RESEARCH PAPER

Oscar Andersson1& Nesrin Budak2

& Arne Melander1,3 & Niclas Palmquist4

Received: 9 September 2016 /Accepted: 8 June 2017 /Published online: 29 June 2017# The Author(s) 2017. This article is an open access publication

Abstract Distortions of mild steel structures caused bylaser welding were analyzed. One thousand-millimeterU-beam structures were welded as overlap joints withdifferent process parameters and thickness configura-tions. Final vertical and transverse distortions aftercooling were measured along the U-beam. Significantfactors, which affect distortions, were identified. Heatinput per unit length, weld length, and sheet thicknessshowed a significant effect on welding distortions.Furthermore, the welding distortions were modeledusing FE simulations. A simplified and computationallyefficient simulation method was used. It describes theeffect of shrinkage of the weld zone during cooling.The simulations show reasonable computation timesand good agreement with experiments.

Keywords (IIW Thesaurus) Laser beamwelding .

Distortions . FE simulation . Volume shrinkagemethod .Mildsteel

1 Introduction

Laser beam welding (LBW) is an increasingly used joiningmethod in several industries due to its high-strength continu-ous joints, high production efficiency, high precision, and lowmetallurgical impact on the welded material. However, as anyfusion joining method, the heating and subsequent cooling ofthe material will induce stresses in the material and causegeometrical distortions, which may require modifiedfixturing, result in rejected components, or need for post-joining repair in industry.

Experimental results of distortions due to LBW of var-ious materials including 4.0-mm butt-welded steel sheets[1], 2.5-mm butt-welded aluminum sheets [2], and 0.4-mmoverlap-welded Inconel tube structures [3] have been pre-sented. Moreover, the results of distortions in laser-hybridwelding of 9.0-mm-thick steel parts were presented in [4].The effect of clamping conditions on distortions has alsobeen highlighted [5]. In addition, various methods to de-crease welding distortions have been presented, such asoptimization of process parameters [6] or intermittentwelding patterns [7].

Researchers have also provided models to predict the mag-nitude and distribution of welding distortions through bothsimplified empirical models and detailed numerical analysesby finite element (FE) modeling. The simplified models relyon general assumptions, which predict the magnitude of dis-tortions due to heat input or weld sheet geometry. An impor-tant assumption is that cooling contraction is the dominantsource of distortions, as proposed by Okerblom [8] andfollowed by several other authors.

With increased computer power, numerical modeling of theLBW process through FE analyses has become more wide-spread. The new techniques include transient modeling of themoving heat source which models dynamic heating and

Recommended for publication by Commission IV - Power BeamProcesses

* Oscar Anderssonoanderss@kth.se

1 Department of Production Engineering, XPRESKTHRoyal Instituteof Technology, 100 44 Stockholm, Sweden

2 Department of SolidMechanics, KTHRoyal Institute of Technology,Stockholm, Sweden

3 Swerea KIMAB, Stockholm, Sweden4 Volvo Car Corporation, Gothenburg, Sweden

Weld World (2017) 61:927–934DOI 10.1007/s40194-017-0496-z

Experimental measurements and numerical simulationsof distortions of overlap laser-welded thin sheet steelbeam structures

cooling of the material. The temperature history of the mate-rial generates thermal expansion and contraction, changes inmaterial behavior due to phase transformations, and changesin material properties. The reduced mechanical strength atelevated temperatures increases plastic strains in the structureduring welding, and martensitic transformation introduces ad-ditional volumetric strains during the rapid cooling afterwelding.

Transient coupled thermo-mechanical FE models are ableto predict distortions with high accuracy by extensivetemperature- and metallurgy-dependent material models anddetailed conductive heat sources. However, they are also com-putationally time-consuming and rely on extensive materialdata [9], which hinders widespread industrial use. Simplifiednumerical methods have long been used to approximatelypredict welding distortions for idealized geometries [10].Simplified simulation methods have also been used to predictwelding distortions for more complex geometries by relyingon calibration of the model [11].

In the automotive industry, LBW is often used for steel andaluminum sheets of thicknesses between less than 1 mm andup to 4 mm. Such slender structures are more prone to weldingdistortions compared to stiffer structures with thicker sheets. Itis also of practice in the automotive industry to join thin sheetsin overlap configurations, as opposed to fillet or butt welds asfor thicker sheet materials. Common applications of LBW inbody in white design are in the case of low-strength steels,exterior panels such as roofs, doors, or trunk lids and in thecase of high-strength steels closed beam structures such as A-or B-pillars. The main advantages of the LBW joints are thehigh structural strength and desirable visual appearance com-pared to other joining methods such as resistance spotwelding. The present paper focuses on the applications inlow-strength steels since such applications are usually verysensitive to distortions and shape deviations.

In summary, the present paper provides new informationon distortion of overlap laser-welded mild steel thin sheetbeam structures relevant for automotive applications. It de-fines how sheet thickness and process parameters influencethe distortions. Finally, it is shown how a simplified FE sim-ulation technique can be used to predict the magnitude of thedistortions. This method allows quick calculations and doesnot require initial fitting procedures contrary to some othermethods.

2 Experimental procedure

Two closed beam structures have been developed by combin-ing two sheet components; a U-beam and a flat sheet, see Fig.1. This resulted in a symmetrical geometry as in the upperpicture of Fig. 1 and an asymmetric geometry as in the lowerpicture. The red arrows in Fig. 1 represent the welds, weld

direction, and weld order. The total weld length per flange is980 mm. The components were made of uncoated mild steel,VDA-100 CR-3, a widely used material in the automotiveindustry. The chemical composition of the steel material isshown in Table 1.

Awelding fixture was used for the experiments as illustrat-ed in Fig. 2. The fixture included six vertical supports, whichthe beam flanges were resting on, located at every 200 mmalong the beam length. The vertical supports prevented down-ward vertical displacement of the flanges, but the beams werefree to move upwards. The supports prevented transverse dis-placement only by friction through contact with the flanges.

The fixture also included a toggle clamp at one end of thebeam to stabilize the beam. In the symmetrical beam case, thetoggle clamp was located at the center of the top of the U-beam, as illustrated in Fig. 2 and in the asymmetrical case, thetoggle was located at the center of the flat sheet. The toggleclamp initiates a downward force on the structure at the end ofthe beam, pushing the beam towards the vertical supports atthe flanges. The fixture prevents both upward and downwardvertical displacements at the location of the toggle clamp. Therest of the beam is free to move upwards vertically.

The welding was performed with a Haas 4006D Nd:YAGweld laser with a nominal beam parameter product of25 mm.mrad and Gaussian intensity profile. A focal lengthof 200 mm, an aperture of 48 mm, and a focus spot diameterof 600 μm were used. The spot focus was located at the topsheet’s top surface. Compressed air was used as shielding gaswith a flow of 30 l min−1. An experimental campaign, seeTable 2, was designed investigating the following points ofinterest:

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 sam-ples R1, H1, and H2.

3. The effect of sheet thickness on welding distortions, seesamples R1, T1, T2, and T3.

The intermittent welding was carried out as 10 weldstitches, 50 mm each evenly distributed along the originalweld path, resulting in a reduction of the weld length perflange from 980 to 500 mm.

After welding and cooling, a digital Vernier caliper wasused to measure the distortions as illustrated with green arrowsin Fig. 1. For the asymmetrical geometry, vertical (out-of-plane) distortions were measured at the centerline of the topof the beam. For the symmetrical geometry, transverse distor-tions 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. Allmeasurements were taken while the beams were still clamped.

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3 Finite element model

An FE model was formulated which describes the effect ofshrinkage of the weld zone during cooling after welding. Themodel only relies on the measuredmaterial parameters, and nofitting procedure is used. The model uses a quasi-static anal-ysis to simulate the welding process.

In the initial step, nodes near the weld of the undeformedgeometry are set to a temperature of 1500 °C, approximatelyequal to the solidus temperature of the material, as illustratedin Fig. 3. The extension of the region of the elevated temper-ature is dependent of the weld process parameters. In the lon-gitudinal direction, the region matches the weld pattern, i.e.,continuous or intermittent. In the transverse direction, thewidth of the region, W in Fig. 3, is proportional to the heatinput per unit length. The exact derivation ofW is described inmore detail below. The initial step of the model represents anidealized state of the structure after welding but before coolingand solidification. Thus, the modeling assumes that all distor-tions occur during the cooling of the weld process.

The extension of the weld shrinkage zone is derived from amodel, presented by Leggatt [13], which assumes pure shrink-age due to cooling and expresses the shrinkage transverse tothe welding direction. The assumption of pure shrinkage dueto cooling is equivalent to the assumption of the static model-ing of the FE model, where the initial step is defined as thestate when the weld region has a temperature equal to the

solidus temperature. The model of pure shrinkage is definedas below.

Δw ¼ 1þ νð Þη αρc

qvt

ð1Þ

whereΔw is the transverse shrinkage (m), ν is the Poisson’sratio (−), η is the process efficiency (−), α is the thermalexpansion 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 nominalheat source power (W), v is the velocity of the moving heatsource (m s−1), and t is the total sheet thickness (m).

Equation (1) is derived in [14] by considering a sheetcross section with free contraction transverse to thewelding direction and by assuming that the total heatinput per unit length is equal to the heat input per unitlength of the moving heat source. However, there arealso contractions in the longitudinal direction whichcause contractions in the transverse direction. By model-ing 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 theextremely high absorptivity of the material in the plasma afterthe formation of the keyhole. Furthermore, the process effi-ciency also takes heat losses from the surface into account. Byapplying the properties of steel at the ambient temperature andthe 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 expressedin millimeter as below.

Δw ¼ 0:00348qvt

ð2Þ

By considering an isolated region near the weld line ofwidth w, the transverse thermal strains of the region can be

Fig. 1 The two experimentalbeam configurations with weldson the flanges indicated with redcolor and the location of verticaland horizontal distortionmeasurements indicated withgreen color

Table 1 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%

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described by Eq. (3), assuming a constant coefficient of ther-mal expansion.

ε ¼ ΔwW

¼ αΔT ð3Þ

where ΔT is the temperature gradient from the solidus temper-ature to ambient temperature (20 °C). By combining theshrinkage of the local shrinkage model, Eq. (2), and the strainsof the isolated weld region, Eq. (3), the extension of the weldshrinkage zone can be found as in Eq. (4).

W ¼0:00348

qvt

αΔTð4Þ

The extension of the weld region can thus be implementedinto the FE model defining the nodes which are imposed bythe elevated temperature. The mesh was adjusted to fit theextension of the elevated temperature region with six elementswithin the weld region in the transverse direction.

The material model is defined by the mechanical propertiesat ambient temperature; the elastic parameters (E = 210 GPa,v = 0.3), a plastic behavior adapted from [14] where an equiv-alent mild steel material was used (σY = 165 MPa), and aconstant 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 mod-ulus and yield stress are significantly reduced at elevated tem-peratures resulting in larger elastic and plastic strains.However, as only a narrow zone near the weld center line isheated during LBW in keyhole mode, most part of the struc-ture behaves according to the material properties close to theambient temperature. Moreover, the thermal expansion andcontraction of the steel do not follow a true linear behaviorwhen heated to above liquidus temperature and cooled downto room temperature again, as observed from dilation curves[9]. Rather, during austenite transformation, a contraction isoccurring when heated from Ac1 to Ac3. Conversely, duringmartensite transformation, an expansion is occurring whencooled from Ms to Mg. In order to reduce computation timesand to reduce material data requirements, these non-lineareffects were neglected in the present study.

The clamping was modeled as boundary conditions wherefour corner nodes at the shorter edge were locked in all dis-placement directions, see Fig. 3. The vertical supports weremodeled by non-linear 1-D spring elements, which hindereddownward displacement. The simulations were done in theESI Group’s software Weld Planner [15] using Intel Xeon E-4750 2.00 GHz processors.

Table 2 Welding experiment matrix

Sample number Structure geometry Welding pattern Nominal weldingpower (W)

Welding velocity(mm/s)

Thickness,upper sheet (mm)

Thickness, lowersheet (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

Fig. 2 Clamping conditions ofexperimental setup

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4 Results and discussion

As described earlier, the experimental campaign was designedto investigate and quantify the effects of intermittent welding,heat input, and sheet thickness on the magnitude of weldingdistortions. The results from the experiments investigatingthese effects are shown and discussed separately in the sub-sections below.

In all welding, distortions are formed due the thermal volu-metric strains generated in the material during the temperaturecycle during welding and cooling. Furthermore, in steel, theincrease in temperature significantly affects themechanical prop-erties by decreasing Young’s modulus and the yield strength,which enhance the elastic and plastic deformations in the mate-rial. During the subsequent cooling, the steel recovers its me-chanical strength and the distortions are formed. In summary, thematerial properties, the welding parameters, i.e., how the heat isapplied to the material, and the structure’s restraint to deforma-tions dictate the distortional behavior of the structure. In thischapter, the variations of heat input, sheet thickness, and inter-mittent welding are described in terms of the effect of the heatand the structure’s restraint to deformations.

It was seen that longitudinal bending and transverse expan-sion were the dominant distortion modes of the asymmetricaland symmetrical geometries, respectively, as shown in Fig. 4.Longitudinal bending occurs due to the axial forces, concen-trated 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 weldline and the neutral plane of the cross section. The upwardbending distortion of the asymmetric geometry supports theassumption that cooling forces are dominant for the finalshape of the structure. The symmetric geometry is a specialcase where the weld line and the neutral plane coincide.Therefore, the lever arm is close to zero and the bending mo-ment is negligible and no longitudinal bending occurs.

On the other hand, the asymmetric case has a highrestraint to transversal distortions due to the planesheet’s high restraint to in-plane deformations. In thesymmetric case, the two U-beams are more prone totransverse distortions as seen in Fig. 4. It was seen thatthe dominant distortions were large enough for a digitalcaliper to be used for relevant measurement.

4.1 Influence of intermittent welding

Intermittent welding is a common method of reducing heatinput while maintaining joint strength. It is of interest to quan-tify the effect of intermittent welding on distortions to showhow effective intermittent welding is in order to mitigate dis-tortions. Intermittent welding patterns, where the total weldlength was reduced from 980 to 500 mm, were carried outfor both geometries and the distortions were compared to thecontinuous welding pattern. It was expected that the intermit-tent welding will significantly reduce distortions.

Fig. 3 FE mesh and highlighted nodes modeling clamping and elevated temperature for continuous (left) and intermittent welding (right)

Fig. 4 Dominant distortionbehavior of the asymmetric (left)and symmetric (right) geometries

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Figure 5a, b compares the distortions of the continuous (redpoints) and intermittent welding (blue points) for the asymmet-ric and symmetric geometries. The results show that the inter-mittent welding has a clear effect on the magnitude of bothvertical and transverse welding distortions. Both the axial andthe transverse stresses, and thus the distortions, are proportionalto the total accumulated length of the weld. The asymmetricaland symmetrical geometries showed a reduction in the maxi-mum distortion from 16.1 to 8.3 mm and 3.4 to 1.6 mm, re-spectively. As the total accumulated weld length was shortenedfrom 980 to 500 mm, a near linear relationship between weldlength and distortion magnitude can be established.

The simulation results, shown as lines in Fig. 5a, b, are ingood agreement with the experiments regarding continuousand intermittent welding for both geometries. The intermittentwelding is modeled by applying the temperature gradient tointermittent nodes equivalent to the intermittent weld line.Consequently, heat contraction strains are imposed at a small-er region compared to the continuous weld, causing smallerdistortions. The results suggest that the modeling approachaccurately models the effect of intermittent welding.

4.2 Influence of welding heat input

A common method of mitigating welding distortions is bydecreasing heat input. In the experiments, three heat inputswere analyzed, 30, 50, and 100 J/mm, shown as points in

Fig. 5c. In general, lower heat input creates smaller distortionsbut reduces weld strength and production tolerances. A fullpenetration weld is desirable from a verification point of viewsince the weld penetration can be visibly observed at the bot-tom surface. However, only partial penetration is necessary forfull bonding and interfacial strength of the joint. A partial pen-etration weld also results in a smaller size of the HAZ whichwill reduce the metallurgical impact of the material.

The heat input will affect stresses in both axial and transver-sal directions. When decreasing the heat input from 50 to 30 J/mm, the mean distortion at the free end of the symmetric ge-ometry decreased from 16.1 mm (red points) to 9.7 mm (bluepoints), suggesting a linear relation between heat input anddistortions. However, an increase in heat input to 100 J/mmshows a mean distortion of 21.2 mm (black points), which doesnot follow the linear relation. Several explanations can be givenfor this trend. In the 100-J/mm welding specimens, both sag-ging defects of the weld, intermittent burn-through and cuttingalong the weld line and significant plastic distortions at thevertical supports were observed. The interpretation of this isthat not all of the additional heat input results in additionalstresses in the material but also in evaporation and ablation ofmaterial. Furthermore, heat losses to the ambient surroundingsare increasingly significant with higher temperatures.

In the FE model, the relationship between heat input anddistortion magnitude is captured by the simulations by theextension of the weld shrinkage zone. Following Eq. (4), the

Fig. 5 Results of experiments(points) and simulations (lines)

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model relies on a linear relation between heat input andshrinkage zone. Consequently, the model shows good agree-ment for the experiments within the linear interval, i.e., 50 and30 J/mm. However, for the 100 J/mm case where the modelassumes that all of the heat creates distortions, the simulationresults are overestimating the distortions. In order to improvethe accuracy of the model for high heat input welding, a cri-terion for the reduction of the shrinkage zone would be re-quired. The model should also be able to describe the lack offusion due to the burn-through of the excessive heat, which isnot implemented in the present model.

4.3 Influence of sheet thickness

Variations of sheet thickness are an important design parame-ter for practicing engineers. By increasing the sheet thicknessof a structure, the stiffness and crashworthiness can be effec-tively improved. Reversely, by using thinner sheets, theweight 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 pro-portional to the lever arm between the weld line and the neu-tral plane. By altering the sheet thickness, the length of thelever arm is also altered, which will affect bending stresses. Astructure’s resistance to bending deformations is controlled bythe 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 sheetthickness configurations are shown as points in Fig. 5d. Byincreasing the thickness of the U-beam from the 1.0 mm (redpoints Fig. 5d) to 1.5 mm (black points in Fig. 5d), the areamoment of inertia is increased by 29%. However, the neutralplan is shifted away from the faying surface by 14%. The newthicknesses result in an increase in distortion of merely0.6 mm indicating that the two factors counteract each other.In the other cases, the variations in sheet thickness, the areamoment of inertia, and the lever arm do not counteract eachother. In all cases, the ratio between the two properties showsgood agreement with the distortion magnitude.

The simulation results, shown as lines in Fig. 5d, are gen-erally in good agreement with the experiments. It shows thatthe shell element thickness can model the sheet behavior dueto longitudinal bending. In the special case with two sheets of1.5 mm thickness, the simulation underestimates the distor-tions. In the experiment, this configuration showed a partialpenetration weld, where the non-molten metal acts as a re-straint for distortions. In the model, the same thermal strainsare applied to both the upper and bottom sheet based on anassumption of complete penetration and symmetrical welddistribution in the thickness direction. In order to model dis-tortions of partial penetration welds, it is necessary to applydifferent thermal strains in the upper and lower sheets.

4.4 Capabilities of the FE model

A comparison between the maximum distortions in simula-tions and the mean maximum distortion in the experimentshas been summarized as a correlation figure in Fig. 6. TheFE model can accurately predict the effect of intermittentwelding, heat input variations, and variations of sheet thick-ness on welding distortions by altering the distribution andextension of the weld shrinkage zone and the elementthickness.

As described above, the FEmodel relies on certain assump-tions. One assumption is that the thermal strains are constantthrough the sheet thickness, i.e., identical temperature cycle inthe top and bottom sheet. This assumption is valid in almostall of the experiments. However, in some special cases, theentire thickness is not fused and will not contribute to thecontraction. In opposite, the unfused material closer to thebottom surface will restrain distortions. This restraining effectis not modeled in the simulations. This is illustrated in sampleT3 in Fig. 6.

The opposite condition, excessive heat input leading toburn-through of the weld zone, will also reduce distortionsby reducing the interaction between the sheets in overlap con-figuration. In the simulations, full interaction between thesheets is assumed and all heat input contributes to the weldingdistortions, which overestimates the distortions in the simula-tion. This overestimation is illustrated in sample H2 in Fig. 6.

In the other samples, good agreement between the simula-tions and the experiments can be observed, which suggeststhat the simplified FE model can be effectively used for prac-ticing engineers for time-efficient prediction of weldingdistortions.

It should also be noted that in the present study, the heatinput was sufficient to achieve a keyhole mode welding—if

Fig. 6 Correlation between maximum distortion in experiments andsimulations

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the heat input is further reduced, a conduction mode weldingis reached. In the case of conduction mode welding, the phys-ical behavior of the melt pool is changed as no metal vapor isproduced. The metal vapor in the weld pool has higher ab-sorption compared to metal in liquid phase which increasedthe power efficiency of the process. Thus, if conduction modewelding is achieved, the process efficiency [η] may need to bemodified to achieve accurate predictions of weldingdistortions.

The maximum simulation time was 79 min in case H2. Thesimulation times are considered relevant for industrial appli-cation, particularly, as the time needed is significantly reducedcompared to the time needed for corresponding experimentsor for more detailed simulations.

5 Conclusions

In this paper, both experiments and simulations are used toinvestigate distortions of thin sheet structures of mild steel dueto overlap laser beam welding. Factors which significantlyaffect the magnitude of distortions have been identified.Also, an FE model to predict welding distortions was gener-ated and evaluated. The conclusions of the paper are summa-rized as follows:

& Overlap LBW of beam structures creates significant dis-tortions through longitudinal bending or transverse to theweld direction depending on the geometry of the structure.If the weld coincides with the neutral plane of the struc-ture, as in the symmetrical case, longitudinal bending dis-tortions are negligible. Flat sheets, as included in theasymmetrical case, increase transverse stiffness and great-ly reduce transverse distortions.

& Three factors which significantly affect the magnitude ofdistortions have been identified; firstly, intermittingwelding, secondly, heat input per unit length, and thirdly,the ratio between the distance from the neutral axis to theweld line and the area moment of inertia of the crosssection.

& A simplified FE model was developed to accurately pre-dict welding deformations. The model shows great reduc-tions in computation power and material data require-ments compared to full transient models. However, themodel is limited to welding conditions where no burn-through is occurring and full penetration of the weld istaking place.

Compliance with ethical standards

Funding This research was supported by the Swedish GovernmentalAgency for Innovation Systems, VINNOVA, through the projectLaserLight (2012-03656) which is a part of the FFI program.

Open Access This article is distributed under the terms of the CreativeCommons At t r ibut ion 4 .0 In te rna t ional License (h t tp : / /creativecommons.org/licenses/by/4.0/), which permits unrestricted use,distribution, and reproduction in any medium, provided you give appro-priate credit to the original author(s) and the source, provide a link to theCreative Commons license, and indicate if changes were made.

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