A New Software Application for Thin Wall Section Analysis
Advanced High-Strength Steel (AHSS) grades offer increased performance in yield and tensile strength. However, to fully utilize this increased strength, automotive beam sections must be designed carefully to avoid buckling of the plate elements in the section. A new software application, Geometric Analysis of Sections—GAS2.0, available through the American Iron and Steel Institute, is a tool to aid in this design effort.
Plate Buckling in Automotive Sections
To understand how plate buckling affects the strength of a thin walled beam consider Figure 1. A square beam is made of four identical plates connected at their edges. Under an axial compressive load each plate may buckle. Considering just one of the plates, the stress that will cause buckling depends on the ratio of plate width and thickness (b/t). Thinner wider plates with large b/t ratio will buckle at a lower stress than thicker narrower plates.
Figure 1: Plate Buckling Behavior.
Now consider a plate of mild steel (200 MPa yield stress) which has been designed to buckle just as yield stress is reached, Point A in Figure 2. The plate would have a b/t ratio of approximately 60. This design is taking full advantage of the yield strength of the material.
Now consider the same plate but substituting an AHSS grade (600 MPa yield stress) as shown in Figure 2. The plate will buckle at the same 200 MPa before reaching the material’s potential, Point B in the figure. To take advantage of this materials yield strength, the proportions of the plate will need to be changed, Point C. This illustration demonstrates the need to consider plate buckling particularly in the application of AHSS grades.
Figure 2: AHSS Substitution in a Plate.
Moving from a single plate to the more complex case of a beam section of several plates, consider Figure 3. On the left is the beam made of four plates with a compressive load causing the plates to just begin to buckle. However, this condition does not represent the maximum load carrying ability of the beam. The load can be increased until the stress at the corners of the buckled plates are at the material yield stress, center in Figure 3. Note that in this condition the stress distribution across the plate is nonlinear with lower stress in the center of each plate. One means to model this complex state is by using an imaginary Effective Section. Here the center portion is visualized as being removed and the remainder of the section is stressed uniformly at yield. The amount of plate width to be removed is determined by theory.1, 2, 3, 4 The effective section is a convenient way to visualize the efficiency of a section design given the material grade and provides an estimate of the maximum load carrying ability of the beam.
Figure 3: Concept of Effective Section.
Geometric Analysis of Sections – GAS2.0
Geometrical Analysis of Sections software determines the effective section for complex automotive sections. Figure 4 illustrates the GAS2.0 user interface. The user has the ability to construct sections or to import section data from a CAD system. Material properties for 63 steel grades are preloaded with the ability to also add user-defined steel grades. Two types of analysis are available. Nominal analysis, which provides classical area properties of the section, and Effective analysis which determines the effective section at material yield. Figure 5 summarizes both the tabular results and graphical results for each type of analysis.
Figure 4: GAS2.0 User Interface.
Figure 5. GAS2.0 Analysis Results.
Figure 6 illustrates an example of an Effective Analysis for a rocker section. In the graphical screen, the effective section is shown in green. Ideally, the whole section would be effective to fully use the materials yield capability. Also shown in the graphical screen are the section centroid, orientation of the principle coordinates, and stress distribution. In the right text box are tabular results. At the bottom of the tabular results is the axial load that causes this stress state and represents the ultimate load carrying ability of this section.
Figure 6: GAS2.0 Graphical Results.
It is clear that much of the material in the section of Figure 6 is not fully effective. GAS2.0 allows the user to conveniently modify the section. For example, in Figure 7 a bead has been added to the left side wall increasing its bulking resistance. Note that the side wall is now largely effective, and the ultimate load at the bottom of the text box has increased substantially.
Figure 7: Improved Design Concept.
Role of GAS in the Design Process
GAS2.0 can play a significant role in early stage design, see Figure 8, by quickly creating initial designs which are more likely to function and to ensure that adequate package space is set aside for structure. This will result in fewer problems to fix later in the design sequence. During the detail design stage, GAS2.0 can supplement Finite Element Analysis by identifying problems earlier, and by screening design concepts for those with the greatest promise prior to more detailed analysis by FEA.
Figure 8: Role of GAS2.0 in Design Process.
GAS2.0 is available for free download at www.autosteel.org, Included in the resources at autosteel.org is an American Iron and Steel Institute introductory webinar conducted by Dr. Don Malen on 16 June 2020, as well as a number of GAS2.0 tutorials and training modules.
You are most likely wondering why WorldAutoSteel is writing a blog about a bicycle. It is because when we talked to Jia-Uei Chan, Regional Business Development at our member company, thyssenkrupp Steel Europe (TKSe), about the journey of inventing the world’s first Advanced High-Strength Steel road bike, we were incredibly inspired. This is more than a story about a steel bicycle. This is the story of steel innovation, conceived in a WorldAutoSteel members workshop to brainstorm ideas on transforming steel’s image to the sophisticated and advanced material it is. Their journey led to new steel applications, patentable processes, and in the steelworks bicycle, ideas that we think can inspire new automotive applications as well. And anyway, who doesn’t like an inspiring story?
Bikes of this genre have some of the same requirements of modern vehicles: lightweight, strength and durability, affordability, and high performance. To achieve these, the thyssenkrupp steelworks team developed what they called inbike® technology, which combines high-strength steel, half-shell technology and automated laser welding.
How it was made
The bike frame is made from DP 330/590 steel, used for its cold forming abilities, stamped as thin as 0.7mm. The steel blanks are pressed into a die to form two half-shells in a deep-drawing process.
A major challenge was to bring these two half shells together in such a way that minimized gaps and achieved a tight fit, enabling automated laser welding (this process requires no gaps over 6 meters of contact length), while ensuring that the frame achieves an elegant, seamless look. Enter innovation.
At the stamping plant, the half-shells were fitted with “dimples,” (See Figure 1) tiny bumps on the welding flanges that create channels at the weld seam for the zinc, preventing vaporized zinc from remaining trapped in the seam during subsequent welding. The half shells were then clamped in a special device and shipped to the laser specialist (See Figure 2).
Figure 1: Tiny bumps prevent vaporized zinc from remaining trapped in the seam during subsequent welding.
Figure 2: Frame half-shells clamped in the device for laser welding.
The particular challenge lay in the reliable processing and fusing of both frame halves by means of automated laser welding in such a way that no damage to the frame would occur, while also ensuring the weld seam lay as close as possible to the bend radius of the frame halves. The complex frame shape is welded by following a sophisticated trajectory in a 3-D space. After countless continuous improvement exercises, the steelworks team was able to achieve a very flat, elegant weld seam design. This translates into a very stable bike, with a frame that has the needed rigidity in the bottom bracket area to enable high biomechanical power transmission, but with high elasticity in the seat tube configuration to make for an unusually comfortable ride. In comparison, aluminium and carbon fiber bikes are very stiff and characteristic of an unpleasant ride experience.
Inventing the possibility
Tackling a project that is such a reach beyond the norm is never easy. The thyssenkrupp steelworks team repeatedly heard from qualified experts that the project was actually not feasible. At the same time, they had partners who were so fascinated by the challenge that they wanted to make it possible. Chan related to WorldAutoSteel that there were many times when giving up was the more attractive option. Endurance won out. And as it turns out, the half-shell technology invented out of necessity for this bike could find an application in the tough requirements of an electric vehicle battery case.
Says Chan, “We genuinely believed that steel is the perfect material for a road bike. And we wanted to break with convention and make the most out of steel with high-tech engineering.” Have a look at steelworks.bike, and you will undoubtedly agree they did just that.
Dr. Donald Malen, College of Engineering, University of Michigan, reviews the use of two recently developed Powertrain Models, which he co-authored with Dr. Roland Geyer, University of California, Bren School of Environmental Science.
The Need For The Powertrain Models
The use of Advanced High-Strength Steel (AHSS) grades offer a means to lightweight a vehicle. Among the benefits of this lightweighting are less fuel used over the vehicle life, and better acceleration performance. Vehicle designers as well as Greenhouse gas analysts are interested in estimating these benefits early in the vehicle design process 5.
Models are constructed for this purpose which range from the use of a simple coefficient, (for example fuel consumption change per kg of mass reduction), to very detailed models accessible only to specialists which require knowledge of hundreds of vehicle parameters. Draw backs to the first approach is that the coefficient may be based on assumptions about the vehicle which do not match the current case. Drawbacks to the detailed models are the considerable expense and time needed, and the lack of transparency in the results; It is difficult to relate inputs with outputs.
A middle way between the simplistic coefficient and the complex model, is described here as a set of Parsimonious Powertrain Models 1, 2, 3. Parsimony is the principle that the best model is the one that requires the fewest assumptions while still providing adequate estimates. These Excel spreadsheet models cover Internal Combustion powertrains, Battery Electric Vehicles, and Plug-in Electric Vehicles, and predict fuel consumption and acceleration performance based on a small set of inputs. Inputs include vehicle characteristics (mass, drag coefficient, frontal area, rolling resistance), powertrain characteristics (fuel conversion efficiency, gear ratios, gear train efficiency), and fuel consumption driving cycle. Model outputs include estimates for fuel consumption, acceleration, and a visitation map.
Physics of the Models
Fuel consumption is determined by the quantity of fuel used over a driving cycle. The driving cycle specifies the vehicle speed vs. time. An example of a driving cycle is the World Light Vehicles Test Procedure (WLTP) cycle shown in Figure 1.
Figure 1: Fuel Consumption Driving Cycle (WLTP Class 3b).
Given the velocity history of Figure 1, the forces on the vehicle resisting forward motion may be calculated. These forces include inertia force, aerodynamic drag force, and rolling resistance. The total of these forces, called tractive force, must be provided by the vehicle propulsion system, see Figure 2.
Figure 2. Tractive Force Required.
Once vehicle speed and tractive force are known at each point of time during the driving cycle, the required torque and rotational speed may be determined for each of the drivetrain elements, as shown in Figure 3 for an Internal Combustion system, and Figure 4 for a Battery Electric Vehicle.
Figure 3. Internal Combustion Powertrain.
Figure 4. Battery Electric Vehicle Powertrain.
In this way, the required torque and speed of the engine or motor may be determined. Then using a map of efficiency, shown to the right in Figures 3 and 4, the energy demand is determined at each point in time. Summing the energy demand over time yields the fuel used over the driving cycle. The reader is referred to References 1 and 2 for a much more in depth description of the models.
As an example application, consider the WorldAutoSteel FutureSteelVehicle (FSV)4. The FSV project, completed in 2011, investigated the weight reduction potential enabled with the use of AHSS, advanced manufacturing processes and computer optimization. The resulting material use in the body structure is shown in Figure 5.
This use of AHSS allowed a reduction in the vehicle curb mass from 1200 kg to 1000 kg. What are the effects of this mass reduction on fuel consumption and acceleration performance?
The inputs required for the powertrain model are shown in Table 1 for the base case.
Table 1: Model Inputs for Base Case
The results provided by the powertrain model are summarized in the acceleration-time vs. fuel consumption graph of Figure 6. Point A is the base case at 1200 kg curb mass. The lightweight case with same engine is shown as Point B. Note the fuel consumption reduction and also the acceleration time reduction. Often the acceleration time is set as a requirement. For the lighter vehicle, the engine size may be reduced to achieve the original acceleration time and an even greater reduction in fuel consumption as shown as Point C.
Figure 6. Summary of results of base vehicle and reduced mass vehicle.
Using the parsimonious powertrain models allows such ‘what-if’ questions to be answered quickly, with minimal data input, and in a transparent way. The Parsimonious Powertrain Models are available as a free download at worldautosteel.org.
WorldAutoSteel releases today the results of a three-year study on Liquid Metal Embrittlement (LME), a type of cracking that is reported to occur in the welding of Advanced High-Strength Steels (AHSS).The study results add important knowledge and data to understanding the mechanisms behind LME and thereby finding methods to control and establish parameters for preventing its occurrence. As well, the study investigated possible consequences of residual LME on part performance, as well as non-destructive methods for detecting and characterizing LME cracking, both in the laboratory and on the manufacturing line (Figure 1).
Figure 1: LME Study Scope
The study encompassed three different research fields, with an expert institute engaged for each:
A portfolio containing 13 anonymized AHSS grades, including dual phase (DP), martensitic (MS) and retained austenite (RA) with an ultimate tensile strength (UTS) of 800 MPa and higher, was used to set up a testing matrix, which enabled the replication of the most relevant and critical material thickness combinations (MTC). All considered MTCs show a sufficient weldability under use of standard parameters according to SEP1220-2. Additional MTCs included the joining of various strengths and thicknesses of mild steels to select AHSS in the portfolio. Figure 2 provides the welding parameters used throughout the study.
Figure 2: LME Study Welding Parameters
In parallel, a 3D electro-thermomechanical simulation model was set up to study LME. The model is based on temperature-dependent material data for dual phase AHSS as well as electrical and thermal contact resistance measurements and calculates local heating due to current flow as well as mechanical stresses and strains. It proved particularly useful in providing additional means to mathematically study the dynamics observed in the experimental tests. This model development was documented in two previous AHSS Insights blogs (see AHSS Insights Related Articles below).
The study began by analyzing different influence factors (Figure 3) which resembled typical process deviations that might occur during car body production. The impact of the influences was analyzed by the degree of cracking observed for each factor. A select number of welding set-ups from these investigations were rebuilt digitally in the simulation model to replicate the process and study its dynamics mathematically. This further enabled the clarification of important cause-effect relationships.
Figure 3: Overview of All Applied Influence Factors (those outlined in yellow resulted in most frequent cracking.)
Generally, the most frequent cracking was observed for sharp electrode geometries, increased weld times and application of external loads during welding. All three factors were closely analyzed by combining the experimental approach with the numerical approach using the simulation model.
Destructive Testing – LME Effects on Mechanical Joint Strength
A destructive testing program also was conducted for an evaluation of LME impact on mechanical joint strength and load bearing capacity in multiple conditions, including quasi-static loading, cyclic loading, crash tests and corrosion. In summary of all load cases, it can be concluded that LME cracks, which might be caused by typical process deviations (e.g. bad part fit up, worn electrodes) have a low intensity impact and do not affect the mechanical strength of the spot weld. And as previously mentioned, the study analyses showed that a complete avoidance of LME during resistance spot welding is possible by the application of measures for reducing the critical conditions from local strains and exposure to liquid zinc.
In welding under external load experiments, the locations of the experimental crack occurrence showed close correlation with the strains and remaining plastic deformations computed by the simulation model. It was observed that the cracks form at the location of the highest plastic strains, and material-specific threshold values for critical strains were derived. The threshold values then were used to judge the crack formation at elongated weld times.
At the same time, the simulation model pointed out a significant difference in liquid zinc diffusion during elongated weld times. Therefore, it is concluded that liquid zinc exposure time is a second highly relevant factor for LME formation.
The results for the remaining influence factors depended on the investigated MTCs and were generally less significant. In more susceptible MTCs (AHSS welded with thick Mild steel), no significant cracking occurred when welded using standard process parameters. Light cracking was observed for most of the investigated influences, such as low electrode cooling rate, worn electrode caps, electrode positioning deviations or for gap afflicted spot welds. More intense cracking (higher penetration depth cracking) was only observed when welding under extremely high external loads (0.8 Re) or, even more, as a consequence of highly increased weld times.
For the non-susceptible MTCs, even extreme situations and weld set-ups (such as the described elongated weld times) did not result in significant LME cracks within the investigated AHSS grades.
Methods for avoidance of LME also were investigated. Changing the electrode tip geometry to larger working plane diameters and elongating the hold time proved to eliminate LME cracks. In the experiments, a change of electrode tip geometry from a 5.5 mm to an 8.0 mm (Figure 4) enabled LME-free welds even when doubling the weld times above 600 ms. Using a flat-headed cap (with small edge radii or beveled), even the most extreme welding schedules (weld times greater than 1000 ms) did not produce cracks. The in-depth analysis revealed that larger electrode tip geometries clearly reduce the local plastic deformation around the indentation. This plastic strain reduction is particularly important, as longer weld times contribute to a higher liquid zinc exposure interval, leading to a higher potential for LME cracks.
Figure 4: Electrode Geometries Used in Study Experiments
It was also seen that as more energy flows into a spot weld, it becomes more critical to parameterize an appropriate hold time. Depending on the scenario, the selection of the correct hold time alone can make the difference between cracked and crack-free welds. Insufficient hold times allow liquid zinc to remain on the steel surface and increased thermal stresses that form after the lift-off of the electrode caps. Elongated hold times reduce surface temperatures, minimizing surface stresses and thus LME potential.
NON-Destructive Testing: Laboratory and Production Capabilities
A third element of the study, and an aid in the control of LME, is the detection and characterization of LME cracks in resistance spot welds, either in laboratory or in production conditions. This work was done by the Institute of Soudure in close cooperation with LWF, IPK and WorldAutoSteel members’ and other manufacturing facilities. Ten different non-destructive techniques and systems were investigated. These techniques can be complementary, with various levels of costs, with some solutions more technically mature than others. Several techniques proved to be successful in crack detection. In order to aid the production source, techniques must not only detect but also characterize cracks to determine intensity and the effect on joint strength. Further work is required to achieve production-level characterization.
The study report provides detailed technical information concerning the experimental findings and performances of each technique/system and the possible application cost of each. Table 1 shows a summary of results:
Table 1: Summary of NDT: LME Detection and Characterization Methods
Suitable measures should always be adapted to the specific use case. Generally, the most effective measures for LME prevention or mitigation are:
Avoidance of excessive heat input (e.g. excess welding time, current).
Avoidance of sharp edges on spot welding electrodes; instead use electrodes with larger working plane diameter, while not increasing nugget-size.
Employing extended hold times to allow for sufficient heat dissipation and lower surface temperatures.
Avoidance of improper welding equipment (e.g. misalignments of the welding gun, highly worn electrodes, insufficient electrode cooling)
In conclusion, a key finding of this study is that LME cracks only occurred in the study experiments when there were deviations from proper welding parameters and set-up. Ensuring these preventive measures are diligently adhered to will greatly reduce or eliminate LME from the manufacturing line. For an in-depth review of the study and its findings, you can download a copy of the full report at worldautosteel.org.
LME Study Authors
The LME study authors were supported by a committed team of WorldAutoSteel member companies’ Joining experts, who provided valuable guidance and feedback.
Related Articles: More on this study in previous AHSS Insights blogs:
Christoph Böhne, Gerson Meschut, Max Biegler & Michael Rethmeier(2020)Avoidance of liquid metal embrittlement during resistance spot welding by heat input dependent hold time adaption,Science and Technology of Welding and Joining,DOI: 10.1080/13621718.2020.1795585
In static or dynamic conditions, the spot weld strength of Advanced High-Strength Steels (AHSS) may be considered as a limiting factor. One solution to improve resistance spot weld strength is to add a high-strength adhesive to the weld. Figure 1 illustrates the strength improvement obtained in static conditions when crash adhesive (in this case, Betamate 1496 from Dow Automotive) is added. The trials were performed with 45-mm-wide and 16-mm adhesive bead samples.
Figure 1: Tensile Shear Strength and Cross Tensile Strength on DP 600.1
Another approach to improve the strength of welds is done by using laser welding instead of spot welding. Compared to spot welding, the main advantage of laser welding, with respect to the mechanical properties of the joint, is the possibility to adjust the weld dimension to the requirement. One may assume that, in tensile shear conditions, the weld strength depends linearly on the weld length as indicated in the results of a trial 1, shown in Figure 2.
Figure 2: Tensile-shear strength on laser weld stitches of different length.1
However, a comparison of spot weld to laser weld strength cannot be restricted to the basic tensile shear test. Tests were also conducted to evaluate the weld strength in both quasi-static and dynamic conditions under different solicitations, on various AHSS combinations. The trials were performed on a high-speed testing machine, at 5 mm/min for the quasi-static tests and 0.5 m/s for the dynamic tests (pure shear, pure tear or mixed solicitation, as shown in Figure 3). The strength at failure and the energy absorbed during the trial were measured. Laser stitches were done at 27mm length. C- and S-shape welds were performed with the same overall weld length.
Figure 3: Sample geometry for quasi-static and dynamic tests.1
The weld strength at failure is described in Figure 4, where major axes represent pure shear and tear (Figure 4). For a reference spot weld corresponding to the upper limit of the weldability range, globally similar weld properties can be obtained with 27mm laser welds. The spot weld equivalent length of 25-30 mm has been confirmed on other test cases on AHSS in the 1.5- to 2 mm thickness range. It has also been noticed that the spot weld equivalent length is shorter on thin mild steel (approximately 15-20 mm). This must be considered when shifting from spot to laser welding on a given structure. There is no major strain rate influence on the weld strength; the same order of magnitude is obtained in quasi-static and dynamic conditions.
Figure 4: Quasi-static and dynamic strength of welds, DP 600 2 mm+1.5 mm.1
The results in terms of energy absorbed by the sample are seen in Figure 5. In tearing conditions, both the strength at fracture and energy are lower for the spot weld than for the various laser welding procedures. In shear conditions, the strength at fracture is equivalent for all the welding processes. However, the energy absorption is more favorable to spot welds. This is due to the different fracture modes of the welds; for example, interfacial fracture is observed on the laser welds under shearing solicitation. Even if the strength at failure is as high as for the spot welds, this severe failure mode leads to lower total energy absorption.
Figure 5: Strength at fracture and energy absorption of Hot Rolled 1500 1.8-mm + DP 600 1.5-mm samples for various welding conditions.1
Figure 6 represents the energy absorbed by omega-shaped structures and the corresponding number of welds that fail during the frontal crash test (here on TRIP 800 grade). It appears clearly that laser stitches have the highest rate of fracture during the crash test (33%). In standard spot welding, some weld fractures also occur. It is known that AHSS are more prone to partial interfacial fracture on coupons, and some welds fail as well during crash tests. By using either Weld-Bonding or adapted laser welding shapes, weld fractures are mitigated, even in the case of severe deformation. As a consequence, higher energy absorption is also observed.
Figure 6: Welding process and weld shape influence on the energy absorption and weld integrity on frontal crash tests. 1
Up to a 20% improvement can be achieved in torsional stiffness, where the best results reflected the combination of laser welds and adhesives. Adhesive bonding and weld- bonding lead to the same stiffness improvement results due to the adhesive rather than the additional welds. Figure 7 shows the evolution of the torsional stiffness with the joining process. Optimized laser joining design leads to the same performances as a weld bonded sample in fracture modes, shown in Figure 8.
Figure 7: Evolution of the torsional stiffness with the joining process.1
Figure 8: Validation test case 1.2-mmTRIP 800/1.2-mm hat-shaped TRIP 800.
Top-hat crash boxes were tested across a range of AHSS materials including DP 1000. The spot weld’s energy absorption increased linearly with increasing material strength. The adhesives were not suitable for crash applications as the adhesive peels open along the entire length of the joint. The weld bonded samples perform much better than conventional spot welds. Across the entire range of materials there was a 20-30% increase in mean force when weld bonding was used; the implications suggesting a similarly significant improvement in crash performance. Furthermore, results show that a 600 MPa weld bonded steel can achieve the same crash performance as a 1000 MPa spot-welded steel. It is also possible that some down gauging of materials could be achieved, but as the strength of the crash structure is highly dependent upon sheet thickness, only small gauge reductions would be possible. Figure 9 shows the crash results for spot-welded and weld bonded AHSS.
Figure 9: Crash results for spot-welded and weld bonded AHSS.