Research on Heat Source Model and Weld Profile for Fiber Laser Welding of A304 Stainless Steel Thin Sheet

A heat source model is the key issue for laser welding simulation. ,e Gaussian heat source model is not suitable to match the actual laser weld profile accurately. Furthermore, fiber lasers are widely recognized to result in good-quality laser beam output, a narrower weld zone, less distortion, and high process efficiency, compared with other types of lasers (such as CO2, Nd : YAG, and diode lasers). At present, there are few heat source models for fiber laser welding. Most of researchers evaluate the weld profile only by the bead width and depth of penetration, which is not suitable for the laser keyhole welding nail-like profile. ,is paper reports an experimental study and FEA simulation of fiber laser butt welding on 1mm thick A304 stainless steel. A new heat source model (cylindrical and cylindrical) is established to match the actual weld profile using Marc and Fortran software. Four bead geometry parameters (penetration depth, bead width, waist width, and depth of the waist) are used to compare between the experimental and simulation results. ,e results show that the heat source model of cylindrical and cylindrical can match the actual shape of the fiber laser welding feasibly. ,e error range of the penetration depth, bead width, waist width, and depth of the waist between experimental and simulation results is about 4.1± 1.6%, 2.9± 2.0%, 13.6± 7.4/%, and 18.3± 8.0%, respectively. In addition, it is found that the depth of penetration is more sensitive to laser power rather than bead width, waist width, and depth of the waist. Welding speed has a similar influence on the depth of penetration, weld width, waist width, and depth of the waist.


Introduction
Stainless steel sheet is widely used in the welded structure of biopharmaceutical, medical device, aerospace, and precision instrument manufacturing industry because of its characteristic of smooth surface, nonmagnetic performance, and corrosion resistance [1]. Currently, the common welding methods are MIG-MAG, TIG, and laser welding [2][3][4]. Compared to the methods of MIG-MAG and TIG, laser welding offers a number of attractive features such as high power density, high speed, narrow weld, and small deformation.
Since the weld profile (depth of penetration, weld width, etc.) is an important criterion to evaluate the quality of laser welding and the results of numerical simulation, the weld profile of laser welding is studied by many scholars [5][6][7][8]. Tadamalle et al. [9] investigate the influence of pulsed Nd : YAG laser welding process parameters on weld pool geometry. e results show that the bead width and depth of penetration decrease as the welding speed increases. Liao and Yu [10] investigate that effect of the pulsed Nd : YAG laser welding incident angle on the depth of penetration, bead width, and bead length, and the results show that the bead width and depth of penetration decrease with the increase in incident angle. Balasubramanian et al. [11] conduct experiments using a three-dimensional conical Gaussian heat source and the temperature-dependent thermophysical properties of the A304 stainless steel sheet to be employed for performing a nonlinear transient thermal analysis. e results of numerical simulation match the actual shape of the weld well, and the depth of penetration and bead width increase as the welding power increases, while the depth of penetration and bead width decrease as the welding speed increases. Shanmugam et al. [12] used a three-dimensional conical Gaussian heat source as a heat source model for studying temperature profiles in the A304 stainless steel sheet. e results of numerical simulation match the actual shape of the weld well, and the calculated weld pool shapes resemble the experimentally measured weld pool shapes. e error percentage of the bead width and depth of penetration is about 7-8%.
Laser welding is a complex physical and chemical process, and many researchers have done a lot of research on this process [9][10][11][12][13]. However, the study of the welding temperature field is a prerequisite for the analysis of welding stress and deformation [1]. It is very important to measure accurately the welding temperature field. Fortunately, with the computer simulation technique used in welding disciplines, the computer simulation technique provides a fast and effective method for measurement of the temperature field. At present, many researchers sum up many combination heat source models for numerical simulation of the temperature field of laser welding of stainless steel. Kim et al. [14] design the combination heat source model of conical and inverted conical to simulate the temperature field of pulsed Nd : YAG laser welding of A304 stainless steel in different conditions. e maximum error of the bead width and depth of penetration is about 0.132 mm (13%). Chukkan et al. [15] simulate the pulsed Nd : YAG laser beam welding profile, temperature field, and welding stress using three combination heat source models (conical, double ellipsoid, and conical, conical, and cylindrical). e calculated weld pool shapes of three combination heat source models resemble the experimentally measured weld pool shapes with a maximum error about 0.082 mm (5.5%), 0.13 mm (8.7%), and 0.02 mm (1.3%), respectively. e results of numerical simulation using conical and cylinder are more accurate than others. Shi et al. [16] establish the combination heat source model of conical, inverted conical, and ellipsoid to simulate the heat source of laser lap welding of stainless steel car body. e error of the bead width and depth of penetration is less than 0.092 mm (8.0%).
Many researchers sum up some combination heat source models for pulsed Nd : YAG laser welding or CO 2 laser welding. However, there are no well heat source models for fiber laser welding of the A304 stainless steel sheet. ere are a wide variety of laser types available for welding, each of which has its own specific characteristics [17]. Unlike most other types of lasers, the wavelength of the fiber laser is about 1.06 μm and the attenuation of the fiber laser is about 10 dB/km. Fiber lasers offer a compact, electrically efficient alternative to Nd : YAG technology. Furthermore, other researchers evaluated the weld profile only by the bead width and depth of penetration. So, in this paper, fiber laser butt welding of A304 stainless steel of thickness 1 mm is carried out to study the change of weld profile in different conditions, and a new heat source model is established to match the actual weld profile using Marc and Fortran software. e combination heat source mode of cylindrical and cylindrical is employed for performing a nonlinear transient thermal analysis. e weld pool shapes are evaluated by the weld width, depth of penetration, waist width, and depth of the waist. e correct heat source model is a solid foundation to analyze temperature field, welding stress, and deformation.

Experimental Materials and Procedure
In this experimental work, an A304 stainless steel workpiece of 100 × 100 × 1 mm thick sheet is chosen. e chemical compositions of the materials are shown in Table 1.
A MFSC-500W fiber laser welding machine (Maxphotonics, Shenzhen, China) is used for all experiments. e materials are completely cleaned prior to welding. e laser wavelength is 1.06 μm, and the maximum output power is 500 W. During the welding process, the plates are fixed by a fixture to prevent deformation. An argon volume fraction of 99.999% is used as shielding gas to avoid atmospheric contamination. In the same conditions, the first set of the experiment is conducted by varying the laser power from 200 W to 400 W and the second set of the experiment is conducted by varying the welding speed from 0.4 m/min to 2 m/min. e process parameters in different conditions are given in Table 2. e way of fixing the plates is shown in Figure 1.
A304 stainless steel plates are butt welded according to the welding parameters in Table 2, and the size of samples which are cut in the welded joints is 10 × 10 × 1 mm. e samples are grounded with 240-, 400-, 800-, and 1200-mesh silicon carbide papers and polished to a mirror finish. en, the weld profile in different welding parameters is observed using a metalloscope in 100x. Before the simulation, a 2 mm thick A304 stainless steel thin sheet was used for trial welding. e actual welding situation is simulated using Marc and Fortran software by mesh generation, with material properties, boundary conditions, heat source model, and so on. e results of simulation are compared with the actual result to verify the correctness of the model. Figure 2(a) shows the analysis model. Due to the structural characteristics of A304 stainless steel sheet butt welding and geometric symmetry, only one plate is used to reduce the simulation computation time. A fine mesh is used for areas in contact with the laser beam since they experienced a complicated thermal sequence of momentary heating and cooling. e size of elements becomes larger from the center of the weld to reduce the calculating time.

Model and Mesh Generation.
e size of elements is 0.2 × 0.2 × 0.25 mm in the weld; while far away from the weld, the size of elements is 0.2 × 0.2 × 0.25 mm; after the

Material Properties and Boundary Conditions.
e physical properties of A304 stainless steel are quoted directly from Marc. ermal-physical properties of A304 stainless steel are shown in Table 3. e initial temperature of the environment is 20°C. When de ning boundary conditions, three directions (X, Y, Z) of the specimen are designed according to the actual situation to ensure zero displacement. e heat exchange between the base metal and the   Advances in Materials Science and Engineering environment is going in the welding process and is ignored between the base metal and the xture. e heat exchange is designed as surface heat transfer, the temperature of the environment is 20°C, and the heat transfer coe cient is 0.04. en, the boundary condition of heat input needs to be de ned. ere is no heat a ected zone in the laser welding A304 stainless steel welded joint. A new subroutine is created about the heat source model by Fortran and applied to the weld. Figure 2(b) shows the boundary conditions.

Heat Source Model.
It has a great relationship between the selection of the heat source model and the weld pro le [18]. e weld pro le is nail shaped, as shown in Figure 6. According to the weld pro le, the combination heat source mode of cylindrical and cylindrical is designed for numerical simulation. Figure 3(a) shows the Gaussian cylindrical heat source model. In Figure 4, Q 0 is the maximum intensity, r 0 is the radius of the cylindrical shell, and Z e and Z i are the locations of the upper and lower surface. e heat input of this source can be expressed as follows: where Q r is the heat source intensity in r, Q 0 is the maximum intensity, and r 0 is the radius of the cylindrical shell. Figure 3(b) shows the combination heat source mode of cylindrical and cylindrical. In Figure 5, Z e , Z m , and Z i are the locations of the upper, middle, and lower surface; r 1 is the radius of the upper cylindrical; and r 2 is the radius of the lower cylindrical. e essence of the three-dimensional cylindrical heat source is superposition of a series of Gaussian planes along the thickness direction. e power distribution ratio between upper cylindrical and lower cylindrical is 0.54 : 0.46. e parameters of the combination heat source mode of cylindrical and cylindrical are shown in Table 4.

Experimental Results.
e microstructure of the trial welding sample is shown in Figure 4. e weld pool shapes of ber laser welding A304 stainless steel are like nail which is z y  typically the shape of laser keyhole welding. Laser power brings A304 stainless steel to vaporization, after few milliseconds of irradiation, and it is termed as keyhole welding. e pressure created by the intense vaporization tends to dig the molten metal zone, which allows the laser beam to penetrate deeper, and it makes the irradiated zone a thin hole, known as keyhole [19]. Laser power makes a waist by thermodynamic cycles, fluid flows, and heat transfer phenomena in the upper part of the fusion zone. e parent material and fusion zone could be discriminated easily. e microstructure of the parent material is composed of coarse equiaxed grains (around 20 μm). e grain near the base parent metal did not grow up obviously, so there are no apparent transition zone and heat affected zone in the welded joint. e columnar dendrite, whose orientation is perpendicular to the fusion line, exists in a welding seam. e dendrite arm spacing of the δ-Fe in the fusion zone is about 3.5 μm. For the reason of high thermal conductivity, large temperature gradient, and slow crystallization rate, the undercooling zone at the edge of the weld is small, which is beneficial for the formation of columnar crystals [20]. e weld profile is shown in Figures 5 and 6. e change of depth of penetration, weld width, waist width, and depth of the waist in different conditions is analyzed by Figures 5  and 6. e effect of laser power on the depth of penetration, bead width, waist width, and depth of the waist for butt joint welds at a constant weld speed of 2 m/min and focus position of 0 mm is shown in Figure 7. With the increase of laser power, the depth of penetration increases, but the increase of weld width, waist width, and depth of the waist is not obvious. e increase of weld width, waist width, and depth of the waist is 0.322-0.415 mm, 0.145-0.175 mm, and 0.190-0.320 mm, respectively. So, the depth of penetration is more sensitive to the welding power than bead width, waist width, and depth of the waist. is is due to the increase of laser energy density with the increase of laser power. e area of keyhole increases and the keyhole deepens into the interior of the sheet, which result in the increase of energy absorption and energy concentration in the lower part of the pool. e laser power covers a wide area on the top surface of the sheet. erefore, there is a slight increase in the bead width of the laser weld [21]. e effect of welding speed on the depth of penetration, bead width, waist width, and depth of the waist for butt joint welds at a constant laser power of 250 W and focus position of 0 mm is shown in Figure 8. e depth of penetration, bead width, waist width, and depth of the waist decrease with the increase of welding speed, which is due to the decrease in the amount of heat input and less interaction time period between the laser beam source and the weld material [6]. e decrease range of the depth of penetration,  Comparing Figure 7 with Figure 8, the change of bead width, waist width, and depth of the waist is more sensitive for welding speed than for laser power. Welding speed has      Advances in Materials Science and Engineering a similar in uence on the depth of penetration, weld width, waist width, and depth of the waist. is is because the welding speed determines residence time somewhere, when welding the material. e residence time is longer, and the bead width, waist width, and depth of the waist are larger. However, when the power increases, the area of keyhole increases and the keyhole deepens into the interior of the workpiece, which result in the increase of energy absorption and energy concentration in the lower part of the pool. e increase of laser power has no obvious e ect on the shape of the upper part of the weld pro le. So, the change of weld width, waist width, and depth of the waist is not obvious.

Simulation
Results. Generally, A304 stainless steel melts at about 1400-1455°C [16]. In this paper, the choice of the melt point is 1450°C [9]. For comparing the pool shape, the isotherm of the melting point is regarded as the fusion interface. Figure 9 shows the numerical simulation results of temperature distribution and weld pro le at a point 42 mm along the welding direction using the combination heat source mode of cylindrical and cylindrical for two of the laser conditions: 250 W, 2 m/min, 0 mm and 250 W, 1.2 m/min, 0 mm. e depth of penetration of the weld is large, and the weld pro le is nail shaped. e numerical simulation results of the depth of penetration, bead width, waist width, and depth of the waist are 0.770 mm, 0.370 mm, 0.190 mm, and 0.250 mm, respectively, when the welding parameters are 250 W, 2 m/min, and 0 mm. e numerical simulation results of the depth of penetration, bead width, waist width, and depth of the waist are 0.795 mm, 0.425 mm, 0.246 mm, and 0.250 mm, respectively, when the welding parameters are 250 W, 1.2 m/min, and 0 mm. Figure 10 shows the comparison of experimental and simulation results for the depth of penetration, bead width, waist width, and depth of the waist for di erent powers. e error range of the depth of penetration, bead width, waist width, and depth of the waist between experimental and simulation results is about 4.8%, 3.6%, 15.6%, and 18.9%, respectively. Figure 11 shows the comparison of experimental and simulation results for the depth of penetration, bead width, waist width, and depth of the waist for di erent welding speeds. e error range of the depth of penetration, bead width, waist width, and depth of the waist between experimental and simulation results is about 3.6%, 2.0%, 11.9%, and 17.7%, respectively. e error range of the depth of penetration and bead width is better than the error range of the waist width and depth of the waist. e possible reason may be that the ow of the fusion zone is not considered in simulation. e larger the fusion zone area of laser keyhole welding is, the higher the ow of the fusion zone is. e ow in the top of the fusion zone has obvious e ect on the shape of the waist, while ow has no obvious in uence on the heat transfer in the depth direction. is means that the ow of the weld pool is directional, and the material is isotropic in simulation. Combining with the literature [10][11][12], Table 5 shows the simulation error of six heat source modes about laser welding of the stainless steel Advances in Materials Science and Engineering 7

Comparison of Experimental and Simulation Results.
sheet. By comparing the simulation error of the combination heat source mode of cylindrical and cylindrical with the simulation error of other ve heat source modes in Table 5, the results show that the simulation error of the heat source model of cylindrical and cylindrical is in the acceptable range. Figures 12 and 13 show the comparison of experimental and simulation results for the weld pro le at a point 42 mm along the welding direction. e simulation results of the heat source model of cylindrical and cylindrical can match the actual shape of the weld well. So, it can be proved that a new combination heat source mode of cylindrical and cylindrical is established according to the results of error analysis and shape matching. respectively. e gures clearly show the large temperature gradients at the area close to the laser source and the cooling of the workpiece away from the heat source. e total duration of the welding process is 4.29 s. It is noted that there is a small preheated zone in front of the laser source. e maximum temperature of the melt pool is 2164°C, which is far higher than the melting point of A304 stainless steel. In the middle of the workpiece, the heat source is in the form of ellipse on the surface of the workpiece. is elliptical shape of the molten pool varies depending on welding speed and beam power. In front of the melt pool, the isotherm is intensive and the temperature gradient is large. e isotherm behind the melt pool is more extensive. It seems from Figure  14(d) that the maximal temperature of the melt pool is 164°C   Figure 15. When the heat source reaches the position of the point in the center line, the temperature reaches the maximum, and the heating rate is very high about 1.0 × 104°C/s. After that, the heat source is far away, the temperature drops rapidly, and the cooling rate can be 1.4 × 104°C/s. e tendency of the thermal cycling curve of each point is similar, which shows that the weld pool remains quasi-steady in the welding process, and the maximum temperature at each point is kept at about 2160°C. e maximum temperature of each point vertical to the center line is different. Point A is in the center of the weld joint, so its maximum temperature is the highest. Points B, C, and D are in turn away from the center of the weld joint, and the maximum temperature is decreased. e closer to the center of the weld joint, the higher the rate of temperature increase and the cooling velocity. e maximum temperature of each point in direction of thickness varies little because the A304 stainless steel sheet is very thin.

Conclusion
is paper analyzes the change of the weld profile for laser butt welding of A304 stainless steel in different conditions. By a new heat source model and numerical simulation technology, the following conclusions are obtained: (1) With the increase of laser power, the depth of penetration increases from 0.54 (at 200 W) to 1.00 mm (at 400 W), but the increase of weld width, waist width, and depth of the waist is not obvious. e increase of weld width, waist width, and depth of the waist is 0.322-0.415 mm, 0.145-0.175 mm, and 0.190-0.320 mm, respectively. e depth of keyhole increases as the laser power increases, so the depth of penetration is more sensitive to the welding power than bead width, waist width, and depth of the waist. e depth of penetration, bead width, waist width, and depth of the waist decrease with the increase of welding speed. e decrease of the depth of penetration, weld width, waist width, and depth of the waist is 1.00-0.715 mm, 0.765-0.355 mm, 0.485-0.145 mm, and 0.820-0.231 mm, respectively. Welding speed has a similar influence on the depth of penetration, weld width, waist width, and depth of the waist.
(2) e simulation results of the heat source model of cylindrical and cylindrical can match the actual shape of the fiber laser welding feasibly. e error range of the depth of penetration, bead width, waist width, and depth of the waist between experimental and simulation results is about 4.1 ± 1.6%, 2.9 ± 2.0%, 13.6 ± 7.4/%,  18.3 ± 8.0%, respectively. e error range of the depth of penetration and bead width is better than the error range of the waist width and depth of the waist. e possible reason may be that the flow of the fusion zone is not considered in simulation.
(3) e heat source is in the form of ellipse on the surface of the workpiece. e maximum temperature of the melt pool is 2164°C. e heating rate is about 1.0 × 104°C/s, and the cooling rate can be 1.4 × 104°C/s.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.