABAQUS,实现了晶体塑性学有限元模拟.直接将电子背散射衍射(EBSD)获取的晶粒初始取向输入晶体塑性有限元模型,预测了两种不同应变情况下面心1050纯铝轧制织构的演化.模拟结果与EBSD实验测得的织构演化结果有较好的一致性,随着变形程度的增加,预测织构与实测织构变得更加锋锐.经过比较,Taylor型模型预测出了{4411}〈11118〉的Dillamore取向,而有限单元模型预测出了铜型织构取向,比Taylor模型预测结果更接近实验验证结果.两种模型并不能预测出{011}〈211〉黄铜取向、{123}〈523〉S取向、{011}〈100〉Goss取向及其他理想取向.     

Biomechanical aspects of the insect wing: an analysis using the finite element method

Insect wings appear as highly functional and largely optimized mechanical constructions. A series of stabilizing constructional elements have been 'designed' to cope with loading during flight. One such element is the expenditure of material in constructing the wing, i.e. the vein system of the wing and its arrangement. It functions like a zig-zag folding framework which stiffens the wing against aerodynamic bending moments. To quantify the quality of material distribution, models of a dragonfly wing and of a fly wing were calculated using the finite element method (FEM).     

宽厚板压力矫平压下模型理论建模与有限元分析

宽厚板压力矫平过程由于缺少精准可靠的压力矫平模型,工艺参数的设定主要依靠人工经验,制约了生产效率和产品质量的提升。针对实现全自动压力矫平关键瓶颈问题——压力矫平模型进行研究。采用弹塑性力学理论,结合压力矫平过程的特点,建立宽厚板压力矫平数学模型;在材料力学性能参数、初始平直度或曲率已知的情况下,自动计算出压平力、压头行程等参数;根据压力矫平模型计算出的数据,采用有限元方法模拟压力矫平过程,获得板材各节点位置和位移数据,计算出压力矫平后宽厚板的平直度。结果表明,各种工况下宽厚板的平直度小于2 mm/m,优于宽厚板的交货标准,证实了模型的可靠性。     

Bayesian registration of models using finite element eigenmodes

This paper is concerned with registering three-dimensional wire-frame organ models. This involves finding correspondences between points on the models of two different examples of the same organ. Such registration is widely used in the processing of medical data; for example in segmentation, or to superimpose functional information on a more detailed structural map. The algorithm described in this paper is based on matching the modes of deformation of organ shapes. Modes with lower spatial frequency characterise large scale organ features whereas small scale variations determine the high frequency modes. First, the organ sizes are normalised using a generalised version of the centroid size metric. The axes of the fundamental frequency modes are then aligned to provide initial rigid-body registration. The registration is refined by matching increasingly high frequency modes using the 'Highest confidence first' algorithm. The matches are evaluated using a Bayesian combination of local prior and likelihood functions. The prior is derived from the Gompertz metric of biological growth and ensures that physically impossible matches are not accepted. The likelihood function is a measure of the similarity between local modal deformation components. The registration algorithm has been applied by the authors in the analysis of three dimensional ultrasound data. Results are presented showing the registration of two liver models derived from 3D ultrasound.     

Investigation of thermal residual stresses in layered composite using the finite element method and X-ray diffraction

A SiC particulate-reinforced 2024Al matrix composite was fabricated using a spray atomization and codeposition process to produce a layered macrostructure. The thermal macro- and microresidual stresses that develop in this layered 2024Al/SiC composite during cooling from the codeposition temperature to ambient temperature were studied using thermoelastoplastic finite element analysis. The calculated residual stresses from finite element method were compared with those obtained from X-ray diffraction (XRD), and good agreement was observed between them. The macroresidual stress distribution was very distinct for the Al and the SiC-rich layers. The macroradial stress was tensile in the Al layers and compressive in the SiC-rich layers. The macroaxial stress was found to be compressive in the vicinity of the center region of the spray-deposited material and to have mostly a continuous distribution in the Al and the SiC-rich layers. The magnitude of the macroaxial stress was noted to decrease with increasing deposition thickness from the bottom. In addition, the spray-deposited material exhibited the highest macro-von Mises’ stress around the outer edge of the deposited material. The microradial stress was in a compressive state in the SiC particulate and in the Al matrix in the vicinity of the SiC particulate. The SiC particulate exhibited compressive microhoop stress, whereas the Al matrix exhibited tensile microhoop stress. The micro-von Mises’ stress was of the highest value at the interface between the SiC particulate and the Al matrix.     

Experimental investigation and finite element modeling of hemispherically stretched steel sheet

Hemispherical stretching experiments and corresponding finite element modeling (FEM) were performed on three aluminum-killed (AK) steels. Strain distributions measured from photogrids on the specimen surface were compared to those predicted by a three-dimensional (3-D), membrane, rigid-viscoplastic FEM program. The material model uses Hill's nonquadratic theory for normal anisotropy and Coulomb friction. The new anisotropy coefficient,M, and friction coefficient, μ, have opposite effects on the strain distribution. Balanced, biaxial simulations of highM materials required unrealistically high friction coefficients to produce agreement with measured strains. The discrepancies call into question the validity of Hill's nonquadratic yield surface and the method of measuringM. J.R. KNIBLOE, formerly Graduate Student, Department of Materials Science and Engineering, The Ohio State University     

增强假设变形梯度有限元方法稳定性计算

讨论了非协调增强假设变形梯度有限元的基本理论、所采用的本构关系和有限元列式.为了克服原先由Simo建议的方法中所固有的缺陷,即在模拟压缩变形时容易出现奇异能量模式而导致计算失稳甚至崩溃,对原方法中有关内变量和应力更新算法进行了改进.计算结果表明,改进的方法在模拟压缩和拉伸模型时,具有较好的计算稳定性.     

基于有限元方法的疲劳裂纹闭合行为

裂纹闭合行为将很大程度改变疲劳裂纹扩展行为。针对316L不锈钢,结合常幅加载和单个拉伸过载试验和动态数值模拟方法,对疲劳裂纹扩展行为中的裂纹闭合现象开展了一系列研究工作。详细对比了不同扩展阶段的裂纹闭合行为随裂纹长度、应力比和过载影响因素的变化,以及对裂纹扩展速率的影响。同时,研究了单个拉伸过载和裂纹闭合行为之间的内在联系和机理。结合裂纹闭合理论和有限元计算结果,等效应力强度因子被用来描述316L不锈钢的裂纹扩展过程,并提出316L不锈钢的裂纹扩展速率的预测模型。     

一种新的静态轧制过程有限元模拟方法

提出了一种将欧拉法与拉格朗日法结合起来的静态轧制过程有限元模拟新方法.其主要内容包括:在轧制件纵向上用欧拉坐标, 厚度和宽度方向上用拉格朗日坐标,时间变量是独立的,计算轧制件厚度和宽度方向上的实际位移时采用的流线形积分改用沿纵向的欧拉坐标一元积分.     

Effects of surface active elements on weld pool fluid flow and weld penetration in gas metal arc welding

This article presents a mathematical model simulating the effects of surface tension (Maragoni effect) on weld pool fluid flow and weld penetration in spot gas metal arc welding (GMAW). Filler droplets driven by gravity, electromagnetic force, and plasma arc drag force, carrying mass, thermal energy, and momentum, periodically impinge onto the weld pool. Complicated fluid flow in the weld pool is influenced by the droplet impinging momentum, electromagnetic force, and natural convection due to temperature and concentration gradients, and by surface tension, which is a function of both temperature and concentration of a surface active element (sulfur in the present study). Although the droplet impinging momentum creates a complex fluid flow near the weld pool surface, the momentum is damped out by an “up-and-down” fluid motion. A numerical study has shown that, depending upon the droplet’s sulfur content, which is different from that in the base metal, an inward or outward surface flow of the weld pool may be created, leading to deep or shallow weld penetration. In other words, it is primarily the Marangoni effect that contributes to weld penetration in spot GMAW.     

Beam focusing characteristics and alloying element effects on high-intensity electron beam welding

Effects of focusing characteristics of the beam as well as concentrations of a volatile alloying element in the workpiece on the shape of the cavity produced by a high-energy beam are systematically and quantitatively investigated. The energy flux of the focused energy beam is independently specified by the convergence angle, the energy distribution parameter at the focal spot, and the focal spot location relative to the workpiece surface. Energy flux at any cross section of the beam is a Gaussian distribution. The geometry of the cavity is determined by satisfying interfacial energy and momentum balances. By accounting for beam focusing characteristics, the cavity surface temperatures, depths of penetration, and cavity shapes are found to agree with experimental data. The opening diameter and depth of the cavity depend primarily upon the energy distribution parameter at the workpiece surface for a surface-focused weld t increase in the content of the volatile alloying element zinc in aluminum exhibits a pronounced influence on the shape of the cavity. Formerly Graduate Student, Institute of Mechanical Engineering.     

Semi-automatic computer construction of three-dimensional shapes for the finite element method

Seven patients with idiopathic Parkinson's disease, aged 62 to 76 years, average duration of the disease approximately eleven years, suffering from severe hallucinosis and paranoid delusions of different degree, in whom conventional therapeutic strategies (administration of benzodiazepines and mild neuroleptics) had no antipsychotic effect, received clozapine, a non-classical highly potent neuroleptic, while blood count was strictly monitored. Paranoid ideas disappeared in all seven patients after a maximum of four days administration of 25-125 mg/day. No deterioration of parkinsonian symptoms, quantified according to UPDRS was seen. Given the protection of clozapine, we could increase the L-dopa dose in two cases, thereby improving the patients' motor function. Blood count showed no abnormalities in any of the patients during an average observation period of seventeen months. Our results support the assumption that clozapine has a potent antipsychotic effect in the treatment of psychotic decompensation in advanced Parkinson's disease in carefully selected patients. We saw no negative influence of the neuroleptic on extrapyramidal symptoms.