焊接应力和变形的数值模拟研究
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摘要
焊接是一个牵涉到电弧物理、传热、冶金和力学的复杂过程。焊接现象包括焊接时的电磁、传热过程、金属的熔化和凝固、冷却时的相变、焊接应力与变形等等。要得到一个高质量的焊接结构必须控制这些因素。一旦各种焊接现象能够实现计算机模拟，我们就可以通过计算机系统来确定焊接各种结构和材料时的最佳设计、最佳工艺方法和焊接参数。本文从这一点出发，在总结前人的工作基础上结合数值计算的方法，对焊接过程产生的温度场、应力场、变形以及焊后的残余应力和变形进行了三维实时动态模拟的研究，提出了基于ANSYS软件的焊接温度场、应力和变形的模拟分析方法，并针对平板堆焊问题进行了实例计算，而且计算结果与传统的分析结果和理论值相吻合。
由于焊接是一个局部快速加热到高温，并随后快速冷却的过程。随着热源的移动，整个焊件的温度随时间和空间急剧变化，材料的物理性能参数也随温度剧烈变化，同时还存在熔化和相变时的潜热现象。因此，焊接温度场的分析属于典型的非线性瞬态热传导问题。因为焊接温度场分布十分不均匀，在焊接过程中和焊后将产生相当大的焊接应力和变形。焊接应力和变形的计算中既有大应变、大变形等几何非线性问题又有弹塑性变形等材料非线性问题。
虽然焊接温度场与应力应变场是双向耦合的，由于应力应变场对温度场的影响非常小，加上计算条件的限制，所以本文只考虑温度场对应力应变场的影响这一单向耦合。在模拟计算时，采用州SYS软件的热—结构耦合功能，利用间接法，先计算焊接温度场，温度场模拟准确之后保存其结果，再进行焊接应力和变形的计算。
模拟计算中一个最大的问题就是计算时间过长，分析其原因主要有三点：
(1) 严重的材料和几何非线性导致求解过程收敛困难；
(2) 三维模型中自由度数目庞大；
(3) 因热源移动需采用多步载荷进行计算。
武汉理工大学硕士学位论文
为了解决这一问题并提高计算精度，本文对高温时材料的物理性能参数
进行了适当的选取和处理；采用过渡网格划分形式划分网格以保证焊缝处网
格足够细小；选取高斯函数分布的热源模型，利用ANSYS 软件的
APDL（ANSY Parametric Design Language）语言编写程序实现移动热源的加
载；选取适当的计算时间步长；采用“生死单元”法模拟熔池金属的熔化和
凝固。
通过研究和算例验证，本文建立了可行的三维焊接温度场、应力和变形
的动态模拟分析方法，为复杂焊接结构进行三维焊接温度场、应力和变形的
分析提供了理论依据和指导，促进了有限元分析技术在焊接力学分析以及工
程中的应用。
Welding is a complicated physicochemical process which involves in electromagnetism, heat transferring, metal melting and freezing, phase-change, welding stress and deformation and so on. In order to get high quality welding structure, we have to control these factors. If welding process can be simulated with computer, we will easily determine the best design, procedure method and optimum welding parameter. Based on summing up others' experience, employing numerical calculation method, this paper researches how to realize the 3D dynamic simulation of welding temperature field, stress field and welding deformation when weldment is been welding and welding residual stress and residual deformation when weldment is cooled, then uses the research result to simulate the welding process of board surfacing. At the same time, the calculation result accords with traditional analysis results and theory results.
Welding process is that parts of an area is quickly heated to high temperature and then rapidly cooled. With the heat source moving, the whole weldment's temperature sharply changes, and the material's physical property parameters also sharply change. At the same time, there is latent heat of melt and phase-change. Therefore, the analysis of welding temperature field is a typical nonlinear transient heat conduction problem. Because of non-uniform temperature distribution, at the course of welding and postweld, weldment takes on serious welding stress and deformation. Calculation of welding stress and deformation includes geometrical nonlinear problem and material nonlinear problem.
Although welding temperature field and stress, strain field are bi-directional couple, because stress and strain field have little influence on temperature field, this paper only considers the single couple which temperature field effects on stress and strain field. When calculating, through ANSYS' thermal-structure couple function, firstly calculate welding temperature field and save the result, then use the temperature result as load to calculate welding
stress and deformation.
The most important problem, we have to face when calculating, is that the counting time is too long. There are three reasons:
(1) Serious material and geometrical nonlinear result in difficult solving convergence.
(2) 3D model has enormous degree of freedom.
(3) Have to employ multi-step load for moving heat source.
In order to solve the problem and improve solution accuracy, this paper chooses suitable material property parameter, uses transition mesh, chooses Gauss function heat source model, uses ANSYS' APDL (ANSYS Parametric Design Language) to compile program to apply load of moving heat source, chooses suitable time step, uses the method of "birth and death" method to simulate the weld pool's melting and freezing.
Through research and practical verify, this paper establishes a feasible dynamic simulation method on 3D welding temperature field, stress and deformation, which provides theory foundation and instruction, promotes the application of FEM (Finite Element Method) on welding mechanics analysis and engineering.
由于焊接是一个局部快速加热到高温，并随后快速冷却的过程。随着热源的移动，整个焊件的温度随时间和空间急剧变化，材料的物理性能参数也随温度剧烈变化，同时还存在熔化和相变时的潜热现象。因此，焊接温度场的分析属于典型的非线性瞬态热传导问题。因为焊接温度场分布十分不均匀，在焊接过程中和焊后将产生相当大的焊接应力和变形。焊接应力和变形的计算中既有大应变、大变形等几何非线性问题又有弹塑性变形等材料非线性问题。
虽然焊接温度场与应力应变场是双向耦合的，由于应力应变场对温度场的影响非常小，加上计算条件的限制，所以本文只考虑温度场对应力应变场的影响这一单向耦合。在模拟计算时，采用州SYS软件的热—结构耦合功能，利用间接法，先计算焊接温度场，温度场模拟准确之后保存其结果，再进行焊接应力和变形的计算。
模拟计算中一个最大的问题就是计算时间过长，分析其原因主要有三点：
(1) 严重的材料和几何非线性导致求解过程收敛困难；
(2) 三维模型中自由度数目庞大；
(3) 因热源移动需采用多步载荷进行计算。
武汉理工大学硕士学位论文
为了解决这一问题并提高计算精度，本文对高温时材料的物理性能参数
进行了适当的选取和处理；采用过渡网格划分形式划分网格以保证焊缝处网
格足够细小；选取高斯函数分布的热源模型，利用ANSYS 软件的
APDL（ANSY Parametric Design Language）语言编写程序实现移动热源的加
载；选取适当的计算时间步长；采用“生死单元”法模拟熔池金属的熔化和
凝固。
通过研究和算例验证，本文建立了可行的三维焊接温度场、应力和变形
的动态模拟分析方法，为复杂焊接结构进行三维焊接温度场、应力和变形的
分析提供了理论依据和指导，促进了有限元分析技术在焊接力学分析以及工
程中的应用。
Welding is a complicated physicochemical process which involves in electromagnetism, heat transferring, metal melting and freezing, phase-change, welding stress and deformation and so on. In order to get high quality welding structure, we have to control these factors. If welding process can be simulated with computer, we will easily determine the best design, procedure method and optimum welding parameter. Based on summing up others' experience, employing numerical calculation method, this paper researches how to realize the 3D dynamic simulation of welding temperature field, stress field and welding deformation when weldment is been welding and welding residual stress and residual deformation when weldment is cooled, then uses the research result to simulate the welding process of board surfacing. At the same time, the calculation result accords with traditional analysis results and theory results.
Welding process is that parts of an area is quickly heated to high temperature and then rapidly cooled. With the heat source moving, the whole weldment's temperature sharply changes, and the material's physical property parameters also sharply change. At the same time, there is latent heat of melt and phase-change. Therefore, the analysis of welding temperature field is a typical nonlinear transient heat conduction problem. Because of non-uniform temperature distribution, at the course of welding and postweld, weldment takes on serious welding stress and deformation. Calculation of welding stress and deformation includes geometrical nonlinear problem and material nonlinear problem.
Although welding temperature field and stress, strain field are bi-directional couple, because stress and strain field have little influence on temperature field, this paper only considers the single couple which temperature field effects on stress and strain field. When calculating, through ANSYS' thermal-structure couple function, firstly calculate welding temperature field and save the result, then use the temperature result as load to calculate welding
stress and deformation.
The most important problem, we have to face when calculating, is that the counting time is too long. There are three reasons:
(1) Serious material and geometrical nonlinear result in difficult solving convergence.
(2) 3D model has enormous degree of freedom.
(3) Have to employ multi-step load for moving heat source.
In order to solve the problem and improve solution accuracy, this paper chooses suitable material property parameter, uses transition mesh, chooses Gauss function heat source model, uses ANSYS' APDL (ANSYS Parametric Design Language) to compile program to apply load of moving heat source, chooses suitable time step, uses the method of "birth and death" method to simulate the weld pool's melting and freezing.
Through research and practical verify, this paper establishes a feasible dynamic simulation method on 3D welding temperature field, stress and deformation, which provides theory foundation and instruction, promotes the application of FEM (Finite Element Method) on welding mechanics analysis and engineering.
引文
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[2] 拉达伊著，焊接热效应·温度场、残余应力、变形，熊第京等译．北京：机械工业出版社，1997．1～87
[3] 陈丙森．计算机辅助焊接技术．北京：机械工业出版社，1999，107～168
[4] 陈楚等．数值分析在焊接中的应用．上海：上海交通大学出版社，1985，1～287
[5] H．H．雷卡林著．焊接热过程计算．徐碧宇，庄鸿寿译．北京：中国工业出版社，1958，24～78
[6] 武传松．焊接热过程数值分析，哈尔滨工业大学出版社，1990，22～78
[7] 武传松．焊接过程的计算机模拟，第十次全国焊接学术会议IT与焊接专题会议，2001，10
[8] 陈楚，汪建华，杨洪庆．非线性焊接热传导的有限元分析和计算．焊接学报，1983(3)：139～148
[9] 蔡洪能，唐慕尧．TIG焊接温度场的有限元分析．机械工程学报，1996．32(2)：34～39
[10] 陈楚，汪建华，杨洪庆．水下焊接冷却特性的有限元分析．海洋工程，1983(4)：34～38
[11] 鹿安理，史清宇，赵海燕等．厚板焊接过程温度场、应力场的三维有限元数值模拟．中国机械工程，2001．12(2)：183～186
[12] Wang J. Improvement in numerical accuracy and stability of 3-D FEM analysis in welding. Welding Journal, 1996, 75(4): 1298-134s
[13] 汪建华．焊接结构三维热变形的有限元模拟．上海交通大学学报，1994．28(6)：59～65
[14] 汪建华．三维瞬态温度场的有限元模拟．上海交通大学学报，1996，30(3)：120-125
[15] K. Masubuchi. Prediction and control of residual stresses and distortion in welded structures. Proc. Theoretical Prediction in Joining and Welding, 1996:71-88
[16] K. S. Alfredsson and B. L. Josefson. Harmonic Response of a Spot Welded Box Beam-Influence of Welding Residual Stresses and Deformations. Proc. IUTAM Symposium on the Mechanical Effects of Welding. Lulea, Sweden, June, 1991:1-8
[17] 陈楚．轴对称热弹塑性应力有限元分析在焊接中的应用．焊接学报，1987．8(4)：196～203
[18] 汪建华．管板接头三维焊接变形的数值模拟．焊接学报，1995．16(3)：140～145
[19] 汪建华，压缩机焊接变形的三维数值模拟．机械工程学报，1996．32(1)：85～91
[20] Wang Jianhua et. An FEM model of buckling distortion during welding of thin plate．J．of Shanghai Jiaotong University, 1999, E-4(2):69-72
[21] 董俊惠，霍立兴，张玉凤．低碳钢管焊接残余应力有限元分析．焊接，2000(12)：11～15
[22] 杨庆祥，李艳丽，赵言辉等．堆焊金属残余应力场的计算机模拟．焊接学报，2001．22(3)：44～46
[23] 余作生，颜怡霞等．ANSYS在焊接中的应用，有限元在工程中的应用—98ANSYS中国用户论文专集，陕西师范大学出版社，1998，25～28
[24] 鹿安理，史清宇，赵海燕等．焊接过程仿真领域的若干关键技术问题及其初步研究．中国机械工程，2000．11(1～2)：201～205
[25] 蔡志鹏，赵海燕，鹿安理等．串热源模型及其在焊接数值模拟中的应用．机械工程学报，2001．37(4)：25～28
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[2] 拉达伊著，焊接热效应·温度场、残余应力、变形，熊第京等译．北京：机械工业出版社，1997．1～87
[3] 陈丙森．计算机辅助焊接技术．北京：机械工业出版社，1999，107～168
[4] 陈楚等．数值分析在焊接中的应用．上海：上海交通大学出版社，1985，1～287
[5] H．H．雷卡林著．焊接热过程计算．徐碧宇，庄鸿寿译．北京：中国工业出版社，1958，24～78
[6] 武传松．焊接热过程数值分析，哈尔滨工业大学出版社，1990，22～78
[7] 武传松．焊接过程的计算机模拟，第十次全国焊接学术会议IT与焊接专题会议，2001，10
[8] 陈楚，汪建华，杨洪庆．非线性焊接热传导的有限元分析和计算．焊接学报，1983(3)：139～148
[9] 蔡洪能，唐慕尧．TIG焊接温度场的有限元分析．机械工程学报，1996．32(2)：34～39
[10] 陈楚，汪建华，杨洪庆．水下焊接冷却特性的有限元分析．海洋工程，1983(4)：34～38
[11] 鹿安理，史清宇，赵海燕等．厚板焊接过程温度场、应力场的三维有限元数值模拟．中国机械工程，2001．12(2)：183～186
[12] Wang J. Improvement in numerical accuracy and stability of 3-D FEM analysis in welding. Welding Journal, 1996, 75(4): 1298-134s
[13] 汪建华．焊接结构三维热变形的有限元模拟．上海交通大学学报，1994．28(6)：59～65
[14] 汪建华．三维瞬态温度场的有限元模拟．上海交通大学学报，1996，30(3)：120-125
[15] K. Masubuchi. Prediction and control of residual stresses and distortion in welded structures. Proc. Theoretical Prediction in Joining and Welding, 1996:71-88
[16] K. S. Alfredsson and B. L. Josefson. Harmonic Response of a Spot Welded Box Beam-Influence of Welding Residual Stresses and Deformations. Proc. IUTAM Symposium on the Mechanical Effects of Welding. Lulea, Sweden, June, 1991:1-8
[17] 陈楚．轴对称热弹塑性应力有限元分析在焊接中的应用．焊接学报，1987．8(4)：196～203
[18] 汪建华．管板接头三维焊接变形的数值模拟．焊接学报，1995．16(3)：140～145
[19] 汪建华，压缩机焊接变形的三维数值模拟．机械工程学报，1996．32(1)：85～91
[20] Wang Jianhua et. An FEM model of buckling distortion during welding of thin plate．J．of Shanghai Jiaotong University, 1999, E-4(2):69-72
[21] 董俊惠，霍立兴，张玉凤．低碳钢管焊接残余应力有限元分析．焊接，2000(12)：11～15
[22] 杨庆祥，李艳丽，赵言辉等．堆焊金属残余应力场的计算机模拟．焊接学报，2001．22(3)：44～46
[23] 余作生，颜怡霞等．ANSYS在焊接中的应用，有限元在工程中的应用—98ANSYS中国用户论文专集，陕西师范大学出版社，1998，25～28
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