*3.5. Calibration and Validation of the Model with a Modified Method of Heat Input in the High-Power Diode Laser Bead-On-Plate Welding Process*

To verify the proposed model, numerical analyses were performed using the model of assumptions proposed earlier, and a three-dimensional discrete model was created containing 38,320 3D elements and 41,148 nodes. The applied boundary conditions simulating sample clamping corresponded to its free placement on the laser table throughout the whole process of welding and then its cooling. The boundary condition regarding heat dissipation was met by convective dissipation to the environment at 20 ◦C and radiation defined for all external surfaces of the model. As a heat source model, a double-ellipsoid model was used which acted on selected elements of the model's mesh (Figure 23). In this case, the calculations using the defined material database containing the thermal, mechanical, and metallurgical material properties depended on temperature and metallurgical phase proportions.

**Figure 23.** View (**a**) of a three-dimensional model of the bead-on-plate laser welding process performed on 6.0-mm steel samples using a high-power diode laser together with a double-ellipsoid heat source model and the loaded area (red color), and (**b**) clamping conditions.

For the calibration of the proposed model, the results of the bead-on-plate high-power diode laser welding process on 10-mm X37CrMoV5-1 tool steel samples were used (Tables 6 and 7). Based on the results of metallographic tests, the calculation models were calibrated and the final results of numerical analyses were compared with the corresponding shapes of actual beads obtained in the real tests (Figure 24). On this basis, a comparison was also made of the measured and calculated basic geometric dimensions of the beads obtained (Table 7).


**Table 6.** Chemical composition of X37CrMoV5-1 steel according to ISO 4957:2018 standard [44].

**Table 7.** Process parameters and comparison of geometric dimensions of beads made on 10 -mm WCL (X37CrMoV5-1) steel samples using a ROFIN DL020 high-power diode laser with values obtained from numerical analyses (values in brackets) (Figure 24).


Argon flow rate via cylindrical nozzle: 15 L/min; laser beam spot dimensions: 1.8 mm × 6.8 mm at 82-mm focal length; location of the laser beam focus: on the upper surface of the samples.

To validate the model, similarly to the case of disk laser welding simulations the recorded thermal cycles were used. K-type thermocouples (Ni–NiCr wires with a diameter of 0.2 mm) were welded in the holes made at the bottom of the samples so that the measuring points were located at 0.5, 1.0, 2.0, and 3.0 mm from the welded sample surface (Figure 25). Thermocouples with accuracy ±0.0075 × t in a temperature range from −40 to +1200 ◦C (according to PN-EN 60584-2) were connected via compensation cables with Agilent 34970A recorder. After calibrating the calculation model (Figure 24), the registered and calculated thermal cycles in the points corresponding to the location of thermocouples were also compared (Figure 26).

**Figure 24.** Comparison of the bead shape on the cross-section of sample (**a**) HPDL\_R1 and (**b**) HPDL\_R2 with the results of numerical analyses.

**Figure 25.** Scheme of thermocouple placement on the cross-section of samples in the axis of welded beads.

**Figure 26.** Comparison of recorded and calculated thermal cycles on the bead-on-plate laser welding process performed on 10-mm AISI304 steel samples using the ROFIN DL020 high-power diode laser with (**a**) TC3 and (**b**) TC4 samples. TCx: thermal cycles recorded during the welding process; SIM\_TCx: thermal cycles obtained from numerical analyses.

#### **4. Conclusions**

A properly prepared and conducted numerical analysis consists of three important stages: precise preparation of the material base, calibration, and model validation. A properly developed material base, created based on tests on the behavior of the material under the influence of various temperatures and thermal cycles, allows for a faithful reproduction of the behavior of materials considering its thermometallurgical and mechanical nature. The stage of building and calibrating the model is important because the variety of methods used and the effects obtained as a result do not allow for the creation of one universal model. Each process must be treated individually by the user, considering the special features of the welding heat source used and the most accurate description of the conditions of the process. Model validation allows for obtaining an appropriate degree of model reliability in further applications.

The presented results of preliminary tests using a disk laser proved the need to supplement the portfolio of implemented models of heat sources with those allowing the correct geometry of the beads in laser welding to be obtained (Figures 6 and 7). Bearing in mind the mentioned desire for the greatest convenience and ease of use of models, it was proposed to extend the method of laser beam modeling or another method of welding with the "keyhole" technique (characterized by high power density). The combination of the already-present heat source model with the possibility of defining selected mesh elements which are affected by it allowed for easy and effective control of the shape of the fusion line of the obtained bead (Figures 9 and 12, Figures 13–15). On knowing the shape of the fusion line from real tests it was possible to calibrate the heat source model in such a way that the calculated shape of the molten pool corresponded to that from real tests. This was well-visible from the comparison of the bead cross-sections and calculated results. Interestingly, on the longitudinal cross-sections and in the corresponding results of numerical analyses, the temperature distributions corresponding to the molten pool showed considerable convergence with the obtained fusion shapes, especially when conducting the process using the "keyhole" technique. The liquid metal moved in a specific way in the gas channel formed by the beam, which was not considered in the numerical analyses based on the heat conduction equation.

The results of the validation seem to confirm that a properly calibrated model corresponds thermally to the situation recorded during actual welding tests (Figure 17). It should also be noted that in the case of thermocouple measurements, there may be disturbances in the registration of thermal cycles. In Figure 17b for the cycle recorded by TC3 it can be seen that, after recording the signal increase as a result of melting through the sample, the thermocouple located in the bead axis was damaged by liquid metal. For this reason, the corresponding course of the calculated thermal cycle was not provided. Incorrect registration of a thermal cycle with a thermocouple could also occur with incorrect positioning of the thermocouple, i.e., plane positioning or installation in drilled holes at the wrong depth, as with thermocouple TC3 in Figure 26b. These types of errors can lead to incorrect indications and in extreme situations it is impossible to register the correct thermal cycles. Therefore, in such cases it is also important that the validation is carried out based on more than one signal recorded in the actual process.

When comparing the recorded and calculated thermal cycles, there are sometimes also visible differences in the value of both the maximum value of the registered/calculated temperature as well as the course of the curves themselves (cooling speed). These differences may of course result from a simplified definition of heat exchange with the environment, convection, and emissivity coefficient values (even when they are dependent on temperature changes) [45]. This may also be due to the fact that the thermocouple tip has a certain diameter which is not taken into account when the thermal cycle is collected at a single mesh node. This is especially visible when fine mesh is used where the thermocouple tip can cover few nodes, and in case of laser welding the temperature gradients are much higher in comparison to arc welding and therefore this phenomenon is noticeable. In this situation, several nodes of the grid, differing in the maximum temperatures of the calculated thermal cycle, may be in the area covered by the thermocouple tip in the case of a real test. This should be kept in mind, especially in the case of process validation with numerical simulations, where the thermal cycles are very short and as already mentioned earlier, the temperature gradients are large so the values in the adjacent mesh nodes change very quickly.

Therefore, it is necessary to pay attention to the fact that the correct calibration of the heat source model, ensuring the convergence of the model with reality, is necessary because the heat distribution as well as the cooling speed in individual areas of the welded elements later affect metallurgical phases distribution, , grain size, and plastic deformation, and thus also stresses and strains distributions. This was confirmed by the calculated distribution of reduced stresses in the sample for the variant using the standard heat source model and the proposed extension. There are visible differences in the calculated maximum stress values as well as their distribution (Figure 18). The situation is similar in terms of cumulative plastic strain case distribution in both analyzed cases (Figure 19). It is particularly important that in the second case higher stress values were obtained, and thus a more rigorous assessment of the level of stresses and the possible danger associated with it was found.

The analyzed case of the high-power diode laser with a characteristic rectangular shape of the laser beam focus shows that more and more often the users of this type of program have to resort to the use of more complex calculation techniques to obtain correct results. The combination of knowledge on the construction of the device itself and actual welding tests carried out at the laser station allowed us to propose a simple and effective method for the simulation of an even distribution of laser radiation in this type of device (Figures 21 and 22). Similar values of geometric dimensions obtained for the tested variants of the model testify to the considerable flexibility of this method and thus also guarantee its considerable versatility, as confirmed in this case by tests and calculations carried out to validate the proposed model (Figures 24 and 26, Table 5). The aforementioned lower temperature recorded for TC3 in Figure 26b was caused by the incorrect position of the thermocouple in the measuring hole. As later tests showed, the thermoelement tip was welded on the wall of the hole and not on its bottom as assumed.

As a summary it should be stated, as the presented considerations have shown, that the implemented models of heat sources in commercially available programs for the numerical analyses of welding processes are not the only way to solve the analyzed problems. The possibility of introducing often simple changes or modifications to the built models allows them to be adapted in a much better way to the expected results. However, it is very important in this case that each of these modifications requires accurate calibration and validation of the proposed model based on the real experimental results. Otherwise, the results of numerical analyses may lead to erroneous conclusions.

**Funding:** This research was financed from the own resources of the Silesian University of Technology. **Conflicts of Interest:** The author declares no conflict of interest.

#### **References**


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