WANG Yang,LUO Yu,TIAN Liang,XUE Jian

(1.School of Naval Architecture,Ocean&Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China; 2.Jiangsu Newyangzi shipbuilding Co.,Ltd,Wuxi 214532,China)

Evaluation Method for Inherent Deformation and its Application in Predicting Welding Distortion on Hull Blocks

WANG Yang1,LUO Yu1,TIAN Liang1,XUE Jian2

(1.School of Naval Architecture,Ocean&Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China; 2.Jiangsu Newyangzi shipbuilding Co.,Ltd,Wuxi 214532,China)

To predict the welding distortion of large structures using elastic analysis based on the inherent strain theory,the inherent deformation around the welding line should be evaluated beforehand.The welding residual stress and welding distortion of the welded joint depend on the value and distribution of inherent deformation.Therefore,it is significant to develop methods to evaluate the inherent deformation precisely and establish inherent deformation database for the prediction of welding distortion on large structures.In this paper,three methods(formula method,Thermal-Elastic-Plastic Finite Element Method(TEP FEM)and experimental method)for evaluating inherent deformation are presented.A fillet welded joint is taken as an example,inherent deformations evaluated by these methods are compared.Finally,computations of welding distortion of a typical hull block are conducted based on the inherent deformation database calculated by three methods.By comparing the welding distortion of evaluated results with that of measured ones,the reliability of the inherent deformation database is confirmed.

inherent deformation database;longitudinal inherent shrinkage;transverse inherent shrinkage;formula method;TEP FEM;experimental method

0 Introduction

With the development of advanced computer and numerical analysis technology,the computational approaches especially the Thermal-Elastic-Plastic(TEP)Finite Element Method (FEM)[1]and elastic FEM[2-3]based on inherent strain theory have been applied to predict the welding distortion by many researchers in the welding field.The later one,using shell FE models with elements much larger than those required in thermal elastic plastic FE analysis can effectively predict the welding distortion of large structures.

If the inherent strain(including thermal strain,plastic strain,creep strain and that produced through phase transformation)around the welding line is known,the residual stress and the welding distortion can be computed by an elastic FEM using the inherent strain as an initialstrain.However,the distribution of inherent strain which is related to the residual stress is hard to calculate.And for large structures,engineers mainly care about the welding distortion.As a result,the inherent deformation theory is introduced in the prediction of welding distortion in large structures.The advantage of inherent deformation is that it is not necessary to consider the distribution of inherent strain on the cross section.It is defined as the integration of inherent strain on each cross section normal to the welding line.The welding distortion of welded structures can be conveniently calculated if inherent deformations including longitudinal inherent shrinkage and transverse inherent shrinkage of each welded joint are known.Therefore,the development of inherent deformation database is significant to the convenient and accurate prediction of welding distortion on large structures.In this paper,three methods including formula method,TEP FEM and experimental method are presented to evaluate the inherent deformation of welded joint at first.Secondly,a fillet welded joint is taken as an example. Three methods are utilized to evaluate the longitudinal inherent shrinkage and transverse inherent shrinkage of this welded joint.Finally,the inherent deformation database evaluated by these methods is adopted to predict the welding distortion of a typical hull block.This research can provide a theoretical guideline for the establishment of inherent deformation database.

1 Methods of evaluating inherent deformation

1.1 Formula method

Over the years,many studies of welding distortion were conducted by empirical formulas based on experimental measurement.Verhaeghe[4]investigated welding distortion based on measured deformation available in the literature and reviewed approximate formulae considering various production factors.In this part,formulas of calculating inherent deformation proposed by Wang are introduced[5].

Wang proposed the concept of unitary longitudinal plastic strain volume WLand unitary transverse plastic strain volume WTas given by Eqs.(1)and(2).

1.1.1 Longitudinal inherent shrinkage

(1)Single pass welding

The relationship between the unitary longitudinal plastic strain volume WLand the net heat input per unit length Qnet(J/mm)may be expressed as follows:

(2)Multi-pass welding

The unitary longitudinal plastic strain volume WLof the whole joint can be calculated through the following equation:

where m is the number of the welding pass;WLmis the unitary longitudinal plastic strain volume of the pass with the largest net heat input per unit length;Kmis the influence factor of welding pass,and it can be evaluated by the following equation:

where εsis the yield strain of the material;α is the expansion coefficient;c is the specific heat (J/g·℃);ρ is the density of melted metal(g/cm3);θ is the heating coefficient(J/cm3).

(3)Fillet welded joint

Most of the plastic strain zone of the second welding pass overlaps that of the first one after fillet welding.So the unitary longitudinal plastic strain volume of the second welding pass WL2can be calculated as given by Eq.(6):

where K2is the influence factor and it can be evaluated as follows:

where δpis the thickness of web plate;K is the weld leg length;rais the depth of plastic strain zone,and its value is decided by the smaller one calculated by the following equations:

where δnis the thickness of flange plate.

1.1.2 Transverse inherent shrinkage

(1)Single pass welding

The relationship between the unitary transverse plastic strain volume WTand the net heat input per unit length Qnet(J/mm)can be expressed as follows:

Fig.1 Relationship between ξ and

(2)Multi-pass welding[6]

The unitary transverse plastic strain volume WTiand angular distortion βicaused by the number i welding pass can be evaluated as follows:

where ξiis the scale factor;βiis the angular distortion caused by the number i welding pass; eiis the distance between the center of the cross section and the center of gravity of transverse plastic strain volume of the number i welding pass.Fig.2 shows the distribution of geometrical parameters of Eq.(12).

Theunitarytransverseplastic strain volume WTand angular distortion β can be evaluated by the following equations:

where diis the distance between the center of the cross section of welding line and that of the plate in the thickness direction.

The scale factor ξiis evaluated by the following equation as mentioned in Wang’s paper[6]:

Fig.2 Geometrical parameters of multi-pass welding

where Ktis the influence factor of thickness of welded joint;Kvis the influence factor of welding speed;Kmis the influence factor of longitudinal plastic deformation;Kcis the influence factor of transverse shrinkage;Ksis the influence factor of original stress.And all these factors were calculated in Wang’s paper[6].

1.2 TEP FEM

According to the definition of inherent deformation given by Eq.(1),the longitudinal inherent shrinkage and transverse inherent shrinkage can be evaluated by integrating the longitudinal inherent strain and transverse inherent strain,respectively.As discussed in Luo’s paper[2],in carbon steel,the plastic strain is the dominant component of the inherent strain.Fig. 3 shows the distribution of plastic strain in the longitudinal direction and the transverse direction on the neutral plane in a middle transverse cross section of a typical bead-on-plate[7]. From this figure,one can observe that plastic strains distribute around the welding line.

Fig.3 Distribution of plastic strain on neutral plane in a middle transverse cross section

The longitudinal inherent shrinkageand the transverse inherent shrinkagemay then be evaluated as in the following Eqs.(16)and(17)using the longitudinal inhere strainand the transverse inherent strainon a transverse cross section in the middle of the joint.

For the special case of a very thin plate,the distribution of longitudinal inherent strain isnearly uniform through the thickness.Eqs.(16)and(17)can be simplified as follows:

1.3 Experimental method

Fig.4 is the result of thermal elastic plastic FE analysis of the welded joint of bead-onplate and shows the distribution of longitudinal displacement along the welding line[7].The curve can be divided into a middle part and two ends.The simulated values at two ends are different from those in the middle part due to the effect of free ends.In the middle part,the curve is almost linear with almost a constant slope.From this slope,the longitudinal inherent deformation can be evaluated as follows.

Fig.4 Distribution of longitudinal displacement along welding line

Since the slope of the longitudinal displacement in Fig.4 is the longitudinal strain εLin the welding directionit can be related to the tendon force Ftendonand the longitudinal inherent shrinkagethrough the following equation.That isin X direction of a length equal to B.

where A is the area of cross section;B is the plate width.

The above equation means that,the longitudinal inherent shrinkagecan be evaluated as the longitudinal displacement between two points separated in X direction by a length equal to the plate width B.If the specimen is long enough,this equation can be used to evaluate the longitudinal inherent deformation in experiments by measuring the longitudinal displacement of sampling points along the welding line.Since the restraint of transverse direction is small, the transverse inherent shrinkage can be obtained by directly measuring the transverse displacement of sampling points along the welding line.

2 Inherent deformation of fillet welded joint evaluated by three methods

2.1 Experiment of a typical fillet welded joint

Fig.5 shows a typical fillet welded joint used in the experiment.This model is consisted of a web with 300 mm×100 mm×6 mm and a flange with 300 mm×200 mm×6 mm.The direction of two welding lines is also shown.In order to obtain the displacement near the welding line in welding direction,displacement at the nine points along one side of the flange as shown in Fig.5 is measured.A middle cross section in the weld zone of this joint after welding is shown in Fig.6.The experiment is carried out by Hudong-Zhonghua Shipbuilding(Group)Co.,Ltd. The material of this structure is carbon steel[7].In this experiment,MIG welding is used,and the welding condition is shown in Tab.1.

Fig.5 Dimensions of the fillet welded joint used in the experiment

Fig.6 Cross section in the weld zone of the fillet welded joint showing fillet size

Tab.1 Welding condition of fillet welded joint

2.2 Evaluation of inherent deformation

Fig.7 FE model of the considered fillet welded joint

A solid FE model of fillet welded joint is shown in Fig.7.The model consists of 12 803nodes and 10 020 elements.The size of the FE model is the same as the one in the experiment. Temperature dependent material properties shown in Wang’s paper are used in thermal elastic plastic FE analysis of this joint[8].

According to Tab.1,the Qnetis 949 J/mm.And by considering the equations listed in section 1.1,the unitary longitudinal plastic strain volume of the first welding pass can be calculated as follows:

The parameters of Eq.(7)are listed in Tab.2.

Tab.2 Parameters of Eq.(7)

According to Eq.(8),the value of rais 15.2 mm.And this value is larger than the thickness of the flange plate.Therefore,rain this study is set to be 6 mm.By substituting all the parameters into Eq.(7),we can get:

The unitary longitudinal plastic strain volume of the second welding pass WL2can be calculated by Eq.(6):

Then,we can get the value of longitudinal inherent shrinkage by the following equation:

The transverse inherent shrinkage can be calculated as follows:

By integrating the plastic strain obtained from thermal elastic plastic FE analysis,the value of the longitudinal inherent shrinkages and transverse inherent shrinkages on each cross section along the welding line are computed and plotted in Figs.8 and 9.As may be seen from the figure,if the edge effect is ignored,the longitudinal inherent shrinkage and transverse inherent shrinkage have almost a uniform distribution along the welding line.

Fig.8 Distribution of longitudinal inherent shrinkage along the welding line and the corresponding averaged value

Fig.9 Distribution of transverse inherent shrinkage along the welding line and the corresponding averaged value

Fig.10 Distribution of longitudinal displacement along welding line

Fig.11 Distribution of transverse displacement along welding line

In order to ignore the edge effect,the displacements of seven points in Fig.5(P2,P3, P4,P5,P6,P7 and P8)are linear fitted.Figs.10 and 11show the longitudinal displacement and transverse one of these sampling points.The longitudinal inherent shrinkage can be calculated by substituting the slope of line 1 and the plate width into Eq.(20).

Tab.3 shows the longitudinal inherent shrinkage and transverse inherent shrinkage calculated by three methods.As may be seen from this table,the longitudinal inherent shrinkage and transverse inherent shrinkage evaluated by these methods are consistent.This indicates that the inherent deformation database can be established by any of these methods.

Tab.3 Comparison of estimated longitudinal inherent shrinkage

3 Application

3.1 FE model of a typical hull block

303P which is one part of double bottom block of 4250 TEU container ship is taken as the research object[8].Fig.12 shows the FE model of this block.The length,width and height of 303P are 17 950 mm,13 535 mm,1 700 mm,respectively.The X direction,Y direction and Z direction are along the ship length,width and depth,respectively.This model can be divided into three parts including inner bottom,outer bottom,longitudinal girders and floors as shown in Fig.13.

Fig.12 FE model of 303P

Fig.13 Parts of 303P

Fig.14 shows the process of assembling 303P at the shipyard.As we can see from this figure,the construction of 303P is divided into two steps (bold lines in the figures represent weldlines).22 weldlines can be found in 303P.

3.2 Method to apply inherent deformation

In this study,the inherent deformation of each welded joint in 303P is evaluated by the inherent deformation database of Welding Structure Deformation Analysis System(Weld-sta) which is developed by Structure Mechanics Research Institute of Shanghai Jiao Tong University and Joining and Welding Research Institute of Osaka University.

Taking the longitudinal inherent shrinkage as an example,Fig.15(a)shows the middle cross section of a simple butt welded joint with uniform thickness.The longitudinal inherent shrinkage can be evaluated by integrating the whole longitudinal inherent strain on this cross section.Then it is equally divided into two parts,and applied to the two plates to be welded in the elastic analysis.For a butt welded joint with different plate thicknesses as shown in Fig. 15(b),the longitudinal inherent shrinkages of the two parts can be evaluated separately,andthen applied in the elastic analysis.Similarly,the longitudinal inherent shrinkage of a fillet welded joint as shown in Fig.15(c)can be divided into three parts and applied to the three plates forming the fillet joint.This method can also be applied to other typical welded joints such as a lap welded joint.

Fig.14 Assembly process of 303P

Fig.15 Typical welded joint

3.3 Results and discussion

Fig.16 shows the welding distortion at the first step in X direction of 303P.The dotted lines show the undeformed structure of 303P,and the deformation is magnified 200 times.The method of calculating total welding deformation of each erection is shown in Tab.4.Tab.5 shows the comparison of the welding distortion in X direction and Y direction in inner bottom and outer bottom between simulated results and the measured ones.According to Tab.5,the simulated results are totally consistent with the measured data.Therefore,the reliability of predicting welding distortion of assembling 303P based on the inherent deformation database is proved.

Fig.16 Welding distortion at the first step of 303P in X Direction

Tab.4 Calculation of welding distortion in 303P

Tab.5 Comparison of welding distortion between simulated results and measured results in 303P

4 Conclusions

Based on the inherent deformation theory,three methods of evaluating inherent deformation are presented in this paper.And through the comparison and application of these methods, several conclusions are made.

(1)The accuracy of elastic FE analysis depends on the precision of the value of inherent deformation.Therefore,it is of significance to establish authoritative inherent deformation database in order to insure the accuracy of elastic FE analysis.

(2)The value of longitudinal inherent shrinkage can be quickly calculated by formula method.Researchers can predict the trend of welding distortion by using this method.

(3)By integrating the inhere strain on a transverse cross section,the inherent deformation can be evaluated by TEP FEM.The accurate inherent deformation can be obtained in the middle region of the welding line.

(4)The longitudinal inherent shrinkage can be calculated by the product of the slope of the longitudinal displacement along welding line and the plate width in experimental method. And the transverse inherent shrinkage can be obtained by directly measuring the transverse displacement of sampling points along the welding line.

(5)By considering a typical fillet welded joint,the longitudinal inherent shrinkage and transverse inherent shrinkage evaluated by three different methods based on the concept of inherent deformation are consistent.

(6)The inherent deformation database based on these methods are applied to predict the welding distortion of a typical hull block.By comparing the welding distortion of simulated results with that of measured ones,the reliability of the inherent deformation database is confirmed.

Acknowledgements

This research is technically supported by Jiangsu Newyangzi Co.,Ltd and is financially supported by Science and Technology Department of Jiangsu Province(Grant No.BE2010172).

[1]Goldak J A.Modeling thermal stresses and distortions in welds[C].Proceeding of the 2nd International Journal for Numerical Methods in Engineering,1988,25(2):635-655.

[2]Luo Yu,Deng Dean,Xie L,et al.Prediction of deformation for large welded structures based on inherent strain[J].Transactions of JWRI,2004,33(1):65-70.

[3]Murakawa H,Deng Dean,Ma Ninshu.Concept of inherent strain,inherent stress,inherent deformation and inherent force for prediction of welding distortion and residual stress[J].Transactions of JWRI,2010,39(2):115-116.

[4]Verhaeghe.Predictive formulae for weld distortion-a critical review[M].Cambridge:Abington Publishing,England Cambridge,1999.

[5]Wang Jianhua.Numerical simulation technology of welding and its application[M].Shanghai:Shanghai Jiaotong University Press,2003.

[6]Wang Jianhua,Chen Chu.Modified temperature computer system for various welded joint configuration[J].Transactions of the China Welding Institution,1990,11(1):57-64.

[7]Wang Yang,Luo Yu.Comparison on several kinds of T-E-P FEM software for welding[J].Hot Working Technology,2013, 42(11):5-7,12.

[8]Wang Yang,Xue Jian,Luo Yu.Sequence optimization of hull structure assembly based on prediction of welding deformation[J].China Welding,2013,22(4):47-52.

固有變形計算方法及其在船舶焊接結構變形中的應用

王 陽1，羅 宇1，田 亮1，薛 健2

（1.上海交通大學 船舶海洋與建筑工程學院，上海200240；2.江蘇新?lián)P子造船有限公司，江蘇 無錫 214532）

采用基于固有應變法的彈性有限元分析預測大型復雜結構的焊接變形的前提是必須已知焊縫附近的固有變形。結構的焊接殘余應力與焊接變形取決于其接頭的固有變形大小及分布，因此開發(fā)精確計算接頭固有變形的方法，并依此建立一個完善的固有變形數(shù)據(jù)庫對于大型復雜結構焊接變形的預測有重要意義。文中提出了幾種計算固有變形的方法包括公式法、熱彈塑性有限元法、實測法，并分別采用這幾種方法對典型T型接頭的橫向固有收縮與縱向固有收縮進行計算，三種方法得到的結果比較一致。在此基礎上，進一步以典型船體結構為研究對象，采用依照這三種方法建立的固有變形數(shù)據(jù)庫對其焊接變形進行預測，并與實測數(shù)據(jù)進行比較，驗證了該數(shù)據(jù)庫的有效性。

固有變形數(shù)據(jù)庫；縱向固有收縮；橫向固有收縮；公式法；熱彈塑性有限元法；實測法

TG404

:A

王 陽（1986-），男，上海交通大學船舶海洋與建筑工程學院博士研究生，通訊作者；

TG404

A

10.3969/j.issn.1007-7294.2015.09.009

1007-7294（2015）09-1126-13

羅 宇（1971-），男，博士，上海交通大學船舶海洋與建筑工程學院教授；

田 亮（1985-），男，上海交通大學船舶海洋與建筑工程學院博士研究生；

薛 ?。?967-），男，江蘇新?lián)P子造船有限公司高級工程師。

Received date：2015-03-03

Foundation item:Supported by the Science and Technology Department of Jiangsu Provinde(Grant No.BE2010172)

Biography：WANG Yang(1986-),male,Ph.D.student,E-mail:maible@sjtu.edu.cn;

LUO Yu(1961-),male,Ph.D.,professor;

TIAN Liang(1985-),male,Ph.D.,student;

XUE Jian(1967-),male,senior engineer.