Thermo-Mechanical Industrial Processes: Modeling and Numerical Simulation

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It is a tool that allows determining the deformation of a complex structure caused by the welding process in a very short time, and very quickly and efficiently creating a welding plan, determining the method and sequence of fastening elements, and optimizing the welding sequence. The present problem of numerical welding simulations is that calculations of temperature fields, metallurgical phases, thermal cycles, as well as the the strains, stresses, and distortions connected with them, are strongly connected with many factors which describe the process and use a proper methodology.

Advantages of using new possibilities in simulation techniques are also strictly connected with the continuous development of new construction materials, which usually have significantly higher requirements also for the techniques of joining them. Moreover, it is not only directly about the quality of joints, but also the production capabilities, manufacturing costs, and the possibility of precise control of the technological process [ 6 , 11 , 12 , 13 ].

A very good example of this is the current use of very popular laser heat sources. Of course, they deliver many advantages such as a low heat effect, causing a narrow heat-affected zone HAZ and limited deformations connected with high process efficiency. However, it is also known that a very precise preparation is needed of the welded element edge, and, with an increase in the dimensions of welded elements, there are also problems with positioning [ 10 , 11 , 12 ].

Additionally, if we attach a very short thermal cycle to these problems, then, in many modern steels, this may be related to the existence of zones in which the structures obtained as a result of welding will be fragile and will not provide adequate plasticity of joints. Another disadvantage of these modern heat sources is a relatively small efficiency.

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It is especially important if we also take into account the current energy problems of the world in which we live, as well as striving to reduce costs at every stage of the production process, wherever possible [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ]. The comparison of the mentioned advantages and disadvantages of the classical arc methods of welding forces us to look for new solutions that combine the advantages of using high-density heat sources with methods that allow maintaining high strength and operational properties of modern and, therefore, more expensive construction materials.

A certain solution to this problem, combining the advantages of laser welding while increasing the efficiency of the process is called hybrid welding HLAW—hybrid laser arc welding [ 24 , 25 , 26 , 27 , 28 ].

The addition of the arc welding process ensures the correct filling of the groove, decreasing the requirements for precise preparation of the edges of welded elements. It can be said that this method combines the laser welding speed with the advantages of arc welding, allowing a reduction in the number of beads compared to traditional methods [ 28 , 29 , 30 , 31 , 32 ]. However, the use of two significantly different heat sources brings with it the need to control a much larger number of parameters at the same time.

The use of numerical techniques at the design and preparation stage of welding technology is particularly recommended in this case. This way of thinking by a modern engineer leads to a significant increase in the quality of manufactured products [ 33 , 34 ].

This study aimed to determine the influence of the thermal cycle of the laser and hybrid welding process on the structure and stress distribution in T-joint welds of SMC steel plates with a thickness of 10 mm. The article presents selected results of numerical analyses of the laser and hybrid welding process of the same type of joint. As a result, it was possible to show differences in the metallurgical phases, hardness, and stress distributions in both cases. SMC, used as a base material, is a hot-rolled, high-strength, low-alloy steel and combines high strength with outstanding formability and consistent quality Table 1.

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As provided by the producers and supplier, it also delivers exceptional weldability for fast and efficient processing. However, along with the change in the thickness of the welded elements, as well as the use of welding methods with a very sharp thermal cycle, unexpected problems are associated with the weldability of components made of this type of steel, as well as with the expected functional properties of the welded joints [ 21 , 24 , 29 , 30 , 35 ]. Welding parameters determined on the basis of tests are shown in Table 2 and Table 3. Laser T-joint welding parameters of SMC steel plates with a thickness of 10 mm.

The chemical composition and the properties of the weld deposit are presented in Table 4. It is a modern, widely used commercial simulation software for welding and heat treatment processes. For calculations, it was, therefore, necessary to acquire the temperature dependence of the heat conductivity coefficient, specific heat, and density [ 6 , 11 , 12 , 36 ]. A correctly performed numerical analysis of the welding process involves the appropriate definition of the method of introducing heat to the material.

The available literature describes many possible mathematical descriptions of this issue. It lists, among others, the two-dimensional 2D Gaussian surface heat source model, the Goldak double-ellipsoidal heat source model, and the three-dimensional 3D Gaussian conical heat source model.

Each of the mentioned models of heat source finds its application in the modeling of selected welding processes. The 3D-Gaussian conical model reflects very well the conditions in which heat sources with high power density laser or electron beam are used [ 6 , 7 , 8 , 36 , 37 ]. The prepared calculation 3D model consisted of 45, 3D solid elements with 48, nodes in the case of the laser welding model, and 47, 3D solid elements with 50, nodes in the case of hybrid welding.

The mesh was concentrated in the weld area to increase calculation accuracy Figure 2.

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Boundary conditions related to clamping conditions during welding were set to simulate welding without any additional clamps. This means that analyses were continuous with time steps defined automatically by the solver, based on mesh dimensions and the size of heat source models. In the case of hybrid welding, the arc heat source was placed 4 mm behind the laser beam. View of calculation three-dimensional 3D solid models for laser and hybrid welding simulations: a laser and b hybrid.

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Additionally, this heat source model moves along the welding trajectory. All heat source parameters i. The volumetric density of energy defined by this Fortran function on the current point depends on the distribution of density around the center of the source and trajectory. The 3D conical model is a type of source which is used for the correct design of a welding simulation using a laser or electron beam characterized by high power density.

From a parametric point of view, the model is determined by the power of the heat source, its radius, and the depth of penetration [ 6 ]. Mathematically, it can describe the conical model with Equations 3 and 4 Figure 3. Firstly, Equation 3 describes the heat transfer to the material depending on the coordinate data.

It is supplemented by Equation 4 , defining the change in radius along the depth.

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The conical model is mainly used to simulate laser welding and electron beams, but it can also be used for other heat sources, such as plasma arc during keyhole technique welding. The efficiency of the heat transfer into the parent material is given by the applied welding method. The geometry of the double-ellipsoidal model can be modified by changing coefficients a, b, and c contained in the equations. By changing these parameters, we have the advantage of greater flexibility in the modeling of a heat source shape.

Because of it, the energy is divided into O f and Q r values. The first value is the heat energy density in the front half of the ellipsoid maximum source frontal intensity , and the second is that in the rear part maximum source rear intensity Figure 3. Transferred heat is described by the equations below [ 6 ]. Another advantage of the VisualWeld SYSWELD package is the possibility of changing the thermal load area shape and achieving the possibility of the very precise modeling of fusion line geometry.

Numerical Simulations of Laser and Hybrid S700MC T-Joint Welding

After model preparations, the calibration of the described heat source models was done. To achieve the best correlation with real welding tests comparison of molten areas on macro views and registered thermal cycles , 3D numerical models were calibrated using the heat input fitting module to optimize the virtual molten metal pool shape. Final values of parameters used in the finite element modeling FEM analyses are presented in Table 5. Due to THE large number of results, one of the analyses for the laser and hybrid welding process was selected for comparison. Used parameters for the laser welding analysis correspond with the parameters used for joint LAS7 Table 2.

In the case of hybrid welding, parameters used in numerical simulations were set as for the HYB1 joint Table 3. Welding parameters used in welding simulations. The above parameters were used in the main simulations. The thermo-metallurgical analysis allows not only determining values and temperature distribution, but also determining each metallurgical phase in calculated joints after welding and cooling to the ambient temperature Figure 4 , Figure 5 , Figure 6 and Figure 7.

Martensitic transformation was calculated based on the Koinstinen—Marburger formula. There was a visible difference between both laser and hybrid distributions of the temperature fields. Heat range understood as the area of heat influence in the hybrid method was bigger than that using the laser.


The distribution of the initial phase, which is possible to calculate, gives the information about the material that undergoes metallurgical changes as a result of the interaction of the welding thermal cycle. Of course, it is clear that the transformed part of these figures is bigger than the real melted area, and also includes the heat-affected zone HAZ. However, the shape of this distribution gives the main information about the weld geometry Figure 4 and Figure 5.

Distribution of a , c martensite and b , d bainite phases after laser welding of SMC steel T-joints with a thickness of 10 mm cross-sections were made in the half-length of the joint. Distribution of martensite a , c and bainite b , d phases after hybrid welding of SMC steel T-joints with a thickness of 10 mm cross-sections were made in the half-length of the joint. The connection of a very short laser thermal cycle and the thickness of the welded elements resulted in a high cooling speed in the area of the weld and the HAZ. In the case of hybrid welding, the cooling rates were lower due to the presence of additional heat from the MAG heat source.

This additional portion of heat coming from the MAG electric arc resulted in a significant decrease in cooling speed, and it is clearly visible in the thermal cycle graph, in addition to the distribution of bainite and martensite at the distribution of metallurgical phases. The distribution of bainite also corresponded to the decrease in cooling rates mentioned above. Using a coupled thermo-metallurgical analysis gave us the possibility of hardness distribution calculations.

They were calculated based on the metallurgical phases, the chemical composition, and the cooling speed rates. It is visible that the hardness values confirmed the martensite and bainite distribution presented above Figure 8. Calculated results were also compared with the real hardness measurements, as shown in Table 6. Distribution of calculated Vickers hardness after laser and hybrid welding of SMC steel T-joints with a thickness of 10 mm cross-sections were made in the half-length of the joint.

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Comparison of measured and calculated hardness values in laser and hybrid welding of SMC steel T-joints with a thickness of 10 mm. For comparison, the same time for hybrid welding was about 1. Calculated thermal cycles for laser and hybrid welded SMC steel T-joints with a thickness of 10 mm.