Blog, main-blog, RSW Modelling and Performance
Modelling resistance spot welding can help to understand the process and drive innovation by asking the right questions and giving new viewpoints outside of limited experimental trials. The models can calculate industrial-scale automotive assemblies and allow visualization of the highly dynamic interplay between mechanical forces, electrical currents and thermal flow during welding. Applications of such models allow efficient weldability tests necessary for new material-thickness combinations, thus well-suited for applications involving Advanced High -Strength Steels (AHSS).
Virtual resistance spot weld tests can narrow down the parameter space and reduce the amount of experiments, material consumed as well as personnel- and machine- time. They can also highlight necessary process modifications, for example the greater electrode force required by AHSS, or the impact of hold times and nugget geometry. Other applications are the evaluation of whole-part distortion to ensure good part-clearance and the investigation of stress, strain and temperature as they occur during welding. This more research-focused application is useful to study phenomena arising around the weld such as the formation of unwanted phases or cracks.
Modern Finite-Element resistance spot welding models account for electric heating, mechanical forces and heat flow into the surrounding part and the electrodes. The video shows the simulated temperature in a cross-section for two 1.5 mm DP1000 sheets:
First, the electrodes close and then heat starts to form due to the electric current flow and agglomerates over time. The dark-red area around the sheet-sheet interface represents the molten zone, where the nugget forms after cooling. While the simulated temperature field looks plausible at first glance, the question is how to make sure that the model calculates the physically correct results. To ensure that the simulation is reliable, the user needs to understand how it works and needs to validate the simulation results against experimental tests. In this text, we will discuss which inputs and tests are needed for a basic resistance spot welding model.
At the base of the simulation stands an electro-thermomechanical resistance spot welding model. Today, there are several Finite Element software producers offering pre-made models that facilitate the input and interpretation of the data. First tests in a new software should be conducted with as many known variables as possible, i.e., a commonly used material, a weld with a lot of experimental data available etc.
As first input, a reliable material data set is required for all involved sheets. The data set must include thermal conductivity and capacity, mechanical properties like Young’s modulus, tensile strength, plastic flow behavior and the thermal expansion coefficient, as well as the electrical conductivity. As the material properties change drastically with temperature, temperature dependent data is necessary at least until 800°C. For more commonly used steels, high quality data sets are usually available in the literature or in software databases. For special materials, values for a different material of the same class can be scaled to the respective strength levels. In any case, a few tests should be conducted to make sure that the given material matches the data set. The next Figure shows an exemplary material data set for a DP1000. Most of the values were measured for a DP600 and scaled, but the changes for the thermal and electrical properties within a material class are usually small.
Figure 1: Material Data set for a DP1000.S-73
Next, meaningful boundary conditions must be chosen and validated against experiments. These include both the electrode cooling and the electrical contact resistance. To set up the thermal flow into the electrode, temperature measurements on the surface are common. In the following picture, a measurement with thermocouples during welding and the corresponding result is shown. By adjusting the thermal boundary in the model, the simulated temperatures are adjusted until a good match between simulation and experiment is visible. This calibration needs to be conducted only once when the model is established because the thermal boundary remains relatively constant for different materials and coatings.
Figure 2: Temperature measurement with thermocouples during welding and the results. The simulated temperature development is compared to the experimental curve and can be adjusted via the boundary conditions.F-23
The second boundary condition is the electrical contact resistance and it is strongly dependent on the coating, the surface quality and the electrode force. It needs to be determined experimentally for every new coating and for as many material thickness combinations as possible. In the measuring protocol, a reference test eliminates the bulk material resistance and allows for the determination of the contact resistances using a µOhm-capable digital multimeter.
Finally, a metallographic cross-section shows whether the nugget size and -shape matches the experiment. The graphic shows a comparison between an actual and simulated cross section with a very small deviation of 0.5 mm in the diameter. As with the temperature measurements, a small deviation is not cause for concern. The experimental measurements also exhibit scatter, and there are a couple of simplifications in the model that will reduce the accuracy but still allow for fast calculation and good evaluation of trends.
Figure 3: Comparison of experimental and virtual cross-sections.F-23
After validation, consider conducting weldability investigations with the model. Try creating virtual force / current maps and the resulting nugget diameter to generate first guesses for experimental trials. We can also gain a feeling how the quality of each weld is affected by changes in coatings or by heated electrodes when we vary the boundary conditions for contact resistance and electrode cooling. The investigation of large spot-welded assemblies is possible for part fit-up and secondary effects such as shunting. Finally, the in-depth data on temperature flow and mechanical stresses is available for research-oriented investigations, cracking and joint strength impacts.
Note: The work represented in this article is a part a study of Liquid Metal Embrittlement (LME), commissioned by WorldAutoSteel. You can download the free report on the results of the LME study, including how this modelling was used to verify physical tests, from the WorldAutoSteel website.
RSW Modelling and Performance
This article summarizes the findings of a paper entitled, “Prediction of Spot Weld Failure in Automotive Steels,”L-48 authored by J. H. Lim and J.W. Ha, POSCO, as presented at the 12th European LS-DYNA Conference, Koblenz, 2019.
To better predict car crashworthiness it is important to have an accurate prediction of spot weld failure. A new approach for prediction of resistance spot weld failure was proposed by POSCO researchers. This model considers the interaction of normal and bending components and calculating the stress by dividing the load by the area of plug fracture.
Background
Lee, et al.L-49 developed a model to predict spot welding failure under combined loading conditions using the following equation, based upon experimental results .
|
Equation 1 |
Where FS and FN are shear and normal failure load, respectively, and n is a shape parameter.
Later, Wung and coworkersW-38 developed a model to predict the failure mode based upon the normal load, shear load, bending and torsion as shown in Equation 2.
 |
Equation 2 |
Here, FS, FN ,Mb and Mt are normal failure load, shear failure load, failure moment and failure torsion of spot weld, respectively. α, β, γ and μ are shape parameters.
Seeger et al.S-106 proposed a model for failure criterion that describes a 3D polynomial failure surface. Spot weld failure occurs if the sum of the components of the normal, bending and shear stresses are above the surface, as shown in the Figure 1.
Figure 1: Spot weld failure model proposed by Seeger et al.S-106
The failure criterion can be expressed via Equation 3.
 |
Equation 3 |
Here, σN , σB , and τ are normal, bending and shear stress of the spot weld, respectively. And nN, nB and nc are the shape parameters. Toyota Motor CorporationL-50 has developed the stress-based failure model as shown in Equation 4.
 |
Equation 4 |
Hybrid Method to Determine Coefficients for Failure Models
This work used a unique hybrid method to determine the failure coefficients for modeling. The hybrid procedure steps are as follows:
- Failure tests are performed with respect to loading conditions.
- Finite element simulations are performed for each experiment.
- Based on the failure loads obtained in each test, the instant of onset of spot weld failure is determined. Failure loads are extracted comparing experiments with simulations.
- Post processing of those simulations gives the failure load components acting on spot welds such as normal, shear and bending loads.
These failure load components are plotted on the plane consisting of normal, shear and bending axes.
The hybrid method described above is shown in Figure 2.L-48
Figure 2: Hybrid method to obtain the failure load with respect to test conditions.L-48
New Spot Weld Failure Model
The new proposed spot weld failure model in this paper considers only plug fracture mode as a normal spot weld failure. Secondly normal and bending components considered to be dependent upon each other. Stress generated by normal and bending components is shear, and shear component generates normal stress. Lastly authors have used πdt to calculate the area of stress instead of πd2/4. The final expression is shown in the Equation 5.
 |
Equation 5 |
Here τn is the shear stress by normal load components, σS is the normal stress due to shear load component. And 
, 
, c, α and β are coefficients.
This work included verification experiments of 42 kinds of homogenous steel stack-ups and 23 heterogeneous stack-ups. The strength levels of the steels used was between 270 MPa and 1500 MPa, and thickness between 0.55 mm and 2.3 mm. These experiments were used to evaluate the model and compare the results to the Wung model.
Conclusions
Overall, this new model considers interaction between normal and bending components as they have the same loading direction and plane. The current developed model was compared with the Wung model described above and has shown better results with a desirable error, especially for asymmetric material and thickness.
Joining, Laser Welding
Optimizing weld morphology and mechanical properties of
laser welded Al-Si coated 22MnB5 by surface application of
colloidal graphite
Researchers at University of Waterloo discovered the microstructural effects of adding colloidal graphite to Al-Si coated 22MnB5 Press Hardened Steel.K-51 Laser welds were made on 1.5 mm thick Al-Si coated 22MnB5 PHS perpendicular to the rolling direction. Pure colloidal graphite suspended in isopropanol base was applied to the area being welded and the resulting graphite coating after evaporation ranged from 5 µm to 130 μm for testing. Parameters used for the weld are: 4kW power, 6m/min welding speed, beam diameter of 0.3 mm, and laser defocus of 6mm. Samples were then hot stamped by heating for 6 min to 930 ᵒC in a furnace and then water quenched at a cooling rate greater than 30 ᵒC/s.
Al-Si coating is excellent at preventing oxidation and decarburization of high strength steel at elevated temperatures. However, during welding there is diffusion of Al into the fusion zone which stabilizes ferrite at elevated temperature reducing the strength of the welded joint. Colloidal graphite coating decreases the Al content and increases C content of the fusion zone. As shown in Figure 1, The mechanism for reduction in Al content is due the graphite coating acting as an insulator to the Al-Si coating which then causes an ejection of the molten Al-Si coating from the surface. Figure 2 displays a proportional reduction of Al in the fusion zone with increasing graphite coating thickness up to 40 μm where after the reduction in Al is minimal. This is attributed to the initial reduction of Al being caused by the ejection of the molten Al-Si from underneath the graphite coating. Graphite coating greater than 40 µm does not aid in additional ejection of Al-Si and the Al-Si coating already diluted in the weld pool will not be removed.
Figure 1: Al-Si ejection mechanism.K-51
Figure 2: Al and C content in weld with increasing graphite thickness.K-51
Summary
Ferrite concentration in the fusion zone was reduced from approx. 40% with no graphite coating to approx. 2% with 130 μm graphite coating thickness (Figure 3). The increase in C content and reduction in Al content resulted in an increase in austenite being stabilized at elevated temperature rather than ferrite and therefore a larger percentage of martensite results after hot stamping. The average fusion zone hardness increased from 320 HV with no coating to 540 HV with 130 μm coating thickness (Figure 4). The weld strength of the sample with no graphite coating was 1249±15MPa whereas the weld strength with a coating of 130 µm was 1561±7MPa which matches the base metal (Figure 5). With an increase in graphite coating thickness there is an increase in weld strength that can eventually match the base metal strength.
Figure 3: Ferrite concentration in weld.K-51
Figure 4: Fusion Zone Hardness vs. Graphite Thickness.K-51
Figure 5: Weld strength vs. Graphite Thickness.K-51
Joining, Laser Welding
In this study by Shanghai Jiao Tong University and General Motors Company on liquid metal Embrittlement (LME)Z-11, hot dipped 1.2mm galvanized QP980 steel sheets with a 6 micron thick zinc rich coating on top of a 2 micron thick transition zone to the base metal were used. The laser welder is tilted 5º ahead of weld pool to avoid back reflection. The welding velocity was varied from 4-6 m/min and laser power from 4-6.5 kW. Referencing Table 1, Schedules #1–4 were intended to investigate effects of laser power on LME cracks using 6 m/min. schedules #4–6 varied velocity with the laser power staying constant at 4.5 kW. In addition, schedules #6 and #7 varied laser power at a relatively lower welding velocity of 4 m/min.
Table 1: Process Parameters.Z-11
Full penetration welds did not result in cracking while partial penetration welds with lower energy density did. The lowest energy density welds resulted in no cracking but the penetration was barely beyond the faying surface. Cracks resembles an inverse “Y” where the cracks initiated at the faying surface and propagated along the direction of solidification towards the weld centerline. Cracks at notch root were wider than centerline crack indicating grain boundary separation. The fracture method is characteristic of quasi-cleavage indicating that the grain boundaries were embrittled by Fe-Zn intermetallics. Crack initiation at the faying surface can be explained by the residual stresses that form highest at the faying surface during cooling. This stress concentration is eliminated with full penetration weld pass as well as in wide and shallow passes as seen in Figure 1.
Figure 1: Von Mises Stress Distribution.Z-11
Because the process of laser welding is so short, the vaporized zinc and intermetallics do not have time to outgas completely. The liquid zinc diffuses along the austenite grain boundaries and stabilize ferrite given ferrite has a higher solubility of Zn compared to austenite. The remaining liquid Zn reacts with the ferrite to form the solid Γ-Fe3Zn10 which is a hard brittle intermetallic that can easily induce cracking. Another peritectic reaction occurs with Γ-Fe3Zn10 and liquid zinc forming another brittle intermetallic δ-FeZn10. The stabilized ferrite and intermetallics occur before austenite transform to martensite and remains even after this reaction occurs.
The formation of the intermetallics between the grain boundaries decreases ductility and with the combination of the high residual stress and stress concentration at the faying surface, the crack initiates and propagates. The cracking follows the grain growth to the center of the weld. Liquid Zn accumulates at the center of the weld and results in Fe-Zn intermetallics with low ductility that can eventually propagate cracking that occurs at the edge of the weld. Welds that result in a smaller cross-sectional area on the faying surface benefit from the reduction in vaporized Zn that cannot be outgassed while full penetration welds with keyhole mode can allow Zn to out gas from both the top and bottom of the weld as well as increased nugget size decreasing the Zn concentration to where brittle Fe-Zn phases do not form. Full penetration welds are recommended to reduce residual stress as well as allow sufficient outgassing of vaporized Zn in the weld pool.
Figure 2: LME illustration.Z-11
Figure 3: Zn diffusion.Z-11
Summary
LME cracks initiated at the weld notch root on the faying surface and propagated towards the center of the weld along the direction of columnar growth. Brittle intermetallic help induce cracking in the weld metal in addition to restraint from the weld joint. Full penetration welds were found to reduce Zn content from the weld in addition to reducing restraint as compared to partial penetration welds. The full penetration weld allowed for zinc to be outgassed from the weld on both sides reducing the Zn content in the weld to an acceptable level. Full penetration welds also reduced the residual stresses that formed during partial penetration welds due to the restraint on the root side of the weld.
Joining, Laser Welding, Press Hardened Steels
This studyR-25, conducted by the Centre for Advanced Materials Joining, Department of Mechanical & Mechatronics Engineering, University of Waterloo, and ArcelorMittal Global Research, utilized 2mm thick 22MnB5 steel with three different coating thicknesses, given in Table 1. The fiber laser welder used 0.3mm core diameter, 0.6mm spot size, and 200mm beam focal length. The trials were done with a 25° head angle with no shielding gas but high pressure air was applied to protect optics. Welding passes were performed using 3-6kW power increasing by 1 kW and 8-22m/min welding speed increasing by 4m/min. Compared to the base metal composition of mostly ferrite with colonies of pearlite, laser welding created complete martensitic composition in the FZ and fully austenized HAZ while the ICHAZ contained martensite in the intergranular regions where austenization occurred.
Table 1: Galvanneal Coatings.R-25
Figure 1: Base metal microstructure(P=pearlite, F=ferrite, Γ=Fe3Zn10, Γ1=Fe5Zn21 and δ=FeZn10).R-25
Figure 2: Welded microstructure — (a) overall view, (b) HAZ, (c) ICHAZ at low and (d) high magnifications, (e) UCHAZ (f) FZ, and (g) coarse-lath martensitic structure (where M; martensite, P: pearlite, F: ferrite).R-25
Given the lower boiling temperature of Zn at 900 °C as compared to Fe, the interaction of the laser with the Zn plasma that forms upon welding affects energy deliverance and depth of penetration. Lower coating weight of (100 g/m2) resulted in a larger process window as compared to (140 g/m2). Increased coating weight will reduce process window and need higher power and lower speeds in order to achieved proper penetration as shown in Figure 3 and Figure 4. Depth of penetration due to varying welding parameters was developed:
d=(H-8.6+0.08C)/(0.09C-4.8)
[d= depth of penetration(mm), H= heat input per unit thickness(J/mm2), C= coating weight(g/m2)]
Given the reduction in power deliverance, with an increase in coating weight there will be an expected drop in FZ and HAZ width. Regardless of the coating thickness, the HAZ maintained its hardness between BM and FZ. No direct correlation between coating thickness and YS, UTS, and elongation to fracture levels were observed. This is mainly due to the failure location being in the BM.
Figure 3: Process map of the welding window at coating weight of (a) 100 g/m2, (b) 120 g/m2, and (c) 140 g/m2.R-25
Figure 4: Heat input per unit thickness vs depth of penetration.R-25
Joining Dissimilar Materials, Laser Welding
Given the use of many different metals in the Body in White construction, it is important to understand the effects of dissimilar welding AHSS. Researchers at Indian Institute of Technology Madras in Chennai, India and Centre of Laser Processing of Materials in Hyderabad, India developed tests to study the resulting microstructure from laser welding 2.5 mm thick DP600 steel to 3 mm thick AA6061 aluminium alloy using a laser beam diameter of 1.5 mm.I-1 They discovered a softening in the steel HAZ due to a tempering effect and an increase in hardness in the aluminum HAZ due to the presence of aluminium intermetallic phases present. Maximum shear strength was observed when the thickness of intermetallics was reduced to 8-11 microns. They concluded that best quality welds were made under power densities and interaction times of 1.98kW/mm2, 0.15s and 2.26 kW/mm2, 0.187s.
The laser power was varied from 3 kW to 4.5 kW and the scanning speed of 8 mm/s, 10 mm/s, and 12 mm/s. Power density and interaction time were two parameters they used to compare trials where:
| Power density (Pd) = |
|
and
| interaction time (It) = |
 |
The resulting welding parameters are shown in Table 1 below. Figure 1 shows the microstructure of the fusion boundary and HAZ on the DP600 side of the welded joint. Figure 2 shows the microstructure of the weld interface on the AA 6061 side. Figure 3 displays the hardness data with (a) representing 3.5 kW and 10 mm/s, (b) representing 3.5 kW and 8 mm/s, and (c) representing 4 kW and 8 mm/s. Figure 4 represents the Shear Stress-Strain of the welds given different IMC thickness.
Table 1: Welding Parameters.I-1
Figure 1: Weld Metal, DP 600 Base Metal and HAZ microstructure.I-1
Figure 2: Fe-Al interface microstructure.I-1
Figure 3: Microhardness Plot.I-1
Figure 4: Load vs. Displacement.I-1
