Figure 2: Experimental setup for tube welding
Testing
The porosity of welds was observed before and after welding using the X-ray technique to check the quality of these welds according to the standard ASTM E155. The whole welded tubes were then tested by traction on a MTS testing machine. The final dimensions of the welded tubes are measured on a CMM machine at many points on the tubes. The distortion of the welded tubes is determined by comparing the final positions with the initial positions of the tubes.
Numerical analysis
In Sysweld, a welding analysis is performed based on a weak-coupling formulation between the heat transfer and mechanical problems. Only the thermal history will affect on the mechanical properties, but not in reverse direction. Therefore, a thermal metallurgical mechanical analysis is divided into two steps. The first step is a thermal metallurgical analysis, in which the heat transferred from the welding source makes phase changes during the welding process. The results of temperature and phase changes from the first step are then used as input for the second analysis. It is a pure thermo-elasto-plastic simulation [6].
Heat source model identification
Before running a welding simulation, it is necessary to determine the parameters of the heat source model. This is called heat source fitting. Actually, it is a thermal simulation using this heat source model in the steady state, which iscombined with an optimization tool to obtain the parameters of the heat source. Figure 3 presents the form of a 3D conical heat source of which the energy distribution is described in Eq (1) as follows:
F=Q0exp(-r²/r0²)                                  (1)
in which Q0 denotes the power density; and r，r0 are defined by
r²=(x-x0)²+(x-x0-vt)²                               (2)
and
r0=re-(re-ri)(ze-z+z0)/(ze-zi)                          (3)
where（x0,y0,z0)is the origin of the local coordinate system of the heat source; re and ri the radius of the heat source at the positions ze and zi,respectively;v the welding speed and t the time.
In this study, a metallographic cross-section has been used to identify the heat source parameters as shown in Figure 4. The use of a 3D conical heat source fits very well the weld cross-section. The mesh size in the cross-section is around 0.5 mm for this case. The finer is the mesh, the more accurate is the shape of the melting pool, but the longer is the simulation.

Figure 3: 3D conical heat source (Sysweld).
 
a)
 
b)
Figure 4: (a) Metallographic cross-section, (b) Melting pool cross-section.
Analysis model
The mesh of the tubes was created in Hypermesh 7.0. Sysweld 2007 has been used as solver and pre/post processor. A full 3D thermal metallurgical mechanical analysis with brick and prism elements. Two welding sequences have been done such as W1/W2/W3/W4 and W1/W3/W2/W4. The tubes are clamped using four v-blocks during the welding, two for each tube. In the simulations, the positions where the tubes are in contact against the surfaces of the v-blocks are considered as fixed conditions (i.e. Ux = Uy = Uz = 0). In the release phase, the tubes are free from the v-blocks.
Results
The distortion of the welded tube is measured when it is released from the constraints. The distortion is determined by measuring the displacement of the small tube on the top and lateral surfaces along the centre line of the tube. These measures are relative to the large tube. Figures 5a-b depict the distortion predicted by the numerical simulations of the sequence W1/W2/W3/W4 and W1/W3/2/W4, respectively. Good agreements between experimental and numerical results were obtained in the two welding sequences as indicated in Tables 2-3, in both the distortion tendency and distortion range of the process variation.

a)
 
b)
Figure 5: Tube distortion (Norm U): (a) Sequence W1/W2/W3/W4, (b) Sequence W1/W3/W2/W4.
Table 2: Distortion result comparison (welding sequence W1/W2/W3/W4)
      Displacements(mm) 
 Uy Uz
Experimrntal From-0.4to-0.59 From-0.35to-0.51
3D simulation -0.4 -0.51

Table 3: Distortion result comparison (welding sequence W1/W3/W2/W4)
 Displacements(mm) 
 Uy Uz
Experimrntal From-0.07to-0.11 From-0.12to-0.21
3D simulation -0.05 -0.26

a)
 
b)
Figure 7: State of stresses Sxy (a) Clamped, (b) Released. (Red = positive, Blue = negative)
 
a)
 
b)
Figure 8: State of stresses Sxz (a) Clamped, (b) Released. (Red = positive, Blue = negative)
Figures 6-8 shows the state of the stresses of the welded tubes at room temperature for the sequence W1/W2/W3/W4 after welding when clampled and released from constraints (x is the direction along the axe of the welded tube). To show how the welded tube is distorted, positive-negative values are used instead of the true values of stresses. The distortion of the welded tube can be explained as the new equilibrium position due to the residual stresses when there is no external load. It is remarked that in the presence of large gaps, the distortion of the welded tube is very likely in the rotational mode around local welds.
Conclusions
The MIG welding is very good for assembling aluminium cast tubes (hollow parts) in the presence of large gaps.
 The 3D thermal metallurgical mechanical simulation of the cast tube welding using Sysweld has been validated. A very good agreement between numerical and experimental results was obtained for both the distortion tendency and distortion range.
 The welding sequence has a major influence on the distortion of the welded structure. It turns out that the optimization of the welding sequences for a reasonable distortion of a welded structure with a large number of welds becomes very important.
Acknowledgments
The authors would like to thank gratefully Rio Tinto Alcan and General Motor for financial and technical supports, particularly Martin Fortier and Pei-Chung Wang. Also, the authors are grateful to Welding Team at ATC (Audrey Boily, Martin Larouche, François Nadeau and Mario Patry) for experimental works.
References
1. K-H. Von Zengen, Aluminium in future cars – A challenge for materials science, Materials Science Forum, 519-521 (Part 2), 1201-1208 (2006).
2. S. Wiesner S., M. Rethmeier and H. Wohlfart, MIG and laser welding of aluminium alloy pressure die cast parts with wrought profiles, Welding International, 19 (2), 130-133 (2005).
3. R. Akhter, L. Ivanchev, C.V.Rooyen, P. Kazadi and H.P. Burger, Laser welding of SSM Cast A356 aluminium alloy processed with CSIR-Rheo technology, Solid State Phenomena, 116-117, 173-176 (2006).
4. J.F. Lancaster, Metallurgy of welding, Abington Publishing (1999).
5. Φ. Grong, Metallurgical modelling of welding, The institute of materials (1997).
6. Sysweld, Sysweld reference manual, ESI Group (2005).

译文
铸造A356铝合金的焊接模拟
X-T. Pham*, P. Gougeon and F-O. Gagnon
Aluminium Technology Centre, National Research Council Canada Chicoutimi, Quebec, Canada
摘要：
空心铝铸造件的焊接是一个很有前途的新结构组件技术的趋势。然而，组件之间的差距较大，焊接孔隙度，大变形和热裂需要处理的风险。在这篇文章中，对铸造A356铝合金的方管的MIG焊接进行了研究。并对焊接管弯曲变形进行了数值模拟预测。实验结果和数值模拟结果的相似度很高。
1前言：
由于铝合金结构自身的重量轻，所以它变得越来越流行，尤其是在汽车制造业。此外，空心铝铸造件的焊接是一种新的有前途的结构组件技术的趋势[1-3]。但是它可能有很大的挑战，由于大的差距，例如组件之间，焊接孔隙度，大变形和热裂的危险等很多问题[4,5]。由于局部加热，复杂的热应力发生在焊接中；焊后会出现残余应力和变形的结果。在这篇文章中，关于铸造A356铝合金的方管的MIG焊接进行了研究。Sysweld软件[6]被用于焊接模拟。其目的是验证这个软件在大差距的焊接管扭曲变形的预测中的能力。在这项工作中，在焊接后利用X射线技术来检查焊缝的孔隙率。在热源参数的基础上，确定了焊缝截面和焊接参数。冶金力学的3D热量模拟已经被使用。用数值模拟所预测出来的扭曲值与焊后用CCM机器所测量的实验结果进行了比较。
2实验：
2.1实验方案
两个成直角的管子是用A356通过砂型铸造然后在加工形成的。他们是由四个管MIG焊接组装而成 ，命名为W1至W4。他们的尺寸和焊接配置描绘如图1.不论小还是大的管子都很好的定位在一个采用V形块的夹具上，如图2所示。管子的规模使它们之间产生了一个1毫米厚的不主要的缝隙。这个夹具固定在一个定位上，使焊接过程中总是保持水平位置。每个焊缝的长度是35毫米。被安装在Motoman机器人上的Fronius焊头是用于MIG焊过程中的。表1表明了这个焊接结构的焊接工艺参数。

表1：MIG焊接参数
电压 电流 速度 厚板1 厚板2 缝隙
(V) (A) (m/min.) (mm) (mm) (mm)
23 260 1.25 4 4 1

a)
 
b)

图1：钢管焊接配置:a）截面图 b）钢管尺寸

图2：管焊接实验装置

2.2测试
     焊接前后利用X射线技术观察焊缝气孔，按ASTM E155标准检查这些焊缝质量。然后整个焊接管子通过一个MTS试验机上的牵引来测试。焊接管最终的尺寸被定位在管子上的多个点的CMM机器所测量。扭曲的焊接管的最终位置与初始位置的管子进行比较。
3数值分析
     在Sysweld软件中，焊接分析是基于热传导和力学问题之间的微弱链接而制定的。只有热学经历在相同方向上才将影响力学性能 。因此，热学冶金力学分析分为两个步骤。第一步是一种热学冶金分析，其中在焊接过程的相变过程中从焊接电源的热量被转移。第一步温度和相变的结果将作为第二次的分析。它是一个纯热弹塑性模拟[6]。
4热源模型的鉴定
     焊接模拟运行之前，有必要确定热源模型的参数。这就是所谓的热源配件。实际上，它是一种热模拟中的稳定状态，在这种稳定状态中用一种优化工具来获得的热量来源的参数。图3给出了一个三维锥形热源形式，它的能量分布在方程中描述：举例如下:
F=Q0exp(-r²/r0²)                                 (1)

其中Q0 表示功率密度; r，r0 被定义为：
r²=(x-x0)²+(x-x0-vt)²                              (2)
和
r0=re-(re-ri)(ze-z+z0)/(ze-zi)                         (3)
其中（x0,y0,z0)是局部坐标系原点热源，re和 ri 在位置ze 和zi,分别为半径热源；v为焊接速度，t为时间。
     在这项研究中，金相截面已被用来确定热源，如图4所示的参数。一个三维锥形热源使用非常适合的焊接横截面。在横截面的网状尺寸是这种情况下约为0.5毫米。越细的网状，越是更准确的熔池形状，但不再是模拟。

图3:三维锥形热源 (Sysweld).
 
a)
 
b)
图4: (a) 金相截面(b) 熔池截面
5模型分析
在Hypermesh7.0上创建了管网。Sysweld2007已被用来作为求解器和前后处理器。一个完整的三维热学冶金力学分析用砖和棱镜为元素。两种焊接序列已完成，如W1/W2/W3/W4和W1/W3/W2/W4。在焊接过程中，夹住管子的过程中使用四个V形块，每个管子两个。在模拟中，管子的立场是反对接触的V形块的表面被认为是固定的条件（如Ux = Uy = Uz = 0）。在释放阶段，管子在V形块中是不受力的。
6结果
     当焊接管子从束缚状态被释放时，它的变形被控制。失真是通过测量沿管子的中心线从顶部到两侧面的小管的位移。这些措施是相对于大管的。图5a,b的描述失真通过数值模拟预测序列为W1/W2/W3/W4和W1/W3/W2/W4。在数值计算结果和实验中获得了良好的协议的两种焊接顺序如表2-3所示，在这两种倾向的扭曲和变形的过程中变化的范围。
 
a)

b)
图5：电子管失真（标准U）：（a）序列W1/W2/W3/W4，（b）序列W1/W3/W2/W4

表2：扭曲结果的比较（焊接顺序W1/W2/W3/W4）

     位移 (mm) 
 Uy Uz
实验 -0.4至-0.59 -0.35至-0.51
三维模拟 -0.4 -0.51

表2：畸变结果比较（焊接顺序W1/W2/W3/W4）

    位移 (mm) 
 Uy Uz
实验 -0.07至-0.11 -0.12至-0.21
三维模拟 -0.05 -0.26

a)

b)
图6：规定压力 Sxx （a）夹紧（b）放松（红=正，蓝=负）

a)
 
b)
图7：规定压力 Sxy （a）夹紧（b）放松（红=正，蓝=负）

a)
 
b)
图8：规定压力 Sxz （a）夹紧（b）放松（红=正，蓝=负）
    
图6-8显示了在夹紧和放松后的焊接在室温的规定压力下焊接序列W1/W2/W3/W4的状态（x是沿焊接管斧头方向）。以展示焊管失真，正负值来代替真实的应力值。该焊管失真可以解释为新的平衡位置，由于残余应力在没有外部负载的情况下。这就是说，在存在较大的差距时，在很大程度上对焊管失真是围绕当地的焊缝旋转模式进行的。
7结论
     MIG焊接很好的解决了铝铸造管（中空部分）存在非常大的差距的问题。
     三维热学冶金铸造力学焊接管采用Sysweld模拟已验证。模拟值与实验结果在扭曲趋势和变形范围内非常吻合。
     焊接的序列对焊接结构变形产生重大影响。事实证明，优化的焊接顺序对一个具有大量的焊缝的扭曲焊接结构的合理性非常重要。
致  谢
The authors would like to thank gratefully Rio Tinto Alcan and General Motor for financial and technical supports, particularly Martin Fortier and Pei-Chung Wang. Also, the authors are grateful to Welding Team at ATC (Audrey Boily, Martin Larouche, François Nadeau and Mario Patry) for experimental works.

参考文献
[1] K-H. Von Zengen, Aluminium in future cars – A challenge for materials science, Materials Science Forum, 519-521 (Part 2), 1201-1208 (2006).
[2] S. Wiesner S., M. Rethmeier and H. Wohlfart, MIG and laser welding of aluminium alloy pressure die cast parts with wrought profiles, Welding International, 19 (2), 130-133 (2005).
[3]  R. Akhter, L. Ivanchev, C.V.Rooyen, P. Kazadi and H.P. Burger, Laser welding of SSM Cast A356 aluminium alloy processed with CSIR-Rheo technology, Solid State Phenomena, 116-117, 173-176 (2006).
[4]  J.F. Lancaster, Metallurgy of welding, Abington Publishing (1999).
[5]  Φ. Grong, Metallurgical modelling of welding, The institute of materials (1997).
[6]  Sysweld, Sysweld reference manual, ESI Group (2005).