Experimental measurements and numerical simulations of distortions of overlap laserwelded thin sheet steel beam structures
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Abstract
Distortions of mild steel structures caused by laser welding were analyzed. One thousandmillimeter Ubeam structures were welded as overlap joints with different process parameters and thickness configurations. Final vertical and transverse distortions after cooling were measured along the Ubeam. Significant factors, which affect distortions, were identified. Heat input per unit length, weld length, and sheet thickness showed a significant effect on welding distortions. Furthermore, the welding distortions were modeled using FE simulations. A simplified and computationally efficient simulation method was used. It describes the effect of shrinkage of the weld zone during cooling. The simulations show reasonable computation times and good agreement with experiments.
Keywords (IIW Thesaurus)
Laser beam welding Distortions FE simulation Volume shrinkage method Mild steel1 Introduction
Laser beam welding (LBW) is an increasingly used joining method in several industries due to its highstrength continuous joints, high production efficiency, high precision, and low metallurgical impact on the welded material. However, as any fusion joining method, the heating and subsequent cooling of the material will induce stresses in the material and cause geometrical distortions, which may require modified fixturing, result in rejected components, or need for postjoining repair in industry.
Experimental results of distortions due to LBW of various materials including 4.0mm buttwelded steel sheets [1], 2.5mm buttwelded aluminum sheets [2], and 0.4mm overlapwelded Inconel tube structures [3] have been presented. Moreover, the results of distortions in laserhybrid welding of 9.0mmthick steel parts were presented in [4]. The effect of clamping conditions on distortions has also been highlighted [5]. In addition, various methods to decrease welding distortions have been presented, such as optimization of process parameters [6] or intermittent welding patterns [7].
Researchers have also provided models to predict the magnitude and distribution of welding distortions through both simplified empirical models and detailed numerical analyses by finite element (FE) modeling. The simplified models rely on general assumptions, which predict the magnitude of distortions due to heat input or weld sheet geometry. An important assumption is that cooling contraction is the dominant source of distortions, as proposed by Okerblom [8] and followed by several other authors.
With increased computer power, numerical modeling of the LBW process through FE analyses has become more widespread. The new techniques include transient modeling of the moving heat source which models dynamic heating and cooling of the material. The temperature history of the material generates thermal expansion and contraction, changes in material behavior due to phase transformations, and changes in material properties. The reduced mechanical strength at elevated temperatures increases plastic strains in the structure during welding, and martensitic transformation introduces additional volumetric strains during the rapid cooling after welding.
Transient coupled thermomechanical FE models are able to predict distortions with high accuracy by extensive temperature and metallurgydependent material models and detailed conductive heat sources. However, they are also computationally timeconsuming and rely on extensive material data [9], which hinders widespread industrial use. Simplified numerical methods have long been used to approximately predict welding distortions for idealized geometries [10]. Simplified simulation methods have also been used to predict welding distortions for more complex geometries by relying on calibration of the model [11].
In the automotive industry, LBW is often used for steel and aluminum sheets of thicknesses between less than 1 mm and up to 4 mm. Such slender structures are more prone to welding distortions compared to stiffer structures with thicker sheets. It is also of practice in the automotive industry to join thin sheets in overlap configurations, as opposed to fillet or butt welds as for thicker sheet materials. Common applications of LBW in body in white design are in the case of lowstrength steels, exterior panels such as roofs, doors, or trunk lids and in the case of highstrength steels closed beam structures such as A or Bpillars. The main advantages of the LBW joints are the high structural strength and desirable visual appearance compared to other joining methods such as resistance spot welding. The present paper focuses on the applications in lowstrength steels since such applications are usually very sensitive to distortions and shape deviations.
In summary, the present paper provides new information on distortion of overlap laserwelded mild steel thin sheet beam structures relevant for automotive applications. It defines how sheet thickness and process parameters influence the distortions. Finally, it is shown how a simplified FE simulation technique can be used to predict the magnitude of the distortions. This method allows quick calculations and does not require initial fitting procedures contrary to some other methods.
2 Experimental procedure
The maximum chemical contents of steel material [12]
C  Si  Mn  P  S  Al  Ti  Cu 

0.08%  0.5%  0.5%  0.025%  0.02%  0.01%  0.3%  0.2% 
The fixture also included a toggle clamp at one end of the beam to stabilize the beam. In the symmetrical beam case, the toggle clamp was located at the center of the top of the Ubeam, as illustrated in Fig. 2 and in the asymmetrical case, the toggle was located at the center of the flat sheet. The toggle clamp initiates a downward force on the structure at the end of the beam, pushing the beam towards the vertical supports at the flanges. The fixture prevents both upward and downward vertical displacements at the location of the toggle clamp. The rest of the beam is free to move upwards vertically.
 1.
The effect of intermittent welding on welding distortions, see samples R1, R2, I1, and I2.
 2.
The effect of heat input on welding distortions, see samples R1, H1, and H2.
 3.
The effect of sheet thickness on welding distortions, see samples R1, T1, T2, and T3.
Welding experiment matrix
Sample number  Structure geometry  Welding pattern  Nominal welding power (W)  Welding velocity (mm/s)  Thickness, upper sheet (mm)  Thickness, lower sheet (mm) 

R1  Asymmetrical  Continuous  4000  80  1.0  1.0 
I1  Intermittent  4000  80  1.0  1.0  
T1  Continuous  4000  80  1.0  1.5  
T2  Continuous  4000  80  1.5  1.0  
T3  Continuous  4000  80  1.5  1.5  
H1  Continuous  2400  80  1.0  1.0  
H2  Continuous  4000  40  1.0  1.0  
R2  Symmetrical  Continuous  4000  80  1.0  1.0 
I2  Intermittent  4000  80  1.0  1.0 
The intermittent welding was carried out as 10 weld stitches, 50 mm each evenly distributed along the original weld path, resulting in a reduction of the weld length per flange from 980 to 500 mm.
After welding and cooling, a digital Vernier caliper was used to measure the distortions as illustrated with green arrows in Fig. 1. For the asymmetrical geometry, vertical (outofplane) distortions were measured at the centerline of the top of the beam. For the symmetrical geometry, transverse distortions were measured through the width of the Ubeam. Measurements were taken at the clamped end and 400, 600, and 1000 mm from the clamped end along the beam. All measurements were taken while the beams were still clamped.
3 Finite element model
An FE model was formulated which describes the effect of shrinkage of the weld zone during cooling after welding. The model only relies on the measured material parameters, and no fitting procedure is used. The model uses a quasistatic analysis to simulate the welding process.
where∆w is the transverse shrinkage (m), ν is the Poisson’s ratio (−), η is the process efficiency (−), α is the thermal expansion coefficient (K^{−1}), ρ is the mass density (kg m^{−3}), c is the specific heat capacity (J kg^{−1} K^{−1}), q is the nominal heat source power (W), v is the velocity of the moving heat source (m s^{−1}), and t is the total sheet thickness (m).
Equation (1) is derived in [14] by considering a sheet cross section with free contraction transverse to the welding direction and by assuming that the total heat input per unit length is equal to the heat input per unit length of the moving heat source. However, there are also contractions in the longitudinal direction which cause contractions in the transverse direction. By modeling these effects purely elastically by Poisson’s ratio, the first term in Eq. (1) is added.
The extension of the weld region can thus be implemented into the FE model defining the nodes which are imposed by the elevated temperature. The mesh was adjusted to fit the extension of the elevated temperature region with six elements within the weld region in the transverse direction.
The material model is defined by the mechanical properties at ambient temperature; the elastic parameters (E = 210 GPa, v = 0.3), a plastic behavior adapted from [14] where an equivalent mild steel material was used (σY = 165 MPa), and a constant thermal expansion coefficient (α = 1.2e^{−5} K^{−1}). Thus, the simplified material model excludes the effects of softening of the material at elevated temperatures and nonlinear thermal expansion and contraction.
As previous works have shown [9], both the Young’s modulus and yield stress are significantly reduced at elevated temperatures resulting in larger elastic and plastic strains. However, as only a narrow zone near the weld center line is heated during LBW in keyhole mode, most part of the structure behaves according to the material properties close to the ambient temperature. Moreover, the thermal expansion and contraction of the steel do not follow a true linear behavior when heated to above liquidus temperature and cooled down to room temperature again, as observed from dilation curves [9]. Rather, during austenite transformation, a contraction is occurring when heated from Ac1 to Ac3. Conversely, during martensite transformation, an expansion is occurring when cooled from Ms to Mg. In order to reduce computation times and to reduce material data requirements, these nonlinear effects were neglected in the present study.
The clamping was modeled as boundary conditions where four corner nodes at the shorter edge were locked in all displacement directions, see Fig. 3. The vertical supports were modeled by nonlinear 1D spring elements, which hindered downward displacement. The simulations were done in the ESI Group’s software Weld Planner [15] using Intel Xeon E4750 2.00 GHz processors.
4 Results and discussion
As described earlier, the experimental campaign was designed to investigate and quantify the effects of intermittent welding, heat input, and sheet thickness on the magnitude of welding distortions. The results from the experiments investigating these effects are shown and discussed separately in the subsections below.
In all welding, distortions are formed due the thermal volumetric strains generated in the material during the temperature cycle during welding and cooling. Furthermore, in steel, the increase in temperature significantly affects the mechanical properties by decreasing Young’s modulus and the yield strength, which enhance the elastic and plastic deformations in the material. During the subsequent cooling, the steel recovers its mechanical strength and the distortions are formed. In summary, the material properties, the welding parameters, i.e., how the heat is applied to the material, and the structure’s restraint to deformations dictate the distortional behavior of the structure. In this chapter, the variations of heat input, sheet thickness, and intermittent welding are described in terms of the effect of the heat and the structure’s restraint to deformations.
On the other hand, the asymmetric case has a high restraint to transversal distortions due to the plane sheet’s high restraint to inplane deformations. In the symmetric case, the two Ubeams are more prone to transverse distortions as seen in Fig. 4. It was seen that the dominant distortions were large enough for a digital caliper to be used for relevant measurement.
4.1 Influence of intermittent welding
Intermittent welding is a common method of reducing heat input while maintaining joint strength. It is of interest to quantify the effect of intermittent welding on distortions to show how effective intermittent welding is in order to mitigate distortions. Intermittent welding patterns, where the total weld length was reduced from 980 to 500 mm, were carried out for both geometries and the distortions were compared to the continuous welding pattern. It was expected that the intermittent welding will significantly reduce distortions.
The simulation results, shown as lines in Fig. 5a, b, are in good agreement with the experiments regarding continuous and intermittent welding for both geometries. The intermittent welding is modeled by applying the temperature gradient to intermittent nodes equivalent to the intermittent weld line. Consequently, heat contraction strains are imposed at a smaller region compared to the continuous weld, causing smaller distortions. The results suggest that the modeling approach accurately models the effect of intermittent welding.
4.2 Influence of welding heat input
A common method of mitigating welding distortions is by decreasing heat input. In the experiments, three heat inputs were analyzed, 30, 50, and 100 J/mm, shown as points in Fig. 5c. In general, lower heat input creates smaller distortions but reduces weld strength and production tolerances. A full penetration weld is desirable from a verification point of view since the weld penetration can be visibly observed at the bottom surface. However, only partial penetration is necessary for full bonding and interfacial strength of the joint. A partial penetration weld also results in a smaller size of the HAZ which will reduce the metallurgical impact of the material.
The heat input will affect stresses in both axial and transversal directions. When decreasing the heat input from 50 to 30 J/mm, the mean distortion at the free end of the symmetric geometry decreased from 16.1 mm (red points) to 9.7 mm (blue points), suggesting a linear relation between heat input and distortions. However, an increase in heat input to 100 J/mm shows a mean distortion of 21.2 mm (black points), which does not follow the linear relation. Several explanations can be given for this trend. In the 100J/mm welding specimens, both sagging defects of the weld, intermittent burnthrough and cutting along the weld line and significant plastic distortions at the vertical supports were observed. The interpretation of this is that not all of the additional heat input results in additional stresses in the material but also in evaporation and ablation of material. Furthermore, heat losses to the ambient surroundings are increasingly significant with higher temperatures.
In the FE model, the relationship between heat input and distortion magnitude is captured by the simulations by the extension of the weld shrinkage zone. Following Eq. (4), the model relies on a linear relation between heat input and shrinkage zone. Consequently, the model shows good agreement for the experiments within the linear interval, i.e., 50 and 30 J/mm. However, for the 100 J/mm case where the model assumes that all of the heat creates distortions, the simulation results are overestimating the distortions. In order to improve the accuracy of the model for high heat input welding, a criterion for the reduction of the shrinkage zone would be required. The model should also be able to describe the lack of fusion due to the burnthrough of the excessive heat, which is not implemented in the present model.
4.3 Influence of sheet thickness
Variations of sheet thickness are an important design parameter for practicing engineers. By increasing the sheet thickness of a structure, the stiffness and crashworthiness can be effectively improved. Reversely, by using thinner sheets, the weight of a structure can be reduced. In the present section, the effect of sheet thickness of distortions is investigated.
As described earlier, the longitudinal bending stress is proportional to the lever arm between the weld line and the neutral plane. By altering the sheet thickness, the length of the lever arm is also altered, which will affect bending stresses. A structure’s resistance to bending deformations is controlled by the structure’s crosssection’s area moment of inertia (mm^{4}), which is also affected by the sheet thickness.
The distortion results of the experiments of various sheet thickness configurations are shown as points in Fig. 5d. By increasing the thickness of the Ubeam from the 1.0 mm (red points Fig. 5d) to 1.5 mm (black points in Fig. 5d), the area moment of inertia is increased by 29%. However, the neutral plan is shifted away from the faying surface by 14%. The new thicknesses result in an increase in distortion of merely 0.6 mm indicating that the two factors counteract each other. In the other cases, the variations in sheet thickness, the area moment of inertia, and the lever arm do not counteract each other. In all cases, the ratio between the two properties shows good agreement with the distortion magnitude.
The simulation results, shown as lines in Fig. 5d, are generally in good agreement with the experiments. It shows that the shell element thickness can model the sheet behavior due to longitudinal bending. In the special case with two sheets of 1.5 mm thickness, the simulation underestimates the distortions. In the experiment, this configuration showed a partial penetration weld, where the nonmolten metal acts as a restraint for distortions. In the model, the same thermal strains are applied to both the upper and bottom sheet based on an assumption of complete penetration and symmetrical weld distribution in the thickness direction. In order to model distortions of partial penetration welds, it is necessary to apply different thermal strains in the upper and lower sheets.
4.4 Capabilities of the FE model
As described above, the FE model relies on certain assumptions. One assumption is that the thermal strains are constant through the sheet thickness, i.e., identical temperature cycle in the top and bottom sheet. This assumption is valid in almost all of the experiments. However, in some special cases, the entire thickness is not fused and will not contribute to the contraction. In opposite, the unfused material closer to the bottom surface will restrain distortions. This restraining effect is not modeled in the simulations. This is illustrated in sample T3 in Fig. 6.
The opposite condition, excessive heat input leading to burnthrough of the weld zone, will also reduce distortions by reducing the interaction between the sheets in overlap configuration. In the simulations, full interaction between the sheets is assumed and all heat input contributes to the welding distortions, which overestimates the distortions in the simulation. This overestimation is illustrated in sample H2 in Fig. 6.
In the other samples, good agreement between the simulations and the experiments can be observed, which suggests that the simplified FE model can be effectively used for practicing engineers for timeefficient prediction of welding distortions.
It should also be noted that in the present study, the heat input was sufficient to achieve a keyhole mode welding—if the heat input is further reduced, a conduction mode welding is reached. In the case of conduction mode welding, the physical behavior of the melt pool is changed as no metal vapor is produced. The metal vapor in the weld pool has higher absorption compared to metal in liquid phase which increased the power efficiency of the process. Thus, if conduction mode welding is achieved, the process efficiency [η] may need to be modified to achieve accurate predictions of welding distortions.
The maximum simulation time was 79 min in case H2. The simulation times are considered relevant for industrial application, particularly, as the time needed is significantly reduced compared to the time needed for corresponding experiments or for more detailed simulations.
5 Conclusions

Overlap LBW of beam structures creates significant distortions through longitudinal bending or transverse to the weld direction depending on the geometry of the structure. If the weld coincides with the neutral plane of the structure, as in the symmetrical case, longitudinal bending distortions are negligible. Flat sheets, as included in the asymmetrical case, increase transverse stiffness and greatly reduce transverse distortions.

Three factors which significantly affect the magnitude of distortions have been identified; firstly, intermitting welding, secondly, heat input per unit length, and thirdly, the ratio between the distance from the neutral axis to the weld line and the area moment of inertia of the cross section.

A simplified FE model was developed to accurately predict welding deformations. The model shows great reductions in computation power and material data requirements compared to full transient models. However, the model is limited to welding conditions where no burnthrough is occurring and full penetration of the weld is taking place.
Notes
Compliance with ethical standards
Funding
This research was supported by the Swedish Governmental Agency for Innovation Systems, VINNOVA, through the project LaserLight (201203656) which is a part of the FFI program.
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