**1. Introduction**

Welding methods are based on the thermal effect of melting and crystallization process. Conventional methods use electric arc as a heat source. Alternative to gas metal arc welding (GMAW) are beam welding methods [1,2], in which the concentrated energy of focused electrons or photons achieves high power density. The energy distribution factor allows high-speed welding, and the quantity of thermal energy absorbed in the materials is low. Electron beam welding (EBW) has high energy distribution, but it has to be performed in a vacuum, which is problematic in some welding applications. Laser beam welding (LBW) is an alternative technology in which a high power density of a focused photon beam shielded by inert gas can be used for numerous types of joining applications [3,4]. The keyhole effect in LBW enables deep penetration of the welded material. Moreover, laser beam penetration is possible through more than one material. Rapid development of laser technology has determined LBW for use in advanced joint configuration. Currently, researchers are focusing on welding dissimilar materials, where low-carbon and austenitic steels are welded, and some works are related to joining advanced aluminum, nickel and titanium alloys [5–9]. Nonconventional joining methods, such as laser welding in butt, lap and T-joint configurations, are also being widely studied [10–14]. Numerical analysis of the laser welding process has been undertaken, including lap joints, for a wide range of materials by many researchers [15–18]. However, laser lap welding of low-carbon steel has been

reported in only a few works concentrated mostly on numerical analysis or joints properties [19–24]. The works cited above lack a more comprehensive study of lap joints, laser beams applied to the welding of commonly used constructional steel, or analysis based on mechanical and metallographic study, supported by numerical simulation. The selection of manually programmed laser welding parameters is problematic and requires performing a number of trial joints and an experienced operator. It thus seems reasonable to use some aided methods for supporting welding parameters estimation, such as analytical method, where thermal conduction calculation is based on solving the moving heat-sources equation proposed by Rosenthal [9]. Evolution of analytical computation relies on improving the mathematical description of heat sources. Solving the moving-heat-sources equation enables the use of the thermal distribution to estimate the shape of weld geometry. Analytical solution allows for the estimation of welding parameters in simple cases. In applications such as lap joints of steel sheets, it is more complex and requires using numerical methods [25–27].

Numerical simulation of welding process can be performed by using dedicated software such as SYSWELD or Simufact Welding or advanced multiphase heat-mass flow programs such as ANSYS with FLUENT module. Calculations are based on the Finite Elements Method (FEM) and solver engine. CAD geometry is discretized, and finite elements mesh is generated. During discretization of the area where significant heat effect can occur, FE refinement is performed. Welding simulation requires defining heat-source dimensions and heat-energy volume related to welding parameters [28–33]. If we consider thermo-mechanical simulation, in addition to the results of temperature distribution, a stress–strain analysis can be obtained. Considering lap welding, material properties in the upper plate of joint will differ from those in the lower plate. An analysis of this phenomenon is presented in this article. Properties of stress–strain distribution in the welded material are related to thermo-physical material properties, temperature distribution, heat expansion coefficient and phase transformation, changing in time. Defining these properties is complex; nevertheless, using numerical computation accurate estimation of the results is possible.

When performing a welding simulation, we must remember that, no matter how accurate, the results obtained are just estimations. The quality level depends on the defined boundary conditions and programmed welding parameters; therefore, experimental verification is required. The welding process requires a shielding atmosphere of inert gas. In order to confine ionization effect, helium is recommended as a reference gas. In the case of a sealed lap joint with partial penetration of the lower plate, no shielding atmosphere for the weld root is needed. However, the space between the plates contains some oxygen and may cause inclusions and welding defects; therefore, metallographic analysis was performed in this study. A programming numerical model verification stage needs to be considered, especially for defining some process properties, such as heat-source efficiency and energy distribution (TEM), related to the laser type, which must be included in the simulation [34–38]. The programmed heat-source dimension can be verified by comparing the simulated weld geometry with the trial joint.

In this paper, a numerical-simulation-aided analysis of laser welding of sealed steel sheets' lap joints is presented.

#### **2. Methodology**

#### *2.1. Materials*

Low-carbon constructional steel S235JR in the form of 2.5 mm thick steel sheets was used as a base material for both the simulation and trial joint welding. The commonly used low-carbon steel sheets were welded in lap joint configuration, using an advanced heat source in the form of a laser beam. The S235JR is unalloyed steel with carbon content up to 0.2% and a trace amount of other alloying elements (Table 1).


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amount of alloying elements reduce steel hardening, though some strengthening effect may occur

The structure of S235JR steel is typically ferritic–pearlitic. Low-carbon content and the trace amount of alloying elements reduce steel hardening, though some strengthening effect may occur via steel phase transformations. Thermo-physical properties of the material affect heat expansion and welding results (Table 2). The S235JR steel has high thermal conductivity, with the phase transformation temperature of 725 ◦C for AC<sup>1</sup> and 863 ◦C for AC<sup>2</sup> [39,40]. via steel phase transformations. Thermo-physical properties of the material affect heat expansion and welding results (Table 2). The S235JR steel has high thermal conductivity, with the phase transformation temperature of 725 °C for AC1 and 863 °C for AC2 [39,40]. **Table 2.** Thermal properties of low-carbon constructional steel S235JR.


**Ferrite** 


#### *2.2. Numerical Simulation 2.2. Numerical Simulation*

A numerical simulation of laser welding generally uses two types of heat-source models simulating laser interaction with the material: a surface heat source and a conical heat source. The surface-heat-source model (disc shape) is more accurate and is used for simulating laser energy absorption by steel sheets' surface (in some applications, for conduction welding solutions) [41]. The conical heat source is dedicated to simulating the keyhole effect and is related to energy being directed inside the material through the keyhole walls. Simufact Welding software (Simufact Engineering GmbH, Hamburg, Germany) uses a combination of surface and conical volumetric heat sources with uneven energy intensity distribution (Gaussian parameter), as shown below (Figure 1). A numerical simulation of laser welding generally uses two types of heat-source models simulating laser interaction with the material: a surface heat source and a conical heat source. The surface-heat-source model (disc shape) is more accurate and is used for simulating laser energy absorption by steel sheets' surface (in some applications, for conduction welding solutions) [41]. The conical heat source is dedicated to simulating the keyhole effect and is related to energy being directed inside the material through the keyhole walls. Simufact Welding software (Simufact Engineering GmbH, Hamburg, Germany) uses a combination of surface and conical volumetric heat sources with uneven energy intensity distribution (Gaussian parameter), as shown below (Figure 1).

**Figure 1.** Heat-source model used in laser-welding simulation. **Figure 1.** Heat-source model used in laser-welding simulation.

Conical volumetric heat source with the Gaussian distribution can be described by the following equation: Conical volumetric heat source with the Gaussian distribution can be described by the following equation:

$$Q(x, y, z) = Q\_0 \exp\left(-\frac{x^2 + y^2}{r\_0^2(z)}\right) \tag{1}$$

Moreover, () is defined as follows:

Moreover, *r*0(*z*) is defined as follows:

$$r\_0(z) = r\_\varepsilon + \frac{r\_i - r\_\varepsilon}{z\_i - z\_\varepsilon}(z - z\_\varepsilon) \tag{2}$$

where *Q*0—maximum volumetric heat flux density; *r<sup>i</sup>* − *re*—upper and lower conical radius dimension; *z<sup>i</sup>* − *ze*—conical heat source depth; and *x*, *y*, *z*—coordinates of heat source.

The numerical simulation was performed by using Simufact software with a Marc solver. The program is dedicated to welding applications; however, some physics phenomena, such as solidification, are simplified. This phenomenon is solved by using the assumption that the latent heat is uniformly released within the solidus and liquidus temperature range, where the solver uses the modified specific heat to model the latent heat effect based on material experimental data calculated by using JMatPro. Thermal conductivity is the dominant heat-transfer method; therefore, the governing equation is based on this phenomenon. Based on Fourier's law, three-dimensional heat conduction is given by the following governing equation:

$$
\rho c(T)\frac{\partial T}{\partial t} = \frac{\partial}{\partial \mathbf{x}} \Big( k(T)\frac{\partial T}{\partial \mathbf{x}}\Big) + \frac{\partial}{\partial y} \Big( k(T)\frac{\partial T}{\partial y}\Big) + \frac{\partial}{\partial z} \Big( k(T)\frac{\partial T}{\partial z}\Big) + q\_{\overline{\nu}} \tag{3}
$$

where *c*(*T*)—temperature dependent specific heat capacity; *k*(*T*)—temperature dependent thermal conductivity; *qv*—volumetric internal energy; *x, y, z*—space coordinates; *T*—temperature; ρ—density; and *t*—time.

The simulation includes the convection effect and uses the Petro–Galerkin convection–diffusion model and nodal velocity vectors, as shown below.

$$\frac{\partial T}{\partial t} + v \cdot \nabla T = \nabla \cdot (\kappa \nabla T) + Q \tag{4}$$

where *v*—nodal velocity vector; *T*—temperature; κ—diffusion tensor; and *Q*—source term.

The obtained numerical model accounts for convection but does not account for surface tension or the Marangoni effect; therefore, some differences in heat transfer compared to the experimental process will occur, reflected in the fusion zone shape.

In the boundary conditions, a rigid restraint for welded elements, using fixed geometry, was programmed (Figure 2). Two 2.5 mm thick sheets were meshed by using finite elements hexahedral in shape. A preliminary research of mesh convergence was carried out, where welding simulations were performed with the same process parameters and different mesh sizes, starting with FE size equal to 1.25 mm, and then 0.5, 0.25 and 0.125 mm up to 0.0625 mm. For 0.0625 and 0.125 mm, no significant differences in the weld or HAZ geometry were observed; however, some differences between 0.125 and 0.25 mm were detected. In order to confirm mesh convergence, a study of temperature distribution was carried out. For all mesh sizes, measurement point, placed 2.5 mm from weld axis (approximately center of HAZ) were sets, and temperature changes shown in graph form were compared (Figure 2). The graphs in Figure 2 show similar results as the HAZ geometry analysis.

Therefore, in order to save simulation time, a general FE size was programmed as 0.25 mm. In order to obtain more accurate and realistic results, a refinement procedure with FE size equal to 0.125 mm was performed near the weld zone (at the temperature exceeding 400 ◦C). Sheets of S235JR low-carbon constructional steel were selected for the simulation (Table 2). The material multiphase library allowed the calculation of the overall thermo-mechanical joint properties.

The performed research assumed keyhole welding and deep material penetration; however, in the first stage before the keyhole effect appears, laser beam reflectivity from the metal surface is high, and when the heat-source efficiency is programmed, this phenomenon must be included. Therefore, for the simulation of CO<sup>2</sup> laser welding, the heat source efficiency coefficient was assumed as 0.77.

analysis.

density; and *t—*time.

() = +

dimension; − —conical heat source depth; and x, y, z—coordinates of heat source.

 ൰ +

heat conduction is given by the following governing equation:

diffusion model and nodal velocity vectors, as shown below.

experimental process will occur, reflected in the fusion zone shape.

൬()

where *—*nodal velocity vector; *T—*temperature; *—*diffusion tensor; and *Q—*source term.

 <sup>=</sup>

()

 − −

The numerical simulation was performed by using Simufact software with a Marc solver. The program is dedicated to welding applications; however, some physics phenomena, such as solidification, are simplified. This phenomenon is solved by using the assumption that the latent heat is uniformly released within the solidus and liquidus temperature range, where the solver uses the modified specific heat to model the latent heat effect based on material experimental data calculated by using JMatPro. Thermal conductivity is the dominant heat-transfer method; therefore, the governing equation is based on this phenomenon. Based on Fourier's law, three-dimensional

൬()

The simulation includes the convection effect and uses the Petro–Galerkin convection–

The obtained numerical model accounts for convection but does not account for surface tension or the Marangoni effect; therefore, some differences in heat transfer compared to the

In the boundary conditions, a rigid restraint for welded elements, using fixed geometry, was programmed (Figure 2). Two 2.5 mm thick sheets were meshed by using finite elements hexahedral in shape. A preliminary research of mesh convergence was carried out, where welding simulations were performed with the same process parameters and different mesh sizes, starting with FE size equal to 1.25 mm, and then 0.5, 0.25 and 0.125 mm up to 0.0625 mm. For 0.0625 and 0.125 mm, no significant differences in the weld or HAZ geometry were observed; however, some differences between 0.125 and 0.25 mm were detected. In order to confirm mesh convergence, a study of temperature distribution was carried out. For all mesh sizes, measurement point, placed 2.5 mm from weld axis (approximately center of HAZ) were sets, and temperature changes shown in graph

where *c*(*T*)—temperature dependent specific heat capacity; *k*(*T*)*—*temperature dependent thermal conductivity; ௩*—*volumetric internal energy; *x, y, z—*space coordinates; *T—*temperature; *—*

 ൰ +

൬()

+ ∙ ∇ = ∇ ∙ (∇) + (4)

൰+௩ (3)

where —maximum volumetric heat flux density; − —upper and lower conical radius

( − ) (2)

**Figure 2. Figure 2.** Graphs showing temperature changes for different FE mesh size. Graphs showing temperature changes for different FE mesh size. assumed as 0.77.

The geometry of the heat source is related to the focal length and focusing power of welding optics, and for the performed research, a single spot spherical mirror with a focal point diameter of 0.3 mm and a focal length equal to 200 mm was used. The disc-shaped heat source with a radius equal to 0.65 mm and a depth of 0.2 mm, and the conical heat source with the upper radius of 0.5 mm and the lower radius of 0.2 mm and the depth of 4 mm were programmed. Geometry of the heat source (HS) is related to welding optics. Nevertheless, some calibration for more accurate results is required, and test welding at the speed of 1 m/min and output power equal to 1 kW was performed. Comparison with the simulation results showed some discrepancy, and the heat-source geometry was adjusted by reducing the HS radius by approximately 10% and Gaussian distribution parameter from 2.9 to 2.8 [42,43]. The geometry of the heat source is related to the focal length and focusing power of welding optics, and for the performed research, a single spot spherical mirror with a focal point diameter of 0.3 mm and a focal length equal to 200 mm was used. The disc-shaped heat source with a radius equal to 0.65 mm and a depth of 0.2 mm, and the conical heat source with the upper radius of 0.5 mm and the lower radius of 0.2 mm and the depth of 4 mm were programmed. Geometry of the heat source (HS) is related to welding optics. Nevertheless, some calibration for more accurate results is required, and test welding at the speed of 1 m/min and output power equal to 1 kW was performed. Comparison with the simulation results showed some discrepancy, and the heat-source geometry was adjusted by reducing the HS radius by approximately 10% and Gaussian distribution parameter from 2.9 to 2.8 [42,43].

Numerical calculation of the laser lap-joint welding using a single pass process simulated by the heat source moving through steel sheets was carried out (Figure 3). Welding simulations with constant speed rate of 1 m/min and changing output power from 1 to 5 kW, changing with a step of 0.5 kW, were performed until the assumed sealed lap joint geometry was obtained. Phase transformation requires cooling time, so for welding equal to 1.2 s, the time for the complete process was programmed as 30 s. The simulation process was performed on a Dell PC class station with the i7 processor and 64 GB RAM, and the simulation calculation time was about 26 h. Numerical calculation of the laser lap-joint welding using a single pass process simulated by the heat source moving through steel sheets was carried out (Figure 3). Welding simulations with constant speed rate of 1 m/min and changing output power from 1 to 5 kW, changing with a step of 0.5 kW, were performed until the assumed sealed lap joint geometry was obtained. Phase transformation requires cooling time, so for welding equal to 1.2 s, the time for the complete process was programmed as 30 s. The simulation process was performed on a Dell PC class station with the i7 processor and 64GB RAM, and the simulation calculation time was about 26 h.

**Figure 3.** Laser-welding simulation model and the weld forming during the lap joint welding process.

#### **Figure 3.** Laser-welding simulation model and the weld forming during the lap joint welding process. *2.3. Experimental Procedure*

LaserCell 1005 work station (Figure 4).

*2.3. Experimental Procedure*  Verification of the numerical model was performed by welding the trial joint with parameters estimated at the simulation stage (laser power equal to 4kW, with the welding speed of 1m/min). For the configuration of the sealed steel sheet lap joint with partial penetration, welding conditions Verification of the numerical model was performed by welding the trial joint with parameters estimated at the simulation stage (laser power equal to 4 kW, with the welding speed of 1 m/min). For the configuration of the sealed steel sheet lap joint with partial penetration, welding conditions equal to those defined in the numerical simulation were established. In order to reduce the plasma ionization effect, helium as a shielding gas, with a flow rate equal to 20 L/min, was used. The welding

equal to those defined in the numerical simulation were established. In order to reduce the plasma ionization effect, helium as a shielding gas, with a flow rate equal to 20 L/min, was used. The

process was performed with a CO<sup>2</sup> laser Trumpf TruFlow 6000 integrated with a 6 axis LaserCell 1005 *Materials*  work station (Figure 4). **2020**, *13*, x FOR PEER REVIEW 6 of 18 

**Figure 4.** Laser-welding station with lap joint low-carbon steel configuration. **Figure 4.** Laser-welding station with lap joint low-carbon steel configuration. Laser-welding station with lap configuration.

The welding head with a focal length of 200 mm and coaxial shielding gas delivery system was used. The focal point was placed on the upper steel-sheet surface, and the welding of the trial joint was performed. The upper sheet was welded through, and the lower plate had the fusion zone approximately in the middle of its thickness. Therefore, the assumed lap joint partial penetration of two 2.5 mm thick S235JR steel sheets was obtained [44–46]. The welding head with a focal length of 200 mm and coaxial shielding gas delivery system was used. The focal point was placed on the upper steel-sheet surface, and the welding of the trial joint was performed. The upper sheet was welded through, and the lower plate had the fusion zone approximately in the middle of its thickness. Therefore, the assumed lap joint partial penetration of two 2.5 mm thick S235JR steel sheets was obtained [44–46]. The welding head a focal 200 mm and coaxial shielding gas system was The focal point placed on upper steel-sheet surface, the welding the trial joint The upper sheet was welded and lower plate the fusion approximately in the of Therefore, assumed lap joint partial penetration of

Weld strength characteristics were defined by the mechanical properties of the obtained joint. The weld properties were investigated by using destructive tests. The hardness test was carried out according to PN-EN ISO 6507-1 standard, using an Innovatest Nexus 4303 machine [47], and the hardness test point distribution for the steel sheets' lap joint is shown below (Figure 5). Weld strength characteristics were defined by the mechanical properties of the obtained joint. The weld properties were investigated by using destructive tests. The hardness test was carried out according to PN-EN ISO 6507-1 standard, using an Innovatest Nexus 4303 machine [47], and the hardness test point distribution for the steel sheets' lap joint is shown below (Figure 5). two 2.5 mm steel sheets obtained [44–46]. Weld strength defined by the mechanical properties joint. weld properties were destructive tests. was carried out to PN-EN an Nexus machine [47], the hardness test point distribution for the steel sheets' lap joint is shown below (Figure 5).

**Figure 5.** Hardness test point distributions in the lap joint.

The three-point test was performed according to the standards for all characteristic zones: base material (BM), heat-affected zone (HAZ) and fusion zone (FZ) in the upper and lower plates. **Figure 5.** Hardness point distributions the lap joint. The three-point according to the standards all zones: base material (BM), heat-affected zone (HAZ) and fusion zone (FZ) in the upper and lower plates. material (BM), heat-affected zone (HAZ) and fusion zone (FZ) in the upper and lower plates.

The material hardness resulting from the crystallographic structure of the welded material affects joint-strength characteristics. Moreover, the properties are related to the thermal cycles and chemical composition of the material. In order to investigate the joint-strength properties, the tensile-strength test was carried out, using an MTS-100 testing machine (MTS Systems Corporation, Eden Prairie, MN, USA) (Figure 6) [48]. The material hardness structure of the welded material affects joint-strength characteristics. Moreover, the properties are related to the thermal cycles and chemical composition of material. In to investigate the joint-strength properties, the tensile-strength test was carried out, using an MTS-100 testing machine (MTS Systems Corporation, MN, USA) [48]. **Figure 5.** Hardness test point distributions in the lap joint.The three-point test was performed according to the standards for all characteristic zones: base The material hardness resulting from the crystallographic structure of the welded material affects joint-strength characteristics. Moreover, the properties are related to the thermal cycles and chemical composition of the material. In order to investigate the joint-strength properties, the tensile-strength test was carried out, using an MTS-100 testing machine (MTS Systems Corporation, Eden Prairie, MN, USA) (Figure 6) [48].

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**Figure 6.** Tensile-strength test stand and specimen scheme. **Figure 6.** Tensile-strength test stand and specimen scheme.

The specimen was prepared by welding two upper plates to a lower plate, with the same process parameters as presented in the scheme (Figure 6). In this configuration, stretching, as well as shearing phenomena, will occur during the test. To confirm the obtained joint properties, an additional test of a specimen welded with the same parameters was performed. No-uniaxial complex-force distribution will certainly affect the test results. Nevertheless, the bonding force of welded sheets in the sealed lap joint will be related to the weld properties; therefore, metallographic The specimen was prepared by welding two upper plates to a lower plate, with the same process parameters as presented in the scheme (Figure 6). In this configuration, stretching, as well as shearing phenomena, will occur during the test. To confirm the obtained joint properties, an additional test of a specimen welded with the same parameters was performed. No-uniaxial complex-force distribution will certainly affect the test results. Nevertheless, the bonding force of welded sheets in the sealed lap joint will be related to the weld properties; therefore, metallographic analysis is required.

analysis is required. Metallographic tests were carried out according to PN-EN ISO 17639 [49]. A microscopic and macroscopic test, using a HiroxKH-8700 confocal digital microscope (Hirox Co Ltd., Tokyo, Japan), Metallographic tests were carried out according to PN-EN ISO 17639 [49]. A microscopic and macroscopic test, using a HiroxKH-8700 confocal digital microscope (Hirox Co Ltd., Tokyo, Japan), was performed, in order to investigate the crystallographic structure of the welded material.

was performed, in order to investigate the crystallographic structure of the welded material. The obtained welded lap joint was analyzed. The low-carbon S235JR steel is not typical hardening steel; nevertheless, phase transformation during laser welding affects the material, and the structure changes. A visual microscopic test was carried out to confirm the weld quality and to The obtained welded lap joint was analyzed. The low-carbon S235JR steel is not typical hardening steel; nevertheless, phase transformation during laser welding affects the material, and the structure changes. A visual microscopic test was carried out to confirm the weld quality and to detect any defects. The crystallographic structure in the upper and lower plate after welding was investigated [50,51].

detect any defects. The crystallographic structure in the upper and lower plate after welding was investigated [50,51]. Laser welding of overlap joints is complex. Thin interspace between welded sheets can affect porosity and oxides' formation. To confirm the uniform structure of the weld, the qualitative and Laser welding of overlap joints is complex. Thin interspace between welded sheets can affect porosity and oxides' formation. To confirm the uniform structure of the weld, the qualitative and quantitative analysis was carried out, using energy-dispersive X-ray spectroscopy with a scanning electron microscope JSM-7100F (JEOL Ltd., Tokyo, Japan).

#### quantitative analysis was carried out, using energy-dispersive X-ray spectroscopy with a scanning electron microscope JSM-7100F (JEOL Ltd., Tokyo, Japan). **3. Results**

#### **3. Results**  *3.1. Simulation Analysis Results*

*3.1. Simulation Analysis Results*  Laser-welding parameters were estimated by using numerical simulation analysis. Weldingsimulation parameters with a speed rate of 1m/min, output power 4 kW, heat source efficiency of 0.77 and the Gaussian parameter of conical and surface heat source equal to 2.8 were programmed (according to laser TEM01\* mod). According to those parameters, the assumed partial penetration in the joint was obtained. Results of the simulation showed that the output power equal to 4 kW provided the partial welding penetration (Figure 7a). Further analysis showed that, by increasing the output power by 0.5 kW, the complete penetration was obtained (Figure 8). For the assumed geometry of heat sources and programmed boundary conditions, partial penetration of the sealed lap joint was achieved and considered in further investigations. The thermo-mechanical simulation, which took into account phase transformation, gave realistic results of the welding process, with a Laser-welding parameters were estimated by using numerical simulation analysis. Weldingsimulation parameters with a speed rate of 1 m/min, output power 4 kW, heat source efficiency of 0.77 and the Gaussian parameter of conical and surface heat source equal to 2.8 were programmed (according to laser TEM01\* mod). According to those parameters, the assumed partial penetration in the joint was obtained. Results of the simulation showed that the output power equal to 4 kW provided the partial welding penetration (Figure 7a). Further analysis showed that, by increasing the output power by 0.5 kW, the complete penetration was obtained (Figure 8). For the assumed geometry of heat sources and programmed boundary conditions, partial penetration of the sealed lap joint was achieved and considered in further investigations. The thermo-mechanical simulation, which took into account phase transformation, gave realistic results of the welding process, with a convex face of the weld and material deformation obtained by a solver mechanism. The recalculation of the contact tolerance or remeshing of the distorted region was performed (Figures 7a and 8). Macroscopic examination of the

convex face of the weld and material deformation obtained by a solver mechanism. The recalculation of the contact tolerance or remeshing of the distorted region was performed (Figures

cross-section of the trial joint was performed by using a confocal digital microscope HiroxKH-8700 with a magnification of ×35 (Figure 7b). 7a and 8). Macroscopic examination of the cross-section of the trial joint was performed by using a confocal digital microscope HiroxKH-8700 with a magnification of x35 (Figure 7b). 7a and 8). Macroscopic examination of the cross-section of the trial joint was performed by using a confocal digital microscope HiroxKH-8700 with a magnification of x35 (Figure 7b).

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 **Figure 7.** Laser lap-joint welding results from (**a**) simulation, (**b**) experiment. **Figure 7.** Laser lap-joint welding results from (**a**) simulation, (**b**) experiment.

**Figure 8.** Laser lap-joint welding results for complete penetration. **Figure 8.** Laser lap-joint welding results for complete penetration.

**Figure 8.** Laser lap-joint welding results for complete penetration. Parameters estimated in the numerical simulation gave similar results: The face of the weld in the simulation was 3.22 mm in width, and in the experimental welding, it was 3.38 mm (for the complete penetration this value was equal to 4.35 mm). Moreover, the weld width in the overlap area for the simulation was equal to 1.99 mm, and it was 2.05 mm for the trial joint. The depth of the obtained welds was 4.33 mm for the trial joint and 4.38 for the simulation. Macroscopic analysis showed differences in heat expansion; the HAZ in the upper plate was wider. This effect is related to dumping and energy decrement during the penetration of the lower sheet. Although the welded surfaces adjoin each other, the spot size of the laser beam on the lower sheet during surface penetration was bigger, indicating lower power density. This phenomenon was also related to the heat-expansion direction. In the upper plate, heat expanded only in the XY direction, and in the lower sheet, it expanded in the XYZ direction. The macroscopic examination confirmed the accuracy of the simulation results, and it was possible to perform further numerical analyses. A thermo-mechanical simulation and a stress–strain analysis were carried out. The overall calculated displacement (Figure 9a) was 0.32 mm, with maximum principal stress (Figure 10a) of 1120 MPa. The changes in the total displacement (Figure 9b) and maximum principal stress (Figure 10b) were recorded against the defined measurement points. Higher displacement values occurred in the steel Parameters estimated in the numerical simulation gave similar results: The face of the weld in the simulation was 3.22 mm in width, and in the experimental welding, it was 3.38 mm (for the complete penetration this value was equal to 4.35 mm). Moreover, the weld width in the overlap area for the simulation was equal to 1.99 mm, and it was 2.05 mm for the trial joint. The depth of the obtained welds was 4.33 mm for the trial joint and 4.38 for the simulation. Macroscopic analysis showed differences in heat expansion; the HAZ in the upper plate was wider. This effect is related to dumping and energy decrement during the penetration of the lower sheet. Although the welded surfaces adjoin each other, the spot size of the laser beam on the lower sheet during surface penetration was bigger, indicating lower power density. This phenomenon was also related to the heat-expansion direction. In the upper plate, heat expanded only in the XY direction, and in the lower sheet, it expanded in the XYZ direction. The macroscopic examination confirmed the accuracy of the simulation results, and it was possible to perform further numerical analyses. A thermo-mechanical simulation and a stress–strain analysis were carried out. The overall calculated displacement (Figure 9a) was 0.32 mm, with maximum principal stress (Figure 10a) of 1120 MPa. The changes in the total displacement (Figure 9b) and maximum principal stress (Figure 10b) were recorded against the defined measurement points. Higher displacement values occurred in the steel sheet plate edge (at points 1 and 3). The higher maximum principal stress concentration was Parameters estimated in the numerical simulation gave similar results: The face of the weld in the simulation was 3.22 mm in width, and in the experimental welding, it was 3.38 mm (for the complete penetration this value was equal to 4.35 mm). Moreover, the weld width in the overlap area for the simulation was equal to 1.99 mm, and it was 2.05 mm for the trial joint. The depth of the obtained welds was 4.33 mm for the trial joint and 4.38 for the simulation. Macroscopic analysis showed differences in heat expansion; the HAZ in the upper plate was wider. This effect is related to dumping and energy decrement during the penetration of the lower sheet. Although the welded surfaces adjoin each other, the spot size of the laser beam on the lower sheet during surface penetration was bigger, indicating lower power density. This phenomenon was also related to the heat-expansion direction. In the upper plate, heat expanded only in the XY direction, and in the lower sheet, it expanded in the XYZ direction. The macroscopic examination confirmed the accuracy of the simulation results, and it was possible to perform further numerical analyses. A thermo-mechanical simulation and a stress–strain analysis were carried out. The overall calculated displacement (Figure 9a) was 0.32 mm, with maximum principal stress (Figure 10a) of 1120 MPa. The changes in the total displacement (Figure 9b) and maximum principal stress (Figure 10b) were recorded against the defined measurement points. Higher displacement values occurred in the steel sheet plate edge (at points 1 and 3). The higher maximum principal stress concentration was measured on the opposite side of the weld (at points 2 and 4).

sheet plate edge (at points 1 and 3). The higher maximum principal stress concentration was

measured on the opposite side of the weld (at points 2 and 4).

measured on the opposite side of the weld (at points 2 and 4).

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 **Figure 9.** Total displacement: (**a**) distribution map and (**b**) displacement chart according to **Figure 9.** Total displacement: (**a**) distribution map and (**b**) displacement chart according to measurement points. **Figure 9.** Total displacement: (**a**) distribution map and (**b**) displacement chart according to measurement points.

 **Figure 10.** Maximum principal stress: (**a**) distribution map and (**b**) stress chart according to **Figure 10.** Maximum principal stress: (**a**) distribution map and (**b**) stress chart according to measurement points. **Figure 10.** Maximum principal stress: (**a**) distribution map and (**b**) stress chart according to measurement points.

measurement points.

measurement points.

#### **Figure 10.** Maximum principal stress: (**a**) distribution map and (**b**) stress chart according to *3.2. Analysis of the Results for Properties 3.2. Analysis of the Results for Properties*

*3.2. Analysis of the Results for Properties*  Numerical simulations with phase transformation allowed for the calculation of material phase change and hardness distribution. As set forth in the standards, the three-point test was performed for all characteristic zones in the upper and down plates, in the cross-section, as defined in *3.2. Analysis of the Results for Properties*  Numerical simulations with phase transformation allowed for the calculation of material phase change and hardness distribution. As set forth in the standards, the three-point test was performed for all characteristic zones in the upper and down plates, in the cross-section, as defined in measurement point distribution (Figure 5). Results from the simulation are shown in Figure 11a, and the results obtained for the trial joint are shown in Figure 11b. Numerical simulations with phase transformation allowed for the calculation of material phase change and hardness distribution. As set forth in the standards, the three-point test was performed for all characteristic zones in the upper and down plates, in the cross-section, as defined in measurement point distribution (Figure 5). Results from the simulation are shown in Figure 11a, and the results obtained for the trial joint are shown in Figure 11b. Numerical simulations with phase transformation allowed for the calculation of material phase change and hardness distribution. As set forth in the standards, the three-point test was performed for all characteristic zones in the upper and down plates, in the cross-section, as defined in measurement point distribution (Figure 5). Results from the simulation are shown in Figure 11a, and the results obtained for the trial joint are shown in Figure 11b.

measurement point distribution (Figure 5). Results from the simulation are shown in Figure 11a,

**Figure 11.** Results of hardness distribution in cross-section from (**a**) simulation and(**b**) experimental **Figure 11.** Results of hardness distribution in cross-section from (**a**) simulation and(**b**) experimental welding. **Figure 11.** Results of hardness distribution in cross-section from (**a**) simulation and(**b**) experimental welding. **Figure 11.** Results of hardness distribution in cross-section from (**a**) simulation and (**b**) experimental welding.

welding.

*3.3. Metallographic Analysis* 

The hardness test results show strengthening in the weld and HAZ. The hardness distribution obtained from the simulation differs from the results measured on the trial joint. The calculated hardness values are greater than those of the welded materials. Hardness simulated for the weld zone does not exceed 240 HV (maximum value is equal to 237 HV). Discrepancies between the upper- and lower-plate values can be observed. In the HAZ for the upper plate, it takes the value from 233 to 249 HV, and for the lower plate, from 222 to 233 HV. The experimental hardness values (trial joint) are lower than the calculated ones. The highest measured value is 231 HV10 and occurs in the weld. In HAZ, the hardness value ranges from 200 to 218 HV10, and in the BM, it is from 160 to 200 HV10. Differences between measured and simulated values amount to 6 HV in the weld and 31 HV in HAZ. Despite the high accuracy of the obtained weld geometry, the results from the simulation and experiment vary. The discrepancies depend on phase-transformation phenomena (temperature gradient and chemical composition of welded material) and affect the calculated and measured hardness values [52,53]. According to PN-EN ISO 15614-11, the maximum allowable limit of Vickers hardness HV10 after welding is 350. Neither calculated nor measured hardness exceeded the allowed value. Therefore, no additional post-weld heat treatment was carried out in the simulation or on the trial joint. The hardness test results show strengthening in the weld and HAZ. The hardness distribution obtained from the simulation differs from the results measured on the trial joint. The calculated hardness values are greater than those of the welded materials. Hardness simulated for the weld zone does not exceed 240 HV (maximum value is equal to 237 HV). Discrepancies between the upper- and lower-plate values can be observed. In the HAZ for the upper plate, it takes the value from 233 to 249 HV, and for the lower plate, from 222 to 233 HV. The experimental hardness values (trial joint) are lower than the calculated ones. The highest measured value is 231 HV10 and occurs in the weld. In HAZ, the hardness value ranges from 200 to 218 HV10, and in the BM, it is from 160 to 200 HV10. Differences between measured and simulated values amount to 6 HV in the weld and 31 HV in HAZ. Despite the high accuracy of the obtained weld geometry, the results from the simulation and experiment vary. The discrepancies depend on phase-transformation phenomena (temperature gradient and chemical composition of welded material) and affect the calculated and measured hardness values [52,53]. According to PN-EN ISO 15614-11, the maximum allowable limit of Vickers hardness HV10 after welding is 350. Neither calculated nor measured hardness exceeded the allowed value. Therefore, no additional post-weld heat treatment was carried out in the simulation or on the trial joint.

*Materials* **2020**, *13*, x FOR PEER REVIEW 10 of 18

Material-strength characteristics change during the welding process, depending on the phase transformation phenomena, and are different for the fusion zone, heat-affected zone and base material. The hardness test showed differences in the trial joint properties relative to the simulation results. Therefore, in order to prove the high quality of the joint obtained by using the estimated parameters, a static tensile test was performed. The properties of the obtained joint were confirmed by performing an additional verifying test of joint strength. Manufactured specimens were stretched by increasing the loading force until failure at the tensile test rate equal to 2 mm/min. The results of the tensile test were compiled as a force vs. displacement graph (Figure 12). Material-strength characteristics change during the welding process, depending on the phase transformation phenomena, and are different for the fusion zone, heat-affected zone and base material. The hardness test showed differences in the trial joint properties relative to the simulation results. Therefore, in order to prove the high quality of the joint obtained by using the estimated parameters, a static tensile test was performed. The properties of the obtained joint were confirmed by performing an additional verifying test of joint strength. Manufactured specimens were stretched by increasing the loading force until failure at the tensile test rate equal to 2 mm/min. The results of the tensile test were compiled as a force vs. displacement graph (Figure 12).

**Figure 12.** Tensile strength test results. **Figure 12.** Tensile strength test results.

The static tensile test results show failure of the lap joint at the maximum force equal to 11.5 kN for the first specimen, and at 11.49 kN for the other specimen. The strength of the obtained joint was 110 and 108 MPa, respectively. The tensile strength of BM was 360 MPa. The failure of both samples occurred along the fusion-zone line. The joint configuration (Figure 6) affected the measurement results. Tension and shear occurred, and the results obtained were mostly dependent on the weld strength [54–57]. The static tensile test results show failure of the lap joint at the maximum force equal to 11.5 kN for the first specimen, and at 11.49 kN for the other specimen. The strength of the obtained joint was 110 and 108 MPa, respectively. The tensile strength of BM was 360 MPa. The failure of both samples occurred along the fusion-zone line. The joint configuration (Figure 6) affected the measurement results. Tension and shear occurred, and the results obtained were mostly dependent on the weld strength [54–57].

Optical and electron microscopes were used for crystallographic structure analysis. The structure of the base material (Figure 13) was examined by using a HiroxKH-8700 confocal digital microscope at a magnification of ×800. It showed a typical low-carbon structure. The microstructure
