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.
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.
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.
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.
- 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
Testing to Determine Inputs for Simulation
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
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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Manufacturing precision welded tubes typically involves continuous roll forming followed by a longitudinal weld typically created by high frequency (HF) induction welding process known as electric resistance welding (ERW) or by laser welding.
Tubular components can be a cost-effective way to reduce vehicle mass and improve safety. Closed sections are more rigid, resulting in improved structural stiffness. Automotive applications include seat structures, cross members, side impact beams, bumpers, engine subframes, suspension arms, and twist beams. All AHSS grades can be roll formed and welded into tubes with large D/t ratios (tube diameter / wall thickness); tubes having 100:1 D/t with a 1mm wall thickness are available for Dual Phase and TRIP grades.
Figure 1: Automotive Applications for Tubular Components.A-35
As roll formed and welded tubes are used with mounting brackets and little else in some Side Intrusion Beams (Figure 2), or they can be used as a precursor to hydroforming, such as the Engine Cradle shown in Figure 3.
Figure 2: Side intrusion beams made from a welded tube with mounting brackets.S-34
Figure 3: The stages of a Hydroformed Engine Cradle: A) Straight Tube, B) After bending; C) After pre-forming; D) Hydroformed Engine Cradle. S-35
The processing steps of tube manufacturing affect the mechanical properties of the tube, increasing the yield strength and tensile strength, while decreasing the total elongation. Subsequent operations like flaring, flattening, expansion, reduction, die forming, bending and hydroforming must consider the tube properties rather than the properties of the incoming flat sheet.
The work hardening, which takes place during the tube manufacturing process, increases the yield strength and makes the welded AHSS tubes appropriate as a structural material. Mechanical properties of welded AHSS tubes (Figure 4) show welded AHSS tubes provide excellent engineering properties. AHSS tubes are suitable for structures and offer competitive advantage through high-energy absorption, high strength, low weight, and cost efficient manufacturing
Figure 4: Anticipated Properties of AHSS Tubes; A) Yield Strength, B) Total Elongation.R-1
The degree of work hardening, and consequently the formability of the tube, depends both on the steel grade and the tube diameter/thickness ratio (D/T) as shown in Figure 5. The degree of work hardening influences the reduction in formability of tubular materials compared with the as-produced sheet material. Furthermore, computerized forming-process development utilizes the actual true stress-true strain curve of steel taken from the tube, which is influenced by the steel grade, tube diameter, and forming process.
Figure 5: Examples of true stress – true strain curves for AHSS tubes made from Dual Phase Steel with 590 MPa minimum tensile strength.A-36
Bending AHSS tubes follows the same laws that apply to ordinary steel tubes. Splitting, buckling, and wrinkling must all be avoided. As wall thickness and bend radius decrease, the potential for wrinkling or buckling increases.
One method to evaluate the formability of a tube is the minimum bend radius. An empirically derived formulaS-36 for the minimum Centerline Radius (CLR) considers both tube diameter (D) and total elongation (A) determined in a tensile test with a proportional test specimen, and assumes tube formation via rotary draw bending:
The formula shows that a bending radius equal to the tube diameter (1xD) requires a steel with 50% elongation. Successfully bending low elongation material needs a greater bend radius. Consider, for example, a dual phase steel grade where the elongation of a sample measured off the tube is 12.5%. Here, the minimum bend radius is 4 times the tube diameter. The tube bending method, the use and type of mandrels, and choice of lubrication may all affect the CLR.
The engineering strain on the outer surface can be estimated as the tube diameter (D) divided by twice the Centerline Radius (CLR):
For example, if you are bending a 40 mm diameter tube around a centerline radius of 100mm, the engineering strain on the outer surface is approximately 40/[2*100] = 20%. As a rough estimate, successful bending requires the tube to have a minimum elongation value from a tensile test in excess of this amount. Otherwise, a larger radius or modifications to the forming process is needed.
Springback is related to the elastic behavior of the tube. Yield strength variation between production batches can lead to variation in the amount of springback. A rule of thumb is that a variation of ± 10 MPa in yield strength causes a variation of approximately ± 0.1° in the bending radius. In addition, a high frequency weld which is harder and stronger than the base material causes a maximum of approximately ± 0.1° variation in bending radius.S-36
The bending behavior of tube depends on both the tubular material and the bending technique. The weld seam is also an area of non-uniformity in the tubular cross section, and therefore influences the forming behavior of welded tubes. The recommended procedure is to locate the weld area in a neutral position during the bending operation.
Figures 6 and 7 provide examples of the forming of AHSS tubes. The discussion on Tailored Products describes tailored tubes, which may be further hydroformed.
Figure 6: DP steel bent to 45 degrees with centerline bending radius of 1.5xD using booster bending. Steel properties in the tube: 610 MPa yield strength, 680 MPa tensile strength, 27% total elongation. R-1
Figure 7: Hydroformed Engine Cradle made from a dual phase steel welded tube by draw bending with centerline bending radius of 1.6xD and a bending angle greater than 90 degrees. Steel properties in the tube: 540 MPa yield strength, 710 MPa tensile strength, 34% total elongation. R-1
- Due to the cold working generated during tube forming, the formability of the tube is reduced compared to the as-received sheet.
- The work hardening during tube forming increases the YS and TS, thereby allowing the tube to be a structural member.
- Successful bending requires aligning the targeted radii with the available elongation of the selected steel grade.
- The weld seam should be located at the neutral axis of the tube, whenever possible during the bending operation.
Three important points collectively highlight the need for high-speed testing:
- Tensile properties and fracture behavior change with strain rate.
- Conventional tensile tests using standard dogbone shapes take on the order of 1 to 2 minutes depending on the grade.
- An entire automotive crash takes on the order of 100 milliseconds, with deformation rates 10,000 to 100,000 faster than conventional testing speeds.
Characterizing the response during high-speed testing provides critical information used in crash simulations, but these tests often require upgraded equipment and procedures. Conventional tensile testing equipment may lack the ability to reach the required speeds (on the order of 20 m/s). Sensors for load and displacement must acquire accurate data during tests which take just a few milliseconds.
Higher speed tensile and fracture characterization also aids in predicting the properties of stamped parts, as deformation rates in stamping are 100 to 1,000 times higher than most testing rates.
Steel alloys possess positive strain rate sensitivity, or m-value, meaning that strength increases with strain rate. This has benefits related to improved crash energy absorption.
Characterizing this response requires use of robust testing equipment and practices appropriate for the targeted strain rate. Some techniques involve a tensile or compressive Split Hopkinson (Kolsky) Bar, a drop tower or impact system, or a high-speed servo-hydraulic system. Historically, no guidelines were available as to the testing method, specimen dimensions, measurement devices, and other important issues which are critical to the quality of testing results. As a result, data from different laboratories were often not comparable. A WorldAutoSteel committee evaluated various procedures, conducted several round-robins, and developed a recommended procedure, which evolved into what are now both parts of ISO 26203, linked below.
Published standards addressing tensile testing at high strain rates include:
The specific response as a function of strain rate is grade dependent. Some grades get stronger and more ductile as the strain rate increases (left image in Figure 1), while other grades see primarily a strength increase (right image in Figure 1). Increases are not linear or consistent with strain rate, so simply scaling the response from conventional quasi-static testing does not work well. Strain hardening (n-value) also changes with speed in some grades, as suggested by the different slopes in the right image of Figure 1. Accurate crash models must also consider how strain rate sensitivity impacts bake hardenability and the magnitude of the TRIP effect, both of which are further complicated by the strain levels in the part from stamping.
Figure 1: Two steels with different strength/ductility response to increasing strain rate.A-7
Tensile testing cannot be used to determine bendability, since these are different failure modes. Failure in bending is like other modes limited by local formability in that only the outermost surface must exceed the failure criteria.
ASTM E290A-26, ISO 7438I-8, and JIS Z2248J-5 are some of the general standards which describe the requirements for the bend testing of metals. In a Three-Point Bend Test, a supported sample is loaded at the center point and bent to a predetermined angle or until the test sample fractures. Failure is determined by the size and frequency of cracks and imperfections on the outer surface allowed by the material specification or the end user.
Variables in this test include the distance between the supports, the bending radius of the indenter (sometimes called a pusher or former), the loading angle which stops the test, whether the loading angle is determined while under load or after springback, and the crack size and frequency resulting in failure.
For automotive applications, the VDA238-100V-4 test specification is increasingly used. Here, sample dimension, punch tip radius, roller spacing, and roller radius are all constrained to limit variability in results. Figure 1 shows a schematic of the test.
Figure 1: Schematic of Bend Testing to VDA238-100, with Bending Angle Definition.
This video, courtesy of Universal Grip Company,U-5 describes the support rollers in the VDA238-100 test.
Calculation of the bending angle is not always straightforward. Bending formulas such as that shown within VDA238-100 assume perfect contact between the sheet metal and the punch radius. However, experimental evidence exists showing this contact does not always occur, especially in AHSS grades.
Figure 2 presents one example testing DP600 where the punch radius is larger than the radius on the bent sheet, leading to a physical separation between the punch and sheet.L-12
Figure 2: DP600 After Testing to VDA238-100. Note punch radius is larger than radius in bent sheet resulting in separation.L-12
Furthermore, bending tests do not always result in a round bent sheet shape and constant thickness around the punch tip, especially when testing 980MPa tensile strength steel grades and higher which have low strain hardening capability. Figure 3 shows pronounced flattening and thinning of the sheet below the punch tip after bending, occurring primarily on the side opposite the punch stretched in tension. Efforts to replicate this phenomenon in simulation have failed, since the underlying mechanism is not yet fully understood.
Figure 3: Flattening and Thinning Behavior after Bending.L-12
Results from bend testing are typically reported as the smallest R/T (the ratio between the die radius and the sheet thickness) that results in a crack-free bend. Many steel companies report minimum bend test limits for various grades and certain automakers include minimum bend test requirements in their specifications as well. Different steel companies and automakers may have different bend test methods and/or requirements, so it is important to understand those requirements and procedures to better match the material characteristics with the customer’s design and process expectations. The test methods could involve a bend of 60°, 90°, 180° as well as various radii, die materials, speeds, etc.
Figure 4 shows etched cross sections of different grades bend to either 0T (fold flat) or 0.5T radii for reference purposes.
Figure 4: Etched cross sections of various grades. Top row, left: 0T bend of DP350/600; Top row, right: 0T bend of HSLA450/550; Bottom left: 0.5T bend of TRIP 350/600; Bottom center: 0T bend of TRIP 350/600; Bottom right: 0.5T bend of DP 450/800.K-1
The ISO 16630 Hole Expansion Test and the VDA238-100 bend test are among the few standardized tests to characterize local formability, the term which describes when part and process design, in addition to sheet metal properties like strength and elongation, influence the amount of deformation the metal can undergo prior to failure.
Researchers have developed alternate tests to further investigate process parameters and more clearly understand and optimize non-steel related variables. Also important is the investigation of different strain states from the ones seen in the hole expansion and bending tests. Comparisons of the stretched or bent edge performance evaluating different process parameters using the same material help to better define optimum process parameters. Repeating the testing with different AHSS grades confirms if similar trends exist across different microstructures and strengths. Standardization of these alternate tests has not yet occurred, so use caution when comparing specific values from different studies.
Hole Tension Test
Microstructural damage in the shear affected zone reduces edge ductility. Damage has been evaluated with a modified tensile dogbone containing a central hole prepared by shearing or reaming, as shown in Figure 1. In contrast with a hole expansion test using a conical punch, the researchers described this as a Hole Tension test, which determines failure strain as a function of grade and edge preparation.
Figure 1: Hole Tension Test Specimen GeometryP-12
Edge Tension Test
A two-dimensional (2-D) edge tension test, also called Half-A-Dogbone test, also evaluates edge stretchability. There are multiple versions of this type of test, but they all are based on the same concept. Like a standard tensile test, the 2-D edge tension test pulls a steel specimen in tension until failure. Unlike a standard tensile test where both sides of the tensile specimen are milled into a “dog bone”, the 2D tension test uses half of a dogbone with different preparation methods for the straight edge and the edge containing the reduced section (Figure 2). The chosen preparation method for each face is a function of the parameter being investigated (ductility, strain, burr, and shear affected zone for example). Potential edge preparation methods include laser cutting, EDM, water jet cutting, milling, slitting or mechanical cutting at various trim clearances, shear angles, rake angles or with different die materials.
Figure 2: 2-D Edge Tension Test Sample. Note the edges are prepared differently based on the targeted property evaluated.
Side Bending Test
Instead of a dogbone or half-dogbone, some studies use a rectangular strip without a reduced section. Bending performance can be evaluated with a rectangular strip having one finished edge and one trimmed edge while preventing out-of-plane buckling, as shown in Figure 3.G-7
Figure 3: The side-bending test expands a trimmed edge over a rolling pin until detection of the first edge crack.G-7
Half-Specimen Dome Test
Deformation in these three tests occur in the plane of the sheet. Typical hole expansion tests, like production stampings, deform the sheet metal perpendicular to the plane of the sheet. However, hole expansion testing does not always give consistent test results. The half-specimen dome test (HSDT) also attempts to replicate this 3-dimensional forming mode (Figure 4), and appears to be more repeatable likely due to creating a straight cut rather than round hole.
In the HSDT, a rectangular blank is prepared with one edge having the preparation method of interest, like sheared with a certain clearance or laser cut or water-jet cut. The sample is then clamped with the edge to be evaluated over a hemispherical punch. The punch then strains the clamped sample creating a dome shape, with the test stopping with the first crack appears at the edge. Edge stretchability is quantified by measuring dome height or edge thinning or other characteristics.
Figure 4: Half-Specimen Dome Test sample. Arrow points to edge crack.S-12
Edge Flange Test
Flanging limits depend on the part contour, edge quality, and material properties. Non-optimal flange lengths – either too long or too short – will lead to fracture. Different tools can assess the influence of flange length, including the one shown in Figure 5 from Citation U-3.
Figure 5: Tool design to investigate flange length before fracture. Flange height: 40mm in left image, 20mm in right image.U-3
Physical tests using this tool show that optimizing sample orientation relative to the rolling direction leads to longer flange lengths before splitting.U-3 Figure 6 highlights the results from testing DP800.
Figure 6: Flange height limits as a function of orientation in DP800.U-3
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The Hole Expansion test (HET) quantifies the edge stretching capability of a sheet metal grade having a specific edge condition. Many variables affect hole expansion performance. By understanding the microstructural basis for this performance, steelmakers have been able to create new grades with better edge stretch capability.
Multiphase microstructures with large hardness differences between the phases, specifically islands of the very hard martensite surrounded by a softer ferrite matrix, may crack along the ferrite-martensite interface (Figure 1). The larger the size of the initiated damage site (due to edge shearing), the smaller the critical stress required for crack propagation.M-6 The microstructure and damage are key components of the Shear Affected Zone, or SAZ.
Figure 1: Features and mechanisms of damage initiation and propagation in Dual Phase steel.M-6
One metallurgical approach to improve sheared edge stretchability is targeting a homogeneous microstructure. Steel suppliers have engineered product offerings like complex phase steel, where extensive grain refinement (reducing the size of the ferrite and martensite grains) is achieved. Consequently, the size of the initial damage resulting from shearing is reduced, raising the critical stress for crack propagation to higher levels and reducing the likelihood for crack propagation. Additionally, reducing the difference in hardness between the soft ferrite phase and the hard martensite phase improves the hole expansion ratio. Changes in chemistry, hot rolling conditions and intercritical annealing temperatures are some of the methods used to achieve this. Such metallurgical trends can include a single phase of bainite or multiple phases including bainite and removal of large particles of martensite. This trend is shown in Figure 2, adapted from Citation M-11.
Figure 2: Hole Expansion as a Function of Strength and Microstructure. Adapted from Citation M-11.
An example of the impact of these modifications is shown in a paper published by C. Chiriac and D. HoydickC-10, where a 1 mm DP780 galvannealed steel was modified to produce a grade with improved hole expansion to achieve greater resistance to local formability failures such as edge fracture and shear fracture. These changes were made while retaining the same base metal chemistry and the same fraction of martensite in the structure, and resulted in similar tensile strength and total elongation but with a 50% increase in hole expansion (Table I and Figure 3). The key difference is a lower martensite hardness, and a smaller difference between the hardness of the martensite and ferrite. The modified DP grade has more homogeneous distribution of martensite with smaller ferrite and martensite grains (Figure 4).
Table I: Comparison of a conventional DP780 steel with a similar chemistry modified to improve hole expansion.C-10
Figure 3: Improvement in Hole Expansion improves with grade modifications and edge quality. DMR = drilled, milled, and reamed hole; EDL = Edge Ductility Loss index, the ratio of the hole expansion of the DMR hole to that of the punched hole.C-10
Figure 4: Comparison of the microstructure of a conventional DP780 steel (left) with a similar chemistry modified to improve hole expansion (right). Overall, there is the same fraction of martensite in both grades, but the modified chemistry has finer features.C-10
A presentation at a 2020 conferenceK-16 described a study which compared DP780 from six different global suppliers. Hole expansion tests were done on 1.4 mm to 1.5 mm mm thick samples prepared with either a sheared edge at 13% clearance, a sheared edge with 20% clearance, or a machined edge. Not surprisingly, the machined edge with minimal work hardening outperformed either of the sheared edge conditions. However, when considering only the machined edge samples, the hole expansion ratio ranged from below 30% to more than 70% (Figure 5). Presumably the only difference was the microstructural characteristics of the six DP780 products.
Figure 5: Variation in hole expansion performance from DP780 from 6 global suppliers.K-56
The microstructural differences that enhance local formability characteristics may be detrimental to global formability characteristics and vice versa. Conventional dual phase steels, with a soft ferrite matrix surrounding hard martensite islands, excel in applications where global formability is the limiting scenario. These steels have a low YS/TS ratio and high total elongation. However, the interface between the ferrite and martensite is the site of failures that limit the sheared edge extension of these grades. On the other end of the spectrum, fully martensitic grades are the highest strength steels available. These have a high YS/TS ratio, and low total elongation. Having only a single phase helps these grades achieve surprisingly high hole expansion values considering the strength, as seen in Figure 6.
Figure 6: Hole Expansion as a Function of Edge Quality and Microstructure. Adapted from Citation.H-7
Knowing that a higher volume fraction of martensite is needed to increase strength, combined with the awareness that minimizing the hardness differences between microstructural phases is needed to increase hole expansion (Figure 7), allows steelmakers to fine-tune their chemistry and mill processing to target specific balances of strength, tensile elongation, and cut edge expandability as measured in a tensile test.
Figure 7: Improved Hole Expansion by Reducing the Hardness Difference between Ferrite and Martensite.H-8
This expands the selection of grades from which manufacturers can choose. Traditional material selection and identification may have been based on tensile strength to satisfy structural requirements – DP980 is a dual phase steel with 980MPa minimum tensile strength. However, newly engineered grade options offer users an extra level of refinement depending on the functional needs of the part. Products can be specified as needing high tensile elongation, high hole expansion, or a balance of these two. In the example shown in Figure 8, note that all 3 grades have nearly identical tensile strength.
Figure 8: Engineered Microstructures Achieve Targeted Product Characteristics. (Data from Citations N-8 and F-5)
The influence of microstructure and the hardness differences between the phases is also seen in the hole expansion values of AHSS grades at strengths below 980 MPa. A study from 2016 shows the impact of a small amount of martensite on a ferrite-bainite microstructure.N-9 Both products compared had a microstructure of 80% ferrite. In one product, the remaining phase was only bainite, while the other had both martensite and bainite. The presence of just 8% martensite was sufficient to decrease the hole expansion capacity by 40%. (Figure 9).
Figure 9: High Hardness Differences in Microstructural Phases Decrease Edge Ductility at All Strength Levels. Adapted from Citation N-9.
Rolling direction may also influence edge fracture sensitivity on some multiphase AHSS grades. When testing a sample, edge fractures may occur first at the hole edge along the rolling direction, which corresponds to a tensile axis in the transverse direction. If the chosen grade exhibits this behavior, locate stretch flanges perpendicular to the rolling direction when possible during die and process development to increase resistance to edge fracture. If this is not practical, identify locations where inserting scallops/notches in the stretch flange will not negatively impact the part structure, fit or die processing.
During die development and die try-out, it is important to use the production-intent AHSS grade – not just one that has the same tensile strength. Blank orientation relative to the rolling direction in these trials must also be production-intent. Often the blank die is the last completed die, so prototype blanks may be prepared by laser, EDM, water jet or even by hand during tryout. These cutting methods will have different sheared edge extension, as measured by the hole expansion test, compared with the production-intent shearing. These differences may be sufficiently significant to prevent replication of production conditions in tryout.