This paper presents an experimentally validated weld joint shape and dimensions predictive 3D modeling for low carbon galvanized steel in butt-joint configurations. The proposed modelling approach is based on metallurgical transformations using temperature dependent material properties and the enthalpy method. Conduction and keyhole modes welding are investigated using surface and volumetric heat sources, respectively. Transition between the heat sources is carried out according to the power density and interaction time. Simulations are carried out using 3D finite element model on commercial software. The simulation results of the weld shape and dimensions are validated using a structured experimental investigation based on Taguchi method. Experimental validation conducted on a 3 kW Nd: YAG laser source reveals that the modelling approach can provide not only a consistent and accurate prediction of the weld characteristics under variable welding parameters and conditions but also a comprehensive and quantitative analysis of process parameters effects. The results show great concordance between predicted and measured values for the weld joint shape and dimensions.
The laser welding process has gained importance in fabrication industries due to its ability to produce precise welds with small heat affected zones [
Conduction mode and keyhole mode are the two basic modes for laser welding. Conduction mode is defined by low energy concentration and shallow penetration. Keyhole mode is defined by high energy concentration and deep penetration achieved when the metal vaporizes and forms a deep and narrow vapour cavity. However, there is no sharp transition between the two modes; a transition zone exists and can be defined by a constant aspect ratio. It has been found that the value of the transition zone ratio varies with laser beam diameter and speed [
The multi-physical aspect of the laser process is the main difficulty in their modelling, as phenomena are coupled and different scales of physics interact [
In butt joint laser welding, the presence of a gap between sheets has an impact on the weld pool. However, gap is hard to add to a simulation without making it very complex. A study has been conducted on the deformation caused by thermally induced stresses that can result in a change of the gap width between the welded parts [
This paper presents a simple heat transfer model based on a moving heat source on a finite medium. The weld pool shape and dimensions are studied in continuous wave butt joint laser welding. The particularity of this simulation is the addition of the gap as a parameter of the simulation, and the prediction of the underfill for a full penetration weld. Conduction mode and keyhole mode are also covered in this model, using different heat sources according to the power density and interaction time. A 3 kW Nd: YAG laser for welding low carbon galvanized steel is used for the experimental investigation.
Heat transfer is the main phenomenon explaining the thermal field in laser welding. The fundamental modes of heat transfer are conduction, convection and radiation. Conduction occurs inside the parts. Convection and radiation occur between the parts and its environment.
The law of heat conduction states that the time rate of heat transfer through a material is proportional to the negative gradient in temperature and to the area. As an equation, it can be written as:
φ = − k ∇ T (1)
where k is the thermal conductivity, ∇ T the temperature gradient and φ the heat flux.
According to the law of conservation of energy, the internal heat transfer equation is:
ρ C p T ˙ − ∇ ( k ∇ T ) = Q ( x , y , z ) (2)
where ρ is the mass density, Cp the specific heat and Q ( x , y , z ) a distributed volume heat source.
In order to solve the differential equations, initial conditions and boundary conditions must be specified. Initial conditions are the ambient temperature and parts temperature. Both are fixed at a temperature T0 equal to 20˚C. Boundary conditions are prescribed, thermal flux coming from radiation and convection. Convection is the thermal exchange resulting from the temperature difference between a body and its environment. The convective heat transfer can be defined by:
Q c o n v = h ( T − T 0 ) (3)
where h defined asthe convective heat transfer coefficient and T0 the room temperature.
The convective heat transfer coefficient highly depends on the fluid flow around the parts. Since ventilation is used during welding, a forced convection coefficient is used. Radiation occurs in the form of electromagnetic waves. According to the Stefan-Boltzmann law, when a hot object is radiating energy to its cooler surroundings, the radiation heat loss can be expressed as:
Q r a y = σ ε ( T 4 − T 0 4 ) (4)
where σ is the Stefan-Boltzmann constant and ε the emissivity. These boundary conditions are applied to the model by specifying the value of the heat flux at the outward boundary of the model. The heat transfer modes through the parts are represented in
The heat source distribution is an influential parameter in laser welding models. Two kinds of heat source models exist for simulating laser welding: surface heat source and volumetric heat source. The surface heat source model is more accurate for conduction welding since in this mode the energy is applied to the component surface, while the volumetric heat source is more adapted for keyhole welding, with the energy being directed inside the medium through the keyhole [
the simulation of laser welding, and many different kinds have been developed over the years [
Q ( x , y , z ) = Q 0 ( 1 − R c ) A c 2 π σ x σ y exp ( − ( ( x − x 0 ) 2 2 σ x 2 + ( y − y 0 ) 2 2 σ y 2 − A c | z | ) ) (5)
where Q0 is the power, Rc the reflection coefficient, Ac the absorption coefficient, σx and σy the radius of the heat source along x and y.
Complex models exist for the conduction mode, such as an adaptive volumetric heat source [
Q ( x , y , z ) = Q 0 ( 1 − R C ) 2 π σ x σ y exp ( − ( ( x − x 0 ) 2 2 σ x 2 + ( y − y 0 ) 2 2 σ y 2 ) ) (6)
The model is based on a moving heat source over a steel plate. The heat transfer equations are used to determine the thermal field using the finite element method. In building the model, the following assumptions were considered: 1) The surfaces of the parts are assumed to be flat permitting perfect contacts; 2) the areas with temperatures higher than liquidus are considered molten; 3) the
vaporisation of elements is not simulated and laser interaction with vapour plumes is not studied; 4) the fluid dynamics are not considered; and 5) The temperature field is supposed to be symmetrical in the welding line.
Since there is geometrical symmetry along the weld line, only one sheet can be modelled using a symmetry boundary condition if the thermal field is also symmetrical. Three stages are present during the laser heating process: a starting stage at which the initiation of the weld begins with the heat source reaching the parts; a quasi-stationary stage at which the heat source is moving along a straight line and the temperature distribution is stationary; and finally an ending stage when the heat source leaves the parts [
During phase transitions, energy is absorbed or released by the body proportionally to its latent heat, with material properties varying according to the new phase. Different methods can be used to develop a finite element model of laser welding that considers phase change [
The main difference between conduction mode and keyhole mode is the power density applied to the welding area. The power density is determined by two laser parameters, laser beam diameter and power. Those parameters are inputs of the simulation. A transition mode exists between the two modes, during which the aspect ratio (depth to width ratio) stays nearly constant with increasing power density. The beginning of the transition mode is called the upper limit of conduction mode. The upper limit of conduction mode depends on the interaction time, which is the laser beam diameter divided by the speed [
represents the welding mode according to previous experimentation. The upper limit for conduction mode has been found to be 0.94 MW/cm2 power density for a 9 ms interaction time, and 1.26 MW/cm2 for a 3.4 ms interaction time. The limit is supposed to vary linearly with the interaction time. In the model the power density and interaction time are calculated and compared to this limit in order to choose the heat source to be used. The conduction heat source is selected below this limit, while the keyhole heat source is selected above it.
A purpose of this simulation is to predict the dimensions of a weld with a gap. Since the melted metal (liquid phase) and the fluid flow are not simulated, a gap cannot simply be placed between the sheets in the model. According to a previous analysis of variance conducted through experimentation, gap effects increase the depth and reduce the width, which are opposite of the effects of diameter. Other parameters used in this study increase or decrease both the penetration and the width. To simulate the effect of the gap a multiplier coefficient G is added to the laser beam diameter in the heat source formula. A heat source with modified diameter can be written as:
Q g a p ( x , y , z ) = Q 0 ( 1 − R C ) A c 2 π σ x σ y G ² exp ( − ( ( x − x 0 ) 2 2 ( σ x G ) 2 + ( y − y 0 ) 2 2 ( σ x G ) 2 − A c | z | ) ) (7)
Since the effect of the gap is the opposite of the diameter, the coefficient has to be less than 1. After some tests, a value of 0.75 has been found to be relevant, which represents a decrease of about 0.1mm in diameter.
In butt joint laser welding, the two main factors that create a lack of material in the weld are edge straightness and sheet positioning. The main factor that generates an excess of material is the stress created during cooling. For partial penetration welds, the underfill has no direct impact on the dimensions of the weld. The presence of an underfill simply moves the weld deeper into the parts. For full penetration welds the underfill reduces the depth of the weld, causing it to be less than the thickness. Since the underfill is not evaluated in this simulation, results will always indicate a depth of penetration equal to the thickness of the sheets. Therefore, another method is used to obtain the dimensions of the underfill in order to estimate the correct dimensions of the full penetration weld. It has been seen in a previous study that the underfill is linked to the thickness, the edge straightness, the gap, and the width of the weld for full penetration welds. Using this information, an estimation of the underfill can be made from those parameters. The empirical formula giving the underfill as a percentage of the thickness for a full penetration weld, inspired from the gap bridging formula [
Underfill = ( 0.05 + g + t ∗ E ) + 10 ∗ exp ( − 0.0065 ∗ B D W ) (8)
where g is the gap size, t the thickness, E the edge preparation coefficient (5% is used here), and BDW the bead width. Simulated full penetration welds calculate the underfill using this formula. The underfill is then subtracted from the penetration in order to determine the effective penetration.
The laser welding simulation can be simplified as a sheet with a laser moving along its length, as represented in
Tetrahedron elements are chosen for the mesh because of their fast, easy meshing and refining. In order to have an accurate temperature field in the region of high temperature gradients, a dense mesh is used close to the weld line, while in the more distant region a coarser mesh is used, as can be seen in
The time steps are chosen according to the welding speed and the diameter. So that for each new time step, the laser beam diameter covers 1/3 of the beam’s coverage during the previous time step.
Many parameters are required to simulate laser welding: materials and optic properties, laser parameters, and parts dimensions [
Material properties have a strong influence on heat transfer. Some material properties are taken dependant of the temperature. During laser welding the temperature varies between 20˚C and over 5000˚C. Since there is no easy theoretical formula to interpolate properties over such a temperature range, experimental data is the main way to access to those values. But experimentation is expensive and difficult. The temperature dependant properties are often not available for a precise grade. The properties of another grade of steel can provide a good approximation. The used properties are supplied by Abhilash for 904L steel [
Property | Symbol | Value |
---|---|---|
Liquidus temperature | T liquidus | 1727 [K] |
Solidus temperature | T solidus | 1672 [K] |
Latent heat of fusion | L fusion | 2.72 × 105 [J/kg] |
Reflectivity | R e | 0.3 |
Absorption coefficient | A c | 800 [1/m] |
Emissivity | ε | 0.6 |
The process parameters such as power, diameter and speed are easily adjustable. The same process parameters are used for the simulation and for the validation. Each parameter have 3 levels, which can be seen in
Parameters | Symbol | Levels | ||
---|---|---|---|---|
Laser beam diameter [mm] | σ x | 0.34 | 0.43 | 0.52 |
Laser beam power [W] | Q 0 | 2000 | 2500 | 3000 |
Welding speed [m/min] | v | 3 | 6 | 9 |
Dimension | Symbol | Value |
---|---|---|
Length | L x | 20 [mm] |
Width | L y | 10 [mm] |
Thickness | L z | 1-2-3 [mm] |
The values of bead width (BDW) and depth of penetration (DOP) of the weld are measured on the thermal fields using the concept that the limit of the melted pool is the liquidus temperature. Since modifications have been added to the simulation for gap, conduction mode, and full penetration weld, each condition is looked at individually.
The predicted and measured BDW and DOP values for tests without gap are presented in
The predicted and measured BDW and DOP for the gap test are presented in
Experiment numbers 4, 5, 6, 16, 17 and 18 are in conduction mode
N˚ | DOP (µm) | BDW (µm) | Conduction mode | Full penetration | ||||
---|---|---|---|---|---|---|---|---|
Meas. | Pred. | %Error | Meas. | Pred. | %Error | |||
1 | 912 | 897 | −2% | 1120 | 1230 | −10% | x | |
2 | 1271 | 1400 | 9% | 1155 | 1210 | 5% | ||
3 | 1280 | 1375 | 7% | 1448 | 1260 | 13% | ||
4 | 608 | 604 | −1% | 893 | 930 | −4% | x | |
5 | 634 | 607 | −5% | 1034 | 890 | 14% | x | |
6 | 552 | 598 | 8% | 985 | 880 | 11% | x | |
7 | 808 | 855 | 5% | 935 | 830 | 11% | x | |
8 | 970 | 983 | 1% | 1003 | 790 | 21% | ||
9 | 1039 | 975 | −7% | 943 | 780 | 17% | ||
10 | 913 | 898 | −1% | 1225 | 1340 | −9% | x | |
11 | 1614 | 1763 | 8% | 1198 | 1320 | −10% | ||
12 | 1777 | 1693 | −5% | 1419 | 1350 | 5% | ||
13 | 901 | 875 | −3% | 839 | 920 | −10% | x | |
14 | 1103 | 1178 | 6% | 1062 | 900 | 15% | ||
15 | 1102 | 1180 | 7% | 1098 | 920 | 16% | ||
16 | 459 | 443 | −4% | 761 | 780 | −2% | x | |
17 | 478 | 434 | −10% | 798 | 790 | 1% | x | |
18 | 400 | 418 | 4% | 799 | 768 | 4% | x | |
19 | 804 | 899 | 9% | 1132 | 1390 | −23% | x | |
20 | 1405 | 1697 | 15% | 1165 | 1380 | −18% | x | |
21 | 2601 | 2401 | −8% | 1208 | 1400 | −16% | ||
22 | 703 | 878 | 17% | 877 | 940 | −7% | x | |
23 | 1607 | 1538 | −5% | 865 | 930 | −8% | ||
24 | 1420 | 1546 | 8% | 850 | 920 | −8% | ||
25 | 709 | 763 | 5% | 659 | 660 | 0% | x | |
26 | 1118 | 1082 | −3% | 575 | 690 | −20% | ||
27 | 964 | 1061 | 9% | 893 | 680 | 24% |
N˚ | DOP (µm) | BDW (µm) | Conduction mode | Full penetration | ||||
---|---|---|---|---|---|---|---|---|
Meas. | Pred. | %Error | Meas. | Pred. | %Error | |||
28 | 810 | 799 | −1% | 1256 | 1460 | −16% | x | |
29 | 1480 | 1497 | 1% | 1197 | 1340 | −12% | x | |
30 | 2151 | 2035 | −6% | 1396 | 1260 | 10% | ||
31 | 795 | 765 | −3% | 1028 | 870 | 15% | x | |
32 | 1408 | 1460 | 4% | 1163 | 1080 | 7% | ||
33 | 1784 | 1720 | −4% | 957 | 920 | 4% | ||
34 | 631 | 644 | 1% | 825 | 640 | 22% | x | |
35 | 992 | 1000 | 1% | 762 | 580 | 24% | ||
36 | 1105 | 1200 | 8% | 857 | 680 | 21% | ||
37 | 761 | 799 | 4% | 1125 | 1380 | −23% | x | |
38 | 1414 | 1498 | 4% | 1204 | 1400 | −16% | x | |
39 | 1969 | 2000 | 2% | 1138 | 1360 | −19% | ||
40 | 711 | 755 | 4% | 820 | 830 | −1% | x | |
41 | 1237 | 1180 | −5% | 855 | 790 | 8% | ||
42 | 1412 | 1380 | −2% | 1023 | 820 | 20% | ||
43 | 702 | 755 | 5% | 844 | 830 | 2% | x | |
44 | 1189 | 1290 | 8% | 740 | 780 | −5% | ||
45 | 1275 | 1420 | 10% | 777 | 730 | 6% | ||
46 | 725 | 797 | 7% | 1018 | 1260 | −24% | x | |
47 | 1218 | 1494 | 14% | 1022 | 1240 | −21% | x | |
48 | 1951 | 1850 | −5% | 879 | 1040 | −18% | ||
49 | 734 | 728 | −1% | 866 | 760 | 12% | x | |
50 | 1399 | 1500 | 7% | 880 | 880 | 0% | ||
51 | 1673 | 1650 | −1% | 1017 | 800 | 21% | ||
52 | 567 | 537 | −3% | 730 | 560 | 23% | x | |
53 | 928 | 1020 | 9% | 565 | 620 | −10% | ||
54 | 1240 | 1150 | −8% | 623 | 550 | 12% |
error of 5% for DOP and 6% for BDW. The use of a conduction heat source turns out to be effective when doing low power density welds. A single heat source cannot be used to generate all the results within a high range of parameters.
Twenty simulations indicated full penetration, with depth equal to the thickness, as shown in
Observation of the weld profile is used to evaluate if the general shape of the weld is in agreement with the experiment. In
In this paper, an integrated approach used to build a weld joint shape and dimensions prediction model in laser welding for low carbon galvanized steel in butt-joint configurations is presented. Based on metallurgical transformations using temperature dependent material properties and the enthalpy method the modelling approach is used to investigate conduction and keyhole modes welding using surface and volumetric heat sources. A commercial 3 kW Nd: Yag laser system, a structured experimental design and confirmed statistical analysis tools are used to evaluate the modelling approach accuracy and to confirm the prediction model accuracy. Numerical simulation carried out through 3D FEM reveal great welds shapes and dimensions concordance between modelling and experimental results. The comparison of predicted and measured weld dimensions reveals similar accuracy for keyhole, conduction, full penetration and for gap welds. The prediction errors may have as sources the experimental errors as well as the adopted assumptions in the formulation, particularly for the fluid flow in the melt pool. The BDW presents a larger relative prediction error than DOP, probably because of the underfill (deeper experimental than simulation measurements). Globally, the results demonstrate that the numerical simulation can effectively lead to a consistent and accurate model and provide an appropriate prediction of the weld joint shape and dimensions under variable welding parameters and conditions.
Jacques, L. and El Ouafi, A. (2017) Prediction of Weld Joint Shape and Dimensions in Laser Welding Using a 3D Modeling and Experimental Validation. Materials Sciences and Applications, 8, 757-773. https://doi.org/10.4236/msa.2017.811055