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 .
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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.
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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.
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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.
Simulation
Evaluating sheet metal formability using computer software has been in common industrial use for more than two decades. The current sheet metal forming programs are part of the transition to virtual manufacturing that includes analysis of casting solidification and rolling at the metal production facility, welding, moulding of sheet/fiber composites, automation, and other manufacturing processes. Computer simulation of sheet metal forming is known by several terms, including computerized forming process development and computerized die tryout.
Many highly developed software programs closely replicate the physical press shop forming of sheet metal stampings. These programs have proven to be accurate in predictions of blank movement, strains, thinning within the blank, wrinkles, buckles, and global formability concerns of necking strains and forming severity as defined by conventional forming limit curves. Accurate prediction of local formability related failures such as cut edge expansion is more challenging due to modeling of the production process influence as opposed to the ideal laboratory edge. Prediction of springback generally provides helpful results in understanding the trends and effects. The quality of springback predictions vary with the specific stamping geometry, the selected metal grade, the input information, and user experience, as discussed in Simulation Inputs.
Virtual forming-process development is ideally suited to the needs of current and potential users of AHSS grades. A full range of analysis capabilities is available to evaluate AHSS behavior in a new stamping. These programs allow rapid “what-if” scenarios to explore the impacts of different grades of AHSS, alternative processing, or even design optimization. A Design of Experiments on actual tooling in a physical press shop is limited to only a few variables and may be subject to noise variables clouding the results. In the virtual press shop, changing variables is done with a stroke of the keyboard, and is far easier to undo than permanent changes to the tooling.
Virtual die tryout has numerous advantages, allowing for assessing the viability of part, process, and die design all before cutting the first hard die. Addressing problems before costly and time-consuming die construction starts leads to improved quality and a better use of resources.
The type of software used depends on the goals and available information at each stage of the process, shown in Figure 1. At the beginning of the styling to production cycle, feasibility – whether the stamping can even be manufactured – is the key question. With only the 3D CAD file of the final part and material properties, One-Step or inverse codes can rapidly ascertain strain along section lines, thinning, forming severity, trim line-to-blank, hot spots, blank contour, and other key information. This approach takes the finished part geometry and unfolds that shape to generate a starting blank, calculating the strain between the two shapes (formed vs. flat). Since it starts with the finished geometry rather than the blank, the process is the inverse of reality. All deformation takes place in a single step, or one step, leading to the description of a one step inverse code. Although this takes reduced computing time, only some simulation packages allow incorporation of the forming process, tooling geometry, and the changes in metal properties associated with deformation.
Figure 1: Software types change during processing stage.
Achieving more accurate results involves incremental simulation, where the virtual forming process attempts to replicate reality. This approach models the tools (punch, die, and blankholder) and process parameters (like the blankholder forces, blank shape, and bead geometry, location and restraining forces). Each increment, or time-step, reflects the sheet metal deformation at a different position of the press stroke. Subsequent increments rely on the output from the prior increments. As the quality of the inputs increase, so does the precision of the results.
During selection of process and die design parameters, software evaluates how each new input affects the strains and blank movement (including wrinkles and splits), and generates a press-loading curve. The analysis creates a visual record of the blank deformation into the final part through a transparent die. Each frame of the video is equivalent to an incremental hit or breakdown stamping. Problem areas or defects in the final increment of forming can be traced backwards through the forming stages to the initiation of the problem, allowing problems to be addressed when before they even occur. Some software packages allow analysis of multi-stage forming, such as progressive dies, transfer presses, or tandem presses. This virtual environment also shows the effects of trimming and other offal removal on dimensional precision and springback.
AHSS grades are suited for load bearing or crash-sensitive applications, and forming simulation helps to optimize performance. Previously, the static and dynamic capabilities of part and assembly designs were analyzed using CAD-generated stamping designs with inputs of initial sheet thickness and as-received yield strength. Often the tests results from real parts did not agree with these early analyses because the effects from forming were not incorporated. State-of-the-art applications now model the forming operation first, allowing for local thinning and work hardening to occur. That point-to-point sheet thickness and strength levels are mapped to the crash simulation inputs, resulting in crash models nearly identical to physical test outputs. Correcting deficiencies of the virtual parts by tool, process, or even part design occurs before tool construction has even begun.
Many simulation packages can evaluate the performance of AHSS grades in many forming environments. A simple constitutive equation with a single n-value sufficiently approximated the stress-strain response of older grades. The n-value of AHSS grades changes with strain, so when simulating AHSS grades, input the full stress-strain curve instead of choosing just one n-value. However, this capability may not be present in some proprietary industrial and university software. Use caution when using these programs to analyze AHSS stampings.
Today’s AHSS grades are not the commodities of yesteryear, but instead are highly engineered products unique to the production equipment and processing route chosen by the steelmaker. Although many companies may be capable of meeting the minimum and maximum mechanical properties associated with a specific grade, different suppliers may take up a different portion of the acceptable window. Working with your production steel supplier helps ensure you are using company-specific forming data.
Also remember that there are multiple products associated with a targeted tensile strength. For example, not only are there different families of 980 MPa minimum tensile strength steels (like dual phase, TRIP, and Q&P), but within each family there are multiple options. A grade designated as “DP980” may have enhanced global formability as measured with total elongation, enhanced local formability as measured in a hole expansion test, or have a balance between those properties. The associated material card for simulation will be different, and use of the incorrect card in development could lead to an under-engineered process when attempting to run with production steel.
Key Points
- A virtual tryout evaluates the stamping and die design, and can detail areas of severe forming, buckles, excessive blank movement, and other undesirable deformation before starting tool construction.
- Evaluating alternative “what-if” scenarios in a virtual environment is faster and more efficient than grinding and welding on physical tooling, and mistakes have no permanent impact.
- Design of Experiments (DOE) studies are challenging to do in the physical press shop. The large number input changes required by the process makes it difficult to attribute changes to the intended variables tested or to some noise factor. Simulation allows for easier and faster evaluations when changing one or more parameters.
- AHSS grades change properties when deformed under different forming conditions. Forming simulation captures these changes to show how the final product will react.
- Observing the sheet metal transition from a flat blank to the engineered stamping in a transparent die is a valuable troubleshooting tool provided by virtual forming.
- Simulation codes accurately capture blank motion, thinning strains within the body of the stamping, and other global formability issues like severity compared with the conventional forming limit curve. However, prediction of local formability concerns like sheared edge stretchability is lacking due to the challenges of capturing all the effects related to creating that cut edge.
- The virtual forming codes do not accurately predict springback or the success of springback correction procedure because of the lack of accurate data everywhere in the stamping during the entire forming operation. However, users report reduction in recuts of the die from 12 or more to three or four based on information from the code.
A well-defined material card and accurate descriptions of metal flow throughout the stamping are critical for precise springback predictions, as discussed in the section on Simulation Inputs. Lacking that, many simulation packages can at least provide guidance on the trends which may help guide springback countermeasures.
RSW of Dissimilar Steel
This article is the summary of a paper entitled, “HAZ Softening of RSW of 3T Dissimilar Steel Stack-up”, Y. Lu., et al.L-15
Electromechanical Model
The study discusses the development of a 3D fully coupled thermo-electromechanical model for RSW of a three sheet (3T) stack-up of dissimilar steels. Figure 1 schematically shows the stack-up used in the study. The stack-up chosen is representative of the complex stack-ups used in BIW. Table 1 summarizes the nominal compositions of the three steels labeled in Figure 1.
Figure 1: Schematics of the 3T stack-up of 0.75-mm-thick JAC 270/1.4-mm-thick JSC 980/1.4-mm-thick JSC 590 steels.L-15
Table 1: Nominal Composition of Steels.L-15
JAC270 is a cold rolled Mild steel with a galvanneal coating having a minimum tensile strength of 270 MPa. JSC590 and JSC980 are bare cold rolled Dual Phase steels with a minimum tensile strength of 590 MPa and 980 MPa, respectively.
The electrodes used were CuZr dome-radius electrodes with a surface diameter of 6 mm. The welding parameters are listed in Table 2.
Table 2: Welding Parameters for Resistance Spot Welding of 3T Stack-Up of Steel Sheets.L-15
Figure 2 shows consistent nugget dimensions between simulation and experiment, supporting the validity of the RSW process model for 3T stack-up. The effect of welding current on nugget penetration into the thin sheet is similar to that on the nugget size. It increases rapidly at low welding current and saturates to 32% when the welding current is higher than 9 kA, as shown in Figure 2C.
Figure 2: Comparison between experimental and simulated results: A) Nugget geometry at 8 kA; B) nugget diameters; C) nugget penetration into the thin sheet as a function of welding current. In Figure 2A, the simulated nugget geometry is represented by the distribution of peak temperature (in Celsius). The two horizontal lines in Figure 2B represent the minimal nugget diameter at Interfaces A and B calculated, according to AWS D8.1M: 2007, Specification for Automotive Weld Quality Resistance Spot Welding of Steel. Due to limited number of samples available for testing, the variability in nugget dimensions at each welding current was not measuredL-15.
The results for nugget formation during RSW of the 3T stack-up are show in Figures 3-5. Figure 2 shows that, at the start of welding, the contact pressure at interface A (thin/thick) has a higher peak and drops more quickly along the radial direction than that at interface B (thick/thick). Due to the more localized contact area (Figure 3), a high current density can be observed at interface A, as shown in Figure 4A. Additionally, due to the high current density at interface A, localized heating is generated at this interface, as shown in Figure 5A.
Figure 3: Calculated contact pressure distribution at interfaces A (thin/thick) and B (thick/thick) at a welding time of 5 ms, current of 8 kA, and electrode force of 3.4 L-15
Figure 4: Calculated current density distribution at interfaces A (thin/thick) and B (thick/thick) at welding time of A — 5 ms; B — 200 and 300 ms.L-15
Figure 5: Temperature distribution during resistance spot welding of 3T stack-up at welding times of A) 5 ms; B) 102 ms; C) 300 ms. Welding current is 8 kA and electrode force is 3.4 kN. Calculated temperature is given in Celsius.L-15
As welding time increases, the contact area is expanded, resulting in a decrease of current density. The heat generation rate is shifted from interfaces to the bulk and the peak temperature occurs near the geometrical center of the stack-up.
Figure 6 illustrates that the predicted value corresponds well with the experimental data indicating a sound fitting to the isothermal tempering experimental data.
Figure 6: Comparison of the measured hardness with JMAK calculation showing the goodness of fit of the JSC 980 tempering kinetics parameters.L-15
Figure 7 shows the predicted hardness map of RSW 3T stack-up as well as the predicted and measured hardness profiles for JSC 980.
Figure 7: A) Predicted hardness map of resistance spot welded 3T stack-up; B) predicted and measured hardness profiles along the line marked in (A) for JSC 980.L-15
