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The rule of thumb estimates used in 1989 during my internship with an automotive stamping supplier were simple calculations for the peak load. Tonnage for trim and pierce operations depended on the length of line of trim, material thickness and the shear strength of the material. Tonnage for forming operations depended on the size of the form, material thickness and material tensile strength. These calculations typically over-predicted the tonnage requirement, but due to the relatively low strength compared to AHSS, the overall part size that dictated the required press size became the limiting factor rather than the tonnage requirement.
Applying these same rules of thumb to the advanced steels in use today will likely under-predict the tonnage requirements. To understand why, let us examine the guidelines I used over 30 years ago.
For piercing a hole: Tonnage = d * t * 80 Equation 1
In this equation d is the punch diameter in inches, t is the material thickness in inches, and it calculates tonnage in tons. This was a simple and effective way to estimate the tonnage of all the holes pierced. Equation 1 is a simplification of the proper calculation being the length of line doing the work, in this case the circumference of a circle, multiplied by the sheet thickness and the material’s shear strength (ꚍ). The generic equation for any type of piercing or trimming is Tonnage = P * t * ꚍ where P is the perimeter or length of line of the trim, t is the sheet thickness and ꚍ is the shear strength of the material. A typical estimate for the shear strength (ꚍ) of mild steel is 60% of the tensile strength (T). Therefore, the equation development for a simple hole piercing looks like:
Generic trim equation: |
Tonnage = P * t * ꚍ |
Equation 2 |
Specific for a round hole: |
Tonnage = πd * t * 0.6T |
|
Simplifying: |
Tonnage = d * t * 0.6Tπ |
|
Mild steel T = 300 MPa = 43.5 ksi: |
0.6 * 43.5 * 3.14 = 82 |
|
Pierce a round hole: |
Tonnage = d * t * 80 |
|
Knowing how the rule of thumb was derived allows us to highlight some possible sources of error. First, the equation assumes trimming of the full thickness. In reality, a typical trim operation for steel consists of 20% to 50% trimming and the remainder is breakage. The press needs to apply load only for the trimming portion. Second, shear strength is not a fixed percentage of tensile strength. The actual shear strength should be measured for each specific grade as the microstructure differences of the AHSS will affect the material strength in shear. Lastly each of these errors are multiplied since today’s AHSS material has a tensile strength of three to five times that of mild steel. To see this, we can consider a simple example of piercing a 1-inch hole in 0.06 inch (1.5 mm) thick mild steel. Mild steel tensile strength typically ranges from 40 ksi to 55 ksi (280 MPa to 380 MPa). Looking at Equation 1 relative to Equation 2 with low- and high -end assumptions:
Equation 1 estimate |
Tonnage = 1 * 0.06 * 80 = 4.8 tons |
Equation 2 minimum |
Tonnage = 3.14 * 0.06(20%) * 0.6(40) = 0.9 tons |
Equation 2 maximum |
Tonnage = 3.14 * 0.06(50%) * 0.6(55) = 3.1 tons |
This simple example shows sources of error that could lead to an estimate ranging from 0.9 to 4.8 tons to pierce a single hole. A similar exercise could apply to a drawing operation. In this situation, most rules of thumb attempt to use the perimeter or surface area of the part, the material thickness and the material tensile strength to predict the tonnage needed. Sources for error in this type of calculation include: 1) Using the perimeter of the draw area, tending to under-predict; 2) Using the surface area of the part, tending to over-predict; and 3) Using the tensile strength of the material, also tending to over-predict as it assumes the material is stretched right to the level of splitting. Correction factors have been developed over time, but it is still easy to see there are many possible sources of error in these types of calculations.
AHSS Magnifies Press Tonnage Prediction Challenges
A number of reasons explain why the inherent challenges with old-school rules of thumb are exaggerated with AHSS:
- Strength: The strength of today’s cold stamped steels is quite incredible. Where a mild steel may have a tensile strength of 280 MPa, it is now common to cold stamp dual phase (DP) steels and 3rd Generation steels with up to 1180 MPa. In addition, new materials having a tensile strength of 1500 MPa with enough elongation to allow for cold stamping are starting to enter the market. This five-fold increase in strength acts as a multiplying factor for any errors in traditional predictions.
- Formability: The formability of AHSS has also increased dramatically. Today a DP 590 steel and even a 980 3rd Generation steel can have nearly the same elongation as a high-strength low alloy (HSLA) steel of 30 years ago. This affords the part designers the ability to incorporate more complex forms into a part including using darts and beads to increase a part’s stiffness, tight radii and deeper draws. All of these add to the tonnage used and are generally not part of the old school rule of thumb calculations.
- Springback Corrections: Springback is linearly related to the yield strength of a material. Therefore, stamping AHSS grades require more features to be added to the die process to control springback. These may include draw beads (used to control material flow early in the press stroke), stake beads (used at the bottom of the stroke to minimize springback) and tighter radii (Figure 2). These features are typically off product, in the addendum, and are easily ignored by typical rule of thumb calculations.

Figure 2: Draw and Stake Bead PlacementA-6
- Hardening Curves: The complex microstructure of AHSS offers many advantages to increase formability. All AHSS grades produce microstructural phase transformations during the stamping process. This allows the lower yield strength in the as-rolled material, which aids in formability, to increase during the stamping operation. This yield strength increase can be as much as 100 MPa. Models that estimate these hardening curves of the material are ignored when doing hand calculations.
- Other Considerations: Lastly the typical rule of thumb calculations, as we have discussed, only consider the part characteristics. They generally do not include the other sources that consume energy during the stamping process including off-product feature (beads, pilot holes, etc.), spring stripper pressure, pad pressure from nitrogen springs or air cushions, driven cams and part lifters. Many of these could be ignored 30 years ago with mild steels, but they become more significant with the strength of today’s AHSS.
Next Steps
Accurately predicting press requirements is a decades-long, industry-wide issue. Auto/Steel Partnership (A/SP), a partnership between automotive OEMs, steel mills and affiliate suppliers, teamed up with formability software suppliers to improve press tonnage prediction accuracy. A/SP’s efforts, including this project, looks to bridge the gap between research laboratories and the shop floor.
Stamping companies should keep press tonnage monitors in good working order, and upgrade to systems that can capture full through-stroke force curves. Engaging with organizations like A/SP, OEMs and steel mills, allows efficient information sharing and capturing best-practices. Get the steel mill involved early, even in the die design phase. All steel mills have teams of application engineers to help OEMs and their suppliers transition into using the newest grades of steel – they want stampers to succeed and have the tools and data to help.
Read more about Press Tonnage Prediction in the expanded article.
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Advanced High-Strength Steel (AHSS) products have significantly different forming characteristics and these challenge conventional mechanical and hydraulic presses. Some examples include the dramatically higher strength of these new steels resulting in higher forming loads and increased springback. Also, higher contact pressures cause higher temperatures at the die-steel interface, requiring high performance lubricants and tool steel inserts with advanced coatings.
These and other challenges lead to issues with the precision of part formation and stamping line productivity. Using a servo-driven press is one approach to address the challenges of forming and cutting AHSS grades. Recent growth in the use of servo presses in the automotive manufacturing industry parallels the increased use of AHSS in the body structure of new automobiles. Click to read more about the Characteristics of Servo Presses and their Advantages.
Figure 1 shows the difference between the available motions of flywheel-driven mechanical presses verses servo driven mechanical presses. The slide motion of the servo press can be programmed for more parts per minute, decreased drawing speed to reduce quality errors, or dwelling or re-striking at bottom dead center to reduce springback.

Figure 1: Comparison of Press Signatures in Fixed Motion Mechanical Presses and Free-Motion Servo-Driven Presses.M-3
Press Force and Press Energy
Categorizing both mechanical and hydraulic presses requires three different capacities or ratings – force, energy, and power. Historically, when making parts out of mild steel or even some HSLA steels, using the old rules-of-thumb to estimate forming loads was sufficient. Once the tonnage requirements and some processing requirements were known, stamping could occur in whichever press met those minimum tonnage and bed size requirements.
In these cases, press capacity (for example, 1000 kN) is a suitable number for the mechanical characteristics of a stamping press. Capacity, or tonnage rating, indicates the maximum force that the press can apply without damaging its components, like the machine frame, slide-adjusting mechanisms, pitman (connection rods) or main gear bushings.
A servo press transmits force (not energy) the same way as the equivalent conventional press (mechanical or hydraulic). However, the amount of force available throughout the stroke depends on whether the press is hydraulic or mechanically driven. Hydraulic presses can exert maximum force during the entire stroke as tonnage generation occurs via hydraulic fluid, pumps, and cylinders. Mechanical presses exert their maximum force at a specific distance above bottom dead center (BDC), usually defined at 0.5 inch. At increased distances above bottom dead center, the loss of mechanical advantage reduces the tonnage available for the press to apply. This phenomenon is known as de-rated tonnage, and it applies to conventional mechanical presses as well as servo-mechanical presses. Figure 2 shows a typical press-force curve for a 600-ton mechanical press. In this example, when the press is approximately 3 inches off BDC, the maximum tonnage available is only 250 tons – significantly less than the 600-ton rating.

Figure 2: The Press-Force curve shows the maximum tonnage a mechanical press can apply based on the position of the slide relative to the bottom dead center reference distance. This de-rated tonnage applies to both conventional mechanical presses as well as servo-mechanical presses.E-2
Press energy reflects the ability to provide that force over a specified distance (draw depth) at a given cycle rate. Figure 3 shows a typical press-energy curve for the same 600-ton mechanical press. The energy available depends on the size and speed of the flywheel, as well as the size of the main drive motor. As the flywheel rotates faster, the amount of stored energy increases, reflected in the first portion of the curve. The cutting or forming process consumes energy, which the drive motor must replenish during the nonworking part of the stroke. At faster speeds, the motor has less time to restore the energy. If the energy cannot be restored in time, the press stalls. The graph illustrates how the available energy of the press diminishes to 25% of the rated capacity when accompanied by a speed reduction from 24 strokes per minute to 12 strokes per minute.

Figure 3: A representative press-energy curve for a 600 ton mechanical press. Reducing the stroke rate from 24 to 12 reduces available energy by 75%.E-2
Case Study: Press Force and Press EnergyH-3
Predicting the press forces needed initially to form a part is known from a basic understanding of sheet metal forming. Different methods are available to calculate drawing force, ram force, slide force, or blankholder force. The press load signature is an output from most forming-process development simulation programs, as well as special press load monitors. The topic of press force predictions will be covered in this Blog in the months ahead.
Most structural components include design features to improve local stiffness. Typically, forming of the features requiring embossing processes occurs near the end of the stroke near Bottom Dead Center. Predicting forces needed for such a process is usually based on press shop experiences applicable to conventional steel grades. To generate comparable numbers for AHSS grades, forming process simulation is recommended.
In Citation H-3, stamping simulations evaluated the forming of a cross member having a hat-profile with an embossment formed at the end of the stroke (Figure 4). The study simulated press forces and press energy involved for drawing and embossing a channel section from four steel grades approximately 1.5 mm thick: mild steel, HSLA 250/350, HSLA 350/450, and DP 350/600. Figures 5A and 5B clearly show that the embossing phase rather than the drawing phase dominates the total force and energy requirements, even though the punch travel for embossing is only a fraction of the drawing depth.

Figure 4: Cross section of a component having a longitudinal embossment to improve local stiffness.H-3

Figure 5: Embossing requires significantly more (A) force and (B) energy than drawing, even though the punch travel in the embossing stage is much smaller.H-3
Figures 6 and 7 highlight the press energy requirements, showing the greater energy required for higher strength steels. The embossment starts to form at a punch displacement of 85 mm, indicated by the three dots in Figure 6. The last increment of punch travel to 98 mm requires significantly higher energy, as shown in Figure 7. Note that compared with mild steel, the dual phase steel grade requires significantly more energy to form the part to home with the 98 mm travel.

Figure 6: Energy needed to form the component increases for higher strength steel grades. Forming the embossment begins at 85 mm of punch travel, indicated by the 3 dots.H-3

Figure 7: Additional energy required to form the embossment increases for higher strength steel grades.H-3
It is not only embossments that require substantially more force and energy at the end of the stroke. Stake beads for springback control engage late in the stroke to provide sidewall stretch. Depending on the design of the forming process, the steel into which the stake beads engage may have passed through conventional draw beads for metal flow control, and therefore are work-hardened to an even higher strength. This leads to greater requirements for die closing force and energy. Certain draw-bead geometries which demand different closing conditions around the periphery of the stamping also may influence closing force and energy requirements.
A more detailed Press Requirements article contains additional information and case studies. Read it here >>>
Resistance Welding Steel to Aluminium
This article summarizes a paper entitled, “Process, Microstructure and Fracture Mode of Thick Stack-Ups of Aluminum Alloy to AHSS Dissimilar Metal Spot Joints”, by Luke Walker, Colleen Hilla, Menachem Kimchi, and Wei Zhang, Department of Materials Science and Engineering, The Ohio State University.W-9
Researchers at The Ohio State University studied the effects of adding a stainless steel (SS) insert to a dissimilar Advanced High-Strength Steel (AHSS) to aluminum (Al) resistance spot weld (RSW). The SS insert was ultrasonically welded to the Al sheet prior to the RSW being performed. The purpose of the SS is to reduce the intermetallic layer that forms when welding steel to aluminum. This process increases the strength and toughness of the weld. In this study, the process is applied to three sheet (3T) stack up that contains one Al sheet and two 1.2 mm thick Press Hardened (PH) 1500 sheets. The joint strength is measured in lap shear testing and the intermetallic thickness/ morphology is studied after cross sectioning the welds.
During the microstructure evaluation it was noted that Al 6022 contained a larger nugget diameter as compared to the Al 5052 welds. A few potential reasons for the hotter welds were proposed including cleanliness of the electrodes, surface oxides, and thickness of the different alloys. The welds on the Al 5052 stack ups were made first on clean electrodes whereas the Al 6022 was made on potentially dirty electrodes that increased the contact resistance. The effects of different surface oxides are not likely given the SS sheet is ultrasonically welded but could still add to the higher heat input in the RSW. The Al 6022 is 0.2 mm thicker, which could increase the bulk resistance and decrease the cooling effect from the electrodes.
The 3T welds likely had much lower strength and toughness due to cracks that formed at the Al-SS insert interface. These can be attributed to an increase in intermetallic compound (IMC) thickness and the residual stress caused by the forge force. The IMC thickness was measured two ways: The first measurement was of the continuous IMC layer and the second was from the Al-Fe interface to the end of the IMC dendrites (Figure 1, 2 and Table 1). The Al 5052 observed the thickest continuous IMC layer but Al 6022 was close to the Al 5052 thickness. This can be attributed to the increased Si content of Al 6022 which has been shown to decrease the growth of Fe-Al intermetallics.

Figure 1: IMC in the Al Alloy 5052 to Stainless-Steel Weld.W-9

Figure 2: IMC in the Al Alloy 6022 to Stainless-Steel Weld.W-9

Table 1: IMC Thickness of Both the 5052 Weld and the 6022 Weld.W-9
Referencing Figure 3, the 2T stack-up has a higher tensile strength as well as significantly higher fracture energy absorbed compared to the 3T stack-ups. This is mainly attributed to the failure mode observed in the different stack-ups. The 2T welds had button pullout failure while 3T stack-ups had interfacial Failure.
![Figure 3: Failure Load and Fracture Energy [(A) Al to steel (Al-Us) welds and (B) steel to steel (Us-Us) welds (the 2T 6022 results are from previous work(10))]W-9](https://ahssinsights.org/wp-content/uploads/2021/12/fig4-process.jpg)
Figure 3: Failure Load and Fracture Energy [(A) Al to steel (Al-Us) welds and (B) steel to steel (Us-Us) welds (the 2T 6022 results are from previous work(10))]W-9
The Al 6022 contains higher Si content which likely decreased the growth of the continuous IMC layer but not the overall IMC layer (as seen in Figure 4 and Figure 5) due to higher weld temperatures. The joint strength of the welds in the 3T stack-ups were closer to the expected weld strength unless there was expulsion that caused a 5-kN drop in strength.

Figure 4: EDS Line Scan of the IMC in Location 2 on the 5052 3T Sample (SS stands for austenitic stainless steel 316).W-9

Figure 5: EDS Line Scan of the Intermetallic Layer at Location 1 on the 6022 3T Sample (SS stands for austenitic stainless steel 316).W-9
Laser Welding
This article is a summary of the paper entitled, “IMPROVEMENT OF DELAYED CRACKING IN LASER WELD OF AHSS AND 980GEN3 STEELS”, by Linlin Jiang, Kyle Kram, and Chonghua Jiang.L-62
Researchers from AET Integration, Inc. worked on developing welding techniques that mitigated delayed cracking issues when laser welding Advanced High-Strength Steels (AHSS) and 3rd Gen AHSS. Stitch welds are most likely to have delayed cracking issues therefore the test specimen were cross tension samples with stitch welds. The test was run with ten specimens for each material with the same parameters. The specimen were visually inspected after welding in intervals from 30 min to 12 hours for 48 hours. The specimen were then inspected using X-ray analysis, cross-sectioning, and scanning electron microscope (SEM) analysis. Cracks were observed in the weld schedules used in Figure 1 and 2, and no cracking was observed in the welding schedules developed by researchers as seen in Figure 3 and 4 by altering parameters such as laser power, travel speed, beam oscillation, and defocusing techniques. The techniques are currently patent-pending and were not discussed in the research paper. Further validation tests on 3rd Gen steels is expected in the future.

Figure 1: Delayed Crack in Weld of Material A. (Top) Crack from top surface, (Bottom) Cross Section of Crack.L-62

Figure 6: Delayed Cracking in Weld of Material B, (Top) X-ray, (Bottom) Cross section of crack.L-62

Figure 3: Examples of Visual Inspection Photographs. (Top) Top surface, Material A, (Middle) Top surface, Material B, (Bottom) Top surface, Material C.L-62

Figure 4: Examples of Cross Section Photographs. (Top) Cross section of weld center, Material A; (Bottom) Cross section of weld crater, Material A.L-62
Simulation
Predicting metal flow and failure is the essence of sheet metal forming simulation. Characterizing the stress-strain response to metal flow requires a detailed understanding of when the sheet metal first starts to permanently deform (known as the yield criteria), how the metal strengthens with deformation (the hardening law), and the failure criteria (for example, the forming limit curve). Complicating matters is that each of these responses changes as three-dimensional metal flow occurs, and are functions of temperature and forming speed.
The ability to simulate these features reliably and accurately requires mathematical constitutive laws that are appropriate for the material and forming environments encountered. Advanced models typically improve prediction accuracy, at the cost of additional numerical computational time and the cost of experimental testing to determine the material constants. Minimizing these costs requires compromises, with some of these indicated in Table I created based on Citations B-16 and R-28.

Table I: Deviations from reality made to reduce simulation costs. Based on Citations B-16 and R-28.
Yield Criteria
The yield criteria (also known as the yield surface or yield loci) defines the conditions representing the transition from elastic to plastic deformation. Assuming uniform metal properties in all directions allows for the use of isotropic yield functions like von Mises or Tresca. A more realistic approach considers anisotropic metal flow behavior, requiring the use of more complex yield functions like those associated with Hill, Barlat, Banabic, or Vegter.
No one yield function is best suited to characterize all metals. Some yield functions have many required inputs. For example, “Barlat 2004-18p” has 18 separate parameters leading to improved modeling accuracy – but only when inserting the correct values. Using generic textbook values is easier, but negates the value of the chosen model. However, determining these variables typically is costly and time-consuming, and requires the use of specialized test equipment.
Hardening Curve
Metals get stronger as they deform, which leads to the term work hardening. The flow stress at any given amount of plastic strain combines the yield strength and the strengthening from work hardening. In its simplest form, the stress-strain curve from a uniaxial tensile test shows the work hardening of the chosen sheet metal. This approach ignores many of the realities occurring during forming of engineered parts, including bi-directional deformation.
Among the simpler descriptions of flow stress are those from Hollomon, Swift, and Ludvik. More complex hardening laws are associated with Voce and Hockett-Sherby.
The strain path followed by the sheet metal influences the hardening. Approaches taken in the Yoshida-Uemori (YU) and the Homogeneous Anisotropic Hardening (HAH) models extend these hardening laws to account for Bauschinger Effect deformations (the bending-unbending associated with travel over beads, radii, and draw walls).
As with the yield criteria, accuracy improves when accounting for three-dimensional metal flow, temperature, and forming speed, and using experimentally determined input parameters for the metal in question rather than generic textbook values.
Failure Conditions
Defining the failure conditions is the other significant challenge in metal forming simulation. Conventional Forming Limit Curves describe necking failure under certain forming modes, and are easier to understand and apply than alternatives. Complexity and accuracy increase when accounting for non-linear strain paths using stress-based Forming Limit Curves. Necking failure is not the only type of failure mode encountered. Conventional FLCs cannot predict fracture on tight radii and cut edges, nor can they account for dimensional issues like springback. For these, failure criteria definitions which are more mathematically complex are appropriate.
Constitutive Laws and Their Influence
on Forming Simulation Accuracy
Many simulation packages allow for an easy selection of constitutive laws, typically through a drop-down menu listing all the built-in choices. This ease potentially translates into applying inappropriate selections unless the simulation analyst has a fundamental understanding of the options, the inputs, and the data generation procedures.
Some examples:
- The “Keeler Equation” for the estimation of FLC0 has many decades of evidence in being sufficiently accurate when applied to mild steels and conventional high strength steels. The simple inputs of n-value and thickness make this approach particularly attractive. However, there is ample evidence that using this approach with most advanced high strength steels cannot yield a satisfactory representation of the Forming Limit Curve.
- Even in cases where it is appropriate to use the Keeler Equation, a key input is the n-value or the strain hardening exponent. This value is calculated as the slope of the (natural logarithm of the true stress):(natural logarithm of the true strain curve). The strain range over which this calculation is made influences the generated n-value, which in turn impacts the calculated value for FLC0.
- The strain history as measured by the strain path at each location greatly influences the Forming Limit. However, this concept has not gained widespread understanding and use by simulation analysts.
- A common method to experimentally determine flow curves combines tensile testing results through uniform elongation with higher strain data obtained from biaxial bulge testing. Figure 1 shows a flow curve obtained in this manner for a bake hardenable steel with 220 MPa minimum yield strength. Shown in Figure 2 is a comparison of the stress-strain response from multiple hardening laws associated with this data, all generated from the same fitting strain range between yield and tensile strength. Data diverges after uniform elongation, leading to vastly different predictions. Note that the differences between models change depending on the metal grade and the input data, so it is not possible to say that one hardening law will always be more accurate than others.

Figure 1: Flow curves for a bake hardenable steel generated by combining tensile testing with bulge testing.L-20

Figure 2: The chosen hardening law leads to vastly different predictions of stress-strain responses.L-20
- Analysts often treat Poisson’s Ratio and the Elastic Modulus as constants. It is well known that the Bauschinger Effect leads to changes in the Elastic Modulus, and therefore impacts springback. However, there are also significant effects in both Poisson’s Ratio (Figure 3) and the Elastic Modulus (Figure 4) as a function of orientation relative to the rolling direction. Complicating matters is that this effect changes based on the selected metal grade.

Figure 3: Poisson’s Ratio as a Function of Orientation for Several Grades (Drawing Steel, DP 590, DP 980, DP 1180, and MS 1700) D-11

Figure 4: Modulus of Elasticity as a Function of Orientation for Several Grades (Drawing Steel, DP 590, DP 980, DP 1180, and MS 1700) D-11
Complete material card development requires results from many tests, each attempting to replicate one or more aspects of metal flow and failure. Certain models require data from only some of these tests, and no one model typically is best for all metals and forming conditions. Tests described below include:
- Tensile testing [room temperature at slow strain rates to elevated temperature with accelerated strain rates]
- Biaxial bulge testing
- Biaxial tensile testing
- Shear testing
- V-bending testing
- Tension-compression testing with cyclic loading
- Friction
Tensile testing is the easiest and most widely available mechanical property evaluation required to generate useful data for metal forming simulation. However, a tensile test provides a complete characterization of material flow only when the engineered part looks like a dogbone and all deformation resulted from pulling the sample in tension from the ends. That is obviously not realistic. Getting tensile test results in more than just the rolling direction helps, but generating those still involves pulling the sample in tension. Three-dimensional metal flow occurs, and the stress-strain response of the sheet metal changes accordingly.
The uniaxial tensile test generates a draw deformation strain state since the edges are free to contract. A plane strain tensile test requires using a modified sample geometry with an increased width and decreased gauge length,
Forming all steels involves a thermal component, either resulting from friction and deformation during “room temperature” forming or the intentional addition of heat such as used in press hardening. In either case, modeling the response to temperature requires data from tests occurring at the temperature of interest, at appropriate forming speeds. Thermo-mechanical simulators like Gleeble™ generate such data.
Conventional tensile testing occurs at deformation rates of 0.001/sec. Most production stamping occurs at 10,000x that amount, or 10/sec. Crash events can be 2 orders of magnitude faster, at about 1000/sec. The stress-strain response varies by both testing speed and grade. Therefore, accurate simulation models require data from higher-speed tensile testing. Typically, generating high speed tensile data involves drop towers or Split Hopkinson Pressure Bars.
A pure uniaxial stress state exists in a tensile test only until reaching uniform elongation and the beginning of necking. Extrapolating uniaxial tensile data beyond uniform elongation risks introducing inaccuracies in metal flow simulations. Biaxial bulge testing generates the data for yield curve extrapolation beyond uniform elongation. This stretch-forming process deforms the sheet sample into a dome shape using hydraulic pressure, typically exerted by water-based fluids. Citation I-12 describes a standard test procedure for biaxial bulge testing.
A Marciniak test used to create Forming Limit Curves generates in-plane biaxial strains. Whereas FLC generation uses 100 mm diameter samples, larger samples allow for extraction of full-size tensile bars. Although this approach generates samples containing biaxial strains, the extracted samples are tested uniaxially in the conventional manner.
Biaxial tensile testing allows for the determination of the yield locus and the biaxial anisotropy coefficient, which describes the slope of the yield surface at the equi-biaxial stress state. This test uses cruciform-shaped test pieces with parallel slits cut into each arm. Citation I-13 describes a standard test procedure for biaxial tensile testing. The biaxial anisotropy coefficient can also be determined using the disk compression testing as described in Citation T-21.
Shear testing characterizes the sheet metal in a shear loading condition. There is no consensus on the specimen type or testing method. However, the chosen testing set-up should avoid necking, buckling, and any influence of friction.
V-bending tests determine the strain to fracture under specific loading conditions. Achieving plane strain or plane stress loading requires use of a test sample with features promoting the targeted strain state.
Tension-compression testing characterizes the Bauschinger Effect. Multiple cycles of tension-compression loading captures cyclic hardening behavior and elastic modulus decay, both of which improve the accuracy of springback predictions. Again, no standard procedure exists. The biggest challenge with this test is preventing buckling from occurring during in-plane compressive loading. Related to this is the need to compensate for the friction caused by the anti-buckling mechanism in the stress-strain curves .
Friction is obviously a key factor in how metal flows. However, there is no one simple value of friction that applies to all surfaces, lubricants, and tooling profiles. The coefficient of friction not only varies from point to point on each stamping but changes during the forming process. Determining the coefficient of friction experimentally is a function of the testing approach used. The method by which analysts incorporate friction into simulations influences the accuracy and applicability of the results of the generated model.
Studies are underway to reduce the costs and challenges of obtaining much of this data. It may be possible, for example, to use Digital Image Correlation (DIC) during a simple uniaxial tensile testing to quantify r-value at high strains, determine the material hardening behavior along with strain rate sensitivity, assess the degradation of Young’s Modulus during unloading, and use the detection of the onset of local neck to help account for non-linear strain path effects.S-110
Application of Advanced Testing to Failure Predictions
Global formability failures occur when the forming strains exceed the necking forming limit throughout the entire thickness of the sheet. Advanced steels are at risk of local formability failures where the forming strains exceed the fracture forming limit at any portion of the thickness of the sheet.
Fracture forming limit curves plot higher than the conventional necking forming limit curves on a graph showing major strain on the vertical axis and minor strain on the horizontal axis. In conventional steels the gap between the fracture FLC and necking FLC is relatively large, so the part failure is almost always necking. The forming strains are not high enough to reach the fracture FLC.
In contrast, AHSS grades are characterized by a smaller gap between the necking FLC and the fracture FLC. Depending on the forming history, part geometry (tight radii), and blank processing (cut edge quality), forming strains may exceed the fracture FLC at an edge or bend before exceeding the necking FLC through-thickness. In this scenario, the part will fracture without signs of localized necking.
A multi-year study funded by the American Iron and Steel Institute at the University of Waterloo Forming and Crash Lab describes a methodology used for forming and fracture characterization of advanced high strength steels, the details of which can be found in Citations B-11, W-20, B-12, B-13, R-5, N-13 and G-19.
This collection of studies, as well as work coming out of these studies, show that relatively few tests sufficiently characterize forming and fracture of AHSS grades. These studies considered two 3rd Gen Steels, one with 980MPa tensile strength and one with 1180MPa tensile.
- The yield surface as generated with the Barlat YLD2000-2d yield surface (Figure 5) comes from:
- Conventional tensile testing at 0, 22.5, 45, 67.5, and 90 degrees to the rolling direction, determining the yield strength and the r-value;
- Disc compression tests according to the procedure in Citation T-21 to determine the biaxial R-value, rb.

Figure 5: Tensile testing and disc compression testing generate the Barlat YLD2000-2d yield surface in two 3rd Generation AHSS Grades B-13
- Creating the hardening curve uses a procedure detailed in Citations R-5 and N-13, and involves only conventional tensile and shear testing using the procedure included in Citation P-15.

Figure 6: Test geometries for hardening curve generation. Left image: Tensile; Right image: Shear.N-13
- Characterizing formability involved generating a Forming Limit Curve using Marciniak data or process-corrected Nakazima data. (See our article on non-linear strain paths) and Citation N-13 for explanation of process corrections]. Either approach resulted in acceptable characterizations.
- Fracture characterization uses four plane stress tests: shear, conical hole expansion, V-bending, and a biaxial dome test. The result from these tests calibrate the fracture locus describing the stress states at fracture.
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