Welding in the World

, Volume 61, Issue 5, pp 927–934 | Cite as

Experimental measurements and numerical simulations of distortions of overlap laser-welded thin sheet steel beam structures

  • Oscar Andersson
  • Nesrin Budak
  • Arne Melander
  • Niclas Palmquist
Open Access
Research Paper


Distortions of mild steel structures caused by laser welding were analyzed. One thousand-millimeter U-beam structures were welded as overlap joints with different process parameters and thickness configurations. Final vertical and transverse distortions after cooling were measured along the U-beam. 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 steel 

1 Introduction

Laser beam welding (LBW) is an increasingly used joining method in several industries due to its high-strength 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 post-joining repair in industry.

Experimental results of distortions due to LBW of various materials including 4.0-mm butt-welded steel sheets [1], 2.5-mm butt-welded aluminum sheets [2], and 0.4-mm overlap-welded Inconel tube structures [3] have been presented. Moreover, the results of distortions in laser-hybrid welding of 9.0-mm-thick 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 thermo-mechanical FE models are able to predict distortions with high accuracy by extensive temperature- and metallurgy-dependent material models and detailed conductive heat sources. However, they are also computationally time-consuming 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 low-strength steels, exterior panels such as roofs, doors, or trunk lids and in the case of high-strength steels closed beam structures such as A- or B-pillars. 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 low-strength 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 laser-welded 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

Two closed beam structures have been developed by combining two sheet components; a U-beam and a flat sheet, see Fig. 1. This resulted in a symmetrical geometry as in the upper picture of Fig. 1 and an asymmetric geometry as in the lower picture. The red arrows in Fig. 1 represent the welds, weld direction, and weld order. The total weld length per flange is 980 mm. The components were made of uncoated mild steel, VDA-100 CR-3, a widely used material in the automotive industry. The chemical composition of the steel material is shown in Table 1.
Fig. 1

The two experimental beam configurations with welds on the flanges indicated with red color and the location of vertical and horizontal distortion measurements indicated with green color

Table 1

The maximum chemical contents of steel material [12]

















A welding fixture was used for the experiments as illustrated in Fig. 2. The fixture included six vertical supports, which the beam flanges were resting on, located at every 200 mm along the beam length. The vertical supports prevented downward vertical displacement of the flanges, but the beams were free to move upwards. The supports prevented transverse displacement only by friction through contact with the flanges.
Fig. 2

Clamping conditions of experimental setup

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 U-beam, 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.

The welding was performed with a Haas 4006D Nd:YAG weld laser with a nominal beam parameter product of 25 mm.mrad and Gaussian intensity profile. A focal length of 200 mm, an aperture of 48 mm, and a focus spot diameter of 600 μm were used. The spot focus was located at the top sheet’s top surface. Compressed air was used as shielding gas with a flow of 30 l min−1. An experimental campaign, see Table 2, was designed investigating the following points of interest:
  1. 1.

    The effect of intermittent welding on welding distortions, see samples R1, R2, I1, and I2.

  2. 2.

    The effect of heat input on welding distortions, see samples R1, H1, and H2.

  3. 3.

    The effect of sheet thickness on welding distortions, see samples R1, T1, T2, and T3.

Table 2

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)

























































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 (out-of-plane) 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 U-beam. 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 quasi-static analysis to simulate the welding process.

In the initial step, nodes near the weld of the undeformed geometry are set to a temperature of 1500 °C, approximately equal to the solidus temperature of the material, as illustrated in Fig. 3. The extension of the region of the elevated temperature is dependent of the weld process parameters. In the longitudinal direction, the region matches the weld pattern, i.e., continuous or intermittent. In the transverse direction, the width of the region, W in Fig. 3, is proportional to the heat input per unit length. The exact derivation of W is described in more detail below. The initial step of the model represents an idealized state of the structure after welding but before cooling and solidification. Thus, the modeling assumes that all distortions occur during the cooling of the weld process.
Fig. 3

FE mesh and highlighted nodes modeling clamping and elevated temperature for continuous (left) and intermittent welding (right)

The extension of the weld shrinkage zone is derived from a model, presented by Leggatt [13], which assumes pure shrinkage due to cooling and expresses the shrinkage transverse to the welding direction. The assumption of pure shrinkage due to cooling is equivalent to the assumption of the static modeling of the FE model, where the initial step is defined as the state when the weld region has a temperature equal to the solidus temperature. The model of pure shrinkage is defined as below.
$$ \varDelta w=\left(1+\nu \right)\eta \frac{\alpha}{\rho c}\frac{q}{vt} $$

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 process efficiency was set to 80% with regard to the extremely high absorptivity of the material in the plasma after the formation of the keyhole. Furthermore, the process efficiency also takes heat losses from the surface into account. By applying the properties of steel at the ambient temperature and the LBW process (v = 0.3, α = 1.2e−5 K−1, ρ = 7800 kg m−3, c = 460 J kg−1 K−1), the transverse shrinkage can be expressed in millimeter as below.
$$ \varDelta w=0.00348\frac{q}{vt} $$
By considering an isolated region near the weld line of width w, the transverse thermal strains of the region can be described by Eq. (3), assuming a constant coefficient of thermal expansion.
$$ \varepsilon =\frac{\varDelta w}{W}=\alpha \varDelta T $$
where ∆T is the temperature gradient from the solidus temperature to ambient temperature (20 °C). By combining the shrinkage of the local shrinkage model, Eq. (2), and the strains of the isolated weld region, Eq. (3), the extension of the weld shrinkage zone can be found as in Eq. (4).
$$ W=\frac{0.00348\frac{q}{vt}}{\alpha \varDelta T} $$

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 non-linear 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 non-linear 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 non-linear 1-D spring elements, which hindered downward displacement. The simulations were done in the ESI Group’s software Weld Planner [15] using Intel Xeon E-4750 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 sub-sections 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.

It was seen that longitudinal bending and transverse expansion were the dominant distortion modes of the asymmetrical and symmetrical geometries, respectively, as shown in Fig. 4. Longitudinal bending occurs due to the axial forces, concentrated at the weld line, occurring during heating and cooling. The axial forces (F in Fig. 4) create a bending moment (M in Fig. 4) due to the lever arm between the position of the weld line and the neutral plane of the cross section. The upward bending distortion of the asymmetric geometry supports the assumption that cooling forces are dominant for the final shape of the structure. The symmetric geometry is a special case where the weld line and the neutral plane coincide. Therefore, the lever arm is close to zero and the bending moment is negligible and no longitudinal bending occurs.
Fig. 4

Dominant distortion behavior of the asymmetric (left) and symmetric (right) geometries

On the other hand, the asymmetric case has a high restraint to transversal distortions due to the plane sheet’s high restraint to in-plane deformations. In the symmetric case, the two U-beams 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.

Figure 5a, b compares the distortions of the continuous (red points) and intermittent welding (blue points) for the asymmetric and symmetric geometries. The results show that the intermittent welding has a clear effect on the magnitude of both vertical and transverse welding distortions. Both the axial and the transverse stresses, and thus the distortions, are proportional to the total accumulated length of the weld. The asymmetrical and symmetrical geometries showed a reduction in the maximum distortion from 16.1 to 8.3 mm and 3.4 to 1.6 mm, respectively. As the total accumulated weld length was shortened from 980 to 500 mm, a near linear relationship between weld length and distortion magnitude can be established.
Fig. 5

Results of experiments (points) and simulations (lines)

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 100-J/mm welding specimens, both sagging defects of the weld, intermittent burn-through 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 burn-through 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 cross-section’s area moment of inertia (mm4), 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 U-beam 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 non-molten 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

A comparison between the maximum distortions in simulations and the mean maximum distortion in the experiments has been summarized as a correlation figure in Fig. 6. The FE model can accurately predict the effect of intermittent welding, heat input variations, and variations of sheet thickness on welding distortions by altering the distribution and extension of the weld shrinkage zone and the element thickness.
Fig. 6

Correlation between maximum distortion in experiments and simulations

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 burn-through 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 time-efficient 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

In this paper, both experiments and simulations are used to investigate distortions of thin sheet structures of mild steel due to overlap laser beam welding. Factors which significantly affect the magnitude of distortions have been identified. Also, an FE model to predict welding distortions was generated and evaluated. The conclusions of the paper are summarized as follows:
  • 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 burn-through is occurring and full penetration of the weld is taking place.


Compliance with ethical standards


This research was supported by the Swedish Governmental Agency for Innovation Systems, VINNOVA, through the project LaserLight (2012-03656) which is a part of the FFI program.


  1. 1.
    Moraitis G, Labeas G (2009) Prediction of residual stresses and distortions due to laser beam welding of butt joints in pressure vessels. Int J Press Vessel Pip 86(2):133–142CrossRefGoogle Scholar
  2. 2.
    Zain-ul-Abdein M, Nelias D, Jullien J-F, Deloison D (2009) Prediction of laser beam welding-induced distortions and residual stresses by numerical simulation for aeronautic application. J Mater Process Technol 209(6):2907–2917CrossRefGoogle Scholar
  3. 3.
    Kim J, Kim C (2010) Design of a laser welded thin metal tube structure incorporating welding distortion and residual stress. Int J Precis Eng Manuf 11(6):925–930CrossRefGoogle Scholar
  4. 4.
    Zhang T, Wu CS, Qin GL, Wang XY, Lin SY (2010) Thermomechanical analysis for laser + GMAW-P hybrid welding process. Comput Mater Sci 47(3):848–856CrossRefGoogle Scholar
  5. 5.
    Schenk T, Richardson I, Kraska M, Ohnimus S (2009) Influence of clamping on distortion of welded S355 T-joints. Sci Technol Weld Join 14(4):369–375CrossRefGoogle Scholar
  6. 6.
    Tsai CL, Park SC, Cheng WT (1999) Welding distortion of a thin-plate panel structure. Weld J 78(5):156s–165sGoogle Scholar
  7. 7.
    Tajima Y, Rashed S, Serizawa H, Murakawa H, Okumoto Y, Akiyoshi K (2009) Prediction and control methods to reduce distortion of deck panels produced during block assembly of car carrier, in Proceedings of the International Offshore and Polar Engineering ConferenceGoogle Scholar
  8. 8.
    Okerblom N (1958) The calculations of deformations of welded metal structures. H.M. Stationery Office, LondonGoogle Scholar
  9. 9.
    Lindgren L-E (2001) Finite element modeling and simulation of welding part 1: increased complexity. J Therm Stresses 24(2):141–192CrossRefGoogle Scholar
  10. 10.
    Verhaeghe G (1999) Predictive formulae for weld distortion: a critical review, WoodheadGoogle Scholar
  11. 11.
    Tikhomirov D, Rietman B, Kose K, Makkink M (2005) Computing welding distortion: comparison of different industrially applicable methods. Adv Mater Res 6-8:195–202CrossRefGoogle Scholar
  12. 12.
    VDA 239-100 Sheet Steel for Cold Forming.Google Scholar
  13. 13.
    Leggatt R (1980) Ph.D. thesis. In: Distortion in welded steel plates. Magdalene College, Cambridge University, CambridgeGoogle Scholar
  14. 14.
    Dziallach S, Bleck W, Blumbach M, Hallfeldt T (2007) Sheet metal testing and flow curve determination under multiaxial conditions. Adv Eng Mater 9(11):987–994CrossRefGoogle Scholar
  15. 15.
    ESI Group (2013) Weld Planner ManualGoogle Scholar

Copyright information

© The Author(s) 2017

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Oscar Andersson
    • 1
  • Nesrin Budak
    • 2
  • Arne Melander
    • 1
    • 3
  • Niclas Palmquist
    • 4
  1. 1.Department of Production EngineeringXPRES KTH Royal Institute of TechnologyStockholmSweden
  2. 2.Department of Solid MechanicsKTH Royal Institute of TechnologyStockholmSweden
  3. 3.Swerea KIMABStockholmSweden
  4. 4.Volvo Car CorporationGothenburgSweden

Personalised recommendations