metals Article
Numerical Simulation on the Origin of Solidification Cracking in Laser Welded Thick-Walled Structures Nasim Bakir 1,2, * ID , Antoni Artinov 1 , Andrey Gumenyuk 1 , Marcel Bachmann 1 Michael Rethmeier 1,2 1
2
*
ID
and
BAM Federal Institute for Material Research and Testing, 12205 Berlin, Germany;
[email protected] (A.A.);
[email protected] (A.G.);
[email protected] (M.B.);
[email protected] (M.R.) Department of Joining Technology, Technische Universität Berlin, 10623 Berlin, Germany Correspondence:
[email protected]; Tel.: +49-30-8104-4622
Received: 17 May 2018; Accepted: 29 May 2018; Published: 1 June 2018
Abstract: One of the main factors affecting the use of lasers in the industry for welding thick structures is the process accompanying solidification cracks. These cracks mostly occurring along the welding direction in the welding center, and strongly affect the safety of the welded components. In the present study, to obtain a better understanding of the relation between the weld pool geometry, the stress distribution and the solidification cracking, a three-dimensional computational fluid dynamic (CFD) model was combined with a thermo-mechanical model. The CFD model was employed to analyze the flow of the molten metal in the weld pool during the laser beam welding process. The weld pool geometry estimated from the CFD model was used as a heat source in the thermal model to calculate the temperature field and the stress development and distributions. The CFD results showed a bulging region in the middle depth of the weld and two narrowing areas separating the bulging region from the top and bottom surface. The thermo-mechanical simulations showed a concentration of tension stresses, transversally and vertically, directly after the solidification during cooling in the region of the solidification cracking. Keywords: laser beam welding; solidification cracking; numerical simulation; CFD model; finite element method (FEM); weld pool; full penetration
1. Introduction For several years, solid-state lasers have been widely applied in metal processing. The high-power of the laser sources and the excellent beam quality allow structures with wall thicknesses of more than 10 mm to be welded in one pass. The high welding speed, low heat input, and low-distortion of the laser beam welding are all advantages that significantly contribute to increasing productivity during the fabrication of thick-walled constructions, and reducing rework [1]. However, when using the laser to weld steels with thickness above 10 mm, the risk of solidification cracking of materials increases due to carelessly coordinated process parameters and mechanical conditions. Due to the complex nature of the hot cracking phenomena, many hypotheses and theories have been presented in the past decades. Apblett and Pellini [2] assumed that solidification cracking first occurs due to a critical strain. They believed that hot cracks occur at a temperature slightly above the solidus temperature when a film of liquid is still present between the dendrite structures. The hot cracks appear when the highly localized strains in the liquid films exceed their critical limit. Prokhorov [3–5] suggested that the materials show a reduced deformation capacity in a specific temperature range, known as the Brittle Temperature Range (BTR). If the strain during solidification exceeds the deformation capacity, hot cracks will occur. Metals 2018, 8, 406; doi:10.3390/met8060406
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According to situ in situ observationsofofcrack crack formation formation and simulations, an approach According to in observations andnumerical numerical simulations, an approach describing the functional relationshipbetween between the the resulting inin thethe weld andand the hot describing the functional relationship resultingstresses stresses weld the cracking hot cracking formation was presented by Zacharia et al. [6,7]. The researchers indicated that the transverse formation was presented by Zacharia et al. [6,7]. The researchers indicated that the transverse compressive stress immediately behindthe thepool pool prevents prevents the of of hothot cracks. The The hot cracks compressive stress immediately behind theformation formation cracks. hot cracks will form if a liquid film is present behind the weld pool, such as when the transverse stress changes will form if a liquid film is present behind the weld pool, such as when the transverse stress changes from compressive to tensile within the mushy zone (see Figure 1). from compressive to tensile within the mushy zone (see Figure 1).
Figure 1. Representation of the influence of the transverse stress development on the hot cracking,
Figure 1. Representation of the influence of the transverse stress development on the hot cracking, according to [6]. according to [6].
Feurer [8] introduced a metallurgical model in which the ratio of the cooling-related volume deformation, the so-calleda rate of shrinkagemodel (ROS), and the ratethe of feeding for closing the cavity Feurer [8] introduced metallurgical in which ratio of(ROF) the cooling-related volume are considered. According theory, the critical will be reached when and ROS arecavity deformation, the so-called ratetoofthis shrinkage (ROS), andpoint the rate of feeding (ROF)ROF for closing the equal. In thisAccording condition, hot can be avoided. In the casewill of a higher shrinkage than feeding are considered. to cracks this theory, the critical point be reached when ROF andrate, ROS are hot cracks will occur. equal. In this condition, hot cracks can be avoided. In the case of a higher shrinkage than feeding rate, In welding of thick-walled structures, the problematic solidification cracking becomes even hot cracks will occur. more complicated. Because of the complex weld pool shape, which is affected by the penetration In welding of thick-walled structures, the problematic solidification cracking becomes even more depth, its solidification behavior plays an additional role in the hot cracking phenomena. complicated. Because the complex weldinpool shape, is affected by the penetrationdepth. depth, its Shida et al. [9]of observed the change the weld poolwhich geometry, depending on penetration solidification behavior plays an additional role in the hot cracking phenomena. In their observations, they found a correlation between the weld pool shape and the solidification Shida et by al. [9] observed the change in the weld pool geometry, on penetration cracking studying the effect of the welding parameter of electrondepending beam welding (EBW) on thedepth. weld pool shape. However, it was reported that a small cavity in the rearshape part ofand the the weld pool at In their observations, they found a correlation between the weld pool solidification approximately one half of the penetration depth resulted from a certain focus position of the electron cracking by studying the effect of the welding parameter of electron beam welding (EBW) on the The observed cavityithas been shown tothat have significant on solidification weldbeam. pool shape. However, was reported a asmall cavityinfluence in the rear part of the cracking. weld pool at Locally delayed solidification in the electron beam welding was studied by Tsukamoto et al. in approximately one half of the penetration depth resulted from a certain focus position of the electron [10,11]. A connection between the delay in the solidification, the formation of the solidification beam. The observed cavity has been shown to have a significant influence on solidification cracking. cracking, and the porosity was identified. Locally delayed solidification in the electron beam welding was studied by Tsukamoto et al. Gebhardt et al. [12,13] observed the same phenomena in laser beam welding for thick-walled in [10,11]. A connection between thecalled delaybulging in the in solidification, the formation of the solidification structures, with the outcome being the weld. Their numerical simulations showed cracking, the porosity identified. that and the bulging has awas significant influence on the temperature field and mechanical stress Gebhardt etwhich al. [12,13] observed same phenomena in laser beam welding for thick-walled distribution, contributes to thethe formation of hot cracking. Barbetta et al. [14] confirmed a high correlation between the bulging in the weld and showed the structures, with the outcome being called bulging in the weld. Their numerical simulations occurrence of solidification cracks, as the solidification crack is always associated with a bulge. These that the bulging has a significant influence on the temperature field and mechanical stress distribution, phenomena, bulging hot cracking, related by the delayed solidification at the rear part of the which contributes to theand formation of hotare cracking. weld pool. Barbetta et al. [14] confirmed a high correlation between the bulging in the weld and the occurrence Schaefer et al. [15] reduced the hot cracks formation in steel by modulation with laser power. of solidification cracks, as the solidification crack is always associated with a bulge. These phenomena, However, additional investigation is still needed to clarify the interaction between the weld pool bulging and hot cracking, are related by the delayed solidification at the rear part of the weld pool. geometry, the thermally induced tensile stresses, and the strain in the weld zone. Schaefer et al. [15] reduced the hot cracks formation in steel by modulation with laser power. However, additional investigation is still needed to clarify the interaction between the weld pool geometry, the thermally induced tensile stresses, and the strain in the weld zone.
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The aim of this study is to use a computational fluid dynamic (CFD) simulation for investigation The aim of this study is to use a computational fluid dynamic (CFD) simulation for investigation and analysis of the weld pool shape for low-alloyed structural steel with a thickness of 12 mm to and analysis of the weld pool shape forby low-alloyed structural steel with a thickness of 12 mm to observe the thermally deduced stresses using a thermo-mechanical model in the weld zone and observe the thermally deduced stresses by using a thermo-mechanical model in the weld zone and analyze its influence on the solidification cracking. analyze its influence on the solidification cracking. 2. Materials and Methods 2. Materials and Methods Low-alloyed steel plates (S355-EN 10025) with 12 mm thickness were used in the welding Low-alloyed steel plates (S355-EN of10025) with 12the mm thickness were used in the experiments. The chemical composition the steel and process parameters are listed in welding Tables 1 experiments. The chemical composition of the steel and the process parameters are listed in Table and 2, respectively. The joint partners were clamped to a device with known restraint intensity (see1 and Table 2, respectively. The joint partners were clamped to a device with known restraint intensity Figure 2). (see Figure 2). Table 1. Chemical composition (in wt. %). Table 1. Chemical composition (in wt. %). C
Si
Mn
C Si Mn 0.088 0.0880.340.34 1.38 1.38
P
P 0.011 0.011
S
S 0.002 0.002
Cr
Cr 0.048 0.048
Cu
Mo
Fe
Cu Mo Fe 0.020 0.007 0.020 0.007 Bal. Bal.
Figure 2. Schematic experiments. Figure 2. Schematic illustration illustration of of the the experiments.
The concept of the intensity of restraint has been introduced by [16,17]. This represents the The concept of the intensity of restraint has been introduced by [16,17]. This represents the stiffness of the surrounding structure around the weld and its influence on the stress development stiffness of the surrounding structure around the weld and its influence on the stress development during solidification. The total restraint intensity of the presented experimental construction before during solidification. The total restraint intensity of the presented experimental construction before welding was 12.6 kN/(mm·mm), estimated according to [18,19]. welding was 12.6 kN/(mm·mm), estimated according to [18,19]. Table 2. Welding parameters used in the experiments. Table 2. Welding parameters used in the experiments.
Parameters Parameters Laser power
Welding Laser power speed Welding Focalspeed position Focal position Weld seam length Weld seam length Plate thickness Plate thickness Shielding Shielding gas gas Restraint intensity Restraint intensity
Value Value 14 kW 2 m/min 14 kW m/min −22mm − 2 mm 100 mm 100 mm 12 12 mm mm N2N2 kN/(mm·mm) 12.612.6 kN/(mm·mm)
To study study more more deeply deeply the the effect effect of of the the weld weld pool pool shape shape on on the the temporal temporal and and spatial spatial distribution distribution To of the stresses, the model was divided into three simulation phases: of the stresses, the model was divided into three simulation phases: CFD model: Calculation of the heat and mass transport in the weld pool to analyze the weld pool shape.
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• •
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pool shape. Thermal FEM model: The CFD-obtained weld pool geometry is used as a heat source in the Thermal FEM model: The CFD-obtained weld pool geometry is used as a heat source in the calculation of the temperature field. calculation of the temperature field. Mechanical FEM model: Using the calculated transient temperature field as a thermal load in Mechanical FEM model: Using the calculated transient temperature field as a thermal load in the the mechanical model to evaluate the stress field. mechanical model to evaluate the stress field.
2.1. 2.1. CFD CFD Model Model The proposedmathematical mathematical model in paper this paper was implemented and solved with the The proposed model in this was implemented and solved with the commercial commercial Software ANSYS Fluent (ANSYS Inc., Canonsburg, PA, USA). In addition, the CFD Software ANSYS Fluent (ANSYS Inc., Canonsburg, PA, USA). In addition, the CFD simulation simulation of full-penetration keyhole laser beam welding wastoused to obtain the weld geometry of full-penetration keyhole laser beam welding was used obtain the weld poolpool geometry by by considering the most relevant physical effects, such as Marangoni and natural convection, considering the most relevant physical effects, such as Marangoni and natural convection, fusion fusion heat heat and and temperature-dependent temperature-dependent material material properties properties up up to to evaporation evaporation temperature. temperature. The The geometrical geometrical dimensions of the the computational computationaldomain domainwere were40 40mm mm×× 25 25 mm × 12 dimensions of mm × 12mm mm(see (seeFigure Figure 3b). 3b). A Asymmetry symmetry plane reduce the the numerical numerical effort effort and and computational computational time while the the computational computational plane was was applied applied to to reduce time while domain polygonal mesh mesh of of tetrahedral tetrahedral elements. elements. The domain was was discretized discretized by by aa polygonal The total total number number of of mesh mesh 5 (see Figure 3b), allowing for a minimum element size of 0.08 mm at the elements was about 9 × 10 5 elements was about 9 × 10 (see Figure 3b), allowing for a minimum element size of 0.08 mm at free surfaces and and the keyhole wall wall to beto used. Because the physical phenomena behind the laser the free surfaces the keyhole be used. Because the physical phenomena behind thebeam laser welding process are strongly coupled and temperature dependent, a highly nonlinear system beam welding process are strongly coupled and temperature dependent, a highly nonlinear system of of equations solution. equations must must be be solved solved to to obtain obtain aa solution.
(a)
(b)
Figure 3. (a) (a)Boundary Boundarycondition condition computational dynamic according to Figure 3. of of thethe computational fluidfluid dynamic (CFD)(CFD) modelmodel according to [20,21]. [20,21]. Theafter model after meshing. (b) The (b) model meshing.
Here, a simplified form of the numerical model was used to guarantee numerical stability and Here, a simplified form of the numerical model was used to guarantee numerical stability and reasonable computing time. The main assumptions in the model were similar to those used in [22], reasonable computing time. The main assumptions in the model were similar to those used in [22], and are given as follows: and are given as follows: Transient approach until reaching a quasi-steady-state. • Transient approach until reaching a quasi-steady-state. Adapted size of the computational domain. • Adapted size of the computational domain. Fixed free surface geometry. Fixed free surface geometry. • Approximated simplified and fixed keyhole geometry from the weld cross-section (see Figure • 4), Approximated simplified and fixed keyhole geometry from weld cross-section Figure 4), used as a model parameter to adapt the numerical to thethe experimental results.(see Thus, effects used asby a model towere adapt the numerical to the experimental results. Thus, effects caused keyholeparameter oscillations not considered. caused by keyhole oscillations were not considered. Shear stress due to the interaction of metal vapor and liquid metal was not considered. • Shearlosses stressby due to the interaction of metal liquid metal not versus considered. Heat radiation were neglected duevapor to theand high relation of was volume surface of the • plate. Heat losses by radiation were neglected due to the high relation of volume versus surface of the plate.
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Figure 4. Cross-section of the weld and the used keyhole geometry in the CFD model.
Figure 4. Cross-section of the weld and the used keyhole geometry in the CFD model. The thermophysical properties of the low-alloyed steel used for the calculation can be taken from [23]. velocity, pressure and temperature of the incompressible werecalculation approximated bybe taken TheThe thermophysical properties of the fields low-alloyed steel used flow for the can the numerical solution of the mass, the momentum and the energy conservation equations by making from [23]. The velocity, pressure and temperature fields of the incompressible flow were approximated use of the simulation framework of ANSYS Fluent. The numerical setup including the geometry of by the numerical solution of the mass, the momentum and the energy conservation equations by the workpiece, the initial state, and the boundary conditions can be seen in Figure 3a. Note, the heat making use of the simulation framework of ANSYS Fluent. The numerical setup including the input was considered as a boundary condition at the keyhole surface by setting the temperature there geometry ofevaporation the workpiece, the initial state, and the boundary be seen in Figure 3a. equal to temperature. A turbulent flow pattern, based conditions on the high can velocities on both Note, the heat inputsides—caused was considered asMarangoni-driven a boundary condition at the by setting the upper and lower by the flow—and the keyhole influence surface of the keyhole temperature there equalwas to considered evaporation temperature. A turbulent flow pattern, based on the high geometry on the flow, by combining the Reynolds-Averaged-Navier–Stokes (RANS) equations withupper the κ-εand turbulence model. Naturalby convection and buoyancy-driven flows the dueinfluence to velocities on both lower sides—caused the Marangoni-driven flow—and of gravity were considered by the Boussinesq approximation and the enthalpy-porosity technique was the keyhole geometry on the flow, was considered by combining the Reynolds-Averaged-Navier–Stokes applied to simulate the solid-liquid phase transformation. The heat conductivity was modified by the (RANS) equations with the κ-ε turbulence model. Natural convection and buoyancy-driven flows due Kays and Crawford heat transport turbulence model and accounts for the amount of produced to gravity were considered by the Boussinesq approximation and the enthalpy-porosity technique was turbulent heat conductivity. To consider the latent heat of fusion by the solid-liquid and liquid-solid applied totransformation, simulate the the solid-liquid phase transformation. heat conductivity was modified by phase method of apparent heat capacity wasThe included.
the Kays and Crawford heat transport turbulence model and accounts for the amount of produced 2.2. Thermo-Mechanical ModelTo consider the latent heat of fusion by the solid-liquid and liquid-solid turbulent heat conductivity. phase transformation, method of apparent heatemployed capacity to was included. A plane strain the two-dimensional model was perform the thermo-mechanical simulation. All out-of-plane strain components were neglected. The thermo-physical material
2.2. Thermo-Mechanical properties were takenModel from [22]. The stress-strain diagram was taken from the Sysweld material database (ESI Group, Paris, A plane strain two-dimensional model was employed to perform the thermo-mechanical France) [23] and the data was supplied for S355J2G3. The material was assumed to follow an elastosimulation. strainbehaviour components wereplasticity neglected. The thermo-physical material plastic lawAll without-of-plane isotropic hardening (von Mises model). properties were taken from [22]. The phase transformation is also considered in the model. The material properties of all elements The stress-strain was taken theduring Sysweld material database Group, Paris, reaching the austenitediagram end temperature (AC3)from changed cooling to austenite. When (ESI austenite is cooled to the (MF),S355J2G3. the materialThe properties of thewas elements changed France) [23] andmartensite the datafinish wastemperature supplied for material assumed to to follow an martensite.law Elements that do nothardening reach the austenite start(von temperature (AC1) maintain the properties elasto-plastic with isotropic behaviour Mises plasticity model). of the base material. Another material model was used for the element, which reaches a temperature The phase transformation is also considered in the model. The material properties of all elements above AC1 and below AC3. This model was composed of 50% of base material and martensite reaching the austenite end temperature (AC3 ) changed during cooling to austenite. When austenite is properties below MF and 50% of base material and austenite properties above MF, until the martensite cooled totemperature the martensite start (MS). finish temperature (MF ), the material properties of the elements changed to
martensite. Elements that do not reach the austenite start temperature (AC1 ) maintain the properties of the base material. Another material model was used for the element, which reaches a temperature above AC1 and below AC3 . This model was composed of 50% of base material and martensite properties below MF and 50% of base material and austenite properties above MF, until the martensite start temperature (MS ).
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with one-dimensional spring elements that have The clamping has been replaced in the model with similar stiffness. Figure Figure 5 shows shows the dimensions and the applied boundary conditions used in the thermo-mechanicalmodel. model.This Thissimplification simplificationhas hasbeen been used [24,25]. The Birth Death feature thermo-mechanical used in in [24,25]. The Birth andand Death feature has ◦ C.1440 Metals 2018, 8,elements x FOR REVIEWreceiving of 15 has been used all PEER elements an average temperature °C. All these 6elements, been used for allfor receiving an average temperature of 1440 of All these elements, reaching reaching thetemperature, melting temperature, were stiffness matrix for these elements by was the melting were “killed”. The“killed”. stiffnessThe matrix for these elements was multiplied a The clamping has been replaced in the model with one-dimensional spring elements that have multiplied by and a penalty factor and all the strains, including the plastic strains, eliminated. The penalty factor all strains, including plastic strains, were eliminated. Thewere computed weld pool similar stiffness. Figure 5 shows the dimensions and the applied boundary conditions used in the computed weld pool geometry from CFD simulation was used as a heat source to calculate geometry from CFD simulation was used as a heat source to calculate the temperature field in thermo-mechanical model. This simplification has been used in [24,25]. The Birth and Death feature the temperature field in the model. thermal model. has been used for thermal all elements receiving an average temperature of 1440 °C. All these elements, reaching the melting temperature, were “killed”. The stiffness matrix for these elements was multiplied by a penalty factor and all strains, including the plastic strains, were eliminated. The computed weld pool geometry from CFD simulation was used as a heat source to calculate the temperature field in the thermal model.
Figure 5. Boundary conditions used in the thermo-mechanical analysis. Figure 5. Boundary conditions used in the thermo-mechanical analysis. Figure 5. Boundary conditions used in the thermo-mechanical analysis. 3. Results and Discussion 3. Results and Discussion Radiographic tests showed that cracks formed in the weld interior (see Figure 6a). In Figure 6b, 3. Results and Discussion Radiographic tests showed that cracks formed in the weld interior (see Figure 6a). In Figure 6b, a micrograph of the weld cross-section presents a typical vertical solidification crack in the weld Radiographic testscross-section showed that cracks formed in the weld interior (see Figure 6a). In Figure 6b, weld a micrograph of the weld presents a typical vertical solidification crack in the centerline. It should of bethe noted that small cracks that can be observed in the weld crack and the heat-affected a micrograph weld cross-section presents a typical vertical solidification in the weld centerline. It should be noted that small cracks that can be observed in the weld and the heat-affected zone were not taken into in thisthat study. theweld low-alloyed steel was not centerline. It should be consideration noted that small cracks can beMoreover, observed in the and the heat-affected zone were not taken into consideration in this study. Moreover, the low-alloyed steel was not zone to were not liquation taken into cracks consideration in this Dip study.Cracking Moreover,(DDC), the low-alloyed steel was notThese susceptible either or Ductility or cold cracks [26]. susceptible to either liquation cracks or or Ductility Dip Cracking(DDC), (DDC), or cold cracks [26]. These to to either liquation cracks Ductility Dip Cracking coldunder crackssimilar [26]. These findingssusceptible are similar those reported by [25], where they welded 15 mm or plate restraint findingsfindings are similar to those by[25], [25], where they welded 15 mm under similar are similar to thosereported reported by where they welded 15 mm plate underplate similar restraint conditions. restraintconditions. conditions.
(a)
(b)
Figure 6. (a) Radiographic film of a welded sample. (b) Weld cross-section at the crack location.
Figure 6. (a) Radiographic film of a(a) welded sample. (b) Weld cross-section at the crack location. (b)
Figure 6. (a) Radiographic film of a welded sample. (b) Weld cross-section at the crack location.
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However, such cracks are related to a high weld depth-to-width ratio. This ratio leads to a pronounced intersection of columnar grains, along with a plane at the weld centerline and the However,ofsuch cracks areinrelated to a high depth-to-width leads totoa accumulation segregations this zone. It is weld believed that if the ratio. weld This metalratio is unable pronounced intersection of columnar along withand a plane at the centerline and the accommodate the contractional strainsgrains, of solidification cooling, hotweld cracks will inevitably accumulation of segregations in this zone. It is believed that if the weld metal is unable to accommodate originate. the contractional of solidification and cooling, hot cracks will inevitably originate. However, thestrains experiments were conducted to create appropriate conditions for solidification However, the experiments were conducted to create appropriate conditions forassolidification cracking initiation. Those boundary conditions and the results of the crack location, well as the cracking initiation. boundary conditions and theused results thecalibration crack location, as well as the cross-section and theThose temperature measurement were forofthe of the numerical cross-section and the temperature measurement were used for the calibration of the numerical models. models. Theaim aimof ofthe theCFD CFDmodel modelwas wasto topredict predictthe thegeometry geometryof ofthe thequasi-steady-state quasi-steady-stateweld weldpool poolin in The thestable stablezone zoneof ofthe theweld. weld.The Thethree-dimensional three-dimensionalweld weldpool poolgeometry geometryisisdefined definedby bythe theliquidus liquidus the temperature(see (seeFigure Figure7a), 7a),and andpart partof ofthis thisisotherm isothermcan canbe beseen seenin inthe thesymmetry symmetryplane planeof ofthe theCFD CFD temperature model(see (seeFigure Figure7b). 7b).In InFigure Figure7,7,three threeregions regionsof ofthe theweld weldpool poolcan canbe berecognized. recognized.The Theweld weldpool pool model shapeisisstrongly stronglyinfluenced influencedby bythe theMarangoni Marangoniconvection convectionininthe theupper upperand andlower lowersides sidesofofthe thepart. part. shape Together with the movement of the laser source, three regions are developed: an upper, a bulging Together with the movement of the laser source, three regions are developed: an upper, a bulging (middle),and andaalower lowerregion. region.The Theobserved observedvelocities velocitiesofofthe themelt meltininthe thebulging bulgingregion regionwere werevery very (middle), smallcompared compared to to the the values values in the upper and small and lower lower regions. regions. Hence, Hence,the theedge edgeofofthe themiddle middleregion regionis the two two backflows backflowsdue dueto tothe the isnearly nearlyaaparallel parallelshift shiftof ofthe thekeyhole keyholeedge, edge, which which forms forms together with the thermo-capillary-drivenflow flowthe theobserved observedbulge. bulge. thermo-capillary-driven Thequasi-steady-state quasi-steady-stateweld weldpool poolrepresents representsthe thestate stateof ofaamass massand andenergy energyequilibrium equilibriumdefined defined The bythe themoving movingenergy energysource sourceand andthe thesolidification solidificationspeed speedat atthe thetrailing trailingpart partof ofthe theweld weldpool. pool.Due Dueto to by themovement movementof ofthe theenergy energysource sourcealong alongthe thepartly partlycold coldmaterial, material,new newmaterial materialisismelted meltedand andadded added the tothe theweld weldpool. pool.This Thisisisthen thentransferred transferredby bythe thedifferent differentflows flowsininthe themolten moltenpool. pool.Simultaneously, Simultaneously, to through transfer,the thesame sameamount amountofof molten material solidifies at the trailing ofweld. the through the the heat transfer, molten material solidifies at the trailing part part of the In theIn present model,model, the flows the upper lower dominate and transfer cooler material weld. the present the in flows in the and upper andregions lower regions dominate and transfer cooler back to the vicinity the keyhole, conservation. The two necking areas are formed material back to theof vicinity of the ensuring keyhole, mass ensuring mass conservation. The two necking areas and, are formed and, consequently, also the bulge7). (see Figure 7). consequently, also the bulge (see Figure
(a)
(b)
Figure Figure7.7.(a) (a)The Theweld weldpool poolgeometry geometrydefined definedby bythe theliquidus liquidustemperature. temperature.(b) (b)Temperature Temperaturefield fieldand and velocity streamlines in the symmetry plane of the model. velocity streamlines in the symmetry plane of the model.
The diameter of the keyhole was used as a parameter to achieve a good match between the The diameter of the keyhole was used as a parameter to achieve a good match between the experiments and the model. This parameter was adjusted until an error of less than 5% was obtained. experiments and the model. This parameter was adjusted until an error of less than 5% was obtained. The fused zone, highlighted with dashed lines, agrees well with the experiment (see Figure 8). The fused zone, highlighted with dashed lines, agrees well with the experiment (see Figure 8).
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Figure Figure 8. 8. Comparison Comparison of of the the fused fused zone zone between between experiment experiment and and CFD CFD model. model.
Figure 9 shows the temperature measurements over time using thermocouples on the top and Figure 9 shows the temperature measurements over time using thermocouples on the top and the the bottom of the specimen surface compared to measurements obtained from calculations. bottom of the specimen surface compared to measurements obtained from calculations.
Figure 9.9.Comparison Comparison of the temperature measurements between experiments and the Figure of the temperature measurements between experiments and the computational computational model. model.
To asas a heat source in the two-dimensional model, it was To use use the thecomputed computedweld weldpool poolgeometry geometry a heat source in the two-dimensional model, it assumed that the temperature within the melt isotherm is homogeneous, constant, and equal to was assumed that the temperature within the melt isotherm is homogeneous, constant, and equal to melting temperature(1440 (1440◦ C). °C). Then, simply consists of multiple of two melting temperature Then, the the weldweld pool pool simply consists of multiple layers of layers two combined combined half-ellipses, as shown schematically in Figure 10. half-ellipses, as shown schematically in Figure 10.
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Figure 10. Schematic representation of the weld pool geometry and the parameters of two combined Figure 10. Schematic representation of the weld pool geometry and the parameters of two half-ellipses. combined half-ellipses.
The equation of the combination of two half-ellipses can be given as flowing: The equation of the combination of two half-ellipses can be given as flowing:
+ ( , )x2 where: where:
=1 ( )y2
c2 ( x, z)
( , ) =
+
b2 ( z )
=1
= 1 if ≤ 0 =c = 2 if 00 c1 if > x≤
(
c( x,ofz)the = ellipses is defined by parameters b and c1 and the rear The front part of the combination c = c2 if x > 0 of the ellipse is defined by b and c2. The parameter c is a function of the weld pool length (xThe front part the combination the ellipses isand defined by parameters c1 andofthe of coordinate) and theofweld pool depth of (z-coordinate), the parameter b is ba and function therear weld the ellipse is defined by b and c2. The parameter c is a function of the weld pool length (x-coordinate) pool depth. and the pool depth (z-coordinate), and the b is apolynomial function of function the weld (see poolFigure depth.11). Theweld parameters c1, c2, and b were fitted withparameter fourth-degree The parameters c1, c2, and b were fitted with fourth-degree polynomial function (see Figure 11). The obtained quartic functions were employed for the calculation of those parameters in the thermal The obtained quartic functions were employed for the calculation of those parameters in the model. thermal Themodel. developed heat source will check at each time step, whether the nodes are located inside The heatifsource check at each step, whether the nodes are located inside one of thedeveloped ellipses, and so, thewill temperature will time be changed to the melt temperature. If not, the one of the ellipses, and if so, the temperature will be changed to the melt temperature. If not, the temperature will be maintained. temperature will be maintained. Figure 12 shows a comparison of the temperature field between calculations, using the CFD Figure 12 shows a comparison the temperature field between calculations, using the CFD on model model on the right and using the of developed heat source, which was previously described, the on the right and using the developed heat source, which was previously described, on the opposite opposite side of the temperature field. A very slight difference can be observed between fusion lines. side of the temperature field. A fitting very slight canparameters. be observedHowever, between fusion lines.ofThis This difference is a result of the of thedifference heat source the results this difference is a resulthigh of the fitting ofinthe source However, the results which of this cannot technique technique showed efficiency theheat transfer ofparameters. computed weld pool geometry, be showed high efficiency in the transfer of computed weld pool geometry, which cannot be achieved by achieved by using common heat sources, such as the conical Gaussian heat source model [27], the using common sources, Gaussian heat [29,30]. source model [27], the cylindrical heat cylindrical heatheat source modelsuch [28],asorthe theconical combination of both source model [28], or the combination of both [29,30].
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Figure 11. 11. Thefitting fitting of of the the parameters parameters c1, c1, c2 and as function of the Figure Figure 11. The The fitting of the parameters c1, c2 c2 and and bbb as as aaa function function of of the the weld weld depth. depth.
Figure Figure 12. 12. Comparison Comparison of of the the temperature temperature fields fields of of the the CFD CFD and and the the thermal thermal model. model. Figure 12. Comparison of the temperature fields of the CFD and the thermal model.
These These heat heat source source models models were were mainly mainly developed developed based based on on the the cross-section cross-section of of the the weld, weld, These heat source models were mainly developed based on the cross-section of the weld, without without considering the weld pool in the longitudinal section. However, this fulfills the purpose of without considering the weld pool in the longitudinal section. However, this fulfills the purpose of considering the weld pool in the longitudinal section. However, this fulfills the purpose of the the the calculation calculation of of residual residual stresses stresses and and the the distortions. distortions. calculation of residualstress stresses and the distortions. The distribution and The transversal transversal stress distribution and the the temperature temperature distribution distribution of of approximately approximately 230 230 ms ms after complete solidification of the melt (i.e., at 1100 °C in the middle of the weld) are shown in after complete solidification of the melt (i.e., at 1100 °C in the middle of the weld) are shown in Figure Figure 13. 13. A A concentration concentration of of the the tensile tensile stress stress can can be be observed observed in in the the middle middle of of the the weld weld in in the the bulging bulging
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The transversal stress distribution and the temperature distribution of approximately 230 ms after complete of the melt (i.e., at 1100 ◦ C in the middle of the weld) are shown in Figure Metals 2018, solidification 8, x FOR PEER REVIEW 11 of13. 15 Metals 2018, 8, x FOR PEER REVIEW 11 of 15 A concentration of the tensile stress can be observed in the middle of the weld in the bulging region. Regions subject tosubject high compressive stresses can be observed the top and bottom of this region. region. Regions to high compressive stresses can be at observed at the top and bottom of The this region. Regions subject to high compressive stresses can be observed at the top and bottom of this same observation can be found for the vertical stress (see Figure 14). region. The same observation can be found for the vertical stress (see Figure 14). region. The same observation can be found for the vertical stress (see Figure 14).
Figure 13. Transversal stress distribution and temperature distribution after solidification of the weld Figure 13. Transversal Transversalstress stressdistribution distribution and temperature distribution solidification the and temperature distribution afterafter solidification of theofweld pool. pool. weld pool.
Figure 14. Vertical stress distribution and corresponding temperature distribution after solidification Figure 14. Vertical stress distribution and corresponding temperature distribution after solidification Figure 14. Vertical of the weld pool. stress distribution and corresponding temperature distribution after solidification of the weld pool. of the weld pool.
To closely evaluate the observed stress distribution at this moment, three evaluation points were To closely evaluate the observed stress distribution at this moment, three evaluation points were chosen, which were positioned belowstress each other. P1 represents the upper narrowing region, the To closely evaluate the observed at this moment, three evaluation pointsP2 were chosen, which were positioned below each distribution other. P1 represents the upper narrowing region, P2 the bulging which region,were and positioned P3 the lower narrowing regionP1(see Figure 13). Figure 15 and Figure 16 indicate chosen, below each other. represents the upper narrowing region, P2 the bulging region, and P3 the lower narrowing region (see Figure 13). Figure 15 and Figure 16 indicate the transversal stress narrowing evolution versus during P1, the P2, bulging region, and and vertical P3 the lower regionthe (seetime Figure 13). cooling Figures at 15the andlocations 16 indicate the transversal and vertical stress evolution versus the time during cooling at the locations P1, P2, and P3. Onand the vertical narrowing regions (P1 and P3),the the transversal stressesatdeveloped in P1, a very similar transversal stress evolution versus time during cooling the locations P2, and P3. and P3. On the narrowing regions (P1 and P3), the transversal stresses developed in a very similar manner because immediately after solidification, tensile stresses appeared for a short period and soon On the narrowing regions (P1after andsolidification, P3), the transversal inaashort very period similarand manner manner because immediately tensile stresses stresses developed appeared for soon became compressive stresses until reaching the value of −30 MPa. Nevertheless, the vertical stresses became compressive stresses until reaching the value of −30 MPa. Nevertheless, the vertical stresses in all regions show tensile development. in all regions show tensile development.
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because immediately after solidification, tensile stresses appeared for a short period and soon became compressive stresses until reaching the value of −30 MPa. Nevertheless, the vertical stresses in all Metals 8, REVIEW 12 Metals2018, 2018, 8,xx FOR FOR PEER PEER REVIEW 12of of15 15 regions show tensile development.
Figure 15. Transversal stress evaluation on the points P1, P2, and P3. Figure15. 15.Transversal Transversalstress stressevaluation evaluationon onthe thepoints pointsP1, P1,P2, P2,and andP3. P3. Figure
Figure 16. Vertical stress evaluation on the points P1, P2, and P3. Figure16. 16.Vertical Verticalstress stressevaluation evaluationon onthe thepoints pointsP1, P1,P2, P2,and andP3. P3. Figure
In In the thebulging bulgingregion region (P2), (P2), transversal transversaland and vertical verticaltensile tensile stresses stresses development developmentcan canbe beobserved observed In the bulging region (P2), transversal and vertical tensile stresses development can be observed immediately immediately after after solidification, solidification, continuing continuing to to rise rise until until reaching reaching aa value value of of 80 80 MPa MPa and and 110 110 MPa, MPa, immediately after solidification, continuing to rise until reaching a value of 80 MPa and 110 MPa, respectively. respectively. The The vertical vertical tensile tensile stress stress along along the the weld weld depth depth can can be be returned returned to to the the restraint restraint of of the the respectively. The vertical tensile stress along the weld depth can be returned to the restraint of the plate to the vertical shrinkage of the weld. However, since the transversal stresses have an opposite plate to the vertical shrinkage of the weld. However, since the transversal stresses have an opposite plate to the vertical shrinkage of the weld. However, since the transversal stresses have an opposite direction direction to to the the dendrites dendrites growth, growth, the the stresses stresses are are held held responsible responsible for for the the formation formation of of these these cracks. cracks. direction to the dendrites growth, the stresses are held responsible for the formation of these cracks. As As previously previously observed, observed, the the chronological chronological order order of of the the solidification solidification of of the the weld weld cannot cannot be be As previously observed, the chronological order of the solidification of the weld cannot be separated from the nature and distribution of the stresses in the weld zone. To explain this mutual separated from the nature and distribution of the stresses in the weld zone. To explain this mutual separated from the nature and distribution of the stresses in the weld zone. To explain this mutual interaction interaction in in the the weld weld during during cooling, cooling, Figure Figure 17 17 schematically schematically shows shows the the melt melt and and the the solid solid interaction in the weld during cooling, Figure 17 schematically shows the melt and the solid distribution distribution in a considered plane orthogonal to the welding direction, while the weld pool passes distribution in a considered plane orthogonal to the welding direction, while the weld pool passes in a considered plane orthogonal to the welding direction, while the weld pool passes through it, at through through it, it, at at three three consecutive consecutive moments moments of of time. time. Moment Moment T1 T1 represents represents the the section section on on the the widest widest three consecutive moments of time. Moment T1 represents the section on the widest location of the location location of of the theweld weld pool poolcrossing crossing the theplane. plane. Until Until this this moment, moment, the the weld weld region region is is heated heated from from room room weld pool crossing the plane. Until this moment, the weld region is heated from room temperature to temperature to melt temperature, and the weld volume expands. This expansion is restrained by temperature to melt temperature, and the weld volume expands. This expansion is restrained by the the melt temperature, and the weld volume expands. This expansion is restrained by the surrounding cold surrounding surroundingcold cold material, material, in in addition addition to to the the restraint restraint of of the the clamping clamping causing causing compressive compressive stress stress in in material, in addition to the restraint of the clamping causing compressive stress in the surrounding the the surrounding surroundingmaterial. material. In In this this moment, moment, no no stresses stresses have have taken taken place place in in the the weld weld zone zone because because the the material. In this moment, no stresses have taken place in the weld zone because the melt has nil melt melt has has nil nil strength strength [2]. [2]. ItIt must must be be noted noted that that the the stress stress resulting resulting from from the the thermal thermal strains strains during during strength [2]. It must be noted that the stress resulting from the thermal strains during solidification is solidification solidification isis relieved relieved as as long long as as the the connection connection to to the the melt melt is is available. available. relieved as long as the connection to the melt is available. As As the the weld weld pool pool moves moves slightly slightly forward forward there there are are still still melted melted regions regions within within the the bulging bulging top top and andbottom bottomparts, parts, whereas whereas the thenarrowing narrowingregions regions solidify solidifybetween between them them (T2). (T2). As As long long as as these these liquid liquid regions regions have have access access to to the the melt melt or or to to the the top top and and bottom bottom free free surfaces, surfaces, the the resulting resulting thermal thermal stresses stresses can can be be relieved. relieved. This This corresponds corresponds to to the the observations observations at at points points P1 P1 and and P3. P3.
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Figure 17. Schematic illustration of the distribution of the melt and solid in three points in time (T1, Figure 17. Schematic illustration of the distribution of the melt and solid in three points in time (T1, T2 T2 and during solidification of the weld pool. and T3)T3) during solidification of the weld pool.
At the last stage of solidification, corresponding to the time T3, the bulging region solidifies and As the weld pool moves slightly forward there are still melted regions within the bulging top the surrounding material is already in a solid state. Then the entire amount of stress resulting from and bottom parts, whereas the narrowing regions solidify between them (T2). As long as these liquid the thermal strain adds to the stresses. Atdistribution this moment, themelt dendrite arms and(T1, feeding Figure 17. Schematic illustration of the of the and solid inhave threecoalesced points in time regions have access to the melt or of tothe theweld top and bottombetween free surfaces, thesolidification resulting thermal and is T3)difficult. during solidification pool. of theT2melt When a melt film is still present the two fronts,stresses due to can be relieved. of This corresponds to the at points P1 and P3. is expected (see Figure 18). the localization high tensile stress, theobservations initiation of solidification cracks At last solidification, corresponding to time T3, the bulging region solidifies and At the the last stage stage of of corresponding to the theuntil time the T3, temperature the bulging region solidifies and The risk of formation ofsolidification, the solidification cracks continues reaches 988 °C, due the surrounding material is already in a solid state. Then the entire amount of stress resulting from the the surrounding material is as already in a solid state. Then the entire amount of stress resulting from to low melting phases such Fe-S [31]. thermal strain adds to the stresses. At this moment, the dendrite arms have coalesced and feeding of the thermal strain adds to the stresses. At this moment, the dendrite arms have coalesced and feeding the melt is difficult. When a melt filmfilm is still present between the the twotwo solidification fronts, duedue to the of the melt is difficult. When a melt is still present between solidification fronts, to localization of high tensile stress, the initiation of solidification cracks is expected (see Figure 18). The the localization of high tensile stress, the initiation of solidification cracks is expected (see Figure 18). risk formation of theofsolidification crackscracks continues until the temperature reachesreaches 988 ◦ C,988 due°C, to due low The of risk of formation the solidification continues until the temperature melting phases phases such assuch Fe-S as [31]. to low melting Fe-S [31].
Figure 18. Schematic representation of solidification cracking in the bulging region.
4. Conclusions In this study, a three-dimensional CFD-simulation model was developed to simulate the fluid flow in the weld pool. The CFD model showed a bulging region in the middle of the depth, which is Figure 18. Schematic representation of cracking in in the bulging bulging region. Figure of solidification solidification separated from the18. topSchematic surface representation and bottom surface by two cracking narrowingthe regions. Itregion. can be concluded that the interaction of the movement of the laser source with the Marangoni vortex leads to a teardrop 4. Conclusions 4. Conclusions shape at the upper and bottom surface of the workpiece. Additionally, it shows that the bulging in In this study, three-dimensional CFD-simulation model was developed to simulate the fluid the weld is astudy, resultaaofthree-dimensional the backflows on the upper and lower sides due to the thermo-capillary-driven In this CFD-simulation model was developed to simulate the fluid flow in the weld pool. The CFD model showed a bulging region in the middle of the depth, which is flows.in the weld pool. The CFD model showed a bulging region in the middle of the flow depth, which is separated from the shape top surface and bottom surface by two narrowing regions. It can be concluded The weld was used a heatsurface source in two-dimensional thermo-mechanical model, separated frompool the top surface andas bottom byatwo narrowing regions. It can be concluded that theallows interaction of the movement of the laser of source with pool the Marangoni vortex leadsfrom to a teardrop which a highly accurate transformation the weld dimensions obtained the CFD shape the upper and bottom surface of the Additionally, shows that the bulging in model.atThis developed technique allows the workpiece. consideration of physicalit aspects, which cannot be the weld is awhen resultusing of thetraditional backflowsheat on the upper and lower sides due to the thermo-capillary-driven considered sources. flows. The weld pool shape was used as a heat source in a two-dimensional thermo-mechanical model, which allows a highly accurate transformation of the weld pool dimensions obtained from the CFD
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that the interaction of the movement of the laser source with the Marangoni vortex leads to a teardrop shape at the upper and bottom surface of the workpiece. Additionally, it shows that the bulging in the weld is a result of the backflows on the upper and lower sides due to the thermo-capillary-driven flows. The weld pool shape was used as a heat source in a two-dimensional thermo-mechanical model, which allows a highly accurate transformation of the weld pool dimensions obtained from the CFD model. This developed technique allows the consideration of physical aspects, which cannot be considered when using traditional heat sources. The mechanical model showed that the chronological order of the solidification of the weld has a significant influence on the nature and distribution of the stresses in the weld. High tensile stress has been observed in the bulging region, i.e., in the susceptible region for solidification cracking, when compared to the other narrowing regions, which show compressive stress. Author Contributions: The numerical simulation models have been developed by N.B. and A.A. Discussion and conclusions have been written with the contribution of all authors. Funding: This work was supported by the Research Association for Steel Application (FOSTA), the Federation of Industrial Research Associations (AiF) and the German Federal Ministry for Economic Affairs and Energy, (BMWi Bundesministerium für Wirtschaft und Energie), (Project 19582N, ‘Investigation of the influence the restraint conditions on hot cracking in laser and laser-hybrid welding of thick structure steels’). Financial funding of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Grant Nr. BA 5555/1-1 is gratefully acknowledged. Conflicts of Interest: The authors declare no conflict of interest.
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