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The objective of the present paper is to develop nonlinear finite element method models for predicting the weld-induced initial deflection and residual stress of plating in steel stiffened-plate structures. For this purpose, t hree-dimensional thermo-elastic-plastic finite element method computations are performed with varying plate thickness and weld bead length (leg length) in welded plate panels, the latter being associated with weld heat input. The finite element models are verified by a comparison with experimental database which was obtained by the authors in separate studies with full scale measurements. It is concluded that the nonlinear finite element method models developed in the present paper are very accurate in terms of predicting the weld-induced initial imperfections of steel stiffened plate structures. Details of the numerical computations together with test database are documented.

Ships and offshore structures are fabricated by welding and thus weld-induced initial imperfections in the form of initial distortions and residual stresses are unavoidable. It is required to predict the weld-induced initial imperfections in magnitude and pattern in association with structural design and construction.

A large number of studies are found in the literature. In recent years, these studies are associated with weld-induced initial distortions [

Simplified methods to predict weld-induced initial distortions are available in the literature [

Nonlinear finite element method is a powerful tool to predict the weld-induced initial imperfections as it can deal with the distribution of heat transfer and general deformation due to welding. Ueda and Murakawa [

Studies on predicting the weld-induced initial distortions using finite element method are also found in the literature [

And, studies on repair welding using finite element method and experiment are also found in the literature [

In this paper, a three-dimensional thermo-elastic-plastic finite element method model is developed to predict the weld-induced distortions and residual stresses of thin-walled structures while achieving the goals in resulting accuracy and computational cost. The validity of the method is confirmed by a comparison with test database separately obtained from the full scale measurements by the authors.

In this section, the finite element model is presented to predict the weld-induced residual stresses. The three-dimensional thermo-elastic-plastic finite element analysis method is applied.

Welding residual stress analysis is a complex problem requiring a lot of knowledge such as solid mechanics, heat transfer, materials science and so on. An important feature of this problem is the nonlinearity of the material. That is, material properties such as thermal conductivity, heat capacity, elastic modulus, yield stress, and Poisson’s ratio vary sensitively with temperature. Particularly in the case of welding, there is sudden change of the temperature from the atmospheric temperature to the melting temperature of the metal. In addition, during the thermal transition period, the material experiences state changes from the solidus to the liquidus, or vice versa. These state changes produce changes in material properties and specific volume. This is generally explained by the coefficient of thermal expansion. For this reason, it is very difficult to obtain an analytical solution to the temperature and stress field. However, recent advances in finite element analysis using computer have led to many improvements in the residual stress analysis of welding. In general, the finite element method provides very detailed information on transition temperature, displacement, strain and stress. This FE method provides an accurate solution to the welding problem. This is possible because the temperature-dependent changes in the material properties of the material can be taken into account and properties such as the state of the weld and the phase change can be sufficiently modeled. As described above, the features of the welding problem requires consideration of many physical phenomena.

The validation of the finite element model is made by a comparison with test database obtained by Paik and Yi [

As heat source moves associated with welding, the heat input can change accordingly. Rosenthal [

q f ( x , y , z ) = 6 3 f f Q a b c f π π exp ( − 3 x 2 a 2 ) exp ( − 3 y 2 b 2 ) exp ( − 3 z 2 c f 2 ) (1)

at z ≥ 0

where q f ( x , y , z ) is the heat flux for the first half-ellipsoidal internal area located at the front of the welding arc, f f is the heat input proportion in the front part, Q is the heat flux of arc which is taken as Q = η I U , a , b and c f are geometric parameters, and η is the arc efficiency, I is the current and U is

the voltage. x, y and z are the coordinate where the origin is located on the weld surface below the heat source as shown in

The arc efficiency η is defined as the ratio of the heat transferred from the arc to the base material and the total heat generated by the arc, which is a constant simply indicative of the complex heat loss between the substrates in the arc. Since the arc efficiency is influenced by various factors such as welding conditions, melting depth and protective gas, it is very challenging to predict it theoretically and it is usually determined experimentally. This is because the arc efficiencies given in the literature are somewhat different from each other. For flux cored arc welding considered in the present method, η = 0.75 is usually taken.

The heat flux at any point ( x , y , z ) in the second semi-ellipsoid covering the rear part of the arc can be defined as follows:

q r ( x , y , z ) = 6 3 f r Q a b c r π π exp ( − 3 x 2 a 2 ) exp ( − 3 y 2 b 2 ) exp ( − 3 z 2 c r 2 ) (2)

at z < 0

where q r ( x , y , z ) is the heat flux at any point ( x , y , z ) in the second semi-ellipsoid covering the rear part of the arc, c r is the geometric parameter, and f r is the heat input proportion in the rear part. It is realized that f f + f r = 2 is approximately taken as far as the following conditions are satisfied:

f f = 2 ( 1 + c r / c f ) , f r = 2 ( 1 + c f / c r ) (3)

Paik and Yi [

Type | a [mm] | b [mm] | t_{p} [mm] | L_{w} [mm] | Stiffener Type | h_{w} [mm] | t_{w} [mm] | b_{f} [mm] | t_{f} [mm] |
---|---|---|---|---|---|---|---|---|---|

Deck | 3200 | 800 | 6 | 6.5 | Longi. | 125 | 7 | 75 | 7 |

8 | |||||||||

10 | Trans. | 350 | 12 | 100 | 17 | ||||

12 |

Note: L_{w} indicates the weld bead length (leg length of welding).

plate thickness is varied as 6, 8, 10 and 12 mm.

Kind of material | E [GPa] | σ_{Y} [MPa] | σ_{u} [MPa] | n [−] | Elongation [mm/mm] |
---|---|---|---|---|---|

Mild A | 203 | 309 | 458 | 0.3 | 0.23 |

Note: E is the elastic modulus, σ_{Y} is the yield strength, σ_{u} is the ultimate tensile strength, and n is the Poisson’s ratio.

As mentioned earlier, a quarter model of the target structure is applied as the extent of the finite element analysis as shown in

Welding heat input is applied using the dual heat source model where thermal loading and boundary conditions with convection and radiation are allocated. With convective conditions, the related constants depending on elevated temperature are defined from the database obtained from experiments and computational fluid dynamics simulations [

Leg length [mm] | Current [A] | Voltage [V] | Speed [CPM] | Speed [mm/s] | Heat input [KJ/mm] |
---|---|---|---|---|---|

6.5 | 320 | 32 | 36 | 6.0 | 1.71 |

a [mm] | b [mm] | c_{f} [mm] | c_{f} [mm] | f_{f} | f_{r} |
---|---|---|---|---|---|

4 | 4 | 4 | 16 | 0.4 | 1.6 |

The observed residual stress distribution is typically characterized by a high tensile stress near the weld bead and a distribution of compressive stress as it moves away from the weld.

Paik and Yi [

It is concluded that the present finite element analysis model gives very good agreements with test database.

In this section, the finite element model is presented to predict the weld-induced distortions. The thermal buckling analysis method is applied. The validation of the finite element model is made by a comparison with test database obtained from Paik and Yi [

analysis is performed using strain-as-direct-boundary (SDB) method [

The mechanical properties of material in

For welding analysis to obtain initial irregularity in thermal buckling analysis, contact analysis is carried out using self-weight and spring elements connected on four vertexes. The spring node constrains all six degrees of freedom to prevent rigid body motion. In order to simulate the actual welding process situation, the planar state is analyzed to the plane and the contact analysis with the structural element is carried out. The contact friction uses a stick-slip model with excellent convergence. A two-bay (1/2 + 1 + 1/2) model both in the longitudinal and transverse directions is taken as the extent for the analysis as shown in

The thermal loads obtained from steps I and II indicated in _{top} and T_{bot}) loads indicated in

t_{p}_{ } [mm] | L_{w} [mm] | Shrinkage force [N] | Imaginary temperature at top, T_{top} [˚C] | Imaginary temperature at bottom, T_{bot} [˚C] |
---|---|---|---|---|

6 | 6.5 | 45,466.49 | 0.174 | −0.174 |

8 | 36,963.12 | |||

10 | 31,861.09 | |||

12 | 28,459.75 |

[

presents the computed results of the weld-induced distortions after welding at the plate center in the longitudinal direction. According to the analysis procedure shown in

Paik and Yi [

The objectives of the present study were to develop finite element modelling techniques to predict weld-induced residual stresses and weld-induced distortions in a stiffened plate structures. The developed techniques were validated using test database obtained from direct measurements from a full scale prototype stiffened plate structures. Based on the results obtained from this study, the following conclusions are drawn.

1) In terms of predicting the weld-induced residual stresses, the modelling of heat source is important. In the present study, a double ellipsoidal shape model was applied to describe the heat source distribution during welding. It was confirmed that the numerical computations applying the proposed model are in good agreement with test data.

2) The procedure for predicting the weld-induced distortions comprises three steps, namely the weld temperature analysis, the shrinkage force computations and the thermal buckling analysis. The proposed procedure was implemented into a commercial computer code. It was confirmed that the numerical computations are in good agreement with test data.

The present study was undertaken in the Korea Ship and Offshore Research Institute at Pusan National University which has been a Lloyd’s Register Foundation Research Centre of Excellence. The support of Samsung Heavy Industries is greatly acknowledged.

Yi, M.S., Hyun, C.M. and Paik, J.K. (2018) Three-Dimensional Thermo-Elastic-Plastic Finite Element Method Modeling for Predicting Weld-Induced Residual Stresses and Distortions in Steel Stiffened-Plate Structures. World Journal of Engineering and Technology, 6, 176-200. https://doi.org/10.4236/wjet.2018.61010