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夹具的约束位置和间距对焊接变形的影响重点通过实验和仿真还原夹具约束角的变形。两种夹具约束对焊接变形的定量研究。探讨夹具位置和间距和焊接变形之间的关系。摘要： 通过实验研究在方形板堆焊非约束自由状态和一个夹具约束条件下焊接变形研究夹具对焊接变形的约束作用。用三维热弹塑性有限元程序来模拟在焊接中的瞬态温度和变形。可以看出焊接角变形大大降低了夹具约束，并且仿真和实验之间非常相似。三方向夹具约束和正常的方向夹具约束是实际工程中典型的约束类型。两个参数a和b，它们代表在焊接方向上的两个夹具和从熔接线的距离之间的间距，分别聚焦。详细讨论了夹具约束对纵向收缩，横向收缩和角变形的影响。关键词：焊接变形；夹具约束位置；约束间距；测量；FEM1.简介焊接过程中通常产生变形和残余应力，是工程意外的结果。焊接变形劣化结构的尺寸，影响了产品的外观。尤其是对外形畸变的诸如薄壁结构容易发生角变形和扭曲变形，以及它们最终需要的的校正工作。附加过程不仅会增加生产周期，而且增加成本。为了降低生产成本，因此有必要通过一些有效的方法，以减少焊接变形。残余应力降低结构中的疲劳强度和填充剂强度方面的性能。要采用适当的焊接后热处理或机械方法，以释放残余应力。McPherson在2010年发表的电弧焊接的反面线加热可以产生相反的弯矩来纠正。如由Ando等在1982年描述的，使用感应加热技术在减少焊接残余应力的潜在益处。通过改变应力分布，屈曲应变也可以有效地缓解。Wang等人在2011年分析了证明了焊接大规模加强结构的变形和屈曲失真可以通过管线加热过程被减少。焊接过程中的额外的加热或冷却是一种可以在过程中控制方法，以防止焊接变形。Mochizuki等人施加的额外的冷却到T形圆角接头的焊接区，并表明旋转失真可以减少数值模拟的结果以外的约束。Guan等人1990年在横截面温差拉伸效应的基础上发明了一种命名为低应力无变形（LSND）的方法。LSND经证实是优越在防止压曲变形的薄板对接焊中。Guan和Zhang在1994年开发了一种动态控制低应力无变形（DC-LSND）的方法，作为另一种在进程屈曲的活性控制方法。在该方法中，一个局部温差拉伸由斑点散热器与焊枪尾随，并且纵向塑性应变在后面的熔池通过动态控制的区域来实现。夹具在焊接工艺中被广泛使用，以避免在焊接热源的前面旋转变形。Hajduk等人在2009年描述关于焊接夹具的机器人细胞点焊车身的设计基于模块化的原则。焊接变形的控制，也有与外部约束和负荷。Park等人2012年通过改变拉伸应力的方向和大小研究了各种拉伸状态角变形和残余应力。Schenk等人在2009年研究了屈曲失真和角变形用于搭接接头和T形角接合的夹紧效果。他们发现夹紧条件对残余应力和焊接变形的影响很大。Shateryana等人在2012年通过执行三维有限元分析研究了在三种类型的本地马蹄形夹具焊接变形和残余应力在铝合金搭接接头的约束效果。Ziaee等人在2009年研究了边界条件的影响屈曲焊接薄板时的模式。人们发现，外部约束可以增加耐压曲性，但不能消除屈曲。然而，由夹紧或夹具焊接变形控制的定量研究是罕见的文献。由于设计参数和焊接结构的复杂多样，一些约束条件的有限的实验结果都不足以概述约束效果。自从Ueda和Yamakawa在1971年确定了热弹塑性有限元法焊接热应力，它已被广泛应用于研究和解决Ueda所描述的工程问题中。随着技术在计算机辅助工程（CAE）的进步，可以有效地执行而无需额外成本的一系列数值实验时的仿真精度验证。在这项研究中，之前被测量调查的夹具约束对焊接变形的影响，堆焊焊缝焊接两个以非约束自由状态测试试样，并在制备的夹具约束条件和焊接变形一个三维坐标测量装置。随后被用于对两个试样分别进行的数值模拟。焊接变形通过数值模拟预测与实验结果进行比较，并准确验证模拟的有效性。此外，为了评估夹具约束定量，夹具约束分为正常方向约束和三方向约束。共41多种约束条件下的数值模型进行了分析。两个参数a和b，这表示在从焊接线焊接的方向和距离的两个夹具之间的间距，分别集中及其对焊接变形效果在进行了细节研究。2.实验研究为了调查由夹具约束的影响，把如图1（a）和（b）中所示非约束自由状态的两个样品焊接在一起，并在夹具的约束条件下，分别用夹具约束样品，所述夹具被固定在平台上，并且平面偏转是固定的。样品的尺寸400毫米的长度400毫米的宽度和9毫米的厚度。该板的基体材料是SS400，焊丝的直径为1.2毫米，材料是MG-50T。为了一个良好的焊接质量在板表面上焊接线周围的锈要在焊接之前除去。实验期间室温约为20。图1待焊接标本：（a）自由状态（b）夹具约束状态。单面堆焊接用的是相同的焊接条件下（240 A，25 V，5毫米/秒），通过一个自动MAG焊接机进行。所述保护气体为100的CO2。约束夹具在焊接结束时间约4分钟后移除。焊接试样分别示于图2（a）和（b）中图2焊后试样：（1）自由状态（b）夹具约束状态。为了获得焊接变形，小型钻洞上盘。每个孔的中心被认为是一个测量点。焊接前在板上测量点的坐标，冷却后进行测定。最终那些减去初始坐标，焊接变形就计算出来了。使用所测量的结果的三个典型的焊接变形部件，纵向收缩，横向收缩和角变形进行评价。在纵向部分的纵向收缩Y= -190，-40，40，190毫米，分别进行评价，如图3所示的横向收缩和角变形的横截面，评价X= 10，50，200，350，390毫米如图4和图5所示。变形值上顶表面和底表面上的测量点的平均值。图3非约束自由状态和夹具约束条件下纵向收缩：（a）4个纵向部分；（b）纵向收缩。图4非约束自由状态和一个夹具约束条件下的横向收缩：（1）5个横截面；（二）横向收缩。图5非约束自由状态和一个夹具约束条件下角变形：（a）5个横截面线；（b）角变形。图3清楚地表明，在焊接线附近纵向收缩比远离焊接线该值大很多。图4和图5显示了横向收缩和角变形在五个部分，分别是相对均匀的，因为每单位焊接长度的焊接热输入是恒定的。在焊接线的精加工结束后，横向收缩率下降，因为压缩横向塑性应变在末端的相对较弱的内部约束变小。通过比较，可以确认，如果用约束夹具夹紧焊接试样，与非约束自由状态下进行比较，角变形可大大减少。对角变形的影响比夹具约束对纵向收缩和横向收缩的影响相对较小。3.数值模拟在这项研究中，三维热弹塑性有限元被采用来模拟焊接热应力和变形。约束夹具在以下的实验条件下进行建模仿真。夹具和样品之间的相互作用被认为是通过夹具的末端固定。焊接过程中用温度变化的材料精确地模拟热机械性能。基体金属和填充金属都在数值模拟分别定义。温度和机械分析进行顺序Murakawa等人提出的迭代子法（ISM）被用于机械分析以节省计算时间。3.1 有限元模型一种固体元件制剂一般需要进行分析瞬态焊接热应力和应变。密实网孔应在焊接线的附近进行以适应周围焊接热源的温度梯度。在这项研究中，六面体元件，其鲁棒性和准确性在处理塑性行为被Benzkey在1995年证实良好，用于焊接模拟。为约束焊接样品的有限元模型示于图6。在有限元模型中的焊接加强件的形状，从实验观察来确定，而宽度和高度分别为10毫米和2.2毫米。在焊接方向2mm的宽度方向和1.8毫米的厚度方向，焊缝区域中的元件的大小是5毫米。单元和节点的数量分别是15736，20448。夹具也仿照由实体单元考虑它的弹性约束。由于夹具的几何形状的复杂性，每个夹具被简化为两个长方体具有相同的长度和横截面为实际夹具，和所述夹持面是大约15mm10毫米。图6有限元网格的标本夹具和焊接热源区。3.2 焊接热的传导分析机械分析之前，进行热传导分析，以获得温度履历为固体元素的所有节点。焊接热源，如由移动体积内均匀的热生成率表示图6。在热传导模拟中所用的温度依赖性的物理性能示于图7（a）中。焊接金属（WM）的热特性被假定是相同的用碱金属（BM）。在高温度超过1000时，材料的性能被认为是相同的与那些在1000。环境温度设定为20，传热系数被假定为24瓦/（米2）的所有的表面上（Ueda等人2012）。图7 碱金属和焊接金属的材料性质：（a）热物理性质；（b）机械性能。在图8中，在40秒的瞬态温度领域进行了绘制的剖视图，从中可以看出，靠近热源的区域具有大的温度梯度，而其后部呈相对均匀的分布。上的横截面的最大到达温度分布表示熔合区示于图9。图8瞬时温度分布从焊接开始40秒：（一）总体视野；（二）截面图。图9在横截面和熔合区最高达到温度分布。3.3 热应力和变形的分析通过施加瞬时温度，焊接热应力及变形计算增量为每个时间步长。碱金属和填料金属的机械特性示于图7（b）中。基体金属和填充金属的特性是除屈服应力相同。该材料按照各向同性硬化法及相关塑性流动规律。对于非约束自由状态下焊接该模型中，只有刚体运动在有限元模型被限制。对于夹具约束试样，夹具的端部被约束在板法线方向（焊接时方向）。夹具约束被焊后获释。相变特性（deng2009），在模拟中没有考虑。迭代子方法（ISM），为了节省计算时间，而不损失精度。基本上，整个模型一个被分成两个区域具有不同的电平的非线性，如图10所示。在本研究中，B区温度高于300。其余区域不包括整个模型A中的B区域被定义为A-B的区域。在A-B区和B区都以互动的方式解决了，而这两个地区之间的边界上的不平衡力迭代计算，直到平衡感到满意。以这种方式，迭代步骤与简单的方案相比为整个区域总数量将大大降低。图10区域A，B和A-B在ISM的框架示意图。4.焊接变形的比较计算出的平面位移中的分布z非约束自由状态与夹具约束条件下方向示于图11，它可以很容易地观察到，面外变形的已被夹具约束大大减少。图11外的面外变形（单位：mm，变形规模：10次）：（a）免费条件下试样；（b）与试样夹具。焊接仿真和测量之间变形，在所述非约束自由状态的比较示于图12（a） - （b）所示。如图中所计算的纵向收缩图12（a）是对称的焊接线由于模型的对称性。板的边缘附近的纵向的收缩远小于其靠近焊接线。图12焊接在非约束自由状态变形和实验和模拟之间的比较：（a）纵向收缩；（b）横向收缩；（c）角变形。从所计算的和测量的结果，可以发现，在横向收缩，在板的中间部分比边缘附近较大，如图12（b）中所示。最小值出现在焊接的精加工结束。角变形变化不大，在所有五个横截面，如图12（c）所示。如果在详细的观察，在焊接线的终端附近的横截面的角变形比焊接线的起始端附近大。这是因为从移动焊接热源的预热效果强附近的熔接线和预角变形的终端已经在焊接热源的前面产生。所计算的纵向收缩，横向收缩和角变形非常接近的实验值。对于夹具的约束条件下的样品，实验和仿真之间的角变形的结果进行了比较，图12所示。无论是实验和仿真结果表明，在角变形减少约70，如果使用约束夹具。图13测量和计算焊接角变形用夹具的约束。5.夹具约束的参数研究5.1 的夹具约束条件模型如果夹具通过接触来限制板，位移仅在接触的法线方向朝向板和夹具之间可以被假定为被约束。如果在板被焊接时被夹具牢固地固定，在夹具约束位置的位移可以被假定为完全固定在三个方向。在这项研究中，两种类型的约束，简单地命名为正常方向夹具约束和三方向夹具约束，并且在示意性图14示出。图14夹具的配置和两种夹具约束。在法线方向夹具约束的建模中，顶部和底部表面的距离上的节点B远离焊接线，表示夹具约束位置，仅在法线方向固定。在节点20毫米远离焊接线附加约束是用来支撑基座上板的底部表面进行建模。在这三个方向的夹具约束条件，夹具在其中的位移分别设置节点，被固定在三个方向。在所有的情况下，在节点处的夹具约束是从焊接的开始施加并且当焊接结束后220 s释放。对于堆焊焊接模型，进行与尺寸模拟400毫米400毫米10毫米。夹具被对称地布置在焊接线的两侧。为简单起见，该约束被直接施加在顶表面和底表面的每个夹具的节点上。调查夹具位置和音调上焊接变形的影响，41例的数值模拟的示于表1，包括一个非约束自由状态下案件。约束类型夹具位置B（毫米）夹具间距一（毫米）占总病例非限制自由状态无无1法线方向夹具约束30，50，100，2005，20，40，80，20020三方向夹具约束30，50，100，2005，20，40，80，20020表1数值模拟的条件和情况下，各种夹具的约束。焊接变形的组件，腱力F，横向收缩和角变形的中间横截面进行了调查。肌腱力的概念最初是由White等人在1980年表示在焊道的纵向的收缩率，并且它可以由下式来定义：方程式（1）分别是杨氏模量和纵向塑性应变。为了使比较更容易，肌腱力F（a，b），横向收缩率S（a，b）和角变形（a，b）在各种夹具约束位置b和俯仰a由方程进行归一化分别为(2)，(3)和(4)。每个焊接变形成分，通过相应的值除以（F0，S0，0）下的非约束自由状态。方程式（2）方程式（3）方程式（4）如果F（a，b），s（a，b），（a，b）比1.0小，则意味着夹具约束减少焊接变形。如果它们是大于1.0，这意味着焊接变形在夹具约束条件下增加。由于纵向弯曲是相当小的，在本研究中，在此不再表述。5.2 法线方向夹具约束在法线方向夹具约束的情况下，位置参数b和螺距参数影响约束夹具的肌腱力F（a，b），所述归一化的横向收缩s（a，b）和归一化的角变形（a，b）在图15（a）-（c）中示出，肌腱力量和横向收缩的效果并不明显。这可以容易地理解的是，在正方向夹具约束没有给出在平面内的塑性应变尤其直接影响平均通过厚度方向的值。图15对焊接变形法线方向夹具约束的影响：（a）受力筋；（b）横向收缩；（c）角变形。可以解释，如果正方向夹具约束施加到焊接板，附加的弯曲应力是由正常的反作用力，如图16所形成。在上表面的拉伸应力可减少横向收缩的塑性应变的量。在底表面上，该压应力将引起更多的横向收缩的塑性应变。因此，横向塑性应变通过厚度的分布将变得更均匀，如图17所示。其结果是，横向弯曲即角变形变小。图16形成了垂直方向夹具约束弯曲应力场。图17在一个非约束自由状态和正常方向夹具约束条件对中间横截面为试样横向塑性应变分布（a=80毫米;B= 30，50毫米）：（a）横向塑性应变；（b）横向塑性应变在中央线（= 0）。如果夹具被放置在靠近焊接区，即，所述夹具位置参数b为30mm螺距a是大于20毫米，角变形引起的夹具约束的减少变小。这是因为，夹具约束位置是塑性变形区内，如图17（a）所示并且由塑性应变夹具位置以外产生的角变形没有被控制。这种现象也通过横向塑性应变通过板厚分布为两所示例图17（b）中所示。如图15（c）中所示，一个小的夹具约束导致一个小的角变形。若间距足够小，例如小于80毫米，节距的效果变小。在这种情况下，如果该参数为大于50毫米的角变形几乎与夹具约束位置增加b呈线性。5.3 三方向夹具约束在三个方向上夹具约束的情况下，夹具约束位置的影响b和归一化a的肌腱力F（a，b），所述归一化的横向收缩s（a，b），并归一化的角变形（a，b）显示在图18（a）-（c）中，夹具约束条件下的归一化腱力和横向收缩率分别变大，这是从正方向夹具约束大不相同。三个方向夹具约束条件下的角变形比那些非约束自由状态下变化小。这种现象与正常的方向夹具约束条件下类似。图18对焊接变形三方向夹具约束条件的影响：（a）受力筋；（b）横向收缩；（c）角变形。肌腱力和横向收缩的三个方向夹具约束条件下的增加，是由于在感应焊接的纵向塑性应变和横向塑性应变的增加，如图19和图20所示。根据夹具的约束条件，在焊接的加热阶段，主要是产生的大的压缩塑性应变。这是因为在热膨胀由夹具强约束，结果压缩塑性应变变大与这些非约束自由状态下进行比较（Murakawa等人 1996年）。图19上中间截面为试样在非约束自由状态和三方向夹具约束条件（纵向塑性应变一个= 20毫米，B= 50毫米）：（a）一部分的轮廓；（b）在宽度方向（分布= 5毫米）。图20在一个非约束自由状态和三方向夹具约束条件（在中间横截面横向塑性应变分布一个= 20毫米，B= 50毫米）：（a）一部分的轮廓；（b）在宽度方向（分布= 5毫米）。6.结论在本研究中，夹具约束对焊接变形的影响进行了研究两者数值模拟和实验测量。位置和间距参数化变更为各种约束条件。根据实验和计算结果，得出如下结论可以得出：（1）焊接变形的有限元计算吻合与非约束自由状态和夹具约束条件下测得的结果。（2）所得到的结果显示，当使用夹具时焊接板角变形得到有效降低。（3）三方向夹具约束，对所有的变形部件有很大的影响。（4）法线方向夹具约束可以有效地减少角变形与肌腱力和横向收缩的影响。（5）一般地，当夹具的位置和间距值较小角变形将会减少。15Effect of jig constraint position and pitch on welding deformationHighlightsReduction of angular distortion by jig constraint is realized by experiment and simulation.Effect of two types of jig constraint on welding deformations is quantitatively investigated.Relationships between jig position & pitch and welding deformations are explored.AbstractQuantitative study on jig constraint effect on welding deformation was carried out. Welding deformation in a square plate with bead welding under a non-constraint free condition and a jig constraint condition was investigated by experiment. A 3D thermal elasticplastic FEM program was employed to simulate the transient temperature and deformation occurred in the welding. It is observed that welding angular distortion has been greatly reduced by the jig constraint, and a good agreement was confirmed between simulation and experiment. Three-direction jig constraint and normal direction jig constraint were defined based on typical constraint types in practical engineering. Two parametersaandb, which represent the pitch between two jigs in the welding direction and the distance from the weld line, respectively, were focused. Effect of jig constraint on longitudinal shrinkage, transverse shrinkage and angular distortion were discussed in details.Keywords:Welding deformation;Jig constraint position;Constraint pitch;Measurement;FEM1. IntroductionWelding process generally produces deformation and residual stresses which are undesired results in engineering. Welding deformation deteriorates the dimensions of structures and influences the appearance of products. Especially the out of plane distortion such as angular distortion and buckling distortion occurs easily in thin-walled structures, and their correcting work is eventually needed. The additional processes will increase not only the production period but also the cost. To reduce the production cost, it is necessary to minimize the welding deformation by some efficient ways. Residual stress degrades the performance of structure in aspects of fatigue strength and bulking strength. Proper post welding heat treatment or mechanical method has to be employed in order to release the residual stresses.Line heating on the reverse side of welding arc can produce an opposite bending moment to correct angular distortion which was reported byMcPherson (2010). As described byAndo et al. (1982), the use of an induction heating technique has potential benefit in reducing welding residual stress. By altering the stress distribution, buckling distortion can also be mitigated effectively.Wang et al. (2011)analyzed welding deformation of a large-scale stiffened structure and proved that buckling distortion can be reduced by line heating process.Additional heating or cooling during welding can be one of the in-process control methods to prevent welding deformation.Mochizuki et al. (2006)applied the additional cooling to the weld zone of a T-shape fillet joint and demonstrated that the rotational distortion can be reduced without tacking and external constraint based on the results of numerical simulation.Guan et al. (1990)invented a process named as the low stress non distortion (LSND) method based on the cross section thermal tensioning effect. LSND was proved to be superior in preventing buckling distortion in butt welding of thin plates.Guan and Zhang (1994)developed a dynamic controlling low stress non distortion (DC-LSND) method as another active in-process buckling control method. In this method, a localized thermal tensioning was realized by a spot heat sink trailing with welding torch, and the longitudinal plastic strain at the zone behind the weld pool was dynamically controlled.Jigs are widely used to assist welding process to avoid rotation distortion in the front of welding heat sources.Hajduk et al. (2009)described the methodological approach about the design of welding fixtures for robotic cells in spot welding of car bodies based on principles of modularity. Regarding control of welding deformation, there are several reports relating to external constraints and loads.Park et al. (2012)investigated the angular distortion and residual stress under the various pre-tension states by changing the direction and magnitude of pre-tension stress.Schenk et al. (2009)studied the clamping effect on buckling distortion and angular distortion for an overlap joint and T-shape fillet joint. They found that residual stresses and welding distortion were strongly affected by clamping condition.Shateryana et al. (2012)investigated the constraint effects on welding deformation and residual stress in aluminum alloy lap joints under three types of local U-shape fixture by performing a 3D finite element analysis.Ziaee et al. (2009)studied the influence of boundary conditions on buckling modes during welding thin plates. It was found that external constraint can increase the buckling resistance but can not eliminate buckling.Nevertheless, the quantitative study on control of welding deformation by clamping or jig is rare in literatures. Due to the diversity of design parameters and complexity of welded structures, the limited experimental results at some constraint conditions are not enough to provide an overview of the constraint effect. Since the thermal elastic plastic FEM for welding thermal stress was established byUeda and Yamakawa (1971), it has been widely used in researches and in solving engineering problems as described byUeda et al. (2012). With the great progress of technology in computer aided engineering (CAE), a series of numerical experiments can be efficiently performed without extra cost when the simulation accuracy was verified previously.In this study, prior to investigate the mechanism of the effect of jig constraint on welding deformation, two testing specimens of bead-on-plate welding at a non-constraint free condition and at a jig constraint condition were prepared and welding deformations were measured by a 3D coordinate measuring device. Then the numerical simulation was performed for the two specimens, respectively. The welding deformation predicted by numerical simulation was compared with the experimental results and the simulation validity was accurately verified.Furthermore, to evaluate the effect of jig constraint quantitatively, the jig constraint is classified into two types named as the normal direction constraint and the three-direction constraint. Totally 41 numerical models under various constraint conditions were analyzed. Two parametersaandb, which represent the pitch between two jigs in welding direction and distance from weld line, respectively, were focused and their effect on welding deformation was investigated in details.2. Experimental studyTo investigate the effect of constraint by jigs, two specimens were welded at a non-constraint free condition and at a jig constraint condition as shown inFig. 1(a) and (b), respectively. In the jig constraint specimen, the jigs were fastened on the platform and out-of-plane deflection was fixed. The dimensions of the specimens are 400mm in the length, 400mm in the width and 9mm in the thickness. The base material of the plate is SS400 and the material of welding wire with a diameter of 1.2mm is MG-50T. The rust on the plate surface around the weld line was removed before welding for a good welding quality. The room temperature was about 20C during experiment.Fig. 1.Specimens to be welded: (a) at free condition (b) with jig constraint.The single pass bead-on-plate welding was performed by an automatic MAG welding machine using the same welding conditions (240A, 25V, 5mm/s). The shielding gas was 100% CO2. The constraint jigs were removed about 4min later from the finishing time of welding. The welded specimens are shown inFig. 2(a) and (b), respectively.Fig. 2.Specimens after welding: (a) at free condition (b) with jig constraint.To obtain the welding deformation, small sized holes were drilled on the plate. The center of each hole was recognized as a measuring point. The coordinates at measuring points on the plate were measured before welding and after cooling. By subtracting the initial coordinates from the final ones, welding deformations were calculated.The three typical welding deformation components, longitudinal shrinkage, transverse shrinkage and angular distortion were evaluated using the measured results. The longitudinal shrinkage at the longitudinal sectionsY=190, 40, 40, 190mm was, respectively, evaluated as shown inFig. 3. The transverse shrinkage and angular distortion were evaluated at the transverse sectionsX=10, 50, 200, 350, 390mm as shown inFig. 4andFig. 5. The deformation values were the averaged ones at the measuring points on the top surface and bottom surface.Fig. 3.Longitudinal shrinkage under a non-constraint free condition and a jig constraint condition: (a) four longitudinal sections; (b) longitudinal shrinkage.Fig. 4.Transverse shrinkage under a non-constraint free condition and a jig constraint condition: (a) five transverse sections; (b) transverse shrinkage.Fig. 5.Angular distortion under a non-constraint free condition and a jig constraint condition: (a) five transverse section lines; (b) angular distortion.Fig. 3clearly shows that longitudinal shrinkage near the weld line has much larger value than that far away from the weld line.Fig. 4andFig. 5show that the transverse shrinkage and angular distortion at the five sections, respectively, are relatively uniform, since the welding heat input per unit weld length is constant. At the finishing end of the weld line, transverse shrinkage decreased because the compressive transverse plastic strain becomes smaller due to the relatively weaker internal constraint at the end. Through the comparison, it was confirmed that if the constraint jigs are employed to clamp the welding specimen, the angular distortion can be greatly reduced compared with that under a non-constraint free condition. The effect of jig constraint on longitudinal shrinkage and transverse shrinkage was relatively smaller comparing with the effect on angular distortion.3. Numerical simulationIn this study, three-dimensional thermal elasticplastic FEM was employed to simulate the welding thermal stress and deformation. Constraint jigs were modeled in the simulation following the experimental conditions. The interaction between jigs and specimen was considered by fixing the end of jigs. To accurately model the thermalmechanical behavior during welding, the temperature dependent material properties were employed. The base metal and filler metal were defined separately in the numerical simulation. Temperature and mechanical analysis were performed sequentially, and iterative substructure method (ISM) proposed byMurakawa et al. (2004)was used in mechanical analysis to save the computation time.3.1. Finite element modelA solid element formulation is generally necessary to analyze the transient welding thermal stress and strain. To fit the temperature gradient around welding heat source, dense mesh should be made in the vicinity of weld line. In this study, hexahedral elements whose robustness and accuracy in dealing with plasticity behavior were proved well byBenzley (1995), were employed for welding simulations. The finite element model for the constrained welding specimen is shown inFig. 6. The shape of the weld reinforcement in the finite element model was determined from experimental observation, and the width and height are 10mm and 2.2mm, respectively. The element size in the weld zone is 5mm in welding direction, 2mm in the width direction and 1.8mm in the thickness direction. The numbers of elements and nodes are 15,736, 20,448, respectively. The jigs are also modeled by solid elements to take into account of its elastic constraint. Due to the complexity of jig geometry, each jig is simplified into two cuboids which have the same length and transverse section as the actual jigs, and the clamping face is approximately 15mm10mm.Fig. 6.Finite element mesh for specimen with jigs and welding heat source zone.3.2. Welding thermal conduction analysisBefore mechanical analysis, thermal conduction analysis was performed to obtain the temperature history for all nodes of solid elements. Welding heat source was represented by uniform heat generation rate within a moving volume as shown inFig. 6. The temperature dependent physical properties used in the thermal conduction simulation, are shown inFig. 7(a). The thermal properties of weld metal (WM) were assumed to be the same with base metal (BM). At the high temperature over 1000C, the material properties were considered to be the same with those at 1000C. The ambient temperature was set to be 20C and the heat transfer coefficient was assumed to be 24W/(m2C) on all the surfaces (Ueda et al., 2012).Fig. 7.Material properties of base metal and weld metal: (a) thermal physical properties; (b) mechanical properties.InFig. 8, the transient temperature field at 40s was drawn with cross sectional view, from which it can be seen that, the region near heat source has large temperature gradient, while the rear part showed relatively uniform distribution. The maximum reached temperature distribution on the transverse section which indicates the fusion zone is shown inFig. 9.Fig. 8.Transient temperature distribution at 40s from start of welding: (a) global view; (b) sectional view.Fig. 9.The maximum reached temperature distribution on transverse section and fusion zone.3.3. Thermal stress and deformation analysisBy applying the transient temperature, welding thermal stress and deformation were computed incrementally for each time step. The mechanical properties of base metal and filler metal are shown inFig. 7(b). The properties of the base metal and filler metal are the same except for the yield stress. The materials follow the isotropic hardening law and related plastic flow rule. For the model welded under a non-constraint free condition, only rigid body motion was restricted in finite element model. For the jig constraint specimen, the end of jigs was constrained in the plate normal direction (Z-direction) during welding. The jig constraint was released after welding. The phase transformation behavior (Deng, 2009) were not considered in the simulation.The iterative substructure method (ISM) was adopted in order to save computation time without loss of accuracy. Basically, the whole model A was divided into two regions with different level of nonlinearity as shown inFig. 10. In the present study, the B region was defined by elements in which the temperature is higher than 300C. The remaining region excluding the B region from whole model A is defined as AB region. The AB region and B region are solved in an interactive manner, and the unbalanced force on the boundary between the two regions is computed iteratively until equilibrium is satisfied. In this way, total number of iteration steps for whole region will be greatly reduced compared with the straightforward scheme.Fig. 10.Schematic drawing of regions A, B and AB in the framework of ISM.4. Comparison of welding deformationThe distributions of computed out-of-plane displacement in thezdirection under the non-constraint free condition and the jig constraint condition are shown inFig. 11. It can be easily observed that the out of plane distortion has been greatly reduced by jig constraint.Fig. 11.Out-of-plane deformation (unit: mm, deformation scale: 10 times): (a) specimen under free condition; (b) specimen with jigs.The comparisons of welding deformation between simulation and measurement at the non-constraint free condition were shown inFig. 12(a)(c). The computed longitudinal shrinkage as shown inFig. 12(a) is symmetrical to the weld line due to the symmetry of the model. The longitudinal shrinkage near the edge of plate is much smaller than that close to weld line.Fig. 12.Welding deformations at a non-constraint free condition and the comparison between experiment and simulation: (a) longitudinal shrinkage; (b) transverse shrinkage; (c) angular distortion.From the computed and measured results, it can be found that the transverse shrinkage at the middle section of plate is larger than that near the edge as shown inFig. 12(b). The smallest value appears at the finishing end of welding. The angular distortion changes a little at all five transverse sections as shown inFig. 12(c). If it is observed in detail, the angular distortion at the transverse sections near the terminal of the weld line is larger than that near the starting side of weld line. This is because the pre-heating effect from moving welding heat source is strong near the terminal of the weld line and a pre-angular distortion has been produced in the front of welding heat source. The computed longitudinal shrinkage, transverse shrinkage and angular distortion were very close to the experimental ones.For the specimen under the jig constraint conditions, comparison of angular distortion between experiment and simulation was made and shown inFig. 13. Both the experimental and simulation results show that there was about 70% reduction in the angular distortion if constraint jigs were employed.Fig. 13.Measured and computed welding angular distortion with jig constraint.5. Parametric study of jig constraint5.1. Models of jig constraint conditionsIf jigs constrain the plates through contact, the displacement only in the normal direction of the contact faces between plates and jigs can be assumed to be constrained. If the jigs are rigidly fixed with the plates to be welded, the displacement at the jig constraint positions can be assumed to be fully fixed in the three directions. In this study, two types of constraint from jigs, simply named as the normal direction jig constraint and the three-direction jig constraint, are assumed and schematically shown inFig. 14.Fig. 14.Configuration of jigs and two types of jig constraint.In the modeling of the normal direction jig constraint, nodes on the top and bottom surfaces with distancebaway from weld line, representing the jig constraint position, are fixed only in the normal direction. Additional constraint at nodes 20mm away from weld line is employed to model supporting base on the bottom surface of plate.In the three-direction jig constraint condition, the displacement at the nodes where jigs were set, is fixed in the three directions. In all cases, the jig constraint at the nodes was applied from the beginning of welding and released after 220s when the welding was finished.The simulations were performed for a bead-on-plate welding model with dimensions 400mm400mm10mm. The jigs were symmetrically arranged on both sides of welding line. For the sake of simplicity, the constraints are directly applied at the nodes on the top and bottom surfaces for each jig. To investigate the effect of jig position and pitch on welding deformation, totally 41 cases of numerical simulations shown inTable 1were performed including one case under a non-constraint free condition.Table 1.Numerical simulation conditions and cases with various jig constraints.Constraint typesJig positionb(mm)Jig pitcha(mm)Total casesNon-constraint free conditionNoneNone1Normal direction jig constraint30, 50, 100, 2005, 20, 40, 80, 20020Three direction jig constraint30, 50, 100, 2005, 20, 40, 80, 20020The welding deformation components, tendon forceF, transverse shrinkage and angular distortion on the middle cross section were investigated. The concept of tendon force was originally proposed byWhite et al. (1980)to represent the longitudinal shrinkage in the weld bead, and it can be defined by the following equation:equation(1)whereare the Youngs modulus and the longitudinal plastic strain, respectively.To make the comparison easier, the tendon forceF(a,b), transverse shrinkageS(a,b) and angular distortion(a,b) under various jig constraint positionband pitchawere normalized by Eqs.(2),(3)and(4), respectively. Each welding deformation component was divided by the corresponding values (F0,S0,0) under the non-constraint free condition.equation(2)equation(3)equation(4)Iff(a,b),s(a,b),(a,b) are smaller than 1.0, it means that the welding deformation is reduced by the jig constraint. If they are larger than 1.0, it means that the welding deformation increased under the jig constraint condition. Since the longitudinal bending was rather small in the present study, it was not discussed here.5.2. Normal direction jig constraintIn the case of the normal direction jig constraint, the effect of position parameterband pitch parameteraof the constraint jigs on the normalized tendon forcef(a,b), the normalized transverse shrinkages(a,b) and the normalized angular distortion(a,b) is shown inFig. 15(a)(c), respectively. The effect on the tendon force and transverse shrinkage is not obvious. This can be easily understood that the normal direction jig constraint did not give direct influence on the in-plane plastic strains especially the average value through the thickness direction.Fig. 15.Effect of normal direction jig constraint on welding deformation: (a) tendon force; (b) transverse shrinkage; (c) angular distortion.It can be explained that if the normal direction jig constraint is applied to the welded plate, an additional bending stress was formed by the normal reaction forces as illustrated byFig. 16. The tensile stress on the top surface can reduce the amount of transverse shrinkage plastic strain. On the bottom surface, the compressive stress will induce more transverse shrinkage plastic strain. Thus, the distribution of the transverse plastic strain through thickness will become more uniform as shown inFig. 17. As a result, transverse bending, i.e., the angular distortion became small.Fig. 16.Formation of bending stress field by normal direction jig constraint.Fig. 17.Transverse plastic strain distributions on middle cross section for the specimens at a non-constraint free condition and normal direction jig constraint conditions (a=80mm;b=30, 50mm): (a) transverse plastic strain; (b) transverse plastic strain at central line(Y=0).If the jigs are placed near the weld zone and when pitch is large, i.e., the jig position parameterbis 30mm and pitchais greater than 20mm, the reduction of angular distortion due to jig constraint became small. This is because the jig constraint position was within the plastic deformation zone as shown inFig. 17(a) and the angular distortion produced by the plastic strain outside of the jig positions was not controlled. The phenomenon was also supported by the distribution