True-stress true-strain curves are less commonly used (Figure 4.1-2a). True stress is defined as the ratio of load to instantaneous area, or s
_T = P/A. Since A decrease faster than P decreases in the necking regime after maximum load on the engineering stress-strain curve, the true stress-true strain curve continues to increase over the entire straining region until the test is terminated by fracture. True strain is defined as the ratio of increase in length to instantaneous length. Thus, true strain, ε is ε = ln l/l_o. Therefor, tensile true strain is less than tensile engineering strain and compressive true strain is greater than compressive engineering strain. This is based on whether l becomes greater (tensile) or less (compressive) than l_o.

When log true stress is plotted as a function of log true strain (Figure 4.1-2b), additional information can be made as to whether the plastic deformation can be described by the common parabolic hardening law: s_T = K ε ⁿ.The values of n and K can be measured. These parameters describe quite accurately the strain hardening behavior of many steels. However, non-parabolic behavior is found for dual-phase steels (B-20, G-22, K-31) and many automotive aluminum alloys (G-10).

Two problems occur for non-parabolic hardening metals. First, the condition for the onset of necking is not predicted by the average n value. In this case, the onset of necking must be obtained by graphical solution of the equations:

ds_T/d ε = s_T for diffuse necking.

ds_T/d ε = s_T /2 for localized necking.

This is schematically shown in Figure 4.1-3 (G-10) where ds_T/d ε is the instantaneous change of true stress for a change in true strain. The terminal n value usually is lower than the average n value and necking occurs at a lower than the average n value and necking occurs at a lower strain than expected.

Second, since the n value is related to the ability of the metal to uniformly distribute strain, changes in n value as a function of strain directly affect its stretch formability. A high initial n value is considered by Rashid (R-5) to be an important factor in the excellent formability of dual-phase steels. Similar data were reported by Bucher (B-20).

A whole field of mathematical plasticity has evolved called “constitutive equations,” which attempt to describe mathematically the metal flow behavior. More than twenty such work hardening laws can be found in the literature (T-15). Four of the most common laws (Hollomon, Ludwik, Voce and Krupskowski/Swift) have been reviewed recently by Ratke and Welch (R-10) and by Truszkowski (T-17). This field of plasticity also was reviewed at the General Motors Research Symposium on “Mechanics of Sheet Metal Forming” (K-48), especially the papers by Hutchinson and Neale (H-44, H-45, H-46), Needleman (N-10), and Tozawa (T-13). Additional studies have also been reported by Mohammed (M-33) and Wagoner (W-2). However, detailed review of this specialized area is considered beyond the scope of this report.

4.1.4 COMMON TENSILE PROPERTIES

4.1.4.1 Yield Strength

Much emphasis in North America is placed on yield strength determination because many metals (especially higher strength steels and automotive alloys) are specified by yield strength. However, the yield strength can be difficult to define. For steels without YPE (Figure 4.1-1a) the yield strength is some arbitrary number, such as 0.2 percent offset form the modulus line. Steels with YPE have an upper and lower yield strength.

The upper yield strength is so dependent on test conditions that any usefulness of the value is questionable; unfortunately, too many upper yield strength values are measured and reported. While the lower yield strength appears to be an easily measured parameter in Figure 4.1-1b, the value is sometimes hard to define in practice because it changes radically depending on the number of active Lüder’s bands (C-6).

A parameter often misunderstood by users of sheet metal is yield point elongation. Special attempts should be made to present the interaction of YPE and formability in an understandable manner. A number of specific areas are:

a) The difference between YPE in an as-produced product and the return of YPE as a time-temperature event (B-10).

b) Discussion of the presence and absence of YPE as a function of different grades of steel (rim, AK, IF, and dual-phase) and aluminum alloys (5182-0 and 5182-SSF).

c) Interrelationship of YPE, Lüder’s bands (see Figure 4.1-4), “worms,” coil breaks, etc.

d) Description of the different methods of removing YPE (temper rolling, flex rolling, tension leveling and others), how they work, speed of return of YPE, etc. (R-18).

e) The reduction in the yield strength by removal of YPE (Figure 4.1-5). While this may assist formability by reducing buckle formation, etc., other formability parameters are not restored by temper rolling (C-5).

f) The increase in YPE as grain size is reduced is displayed in Figure 4.1-6 (B-10). This is especially important in higher strength steels since they have finer grain sizes.

All of the above information is know within the steel industry but has not been definitively accumulated in a single source easily accessible to the users of sheet steel.

Rockwell hardness measurements are related directly to the tensile strength of steel. Relationships between Rockwell hardness values and yield strength are less reliable (K-9). However, a special three scale hardness measurement procedure has been published (G-4) which claims to provide a good measure of the yield strength. Experience with this procedure is far too limited in scope and number of tests to comment on its reliability.

New emphasis is being placed on the wrinkle limit of the steel. While fracture is one forming limit, the other forming limit is wrinkling. Wrinkling has been related to the yield point of the steel (F-12).

4.1.4.2 Tensile Strength

In North America there is limited interest in the tensile strength per se, especially with respect to formability. In Japan, however, higher strength steels are specified by tensile strength is synonymous with the onset of diffuse necking and termination of uniform elongation in the remainder of the specimen for metals with parabolic hardening and no strain rate hardening. The tensile strength is a more precise definition and is easier to obtain from test data. Therefore, the popularity of the tensile strength has increased as the prime specification of strength.

The ratio of tensile to yield strength (TS/YS) sometimes is used as a measure of stretchability. For metals following parabolic hardening, a theoretical relationship between the YS/YS ratio and the work hardening exponent, n, can be derived – provided no yield point elongation is present (Figure 4.1-7). Experimental results show a similar relationship (K-31). A series of curves has been presented for steels with different values of YPE (k-31). Thus, for a given steel with a fixed n value, the TS/YS ratio increases as temper rolling removes YPE.

4.1.4.3 Work Hardening Exponent

The work hardening exponent or n value is important as a parameter that can be related to the ability of sheet metal to distribute strain more uniformly in the presence of a stress gradient (K-24, H-22); a high n value is desirable.

The n value has been shown by Backofen (K-29) to depend strongly on the yield strength of steel (Figure 4.1-8). A primary method to increase the strength of steel is to reduce the mean ferrite path, which in turn would reduce the n value (Figure 4.1-9).

The availability of computerized data acquisition systems has facilitated a closer examination of formability parameters as a function of strain. The work hardening exponent, n, seems to vary with strain for a wide range of sheet steel products.

Thus Lieberg, and Beyer have suggested a new parameter to rank sheet steel stretchability (L-11). Their O_m is the logarithmic strain associated with the maximum force in the tensile test; determination of the value does not require an extensometer, a uniform elongation, or adherence to any power law.

Examination of the n value for many steels will show that it varies as a function of strain for more than dual-phase steels. Lack of agreement between laboratories in n value determination has been shown to be caused by two-point n value determinations made at different portions of the stress-strain curve (K-31, T-22). Perhaps the n value derived from the initial portion of the curve will correlate with springback and other low strain phenomena. The n value at the onset of localized necking establishes the height of the Forming Limit Diagram. The distribution of strain in the stamping probably is related to some weighted average of the n value over the entire strain history.

4.1.4.4 Uniform Elongation

For metals following the equation s_T = K ε ⁿ with no strain rate hardening, elongation is related to the n value by the relation n = ln (1 + e_u) where e_u is the percent uniform elongation divided by 100. More practically, uniform elongation measurements are taken directly from the specimen or the load-elongation chart. However, a very flat load maximum common to sheet steels presents a problem in identifying the exact end point to measure.

sT = K’ ε ⁿ ε ^m

were K’ is a proportionality constant and ε is the strain rate (G-2). Typical values can be n=O and m=0.5 for superplastic material, while n=0.2 and m=0 for most low strength steels at room temperature.

Two methods are commonly used to obtain the m value (Figure 4.1-11). One method is to obtain stress-strain curves at different speeds. The difference in yield stress at a given strain can be measured for different strain rate changes (C-8). An argument opposing the use of this method (k-67) is that different microstructures in the different specimens have undergone different strain-strain-rate histories. A method to overcome this (Figure 4.1-11b) is to rapidly change the testing speed during the course of testing a single specimen. This is easily accomplished on a screw driven tensile test machine with a decade speed control or a computer controlled, hydraulic driven tensile test machine.

It has been known for some time (S-9, C-8, J-6, B-1, H-24, D-16, G-33) that some common tensile properties change as a function of speed. These are shown for an HSLA steel in Figure 4.1-12 and an aluminum alloy in Figure 4.1-13. The strain rate effects have been extensively evaluated (S-9, C-8). These studies reported that the behavior shown in Figure 4.1-12 was typical of all steel tested. It should be noted, however, that the curve labeled uniform elongation in reality is the elongation at the ultimate tensile strength. The elongation at ultimate tensile strength is the uniform elongation only for metals with a zero strain rate hardening exponent, m. Additional work to determine the effect of cold work and aging of steel (Figure 4.1-14) followed the same pattern. The extensive data are summarized in Figure 4.1-15, which shows the m value (obtained by testing different specimens at different speeds in Figure 4.1-11a) is a function of the static flow stress.

Automotive aluminum alloys have m values approaching zero or slightly negative (C-8, G-15). Thus, the data shown in Figure 4.1-13 are typical for these metals.

The previous discussion highlighted the influence of strain rate hardening on tensile properties for increasing testing speed. An even more important strain rate hardening effect takes place during a constant cumulative elongation rate test, during which the cross head speed of the tensile test machine remains constant. In the workpiece, the region undergoing thinning strain hardens and becomes resistant to additional deformation. This forces the deformation to the less deformed neighboring elements. In a like manner, as the local strain rate increases in areas undergoing thinning (or necking), the strain rate hardening in these regions forces deformation to occur in areas undergoing a slow down in the rate of deformation (outside of the neck). For metal s with a positive m value, the neck is “turned off” or at least delayed. For metals with a negative m value, the growth of the neck is accelerated by strain rate softening.

The stress-strain curves in Figure 4.1-16 emphasize the influence of the m value. Even a small m can produce quasistable flow (characterized by a nearly constant maximum load) over an appreciable strain range (G-10). This quasistable flow or post uniform elongation is shown in Figure 4.1-17 as a function of m value. An m value as low as 0.012 can postpone the onset of localized necking long enough to accumulate 40 percent of the specimen’s total elongation. In a dispersion-hardened zinc (Zn-Ti alloy) with a very low n of 0.05 and an m value of 0.06, nearly 90 percent of the total elongation is post-uniform deformation. In contrast, materials with a negative m value (Figure 4.1-16) rapidly localize deformation beyond maximum load.

The strain rate hardening contribution to the Forming Limit Diagram is important (S-4, M-38). This especially applies when comparing FLD’s for different classes of metals for which significant differences of m value can occur for equal n values. Muschenborn and Sonne (m-38) even suggest that the formability of heavily temper rolled steel is not reduced as much as the lowered n value suggests. They indicate that temper reductions less than 10 percent do little to affect the diffuse necking component of the deformation and the evaluating stretchability only by the n value may be in error.

4.1.4.7 Total Elongation

The total elongation is widely used as a ductility and formability parameter. The reasoning is simple: the more a metal can elongate in a tension test before fracture, the more it should elongate in a forming operation. As will be seen later, this is an oversimplified approach but one which has merit in several specific cases.

The total elongation strongly depends on specimen geometry. While a number of equations have been developed to correct total elongation values for different geometry, the following equation (K-57) appears to make the best overall correction:

      L₁²/A1 = L₂²/A₂

where L₁ and A₁ are gage length and cross-sectional area of geometry 1 and L₂ and A₂ are gage length and cross-sectional area of geometry 2. Note, however, that other test parameters, such as specimen alignment, strongly affect the total elongation.

As the strength of the steel increases, the total elongation decreases (Figure 4.1-10). The amount of reduction in total elongation depends on the strengthening mechanism. Total elongation as a function of yield strength and tensile strength is shown in Figure 4.1-18 and Figure 4.1-19 respectively for various hardening mechanisms.

4.1.4.8 Anisotropy

The r and r_m values traditionally have been measured from tensile specimens prepared at 0°, 45 ° , and 90° angles to the rolling direction for steel (K-24, W-19, W-20). Figure 4.1-20 shows that these three directions are excellent representations of the maximum and minimum values for common, low strength 1008 steels. The change of 4 value with angles from the rolling direction is not well defined for other steels; IF steel shows a maximum r value around 55° to the rolling direction (K-31). Other important angles sometimes can exist for aluminum and other FCC metals. The primary method for measurement of anisotropy is the traditional tensile test method. An additional test method is the Modul-r unit. This method may have some advantages for special applications.

The Modul-r does solve two problems associated with the traditional tensile specimen method of r value determination. Because the Modul-r unit functions on the oscillating beam theory, no plastic deformation of the specimen occurs. This avoids problems normally associated with cold worked samples, where the uniform elongation is so low that accurate strain measurements are difficult. In addition, the Modul-r test avoids problems often encountered when tensile samples with large amounts of yield point elongation are tested. The traverse of the sample by Luder’s bands often leads to discontinuities in the width of the sample; these discontinuities can cause significant errors in traditional r value measurements.

For hot-rolled steels, only a random orientation of the texture is developed and the r_m value is approximately one. This r_m = 1 value will persist, independent of yield strength, grain size, etc. (Figure 4.1-22). Therefore, low strength and high strength steels have equal r_m and equal deep drawability. In cold-rolled steels, however, the anisotropy is strongly affected by grain size (Figure 4.1-23). Therefore, unlike hot-rolled steels, the r values of cold-rolled steels should be dependent on strength – decreasing as the strength of the steel increases. Figure 4.1-24 shows r values for a number of steels as a function of tensile strength.

The anisotropy ratios were originally thought to be constant with increasing strain. In fact, one method to obtain accurate r values was to plot width strain as a function of thickness strain for different strain increments; the r value was the slope of the line drawn through the data points. Data (H-39) for steel in Figure 4.1-25 shows a remarkable change in r_m for certain steels. This same work generalizes the results as a function of texture strength and documents opposite effects for r values above and below one (Figure 4.1-26).

Other researchers (W-15, W-16, L-14) also have noted a change of r value with strain. The argument is proposed by Liu (L-14) that an instantaneous strain ratio should be measured. Grzesik and Vlad (G-41), however, argue that in spite of large changes in the preferred orientation which occurs on straining, relatively little variation in the normal plastic anisotropy takes place. For many steels, the slope of the curve of width strain as a function of thickness strain is constant beyond strain levels of 2 to 3 percent. However, extrapolating the curve back to the axes does not intersect at the origin. Thus, any curve drawn between the origin and any point on the curve (standard two point method for r value calculation) would create a slope of a different value. Modern biaxial extensometers, electronic data acquisition, and computer analyses allow for such measurements to be easily obtained during a tensile test.

Changes in steel compositions and processing can increase the r_m values close to the theoretical optimum of 3.0 obtainable in b.c.c. metals (Figure 4.1-27). An r value of 2.8 has been reported (B-14).

4.1.4.9 Shear Strength

An important parameter in calculation of blanking press loads, etc. is the shear strength of the metal, which traditionally has been some fraction of the tensile strength of the metal. Although various tables can be found in the literature (H-41, E-2), an easily remembered approximation (E-1) is:

   Shear Strength = (YS + TS)/2.

Miyauchi (M-30) has developed a simple in-plane shear test to evaluate planar shear deformation caused by differential metal flow in a stamping. Bauer (B-8) describes a torsion test of sheet steel which allows for the calculation of shear stress as a function of shear strain. The primary advantages of the torsion test are attainment of much higher strains than are possible with a tensile test and a principal stress state which corresponds to that found in deep drawing. Miyauchi (M-31) proposes a torsion buckling test.

4.1.5 COMPLICATING FACTORS

As described in Section 4.1.4.8 metals used by the automotive industry do not have properties which are the same in all directions. That is, the metals used are anisotropic. In addition, they respond differently to speed of deformation. Practical forming operations are performed with multiple stresses, different amounts of prestrain, and varying temperatures. In this section, these complicating factors are reviewed.

4.1.5.1 Biaxiality

Most forming is done under biaxial stress states and not uniaxial tension. However, the stress-strain formability parameters obtained by uniaxial tensile test have traditionally been applied to deformation induced under plane strain or balanced biaxial stress states. The developing literature (G-16, L-4, S-34, J-11, G-10, R-2). however, is beginning to show that this assumption is not correct. Figure 4.1-28 indicates the balanced biaxial stress-strain curve to be significantly above the uniaxial curve. Ghosh (G-16) reports that the n45 value for aluminum-killed steel to be 0.226 in uniaxial tension and 0.302 in biaxial tension. Preliminary results on automotive aluminum alloys (l-4) show the reverse to be true in that the biaxial curve is lower than the uniaxial curve. Sang and Nishihawa (S-5, R-15, C-4, D-13) have designed various experimental techniques to measure properties under different conditions of biaxiality. Much more work needs to be done in this important area (J-3).

In an attempt to better describe the relationship between the biaxial stress level versus uniaxial stress level, Yoshida et al (Y-10) have developed an X factor. The X factor takes into consideration the stress ratio dependence of work hardening, by including functions of r value and r-value-like anisotropy and the dependence of n value upon the mode and amount of deformation (Y-10). This X factor is shown to be related to the r value in Figure 4.1-29. Finally, in order to evaluate combined stress states - as opposed to simple uniaxial tension - Tozawa (T-14, T-13) has adhesively bonded stacked sheets together to compress the metal in the plane of the sheet (Figure 4.1-30).

Recent work was completed by Jun and Hosford (J-16), who tested as-received and prestained sheet samples in uniaxial tension, plane strain, and balanced biaxial tension. The prestrain also was conducted in uniaxial tension, plane strain, and balanced biaxial tension to complete a 3 x 3 matrix of prestrain and test conditions.

4.1.5.2 Temperature

Yet another complicating variable affecting the tensile properties of automotive metals is the temperature of deformation. Temperatures during deformation rarely have been measured. Most often, like the m value, the changes have been thought to be too small to be significant. However, experiments have shown that small changes in tensile strength with temperature (Figure 4.1-31) can produce large differences in formability (G-32). These temperature reductions in the sheet metal are made to locally strengthen the sheet metal in areas of high strain. Even without external modification of the temperature, the importance of thermal notches during deformation is being increasingly recognized. An important paper by Ayres (A-33) showed that tensile elongations for 1008 AK steel tested in air are affected adversely by thermal gradients and beneficially by strain-rate sensitivity at strain rates >10^-3 s^-1. These two effects appear to be competing influences that partially cancel out under non-isothermal conditions. However, the ductility can be improved by preventing thermal gradients by using isothermal water baths; the total elongation increased from 42 percent to 54 percent. Improved formability in sheet metal stampings can be expected by controlling these thermal gradients. Similar conclusions were reached by Kleemola and co-workers (K-39).

4.1.5.3 Test Speed

The speed of testing in the tensile test affects the resultant properties in many ways. Similarly, the speed of forming affects formability in a variety of ways. Test speed is not to be confused with deformation speed. Test speed is global – like the rotation of the earth. However, deformation speed can be different for each element of the test specimen.

Strain rate has a dual role. One is the global effect which is established by the test speed of the specimen; this will be discussed here. The other is the strain rate effect in the incipient neck and the resulting beneficial effect of strain rate hardening (discussed in Section 4.1.4.6).

Increased test speed will increase the yield and tensile strength as shown previously in Figure 4.1-12. Therefore, a standard test speed is important for reproducibility within a laboratory and between laboratories. The ASTM specifies test procedures for this purpose (A-16). However, the question is continually raised whether this speed is indicative of the properties encountered during either the forming cycle or in-service environments such as during crash management (K-52). A good case is made for testing at speeds equivalent to forming speeds, especially for predicting press and tool loading. A new problem now introduced is the ability of performing high speed tensile tests without introducing excessive vibrations into the dynamic tensile test machine (S-8). Other test speed effects are more difficult to measure. Faster test speeds decrease the time for dissipation of heat generated by the deformation. This, in turn, increases the thermal gradients developed along the length of the specimen (A-33). Thermal gradients not only affect the strength of the steel at each point along the specimen, but may achieve sufficiently high temperatures to initiate metallurgical modifications within the specimen.

4.1.5.4 Prior Cold Work

Many metals are deformed after being previously cold worked. A number of studies (B-14, H-20, H-23, T-5) have been conducted to evaluate the effect of prior cold work on various properties. Figure 4.1-32 shows the instantaneous n value as a function of strain for a various prior processing studies. Strain rate data for cold work samples are presented in Figure 4.1-14. The drop in uniform strain in Figure 4.1-33 indicates a rapid loss of flow stability when uniaxial tests are conducted after a biaxial prestrain. The residual uniform tensile elongation drops to zero for an effective biaxial prestrain of 0.08. Many questions are unanswered about the effect of prior cold work on metal properties (F-6).

4.1.6 SUMMARY

Of all the common laboratory tests, the tensile test probably is the most defined and best understood test available. The tensile test has certain advantages compared to other laboratory tests, including singular loading mode, no specimen curvature, no interface contact with a forming tool, and a simplified analysis.

Numerous properties can be obtained from the tensile test which, in turn, can be correlated to different forming modes in production stampings. Some properties, however, depend on the specific work hardening law used to best describe the actual behavior of the specimen.

Once a specific property from the tensile test can be correlated to a specific stamping (such as the normal plastic anisotropy ratio with deep drawability), the problem then becomes one of determining the range of the property (both maximum and minimum) which will assist in generating a satisfactory stamping.

Figure 4.1-1 Typical engineering stress-strain curves for steels without and with yield point elongation.

Figure 4.1-2 Comparison of true stress-strain curve with and engineering stress-strain curve.

Figure 4.1-3 The determination of the onset of diffuse necking for metals. The influence of srain rate hardening (m) is shown (G-10).

Figure 4.1-4 The relationship between Lüder's bands for steels having yield point elongation (B-10).

Figure 4.1-5 The lower yield stress decreases as percent temper rolling increases until the yield point elongation is eliminated. Then work hardening causes the yield stress to increase (C-6).

Figure 4.1-6 The relation between yield point elongation and grain size (B-10).

Figure 4.1-7 A theoretical relationship exists between the n value and the TS/YS ratio only for steels with no yield point elongation and parabolic hardening.

Figure 4.1-8 Al linear relationship exists between yield strength and n value for steels with a yield strength greater than 50 ksi (345 MPa) (K-29).

Figure 4.1-9 The strain hardening exponent n correlates with the log of the mean free ferrite path (B-10).

Figure 4.1.10 Both uniform elongation and total elongation decrease as a function of yield strength (F-2).

Figure 4.1-11 Two methods are commonly used to determine the strain rate hardening exponent, m.

Figure 4.1.12 The yield and tensile sterngths increase as fucntion of test speed for a high strength steel due to a positive m value (C-8).

Figure 4.1-13 The yield and tensile strengths typically remain unchanged with test speed for most automotive aluminum alloys with no strain rate hardening (C-8).

Figure 4.1-14 Yield strength as a function of strain rate for a cold-rolled rimmed steel sheet (S-9).

Figure 4.1-15 The strain rate hardening exponent, m, can be correlated to the static flow stress (S-9).

Figure 4.1-16 The shape of the stress-strain curve beyond maximum load (indicated by the vertical arrow is related to the strain rate hardening exponent (m) (G-10).

Figure 4.1-17 Post-uniform elongation is directly related to the strain rate hardening exponent (m) (G-10).

Figure 4.1-18 The total elongation for a given yield strength depends on the strengthening mechanism (K-55).

Figure 4.1-19 Total elongation for a given tensile strength is a function of the hardening mechanism (M-14).

Figure 4.1-20 The r value for sheet steel depends on specimen angle relative to the rolling direction (F-8).

Figure 4.1-21 The traditional correlation curve between E_m from the Module-r unit and manually determing r_m values from tensile specimens (M-35).

Figure 4.1-22 The r values are independent of yield strength for hot-rolled steels (F-2).

Figure 4.1-23 The r_m value is a function of grain size for cold-rolled steels (B-10).

Figure 4.1-24 The r_m can vary greatly as a function of tensile strength depending on the hardening mechanism (M-14).

Figure 4.1-25 The mean anisotropy ratio, r_m, has been shown to be a function of the strain level (H-39).

Figure 4.1-26 Experimental results show the change of r value as a function of strain (H-39).

Figure 4.1-27 The relative values of r₀, r₄₅, and r₉₀ depend upon the chemistry of the steel (B-14).

Figure 4.1-28 For steel, the stress-strain curve for balanced biaxial strain is higher than the curve for uniaxial strain. This causes a strain path change from biaxial prestrain to uniaxial tension to induce a lowering of the FLD (G-16).

Figure 4.1-29 The X factor, the stress ratio dependence of work hardening, is shown as a function of the r_m value (Y-10).

Figure 4.1-30 Sheets of metal are glued together to form pieces thick enough for compressive edge loading (T-14).

Figure 4.1-31 The tensile strength of steel decreases for steel as the test temperature increases (G-32).

Figure 4.1-32 Variation in n value with strain is shown for different amounts of prestrain temper-rolling (B-14).

Figure 4.1-33 The change in properties is given as a function of prestrain. Note how fast the uniform elongation is reduced to zero (G-16).

4.2 Forming Limit Diagrams

4.2.1 INTRODUCTION

Forming Limit Diagrams (FLD’s) have been empirically constructed to describe the strain states, or combinations of major (e1) and minor (e2) principal strains, at which a highly localized zone of thinning, or necking, becomes visible in the surface of sheet metal. The first published FLD for sheet steel appeared in 1963 for stretch forming the low carbon, low strength steel commonly used by the automotive and appliance industry – 0.036 inch (0.9mm) 1008 steel (K-15). Derived from laboratory rigid punch dome tests, the first FLD (Figure 4.2-1) showed the maximum strain (called fracture strain) that this steel and other metals could withstand as a function of the principal strain ratio. The criterion used to define the maximum strain was the onset of a band of highly localized thinning in the sheet surface. This criterion was selected because the appearance of a localized thinning or visible neck is sufficient cause for rejection of exposed stampings in the press shop. For unexposed stampings, the formation of the localized thinning signals the termination of further general deformation throughout the stamping and introduces potential structural defects which can affect in-service performance.

The empirically derived laboratory data were utilized in production press shop experiments from 1963-1965. The results of such work were summarized in a 1965 paper which laid the foundation for the present analysis technique (K-12). This paper showed that the maximum strain limits obtained from stretch formed production stampings were identical to those previously obtained in the laboratory. In addition, the ratio of the principal strains plotted on the absicca was replaced by the minor strain.

Additional press shop experiments conducted during the 1965 to 1968 period led to two companion papers in 1968. One by Keeler (K-21) detailed research conducted on the "right side of the FLD" where e2>0 for stretch forming and on by Goodwin (G-23) detailed research conducted on the "left side of the FLD" where e₂<0 for deep drawing. Taken collectively, the two limiting strain curves represent the onset of localized necking for different values of the minor strain encountered in sheet metal forming.

The FLD just described is known as the necking or instability FLD. Care must be taken not to confuse the instability FLD’s appearing in the literature with two other FLD’s which have appeared in the literature. One is the fracture FLD, measured when the specimen physically separates (G-39, K-35, B-6, N-6, T-3, D-10). The other published FLD is the wrinkling or buckling FLD (H-8, H-33), which details strain states for which wrinkling is possible. These other two types of FLD’s will be described in Sections 4.2-6 and 4.2-7).

4.2.2 SHAPE OF THE FLD

The Forming Limit Diagram (or Forming Limit Curve in some areas of the world) can be plotted in a variety of ways. The most common is shown in Figure 4.2-2. Here the vertical axis is the largest engineering strain in the plane of the sheet or major strain e1. If the circle is used as the grid for geometry, the major strain is obtained form the long axis of the resulting ellipse. The horizontal axis is the smallest engineering strain in the plane of the sheet or the minor strain e₂. This plot encompasses all possible combinations of major and minor strains encountered in practical sheet steel forming; it is sometimes denoted as “strain space” in the literature.

Data to be plotted in the strain space can be obtained in several ways. The most common measurements are made on a series of rectangular strips stretched over a punch. This method was proposed by Nakazima (N-6) and used by Veerman (V-4). Hecker (H-19) developed, streamlined, and studied in depth a comparable method now used by many laboratories. Instead of many punch configurations and test conditions, a single hemispherical punch – usually four inches or 100mm – is used to stretch to necking gridded sheet specimens securely clamped at the periphery. Different minor strains (e₂), and therefore different amounts of strain biaxiality, are obtained by varying the width of the specimen (Figure 4.2-2). Sometimes notched samples are required to avoid die radius failures in narrow strips (A-2).

Recently the literature has detailed other test techniques for obtaining onset of instability data. Some investigators use hydraulic bulge tests using masks of elliptical shape with different aspect ratios to obtain a series of positive minor strain values for establishing the right side of the FLD (M-16). Tensile specimens of varying widths with side incisions are used to generate varying degrees of negative minor strain to establish the left side of the FLD (M-16, H-6).

A completely different approach is suggested by Gronostajski and Dolny (G-35). They use modified Marciniak domes for their tests. Both the specimens and the spacers have circular arcs of varying radii cut into the width dimension of the sample. This specimen configuration is used to determine both the instability FLD and the fracture FLD. These authors argue that the modified Marciniak domes eliminate friction between material and tool surface, retain the flat surface of the specimens during the whole straining process, closely approach proportional straining for all strain paths, and require only one punch and one die to obtain the full FLD. Similar claims could be made by Azrin (A-35) and Ghosh (G-8, G-12). Their in-plane stretching technique consists of an elliptical groove machined in the center of a sheet which is subsequently stretched over a flat punch.

The greatest controversy in FLD determination is the procedure for determining the onset of the instability for which measurements are then plotted to form the FLD. Keeler (K-21) and Hecker (H-19) suggest stopping the deformation at the onset of necking. The strain for the circle directly over the location of the incipient neck is measured and is coded as to unnecked, incipient neck, and necked. The FLD is drawn between the unnecked and necked coded data points and through any incipient neck data points. A similar data acquisition system is used for measurements from production stampings. This technique, though harder to conduct, avoids the problems generated when attempting to measure the next whole circle adjacent to the failure location. The problem with the adjacent circle technique is that it delicately balances the necking strain for circles too close to the neck against the reduced strain level due to gradients for circles too far removed from the neck. Similar problems have been encountered when extrapolation of gradients across the fracture itself have been attempted (I-3). Some strain gradient estimation techniques (A-21) lead “to FLD’s which are quite different from those obtained previously by classical methods”. Keemola and co-workers argue that the change of the strain path towards the plane strain provides the “lowest limit strains” (K-40). Thus, the definition of the FLD and the measurement technique are critical in determining the shape and level of the FLD.

The steel, the shape of the FLD for proportional straining (linear strain path) shown in Figure 4.2-3 is used as a standard shape in many press shop applications (K-28, K-30), especially in North America. The vertical position of the FLD changes depending on the characteristics of the sheet steel which the FLD represents. In other applications, the FLD for a specific steel sample is empirically obtained in the laboratory through the use of Nakazima samples stretched over rigid punches (H-19). In this case, a regression analysis is used to determine the best fit curve. European determination of the FLD is based more on best-fit curves than on standard shape. In addition, the European curves consistently tend to have the minimum of the FLD at a minor strain level of + 0.05 (J-3, K-40). The cause of this is unclear but may be due to the FLD determination procedures used in Europe.

The use of the standard shape curve has simplified press shop application, since the entire curve is now defined by the plane strain intercept (FLD0). However, this standard shape does not apply to stainless steel and other steel alloys (R-6, K-28). A variety of FLD shapes are found for aluminum alloys. Interestingly, however, a number of the automotive aluminum alloys (2036-T4, 6009, 6010, 5182-0, etc.) have FLD’s with shapes similar to that of low carbon steel (H-14, S-35, H-16).

Another method of portraying the data is to plot the curve on a true major strain – true minor strain curve (Figure 4.2-4). The left hand side of the curve has been shown to be a straight line with a slope of -1 when plotted on a major true strain versus minor true strain graph (I-3). This means the left hand curve is equal to the strain allowed in plane strain plus a shear component ∊₁ = ∊₂). The right hand curve remains to be the original curve replotted in the true strain format (K-15, K-12, K-24).

The major – minor strains in the surface of the sheet metal at the onset of instability can be used to calculate the thickness strain (through the constancy of volume rule). Therefore, the curve in Figure 4.2-3 can be used to generate a thickness strain Forming Limit Diagram as shown in Figure 4.2-5 (K-11). This thickness FLD can be presented on either an engineering or true strain axis.

Finally, the Japanese literature portrays the FLD with a rotation of the axis (Figure 4.2-6). Here the traditional North American FLD is mirror imaged (rotated 180 degrees) about the y axis and then rotate 90 degrees clockwise.

A review paper on “Forming Limit Diagram – Sheets” was prepared for the 1974 Sagamore Conference (K-28). All aspects of FLD’s and the literature as of 1974 are detailed in that document. Therefore, the present review will provide only an update of the literature since the Sagamore Conference, and complements a recent review published by Mellor (M-20).

4.2.3 LEVEL OF THE FLD

The FLD is a characteristic of the steel and is independent of the stamping for which the steel is used. For example, different stampings will have different forming modes which are utilized in the formation of the stamping. These forming modes can be plotted on the Forming Limit Diagrams Figure 4.2-7). Therefore, the higher level of the FLD, the higher the strain which can be imparted to the stamping before “failure”. The level of the FLD depends on a number of parameters. These are reviewed below.

4.2.3.1 Sheet Thickness

A previous publication (K-28) indicated a sheet thickness correction in which the plane strain intercept (FLD₀) increases from a value of n for zero thickness sheet as shown in Figure 4.2-8. Additional studies showing this effect include H-1, C-3, H-32, H-25, K-40. Work on 2036-T4 aluminum (K-31) also has shown an increase in the FLD₀ with sheet thickness from an initial value approximately equal to the n value. However, the slope is substantially less. It is suggested that the aluminum and steel both undergo an increase in FLD₀ with sheet thickness simply because the neck is geometrically more diffused as the sheet thickness increases. The steel, however, has a large additional thickness influence which this author suggests is related to the strain rate hardening exponent, m.

The role of strain rate sensitivity in the thickness effect of the FLD has been mathematically modeled by Rao and Caturvedi (R-4, R-3). Studies of the thickness effect for dual-phase steels would be important for additional understanding of the physical basis for the thickness effects.

4.2.3.2 Mechanical Properties

A paper at Microalloying-75 (K-29) first indicated a systematic decrease in the FLD₀ as the n value of HSLA steels decreased below the 0.21 level. Additional work reported in the discussion of the Microalloying 75 paper (K-29) showed a whole family of sheet thickness – n value curves which could be used to determine an FLD₀ for any HSLA steel (Figure 4.2-9). Still to be fully explained is the reason why 70-30 brass (Figure 4.2-10) has an FLD almost equal to that of steel, even though its terminal work hardening exponent (n’) is almost twice that of AK steel. Some of the problem may be explained by the m value and sheet thickness effects described above but it is uncertain whether that is the total solution (A-35, G-12).

It might be expected that the normal plastic strain ratio, rm, affects the level of the FLD since the r value is known to be important in tensile tests, deep drawing, and other deformation modes. However, studies have shown the level of the FLD to be independent of the r value (K-28). The r value, however, does affect the strain path taken during deformation. Figure 4.2-11 shows this effect on the strain path taken by two tensile specimens. Thus, although the level of the FLD is independent of the r value, the permissible FLD ceiling strain is indirectly a function of the r value through the strain path (B-18, K-45).

The traditional FLD details the strain conditions for the onset of localized necking. Therefore, correlations between the level of the FLD and the uniform elongation are not expected. The uniform elongation does not incorporate the effect of the strain rate sensitivity which tends to delay the onset of the localized neck and increases the increment of post-uniform elongation. This is especially evident when the FLD’s of steel and 2036-T4 aluminum are compared (H-19). Both have approximately the same uniform elongation values (work hardening or n value controlled) but widely differing strain rate hardening (m value) characteristics.

Likewise, no correlation exists between the total elongation and the traditional FLD based on instability. The total elongation depends on the strain required for the localized neck to progress to fracture. The total elongation decreases with increasing biaxiality, but the FLD first decreases and then increases.

The literature recognizes this by publishing fracture FLD’s. These are discussed in Section 4.2.6. The literature contains numerous papers and reviews which attempt to show the role, or absence thereof, which steel cleanliness plays on the level and shape of the FLD (K-40, S-16, D-12, A-25, A-11, K-28, S-31, T-7, J-2, K-38). No clear, definitive conclusion can be reached.

4.2.3.3 Bending

Bending adds a positive strain component to the convex surface of the sheet and a negative strain component to the concave surface of the sheet. Somewhere between these two extremes is a neutral axis. The compressive (negative) strain and the zero strain in the neutral axis counteract the tensile strain in the convex surface and do not allow a through-thickness localized neck to develop. Strain readings taken on the convex surface (the surface usually selected for strain measurements) can exceed the FLD without the initiation of localized necking. This leads the press shop to consider the FLD to be too conservative (B-12, A-22).

Three methods have been used to correct the strain readings obtained on stampings before plotting on the FLD (K-31). The first is to average the strains from the convex and concave surfaces. In this manner the bending strains are subtracted from the convex surface strains, which are then plotted on the FLD. This method does not make any assumptions about the location of the neutral axis.

The second method is to calculate the bending strain from the measurement of the inside radius, the sheet thickness, and an estimation of the location of the neutral axis. Such a calculation will show that a 1t bend will add a strain of 33 percent to the convex surface.

The third method is to measure the thickness strain of the sheet, either by ultrasonic thickness measurements, cross-sectioning, or some other method. The major strain component then can be calculated from the thickness strain and the minor strain through the constancy of volume formula.

4.2.4 DEFORMATION PATH AND PRESTRAIN

The initial FLD’s were generated by single path deformation modes. These single paths also are known as proportional straining and will plot as a straight line on the FLD. Even here differences exist as to the definition of proportional straining – whether the strain path is a straight line in engineering strain or true strain space (R-9).

Most experimental research on FLD’s in the last decade has been concentrated on the effect of changes in strain path – especially radical changes. The two extreme boundary cases for steel (Figure 4.1-12) appear to be the upper curve formed by unixial tension followed by balanced biaxial tension and the lower curve formed by balanced biaxial tension followed by uniaxial tension. These multiple path FLD’s have been examined by numerous investigator’s (K-35, G-16, I-7, K-56, R-7, M-15, M-37, K-37, L-4, K-40, A-20, G-37, G-26, G-36).

A rule of thumb has been derived which summarized the results of the strain path research (R-9). This rule states that the addition of two linear strain path increments will cause:

- higher limit strains if the strain increment ratio is greater in the second stage than in the first stage (clockwise shift in strain path).

- lower limit strains if the strain increment ratio of the second stage is less than that of the first stage (counterclockwise shift in the strain path).

Matsuoka and Sudo (M-15) provided an interesting suggestion that strain space be divided into three zones. All strains in Zone 1 can be reached safely under all circumstances. Zone 2 contains strain states that can or can not be reached safely depending on strain path. Zone 3 contains strain states that can not be reached under any conditions. In Figure 4.2-12, Zone 1 is below the minimum forming limits curve (a = 0) and Zone 3 is above the maximum forming limits curve (a = 1.0).

The problem remains, however, to provide press shop documentation and case histories of the practical application of strain path changes in single or multiple forming stage operations (K-41, K-42, K-56, G-39). Most problem areas in forming can be attributed to deformation in the first major forming die.

4.2.5 MATHEMATICAL DESCRIPTION

A mathematical description and derivation of the FLD’s has been the other important research area relative to FLD’s during the last decade.

A mathematical description of FLD’s is important for simplicity of press shop calculations and for entering the FLD’s into computer plotting programs for computer graphic output. Here the conversion of the graphical FLD into an equation form is required. This was done initially for an S'E Recommended Practice (S-27). For low strength steels the following equations can be used to approximate the FLD (S-27, K-32):

When e2 is 0 to plus 30,
   FLD = (0.6e₂ + 25 + 350t) for t in inches
   FLD = (0.6e₂ + 25 + 13.8t) for t in mm.
When e2 is 0 to minus 30,
   FLD = (1.5e₂ + 25 + 350t) for t in inches
   FLD = (1.5e₂ + 35 + 13.8t) for t in mm.

Note that major and minor strains are expressed as a percent (not a decimal value) and the sign of e₂ is disregarded.

A more fundamental approach is the mathematical prediction of FLD’s from basic plasticity analyses of instability. A number of papers have addressed this problem (M-7, M-8, J-3, K-40, L-1, G-20, V-5, T-5) and it was reviewed at the General Motors Symposium on “Mechanics of Steel Metal Formability” (K-48). In general, problems have occurred when experimental FLD’s are compared to mathematical models derived from theory. While numerous “factors” have been introduced into the equations, the physical significance of many of these “factors” eludes many readers (K-40, B-19, D-10). A solid, physical understanding of the FLD still is lacking.

4.2.6 FRACTURE FORMING LIMIT DIAGRAMS

The previous discussion has been restricted to FLD’s derived for onset of a localized neck. The literature also contains FLD’s derived for the actual fracture of the specimen (P-3, B-6, N-6, T-3, D-10, I-3, G-39, K-35).

Fracture strain measurements are very sensitive to a number of test parameters. Grumbach and Sanz (G-39) showed the grid length used for measurements not only influenced the level of the FLD-fracture but also the shape (Figure 4.1-13). For zero gage length the fracture strain (e1) decreased uniformly as the degree of biaxiality is increased. As the gage length is increased, the FLD-fracture measurements included an increasing proportion of the uniform and post-uniform strain. When the gage length becomes large enough, the FLD-fracture duplicated the FLD-localized necking. Baret and Wybo (B-6) observed a grid length effect on the FLD-fracture but no FLD-localized necking.

Other factors which influence the FLD-fracture are steel grade, inclusion size and shape, sample orientation, degree of biaxiality, etc. (N-6, G-39, K-35, D-10, F-1). Because of this extreme sensitivity, it is conceivable that an FLD-fracture would have to be obtained not only for every coil of metal but for locations along the length of the coil to be truly representative of the coil.

The fracture FLD, therefore, seldom is utilized in the press shop. First, the fracture FLD will vary from point to point in a coil of steel as a function of cleanliness. This makes it difficult to generate a FLD representative of the coil. Second, necking is cause of rejection in many stampings, especially for those exposed applications. Third, once the localized neck has begun, all deformation is now confined within the neck. Therefore, even though the strain level at fracture in the neck is much higher than the strain at the onset of the localized neck, the active gage length for the additional straining is so small that little additional stamping depth is achieved.

For low strength steel, the fracture FLD is well above the instability FLD (Figure 4.2-14). As expected, the curve decreases continuously with increasing biaxiality (increasing minor strain, e₂). For some high strength steels, the fracture FLD has dropped below the localized necking FLD (Figure 4.2-15). This is seen in the laboratory as fracture without a localized neck-typically for large positive and large negative minor strains (K-31).

In one special case, the normal sequence of uniform deformation and diffuse necking was interrupted by ductile fracture prior to obtaining strain levels predicted by the FLD-necking (K-31). The steel was a relatively “dirty” 50 ksi (345 MPa) yield strength steel without inclusion shape control. Major strains of 65 percent were achieved in the rolling direction of the sample with a visible neck beginning to form perpendicular to the major strain direction. Suddenly, a sharp fracture occurred parallel to the rolling direction and cut through the neck in a perpendicular direction. Strains across the neck were only 40 percent with no evidence of a neck preceding fracture.

Based on the above discussion, steel producers should use techniques, especially inclusion shape control, to suppress ductile fracture initiation sufficiently to insure that the FLD-fracture is always at a strain level higher than the FLD-localized necking. This will allow for the maximum stretchability the steel is capable of producing.

4.2.7 BUCKLING/WRINKLING DIAGRAMS

Arguments have been made that fracture is not the only “failure” in forming. Wrinkles and buckles also contribute to stamping rejection (h-8, H-33). The criterion for the initiation of buckles is that the thickness strain is positive. An increase in thickness means a propensity of the sheet metal to buckling. The strain states which cause an increase in thickness can be shown on the same strain space used for the Forming Limit Diagram (Figure 4.2-16).

4.2.8 SUMMARY

The Forming Limit Diagram represents the combinations of major and minor surface strains which sheet metal can undergo without satisfying the conditions for the onset of localized necking. For this reason the FLD is a formability characteristic of the metal independent of the specific application of the metal. The data points plotted on the FLD are values obtained from the actual stamping under investigation. The proximity of the various data points to the failure line indicated the severity of the stamping.

For steel, a standard shaped FLD curve is used to make the analysis technique simple and useful for press shop application. The height of the curve-specified by FLD0 – is determined from a nomograph based on the thickness and the work hardening exponent of the steel. These quick analysis techniques are not applicable to alloys of steel or other metals. For these metals, experimental FLD’s must be obtained in the laboratory.

Additional Forming Limit Diagram research is still required for more complex forming conditions, such a prestrained metal and radical changes in strain path.

Figure 4.2-1 First published Forming Limit Diagram showing major strain as a function of the strain ratio (K-15).

Figure 4.2-2 A Forming Limit Diagram commonly is generated in the laboratory by clamping and stretching strips of varying width. The strain at the onset of localized necking (failure points in the diagram) is poltted as a function of the minor strain (H-19).

Figure 4.2-3 A standard shaped Forming Limit Deagram is used in many North American press shops. The height of the curve is set by the FLD₀ determined from the nomograph in Figure 4.2-9 (A-12).

Figure 4.2-4 The axes of the traditional Forming Limit Diagram are engineering strains. When plotted on true strain axes, the left side of the standard shaped FLD becomes a straight line at 45 degrees to the vertical axis (-34).

Figure 4.2-5 The conditions for the onset of localized necking (FLD) can be plotted in terms of the thickness ratio and the minor strain. The conversion is accomplished with the constancy of volume formula. The left side of the standard shaped FLD now becomes a constant thickness ratio (K-11).

Figure 4.2-6 The Japanese version of the FLD is plotted with a different orientation of the axes (I-7).

Figure 4.2-7 Different forming modes can be depicted as different strain paths on the FLD.

Figure 4.2-8 Effects of sheet thickness on the FLD₀ for steel and aluminum (K-31).

Figure 4.2-9 A nomograph to obtain the FLD₀ for a steel when the values of the work hardening exponent, n, and the sheet thickness are known (K-29).

Figure 4.2-10 The level of the FLD's for different metals depends upon both the work hardening exponent, n, and the strain rate hardening exponent, m (G-10).

Figure 4.2-11 The plastic anisotropy ratio, r, determines the strain path a tensile test and other deformation modes will follow prior to the onset of localized necking.

Figure 4.2-12 A variety of "FLD's" are possible if a radical change in strain path takes place (K-56).

Figure 4.2-13 True fracture strain as a function of the minor strain and the gage length used for the strain measurements (G-39).

Figure 4.2-14 Both the FLD-fracture and the FLD-localized necking are shown for an AK DQ steel (G-14).

Figure 4.2-15 A high strength steel with a large number of inclusions can have a FLD-fracture which will intersect the FLD-localized necking (K-31).

Figure 4.2-16 The "wrinkling FLD" delineates conditions for which buckles or wrinkles can occur. These conditions generally are those strain states which cause an increase in thickness.

4.3 Simulative Tests

4.3.1 INTRODUCTION

The Forming System is a complex interaction of material, lubricant, die, and press. By holding the incoming material constant, one of the primary components of the Forming System is held constant. This, in theory, should reduce one of the causes of press shop breakage. Therefore, press shops continually search for a test(s) which will permit evaluation of the formability of the incoming material.

Formability of incoming steel can be evaluated by three general types of tests. These are: 1) fundamental properties, 2) simulative tests, and 3) actual press shop trials.

Fundamental properties utilized for formability evaluation generally are those properties which have previously been shown to correlate to formability. Primary properties include work hardening exponent (n), strain rate hardening exponent (m), and anisotropy ratio (r). Other related properties are yield strength, uniform elongation, and total elongation. These properties are measured from a tensile specimen, which is deformed at a constant rate by a uniaxial stress in free space (no surface contact). These properties are widely used to assess the formability of sheet metal.

Two major determinations must now be made. The first is choosing the correct property or properties which can predict the performance of the sheet metal in stamping under investigation. For example, the work hardening exponent, n, is related to stretch forming but not to cup drawing. The problem now becomes one of determining whether the critical zone in the stamping is formed by the stretch forming mode. This may be difficult without an extensive evaluation of both the stress and strain states. The identical strain state can be created by either a stretch forming mode or a compressive mode. Tensile instability terminates the former but not the latter.

The second determination is selection of the proper test parameters. An argument is made that most sheet metal is formed with a biaxial stress state, while the traditional tensile test are uniaxial. A valid question therefore is whether various degrees of biaxiality change the n value. If so, a multiplicity of n value test would be required to match the exact biaxial stretch conditions of the stamping for which the steel is intended.

Other test parameters must also be selected for effective correlation with the stamping. These include deformation speed, test temperatures, and prior deformation conditions. The argument also is made that the surface/lubrication interactions are important in forming of actual stampings and these interactions are absent in fundamental property tests such as the tensile test. To counter this last complaint, some measurements of surface morphology and coefficients of friction can be made for each sheet material being characterized.

On the other extreme, press shop trials indicate the response of the total Forming System. However, failure of the system to produce a satisfactory stamping does not provide information as to which component(s) is at fault. The Forming System is, unfortunately, a dynamic system. Failure of the system to produce a satisfactory stamping simply means that the system components are mismatched at the time the stamping is made. Without extensive system checks it is difficult to say which component – such as the material – is at fault. Even worse, the current make/break evaluation method does not provide sufficient gradation between materials with different levels of formability. Another problem with press shop trials is the need to create a full size blank and bring it to the press. Finally, interjecting press shop trials into a production schedule is sometimes difficult. Simulative formability tests were designed to overcome these problems – a compromise between fundamental property evaluation and actual and actual press trials.

4.3.2 USES OF SIMULATIVE TESTS

Simulative tests can be used for three purposes in sheet metal forming:

   a. Evaluate incoming metal with respect to a historical baseline.
   b. Predict the success of the metal in a specific press application.
   c. Analyze the effects of modifying various parameters.

4.3.3 FORMING MODES

The most important description of any simulative test is the forming mode which it simulates. Some tests are single mode tests, while others are combinations of different modes.

   SINGLE MODE – STRETCH

Hole Expansion, Yoshida Buckling – (minor strain is negative), LDH, Free Bend, Stretch Bend, Draw Bead – (minor strain is zero), Olsen, Erichsen, Four-inch Dome, Marciniak – (minor strain is positive)

   SINGLE MODE – DRAW

LDR, Swift Flat Bottom

   COMBINATION – STRETCH PLUS DRAW

Fukui, Swift Round Bottom

4.3.4 TEST DESCRIPTIONS

4.3.4.1 Hole Expansion

The hole expansion test measures the ability of a sheet edge to be elongated. No standard test procedures have been developed for this test. Thus, various combinations of hole diameters and punch diameters, as well as different punch configurations, are used by different laboratories. Many test units in operation today have a common diameter of four inches (102mm). The diameter of the hole depends on the sheet metal being tested; a typical hole diameter of two inches (51mm) allows a maximum hole elongation of 100 percent.

One typical test procedure (Figure 4.3-1) starts with either an eight-inch (203mm) diameter circle or square blank placed in the test apparatus and a crimp or lock bead formed. The locking is required to insure that all deformation is confined to the enlargement of the hole and that metal does not move into the die opening from the binder area. The blank is removed from the test apparatus and a central hole is placed in the blank; the crimp bead is used by the punching device to accurately center the hole. The amount of hole expansion depends on the quality of the central hole. A milled hole will expand further than a punched hole which contains damaged edges. A poorly punched will expand less than a good quality hole. The hole expansion test, therefore, will allow different quality holes to be used as one of the test variables. The problem becomes one of reproducing the specific quality of a hole from one test specimen to another. The blank containing the hole is reinserted into the test apparatus and expanded by the punch. Different punch geometries can be used. While the hemispherical punch is the most common, conical and flat-bottom punches have been used in some laboratories. All the punches, however, generate an edge strain path which approximates a tensile test. During the circumferential elongation of the hole, the hole edge is free to contract in the radial direction. This creates the characteristic positive major strain and negative minor strain.

Hole expansion is continued until a predefined end point is reached. This usually is the onset of edge “checks” or edge notches. Deformation beyond this stage will rapidly lead to cracking. Traditionally, punch load measurements are not made for determining the end point since the onset of checking may not cause a sufficient drop in the punch load to terminate the test. For this reason, end point determination usually is done visually.

Directionality of sheet metal properties (anisotropy) usually causes the hole to deviate from a circular shape. Thus a series of diametrical measurements are necessary to determine an average hole expansion. The formula for the hole expansion is

where D_f is the final hole diameter and Di is the initial hole diameter.

A number of papers have been written about the hole expansion test (K-42, D-6, D-8, W-14, N-3). Originally used for studies of container flanging, the hole expansion test has grown in popularity for evaluating higher strength steels and the ability of various steels to withstand blanking damage.

Some general observations can be derived form the hole expansion tests:

• The primary factor which influences the hole expansion values is the condition of the initial hole. This is illustrated in Figure 4.3-2 where the expansion values for different hole qualities and different strengths of steel (with and without inclusion shape control) are presented.
• Substantially greater variability in the hole enlargements were observed with the drilled holes (initiation and propagation of cracks) than with punched holes (propagation only).
• The percent hole expansion is:
• directly related to:
     sheet thickness
     work hardening exponent, n
     total elongation
     normal anisotropy, r_m
     minimum r value
• and, inversely related to:
     yield strength
     tensile strength
     hardness

A good correlation was obtained between the stretch bend tests and the hole enlargement tests (D-2).

4.3.4.2 Yoshida Buckling (Handkerchief)

The Yoshida Buckling test (YBT) is a test to evaluate the susceptibility of sheet metal to buckling (Y-5, Y-8, H-12, J-4, Y-9, S-46, H-31, L-2, M-13, G-5, S-15). In this test, a square sheet metal sample is clamped on one set of diagonal corners and elongated in a tensile test frame (Figure 4.3-3). As the specimen is elongated, a series of wrinkles or buckles are generated parallel to the direction of elongation. The degree of width contraction and height of the wrinkles are measures of buckling.

4.3.4.3 Limiting Dome Height (LDH)

The Limiting Dome Height (LDH) test is a modified hemispherical dome test (A-12). Instead of a fully clamped blank, strips of varying widths are clamped on end by a lock bead and then deformed with a four-inch (102mm) diameter hemispherical punch (Figure 4.3-4). The different widths generate different minor strains at failure. The height at failure (height at maximum load) can be plotted as a function of strip width or minor strain. LDH curves for two different steels are schematically shown in Figure 4.3-5. Superimposed on the LDH curves are the strain paths commonly followed by three traditional laboratory tests.

The total height of the dome depend on two factors. The first is the maximum amount of strain the metal can withstand before failure. Obtained from the Forming Limit Diagram (FLD), this strain represents a limiting (ceiling) value. The second factor is how uniformly the strain is distributed without exceeding the ceiling. Since the dome height is proportional to the area under the strain distance curve, a high uniform strain will generate the largest dome height. The distribution of strain is governed both by the stretchability of the steel and the strain distribution characteristics of the blank-punch interface. These are also the characteristics which lead to good stretchability in a production stamping. Therefore, it is argued that the height in the LDH test can be related to the stretchability of production stampings.

The shape of the LDH curve approximates that of the FLD. However, the ability of the substrate and the interface to distribute strain in the presence of biaxial stress state will affect not only the height but also the shape of the curve.

The most common application of the LDH test is to measure and report only the minimum of the curve – LDH₀. In this case it is necessary only to measure the specimen width; measurement of the minor strain is unnecessary since the minimum occurs at plane strain.

Test procedures for the LDH test have not been standardized. Various researchers (G-9, A-30, M-23), as well as the North American Deep Draw Research Group of the American Society for Metals, have undertaken numerous cooperative programs to converge on the best procedure. The description which follows is intended only as a guide.

To determine the LDH₀, seven-inch (178mm) long specimens of the test metal with various widths are sheared. Five different width strips are tested, each strip being 1/8 inch (3mm) wider than the previous strip. The widths of the five strips are chosen to bracket the width which will generate a plane-strain condition – the minimum of the curve. For uncoated, low carbon, mild steel this width usually is approximately five inches (127mm).

Each blank is processed according to prescribed test procedures. Here testing philosophies diverge. One procedure dictates maximum cleaning and degreasing to remove ill oil and other surface contaminants. A second procedure requires the specimen to be tested as-received, since mill oil, prelubes, etc. affect both the test result and the press shop performance. A third procedure attempts to standardize the interface in order to measure only the steel stretchability. A low viscosity wash oil appears to provide a more standard condition than the various cleaning techniques.

The strip is centered in the test fixture and securely clamped. Absolute clamping is imperative. In this respect, the tooling must be highly standardized to provide interchangeable data. The strip is deformed by the hemispherical punch at a typical speed of ten inches per minute (254mm/min). The punch travel at maximum punch load is the Limiting Dome Height and is determined from autographic records or electronic maximum load detectors. These data allow the minimum of the LDH-width curve to be constructed and LDH0 determined. Different procedures to eliminate test variability include the use of standardized samples and “seasoning” of the punch after changing material type (m-23). The tool material can also be changed to duplicate soft tryout tools or hardened tools (B-16, M-24, B-17).

The common tensile properties which contribute to good stretchability also contribute to high LDH values: work hardening exponent (n), strain rate hardening (m). total elongation, tensile/yield ratio, etc. Experiments indicate that the high mean anisotropy ratio (r_m) important to cup drawing can be detrimental to the LDH value (H-21, N-12). the exact role of surface topography in controlling dome height needs further research. Some complex interactions of sheet surface material, sheet surface profile, lubricant, tool material, tool surface profile, interface pressure, and interface temperatures are present (B-16, B-17).

4.3.4.4 Free Bend

Bend tests are different from most other sheet metal forming tests in that a severe strain gradient is developed through the sheet thickness by the act of bending. A simple bend test (I-4) is made in one direction without reversing direction of bending (Figure 4.3-6). A more controlled variation of the bend test is to clamp a flat specimen against a die plate with a radius on one end and bend the strip to a specified angle by using a slowly applied force (Figure 4.3-7). Specifications may require the specimen used to be from either the rolling direction or the transverse direction of the sheet. The strip then is formed over a flat plate until its sides are parallel and a fixed distance apart relative to the strip thickness. This distance usually is given as a number times strip thickness, such as 4t for a four sheet thickness spacing. When required, no spacer may be specified and the strip is bent flat upon itself through a 180 degree bend angle (Figure 4.3-8). This is called a 0t bend. In simple bend tests, the requirement is to obtain the specified angle or shape under load without regard to possible springback after the load is removed.

The interpretation of results is a matter for the material specification. The metallurgical and mechanical factors important in all bending operations are the strength and ductility of the steel, the degree of inclusion shape control, and the condition of the edge of the test blank. Bendability is described by the radius to thickness ratio (in multiples of thicknesses) that the steel can be bent without developing cracks over a specified length. This, therefore, becomes a pass/fail system.

Typical bend test data are shown in Figures 4.3-9 and 4.3-10. In Figure 4.3-9 poor correlation was obtained between bendability and percent total elongation (T-8). Better correlation was obtained between bendability and percent reduction of area. The effect of stringer inclusions for different yield strength steels is shown in Figure 4.3-10.

A bendability definition which is superior to the pass-fail system is the length of the longest edge crack developed under constant bend conditions (K-55). This test combine outer fiber strain and the strain limits of the material. Using this criterion, the effect of sulfide shape control during bending has been assessed (Figure 4.3-11). The data in this graph shows the reduced bendability of an 80 ksi (550 MPa) steel compared to a 50 ksi (345 MPa) steel when neither steel has inclusion shape control. With inclusion shape control, both steels have equal bendability at a level significantly better than the 50 ksi (345 MPa) steel without inclusion shape control.

Like many other simulative tests, bending tests are often used to evaluate the adhesion of various metallic and painted coatings.

4.3.4.5 Stretch Bend

Some sheet metal forming operations are pure bending operations. Other operations are pure stretching operations. The latter is true for thin sheets and generous radii, where the radius/thickness ratio (R/t) is greater than 15 and the bending component is considered to be negligible compared to the uniform strains through the thickness. Many production parts, however, are made from thicker steels or, more commonly, have tighter radii in character lines, sharp punches, embossments, etc.

The Stretch Band test attempts to duplicate the combination of stretch plus bending. Two types of Stretch Bend tests have been suggested in the literature (D-11). The first is called the Angular Stretch-Bend Test (ASBT) shown in Figure 4.3-12. The angular punch has a single plane of symmetry. The rectangular blank used in the ASBT is eight inches (203mm) across the die opening and four inches (102mm) wide. A series of punches with different radii allow different ratios of R/t to be generated. More combinations can be obtained without increasing the number of punches by varying the thickness of the steel to be tested.

The blank is firmly clamped and stretched. The depth of punch travel (configuration height H) is the measure of stretch-bendability. The test conditions are monitored to insure that fracture occurs over the punch. Fracture in the unsupported region of the strip would simulate tensile failure instead of the desired stretch-bend mode. The second Stretch Bend test, a variation of the angular punch test, is the hemispherical punch test (HSBT). Here the punch has a double curvature. In this case, blanks of varying width are used to provide varying amounts of drawing-in (such as the Limiting Dome Height test).

The test results depend on the steels tested (Figure 4.3-13) and the test parameter R/t (Figure 4.3-14). The test results should be taken as a relative ranking of various steels rather than an absolute value which can be translated into design parameters for die construction.

Another combination test has been proposed by Rasmussen (R-8) whereby the shearing properties of the sheet in the direction of the prior bending axis are used to indicate the severity of the bend and its resistance to subsequent deformation.

4.3.4.6 Draw Bead

Draw Bead tests are used to simulate the deformation a sheet of metal undergoes as it moves through one or more draw beads located in the binder (blankholder) area of the die system. Two very distinct type of Draw Bead tests are in use. One is used to test the adherence of coatings, while the other is used to measure the coefficient of friction of sheet metal passing through the beads.

The coating adherence draw bead test is not a true sheet metal formability test. In these tests, the male bead and the female recess (Figure 4.3-15a) have identical radii. Any sheet metal inserted between the bead and the recess is heavily loaded at each shoulder due to the “negative” clearance which exists. The sheet metal is dragged (even scraped) through the beads. Visual examination of the surface, or a weight loss, is made after, typically, two passes through the beads.

The second type of Draw Bead test is called the Draw Bead Simulator (DBS) because it attempts to simulate the deformation of the sheet metal as it passes through an ideal bead (N-14, N-15). Here a coefficient of friction is calculated for each combination of sheet, lubricant, and bead metal. The interchangeable beads (Figure 4.3-15b) can vary from hardened steel to a soft zinc-based alloy used for die tryout. A positive clearance (gap dimension greater than metal thickness) is used to avoid any pinching or scraping action.

The normal force on the bead is not controlled but allowed to vary. Instead, the beads are interleafed a fixed amount and then locked. The pulling rate generally exceeds 50 inches per minute (1270mm/min) to duplicate more closely actual press speeds. The measured force to pull the specimen through a fixed bead has two components. One is the frictional force, which is used to calculate the coefficient of friction. The other is the force required to bend and unbend the sample as it passes around the beads. This force is obtained separately by pulling a second sample of the metal around frictionless roller beads. The force from the roller beads is subtracted from the force from the fixed beads to calculate a coefficient of friction.

Studies to date (B-16, N-14, N-15, K-16, K-17, B-17, W-13) have shown a unique value of the coefficient of friction for each combination of steel surface morphology, interface lubricant, and bead metal. One test result can not be extrapolated to any other test combination – each combination must be tested. The coefficient of friction generally increases as the test speed is decreased (K-17).

4.3.4.7 Olsen/Erichsen Dome

The Olsen Dome test is used as a stretchability evaluation test in North America. The Erichsen Dome test is a similar test used in Europe and Japan. The simple test procedures makes these two tests popular in the sheet metal forming industry. A good correlation has been found between these two tests (N-12). Therefore, comments will be restricted here to the Olsen Dome test.

The operational procedures of the Olsen Dome test are few (A-26). Specimen preparation requires only sharing a small rectangular blank. The test apparatus consists of a hydraulic cylinder to force a small diameter hemispherical punch into a sheet clamped by an annular die set activated by another hydraulic cylinder (Figure 4.3-16). Measurements are made of punch load and punch travel. Punch travel is stopped when the end-point is detected. The correct end-point is the maximum in the punch load-punch travel curve. This can be determined from a graphical plot of punch load versus punch travel. Some of the more advanced Olsen Dome test machines are equipped with automatic, electronic, load maximum detectors. The common practice for most Olsen tests, however, is to observe the load indicator dial for the load maximum and then to manually stop the punch travel. The load maximum is sometimes difficult to detect accurately. Therefore, some operators observe the test specimen for a visual onset of the necking failure.

Total punch travel is measured in thousandths of an inch; the Olsen value is the dome height in thousandths. Therefore, a 425 Olsen value is really 0.425 inches of punch travel to the point of test cutoff. The degree of necking and the response time for machine shutdown vary from operator to operator and even for repetitive tests with the same operator. This difference, especially for inter-laboratory correlations, can be as large as 60 Olsen units (A-7).

In theory the Olsen Dome test is a pure biaxial stretch test. As such the Olsen values should correlate with common stretchability parameters, especially the work hardening exponent (n). Available data, however, show extreme scatter (H-18, T-8, N-12, K-43). Little correlation is seen as a function of the n value (Figure 4.3-17). or the uniform elongation (Figure 4.3-18). Somewhat better correlation is obtained with percent transverse reduction in area (Figure 4.3-18). Correlation between the Olsen values and n were obtained only when oiled polyethylene sheets were used as a barrier lubricant indicating the extreme importance of frictional factors.

Research studies have highlighted a number of weaknesses in the Olsen Dome test which can account for the lack of correlation between the Olsen value and the work hardening exponent, n (A-7, T-8, H-18, K-27):

However, the Olsen Dome test can be very useful in evaluating certain parameters of the steel. For example, the Olsen Dome test often is used to show the presence of “orange peel” at high levels of strain prior to fracture. In addition, the type of fracture (ring versus highly directional) provides some indication of steel cleanliness.

The Olsen Dome test also is utilized for determining the adhesion of metallic and paint coatings to a substrate during stretch deformation. For this application, a “Scotch-Tape” peel test is usually included. However, even for these applications, a severe strain gradient form the pole to the rim of this small diameter dome complicates the test.

4.3.4.8 Large Diameter Hemispherical Stretch

An improved dome stretching test has been used over the last 20 years to evaluate pure stretch forming (K-15, H-24, H-14, H-18, H-19). The typical diameter of the hemispherical punch is 4 inches (102mm), although diameters from 3 to 12 inches (76 to 305mm) have been used. These dome tests are designed to eliminate the problems enumerated for the Olsen/Erichsen tests described above. They differ from the Olsen/Erichsen test because:

These large diameter dome tests are used for a variety of purposes, including evaluating the influence of steel substrate stretchability, coatings, lubricants, test speed, temperature, tool material, and tool surface coatings on the dome height. In the extreme, the rigid hemispherical punch has been replaced by hydraulic fluid (of fluid pressure simulated by a thick plug of rubber) to create maximum strain under conditions of balanced biaxial stress at the pole of the dome. Examples of the data obtained are shown in Figures 4.3-19 (H-18). The lack of correlation is due to the fact that stretchability is a function of the work hardening exponent (n) plus the strain rate hardening exponent (m). The value of (n + m) correlates with the total elongation when different classes of metals are studied. In Figure 4.3-19 the following property combinations are observed:

   Zn: low n, high m
   Steel: medium n, low m
   Brass: high n, zero m
   Aluminum: medium n, negative m

Thus, the dome heights of the metals shown in Figure 4.3-19 correlate well with total elongation in Figure 4.3-20.

Within a given class of metal, steel for example, correlations between the work hardening exponent (n) and dome height can be observed (Figure 4.3-21). Note here that the old terminology of cup height is used. The current terminology is cup height for cylindrical deep drawn cups and dome height for biaxially stretched, clamped sheets. In Figure 4.3-21, the dome heights for tests run with oiled polyethylene sheets are greater than those run without lubrication (dry). However, the scatter for the polyethylene lubricated domes is greater and the slope of the curve is reduced. Thus, the better lubricant tends to mask the effects of other variables such as material properties. While this masking has useful implications in the press shop, it reduces sensitivity of the simulative tests. Therefore, simulative tests should be designed to maximize the effect of the variable under study. In a like manner, the n values for steel, and therefore the dome heights, decrease as the yield strength of steel increases (Figure 4.3-22).

High normal anisotropy or strain ratio, r_m, (important for good cup drawability) has been shown to be detrimental to pure dome stretching (Figure 4.3-23). Here the circle arc elongation (e_ca) is related to the uniform elongation and therefore the n value of the material. Therefore, for a given e_ca (or n value) the dome height is inversely proportional to r_m values. No explanation for this effect has been proposed. It may be a direct effect of substrate stretchability or an indirect result of interface lubrication effects. Hecker (H-18) could not duplicate these results. Other dome tests have been conducted which evaluate test speed (Figure 4.3-24).

While the Large Diameter Hemispherical Stretch test has many advantages over the Olsen/Erichsen Dome test, it still retains the strain gradient and varying strain states from the pole to the rim of the dome. These point to point variations can cause problems in analysis of results.

Application of the Large Diameter Hemispherical Stretch test to actual production problems has begun. Brazier (B-18) used the four-inch (012mm) dome test to establish permissible pocket depths permissible pocket depths were established by the ratio of the dome height to dome diameter for various metals.

4.3.4.9 Marciniak Stretch

The Marciniak Stretch test (M-9, G-35) is a modified dome test (Figure 4.3-25). It was designed to overcome the severe strain gradients developed by the traditional dome tests using a hemispherical punch.

If a flat sheet of metal is simply clamped and a flat-bottom punch is pushed into the sheet, a very limited amount of stretch is possible, usually around the punch radius, before the strain level reaches failure and tearing occurs over the radius. The low level of strain that does occur under the flat (central) portion of the blank is balanced biaxial because stretching is equal in all directions.

To increase the level of straining in the flat bottom, metal must slide over the punch radius and transmit increasing force to the metal in the flat bottom. Strain can not be allowed to localize in the radius. This is extremely difficult to accomplish with a single sheet of metal. In theory, the punch radius could be replaced with a series of ball bearings to generate a frictionless radius. A more practical solution is to insert a carrier blank between the test blank and the punch (see Figure 4.3-25). A central hole punched in the carrier blank easily expands allowing metal to slide over the punch radius with relatively small applied force. The metal of the test blank on top of the carrier blank rides with the carrier blank. The metal of the test blank within the circumference of the carrier blank hole elongates in all directions.

Several specimen sequences are possible. The simplest is to use a square carrier sheet and test sheet with a minimum dimension of one inch (25mm) greater than the dimension of the lock bead. A common size is eight inches (203mm) for a four-inch (102mm) diameter punch. The carrier blank can be made from any stock steel or other metal with excellent formability; the test bank must fail before the edge of the enlarged hole in the carrier blank checks or tears. Carrier blank thickness is not specified, but must be on the same order as the test blank or else fracture can occur in the carrier blank.

The test blank and carrier blank are mated and placed in the test fixture to be crimped. This insures proper carrier hole alignment. The carrier blank is removed for punching of the central hole and then replaced. A two-inch (50mm) hole is common. The punch is driven into the pair of blanks (Figure 4.3-25) until the desired end point is reached. For a given test configuration, the amount of strain in the flat bottom is a function of punch depth. Therefore, blanks with identical amounts of strain can be generated as prestrained samples for other tests. Another end point is fracture, this end point is best determined by visual monitoring during deformation.

The Marciniak Stretch test is a specialized test used in only a few laboratories. Coated metals (both metallic and painted) can be formed to increasing levels of strain. The balanced biaxial strain state generates maximum increase in surface area. Changes in coating adhesion, ductility, and surface topography are several parameters easily measured. Because no contact is made with the punch in the central test area, print-through problems are eliminated. The specimens are flat for application of different visual tests. All the specimens can be painted after forming to simulate painting of actual deformed panels.

This test also indicates the internal cleanliness of the substrate based on the nature of the incipient fracture. A long, straight, rolling direction, line fracture with no necking elsewhere in the surface indicates a large inclusion. A surface with deep “wormy” necks in all directions over the entire surface indicates a very clean substrate. By evaluating samples from edge to edge of the sheet, a profile of internal cleanliness can be generated. This also can correlated with height at fracture (average strain) for the various samples.

4.3.4.10 Limited Draw Ratio (LDR)

The tests described previously were simulative stretch tests. The Limiting Draw Ratio test is a single mode draw test. This test evaluates the ability of a sheet metal to be drawn into a cylindrical cup (Figure 4.3-26). Test procedures have not been standardized (H-34, W-19, A-28, A-29). Typically, however, circular disks of increasing diameter are machined or punched. After deburring, they are inserted into the draw fixture. A clamping force is applied which is sufficient to prevent wrinkling but which is not so large as to add an unnecessarily large component to the draw load. Cups are drawn with increasing blank diameter until the blank diameter is reached at which breakage is encountered. The Limiting Draw Ratio is defined as that maximum ratio of blank diameter to punch diameter for the onset of breakage.

The absolute value of the LDR for any given lot of metal depends on die and punch geometry (Figures 4.3-27 and 4.3-28), test speed (Figure 4.3-29), temperature (Figure 4.3-30), lubrication, and holddown parameters. Once these are fixed, however, various metals can be ranked according to their relative capacity for deep drawing. The LDR increases with increasing sheet thickness (Figure 4.3-31).

The LDR has been shown to depend linearly on the normal anisotropy of the steel (Figure 4.3-32). The mean Young’s modulus can also be used to predict the LDR (M-35). When evaluated over a wider range of materials, however, the LDR-rm relationship has been shown to be a linear relation on a log-log plot (Figure 4.3-33); this figure by Atkinson and Maclean (A-28) is popular in many paper textbooks. Hosford, however, argues that b.c.c. and h.c.p. metals should not be compared on the same line (H-37). When comparing only b.c.c. metals, the curve sharply decreases slope for increasing rm (Figure 4.3-34). He contends that very large values of rm are not beneficial in increasing the LDR. One Japanese author (Y-10) claims that limiting depth is better defined by their X value rather than the rm values for a wide range of metals (Figure 4.3-35); the X value is a complex term incorporating work hardening anisotropy and changes in the yield locus.

There is a one-blank method for evaluating deep drawability which greatly reduces blank preparation (A-29, W-21). A blank of a given size is drawn into a cup of specified dimensions until the maximum load is exceeded. The blank is then clamped and the load to fracture the cup wall is measured. The greater the ratio of wall fracture load to draw load (Lu/Ld), the greater the deep drawability of the metal. This ratio can be empirically converted to a rm value of the metal (Figure 4.3-36).

4.3.4.11 Fukui Conical Cup

Very few stampings can be identified as being pure stretch or pure draw. Therefore, it can be argued that laboratory simulative tests which are intended to be pure stretch (such as the Olsen Dome test) or pure cup drawing tests (such as the Limiting Draw Ratio) should correlate poorly with actual press performance. A laboratory simulative test is needed which incorporates both modes of deformation.

Fukui Conical Cup test was designed to overcome this problem (F-9). In this test, a circular disk of metal is blanked in a separate operation; its diameter depends on the sheet metal thickness. This disk is then placed into a conical die (Figure 4.3-37). No holddown is used. This is possible because the ratio of blank diameter to sheet thickness is such that buckling does not occur. The absence of holddown eliminates many of the test variables associated with draw type tests, such as holddown load, die radii, roughness of the holddown surfaces, lubrication under the holddown, etc.

The deformation forces are generated by pushing a spherical ball into the center of the blank. Two deformation modes occur. The central portion of the blank is stretched over the ball. This loading also causes the blank to be pulled down the conical cavity. The circumference of the blank must decrease, generating the compressive stress component found in cup drawing. This test sums all the various components to produce a final cup height at failure. The higher the maximum height, the more formable the steel.

The traditional Fukui Conical Cup Values (CCV) – the ratio of final cup diameter to blank diameter – strongly depend on the product of n_m times r_m (Figure 4.3-38). The change in Fukui CCV values for AK steel as a function of test speed is shown in Figure 4.3-39. The end point of this test was modified by Goodwin and is called the “Formability Index” (G-24). The punch travel at maximum load is the Formability Index; in this respect, the modified Fukui test is similar to the Olsen Dome test. Goodwin showed that the Formability Index is related to the product of the minimum r value and the uniform elongation of the sample tested (G-24). The minimum r value for cold rolled steel usually occurs in the 45 degree direction to the rolling direction.

4.3.4.12 Swift Round Bottom Cup

The original Swift Flat Bottom test (C-14) was a pure cup drawing test. To make the test sensitive to both stretch and draw components, the flat bottom of the punch was replaced by a hemispherical head, typically four inches (102mm) in diameter (Figure 4.3-40). The test is conducted similarly to the Limiting Draw Ratio test. Blanks of increasing diameter are formed with the punch until breakage occurs.

4.3.5 SUMMARY

A wide variety of simulative tests are available in the literature. Some are well defined with all variables and test parameters specified. Others are essentially undefined with equipment and procedures varying from one investigator to another.

Each test represents an attempt to duplicate some portion of a complex stamping or a specific forming mode. Many are successful; others are not. As the critical forming mode in any given stamping changes, so the required test changes.

The current trend is to increase the number of simulative tests performed in order to broaden the characterization of a specific metal or lubricant. In addition, the simulative tests provide excellent data for verification of mathematical simulation models.

Figure 4.3-1 Schematic for the Hole Expansion test. Specimen after an increase of deformation is shown as dotted lines.

Figure 4.3-2 Hole expansion results are strongly influenced by edge condition. Steels indicated by l and l' were inclusion shape controlled steels. The 30, 50, 60, and 80 numbers refer to minimum yield strengths in ksi (H-29).

Figure 4.3-3 Yoshida Buckling test specimen (H-12).

Figure 4.3-4 Schematic for the Limiting Dome Height test. Specimen after an increment of deformation is shown as dotted lines.

Figure 4.3-5 Schematic showing Limiting Dome Height (LDH) for two different metals. The minimum is labeled LDH₀ (A-12).

Figure 4.3-6 Simple bend test for sheet metals (A-12).

Figure 4.3-7 Figure 4.3-7 Modified simple bend test. (a) is start of bend. (b) is finish flat using specified spacer designated as 1, 2, 3-t (times sheet thickness) (A-12).

Figure 4.3-8 Bend flat upon itself is the most severe test condition - referred to as 0-t (zero thickness) (A-12).

Figure 4.3-9 Bendability as a function of total elongation and transverse reduction in area for various strength steels (T-8).

Figure 4.3-10 Stringer Inclusions reduce bendability (T-8).

Figure 4.3-11 Using length of edge cracking as a measure of formability (K-55).

Figure 4.3-12 Schematic of the Stretch Bend test. Specimen after an increment of deformation is shown by the dotted lines.

Figure 4.3-13 Stretch-bent height as a function of yield strength (F-2).

Figure 4.3-14 Transverse stretch-band tests with and without rare earth treatment (F-6).

Figure 4.3-15 Schematic showing two types of Draw Bead tests. The coating adhesion test (left) heavily loads the strip with a negative clearance. The coefficient of friction test (right) measures pulling load for friction plus deformation (fixed bead) and pulling load for deformation only (roller bead).

Figure 4.3-16 Schematic of Olsen Dome test. Specimen after an increment of deformation is shown as dotted lines.

Figure 4.3-17 Olsen Dome height does not correlate well with the work hardening exponent, n (H-18).

Figure 4.3-18 Olsen Dome height correlates with transverse percent reduction in area (T-8).

Figure 4.3-19 Poor correlation of stretch dome height with the work hardening exponent, n, exists for different metals.

Figure 4.3-20 The stretch dome height correlates with total elongation (H-18).

Figure 4.3-21 Dome heights for large diameter domes formed with and without lubrication (H-18).

Figure 4.3-22 Maximum dome height of a round bottom dome is dependent on the work hardening exponent, n (F-2).

Figure 4.3-23 Dome height as a function of circle arc elongation (N-12, H-21).

Figure 4.3-24 Dome height at failure as a function of punch speed (G-10).

Figure 4.3-25 Schematic of Marciniak Cup test. Specimen after an increment of deformation is shown as dotted lines.

Figure 4.3-26 Schematic of Limiting Draw Ratio (LDR) test. Specimen after an increment of deformation is shown as dotted lines.

Figure 4.3-27 Limiting Draw Ratio (LDR) decreases as sheet thickness decreases (F-8).

Figure 4.3-28 Maximum Draw Ratio (LDR) as a function of both the die and punch profile radii (H-34).

Figure 4.3-29 Critical blank diameter for flat bottom punches increases with punch speed (F-7).

Figure 4.3-30 Limiting Drawing Ratio (LDR) decreases as the punch temperature increases (G-32).

Figure 4.3-31 Recommended Limiting Drawing Ratio (LDR) as a function of sheet thickness (J-13).

Figure 4.3-32 Limiting Drawing Ratio (LDR) as a function of both r_m and E_m (M-35).

Figure 4.3-33 Linear relationship found between Limiting Draw Ratio (LDR) and r_m for a wide variety of metals (A-28).

Figure 4.3-34 Limiting Draw Ratios (LDR) as a non-linear function of r_m for a variety of metals as published by Hosford (H-37).

Figure 4.3-35 Relationship between limiting depth and X and r values (Y-10)

Figure 4.3-36 Approximation of the r_m value from a single blank cup draw test (A-29).

Figure 4.3-37 Schematic of the Fukui Conical Cup test. Specimen after an increment of deformation is shown by the dotted line.

Figure 4.3-38 The diameter ratio of the Fukui conical cup test correlates well with the product of n_m and r_m (F-8).

Figure 4.3-39 The diameter ratio of the Fukui conical cup test for various punch speeds and test steels (F-7).

Figure 4.3-40 Schematic of Swift Round Bottom Cup Test.

4.4 Coated Steels

4.4.1 INTRODUCTION

The use of coated steels for automotive applications is rapidly increasing. Starting simply many years ago with galvanized rocker panels, the current vehicle designs are candidates for a wide spectrum of coated products – ranging from prepainted cold-rolled steels on one extreme to multi-layers of different electrodeposited metals to the other.

The introduction of coated products into the press shop was not been without problems. Little press shop experience with these new products, if any, has been available to the artisan. Therefore, the artisan has been forced to implement the traditional press shop techniques of trial and error. Sheets of a new coated product have been inserted into available tooling and their press performance compared with that of the existing bare steel sheets. The results have been mixed at best and confusing to most. Some of the products have been so slippery that restraint in the binder has been impossible and the resulting stampings were a series of buckles, waves, and loose metal. Other products have “welded” to the binder and punch and would not flow into the die under any conditions; stampings were removed from the tooling in multiple pieces. When compared with uncoated steel sheets, many coated steels have different characteristics which affect formability in many unpredictable ways.

Attempts at characterizing the formability of coated products by traditional mechanical properties have explained some of the differences in formability. Depending on the process used to make the product, different values of the substrate properties have been obtained. These in turn have influenced the press performance of the coated steels, just as the formability of bare steels would be affected by the same changes in substrate properties. This has explained some of the variations in press performance of galvanized steels. However, press shop experience has also shown that the press performance of some coated products has varied widely – even for steels with identical substrate properties. This has confirmed the long held suspicion that the coatings also have had a major influence on the press formability of the product.

Previous discussions of formability in this document have emphasized the importance of the four components of the Forming System: material, lubricant, die design, and press. Therefore, this section on coated steels also will review formability with respect to the Forming system. Coated products can be directly related to two of the four components – material and lubricant.

One approach to analyzing coated products is to separate the basic formability of the substrate from the effect of the coating (K-13, K-22). In this model, the formability of the substrate, as defined by its mechanical properties, determines the primary formability of the coated product. The mechanical properties of the substrate steel – like uncoated steels – determine the ability of the coated steel to withstand strain in the various modes of forming (A-13).

The coating, in turn, affects the amount of the metal flow over the tool and die surfaces. In this manner, the effect of the coating parallels that of a lubricant. In this section, the coating on the steel, the lubricant in the workpiece-tool interface, and the surface of the tool are considered as a single system interacting together to control the flow of metal over the various tool surfaces. The coefficients of friction are the measured output of the system.

This separation of the substrate formability from the lubricity effects of the coating presupposes no interaction between the coating and the substrate formability.

Some research (S-36, S-37) has suggested that some coatings can reduce the formability of the substrate. For example, the zinc-iron layer formed at the surface of the steel substrate of a hot-dipped galvanized product is said to cause local tensile stresses which lead to premature failure in regions of negative curvature which contact the punch. This model is used to explain some observations that the limiting dome height in punch stretching decreases with increasing intermetallic layer thickness (S-37).

A number of other studies, however, have been conducted comparing the formability of coated and uncoated steels which have led to the opposite conclusion (M-25, M-24). To insure identical substrate formability, the uncoated steel conditions are obtained by stripping the coating off the coated steel; the tool-surface effects are eliminated by isolating the sheet surfaces from the tool surface with an oiled polyethylene sheet. Meuleman, Denner, and Cheng (M-25) have shown that for both plane strain and stretch deformation modes, the zinc coatings had a negligible effect on the formability. In terms of drawability, only hot-dipped zinc-iron alloy coatings exhibited decreased drawability parameters relative to uncoated steels – i.e., reduced r_m values. However, these reduced r_m values can be explained as an artifact of the tensile test method r_m value determination. The corresponding reduction in limiting draw ratios has not been observed (M-26). Additional research is required in this area. Finally, the position can be taken that any failure of the coating itself during the forming process – even without substrate breakage – should be considered a formability problem because the coating failures are affected by the mode and amount of the deformation. This category includes lack of adhesion, decohesion, scoring, galling, and other problems.

The discussion following, therefore, is divided into three topics:

- Substrate formability
- Interface friction
- Coating failures

The primary emphasis of the discussion will be various types of galvanized coatings on steel substrates. However, the discussion is general and is equally applicable to other metallic coatings and paints, as well as substrates other than steel.

4.4.2 SUBSTRATE FORMABILITY

The formability of the substrate can be measured by the traditional formability parameters, including the work hardening exponent (n), strain rate hardening exponent (m), plastic anisotropy ratio (r), uniform elongation, total elongation, and other mechanical properties. Specific combinations of steel composition and processing conditions allow a wide range of different formability parameters to be developed in the steel substrate in order to meet the formability requirements of different stampings. A full discussion of these parameters is provided in Section 4.1.

Historically, the galvanized steels used initially for the automotive industry were produced by the hot-dipped galvanizing process. Two different types of hot-dipped galvanizing processes have evolved (Figure 4.4-1).

One hot-dipped galvanizing process uses cold-rolled steel which has been pre-boxed annealed to obtain a soft, ductile structure that exhibits good formability. This steel then is heated to a temperature range of 850 to 900 degrees F (455 to 483 degrees C) to ensure that the steel is at the same temperature as the molten zinc bath. This “low temperature” process also is known as the “Cook-Norteman” process.

The other process begins with the fully cold worked steel obtained from the tandem mill. This steel is heated to a temperature range of 1250 to 1600 degrees F (695 to 970 C) to achieve in-line annealing to replace the box annealing cycle. This “high temperature” process is known as the “Sendzimir” process. Because the in-line annealing is short in duration compared to box annealing, a slightly less formable steel results (A-13). The rapid heat up does not allow for the recrystallization and growth of crystallographic textures which lead to high normal anisotropy, r_m (B-10).

The rapid heating and the rapid cooling of the strip from the annealing furnace temperature to the temperature of the galvanizing pot causes excess carbon to remain in solution in the steel and a smaller grain size; these reduce the stretchability of the steel through lower values of the work hardening exponent, n. Correspondingly, the yield and tensile strength values are elevated and the total elongation is reduced. For these reasons hot-dipped galvanized steels as a class have been considered to have inferior formability.

The electrogalvanizing process eliminates the heating and cooling of the steel required by the hot-dipped galvanizing process. For this steel, the electrogalvanizing step is added at the end of the normal cold-rolled steel processing cycle. The formability of the substrate of the electrogalvanized steel therefore should be identical to the formability of its cold-rolled steel counterpart.

To improve the formability of the hot-dipped galvanized steel substrate, the steel producers have developed a number of processing options (Figure 4.4.2). The first option is a post batch anneal. While the r_m value is unchanged, a slight increase in the n value and stretchability is achieved. The major change is in the lower yield strength. The second option is both a pre and post anneal in a batch anneal furnace. The properties now are similar to the bare cold-rolled steel. Superior stretchability can be achieved through special chemistry and processing. The most common here are ultra-low carbon steels (with or without additions) processed by vacuum degassing.

The result of these chemistry/processing options is that the galvanized steel product received by a stamping plant may have different formability characteristics depending on the specific route a particular supplier chooses to meet the formability requirements of each stamping. However, as illustrated schematically in Figure 4.4-3, the steel producers have sufficient options available to them with which to produce one or more types of galvanized steels with the formability equal to or even exceeding that available with bare, cold-rolled steel (A-13).

Interestingly, one study (G-38) has shown that the zinc layer improved the formability of steel in the stretching area by raising the FLD. The argument is made that the zinc increase the total thickness of the sheet ad therefore also increases the level of the FLD.

4.4.3 INTERFACE FRICTION

An obvious difference between bare steel and coated steel and coated steel is the frictional effect the coating has on the interface. The coefficient of friction is the resultant of a specific combination of workpiece (coated sheet metal), interface lubricant, and tool surface. Coating the sheet metal can be considered as adding another component (another layer) to the interface lubricant system.

Recent research has shown that no single test can evaluate coated steel/lubricant combinations (M-25, K-13, B-16, B-22, A-13, K-17, M-24, K-16, R-12). Instead, a variety of tests are required which will simulate various forming modes. This is illustrated in Figure 4.4-4. The specific forming mode is more important to coated steels than uncoated steels. In addition to the specific response of the steel substrate to the forming mode, the coating will respond differently to each strain state. One extreme comparison would be cup drawing versus biaxial stretching. In cup drawing the surface area of the flange is decreasing. Here the coating does not have to flow to provide coverage during the generation of new surface area of the substrate. However, the coating is subjected to compressive stresses which could cause a high strength coating to buckle (as opposed to upsetting upon itself) and separate from the substrate.

The opposite occurs in biaxial stretching. Here the deformation is tensile which prevents coating buckling. However, if the ductility of the coating is less than the ductility of the substrate, then the coating will crack and create voids in the coating.

Another deformation mode occurs in the draw bead area of the stamping. This deformation is plane strain bend-and-straighten. However, the coating is on the outer surface of the bend and therefore is subjected to the maximum strain. Even worse, each surface is subject to alternating tension and compression cycles which are demanding both on coating ductility and adhesion.

A single coefficient of friction for each coated steel/lubrication combination – independent of forming mode – would be ideal for the press shop. However, recent research has shown the opposite (M-25, K-17, M-24). The coefficient of friction for each combination of coated steel and lubricant depends on the specific forming mode to which the combination is subjected. Even worse, the rank order of a lubricant changes with variations in steel coating and forming mode. Likewise, for a given steel coating, the rank order of different lubricants changes for different forming modes. Finally, the coefficients of friction are further modified by forming speed, interface pressure, interface temperature, and other forming process variables.

Laboratory prediction of forming performance of coated steel products currently can be accomplished only for a specific set of test parameters. Thus, one laboratory test will be applicable only to one small segment of any complex production stamping. Therefore, current laboratory evaluation of coated steels are even more restricted in scope and applicability than laboratory evaluation of uncoated steels.

The avenues for solving this complex problem appear possible, but need further research to develop press shop feasibility. First, identify test procedures which will provide a significant coefficient of friction for each forming mode which will encompass a large population of steels. For example, the coefficient of friction from a punch radius test conducted at one inch (25mm) per minute may correlate with the severity of most large, rectangular boxes, while a coefficient of friction from a high speed dome test will correlate with pure stretch forming such as a door handle pocket. Thus, one test could be sufficient to predict press shop behavior, to a first approximation.

Second, perfect mathematical modeling and other research such that all forming conditions can be theoretically derived or empirically calculated from one or two key frictional tests.

Third, make stampings insensitive to various types of steel when using a restricted number of mill applied lubricants and then prohibit use of in-plant lubricants. This restricts the number of possible combinations, and therefore restricts variations from a single source supplier.

The problem is compounded when the tool material is changed. One common example is the soft, zinc-based alloys used for die tryout and prototyping. The effect of the zinc coating depends on the deformation mode. For example, a hot-dipped, zinc-iron alloy, coated steel, commonly known as galvannealed steel, shows consistently diminished formability regardless of the deformation mode when tested with soft, zinc-based tools (M-24). In contrast, other hot-dipped free zinc and electrogalvanized steels show decreased formability with soft tooling only when substantial sliding of the blank occurs over the tooling, such as with soft draw beads; these same materials show improved performance in plane-strain stretching with a soft, zinc-based punch. Thus, the galvannealed and the free zinc coated steels have performance changes in the opposite directions for punch stretching, but in the same direction for metal movement in the binder area. Thus even relative performance ranking between these various galvanized coatings is lost when changing from soft, zinc-alloy based tooling to hard, steel tooling.

The reduced formability of the hot-dipped galvannealed steel is sufficiently severe that both Meuleman and Brazier (M-22) suggested that soft tool tryouts with galvannealed steel were not representative of how the galvannealed steel would perform in hard tools. These two authors independently concluded that soft tool tryout with bare steel (with comparable substrate properties) would best duplicate the forming conditions of the galvannealed steel in hard tooling.

Most of the literature addresses problems with galvanized steels. However, identical analyses can be performed on prepainted steels (W-11).

In summary, the coated steel-lubricant-tool interaction is so complex that no specific guidelines can be provided here. This conclusion has a significant impact on the mathematical modeling of coated steels, since many mathematical models are sensitive to the coefficients of friction for accurate calculations.

4.4.4 COATING FAILURES

All of the previous discussion has assumed that the coating has maintained its integrity, has remained bonded to the steel substrate, and has not “welded” itself to the tool. Some coatings do not respond in such a predictable, steady-state manner. These coating failures are yet another type of stamping rejection which depend both on the forming mode and the level of deformation.

This concept is elucidated in a paper by Sudoo, Hayashi, and Nishihara (S-43) where a “Flaking Limit Diagram” is used to define deformation behavior of surface films (Figure 4.4-5). The axes for this diagram are the same as the Japanese Forming Limit Diagrams, which differ from other Forming Limit Diagrams in that the axes are rotated first 180 degrees around the y axis (mirror image) and then 90 degrees clockwise. This paper concluded:

Shiokawa et al (S-20) performed a cylindrical cup test or a hat channel drawing test (including pre and post specimen weighing) in order to standardize an evaluation procedure for powdering. Their tests showed wide differences between different coatings, or even variations of similar coatings, in terms of weight losses due to powdering.

Other papers confirm the complex nature of coating failures (H-36, N-11, E-4). The nature of coating deformation was examined in more detail by Makimattila and Ranta-Eskola (M-2). They found that the biaxial stretching of galvanized steels can be subdivided into two stages. In the first stage cracks nucleate and grow in grains that have brittle crystallographic directions oriented unfavorably with respect to slip directions; this is referred to as partially plastic deformation. After a gradual transition, deformation is characterized by more brittle behavior. Primary cracks widen and secondary cracks nucleate as the base steel is strained.

Schedin, Karlson, and Melander (S-10) suggest a plasticity index (k) for coatings, where k = 0 for a coating which does not deform plastically and k = 1 for a coating which deforms as the base metal without cracking. A value of 0.7 was obtained for unixial tension, plane stain, and equibiaxial stretching for a commercially produced hot-dipped galvanized product.

A two-stage coating evaluation test has been suggested (M-2). The first deformation mode is a biaxial stretching test. If the coatings pass the biaxial stretching test, they are then subjected to the more severe bending test. Other tests proposed to study the adhesion and cohesion of coated steels are they cylindrical cup test and the beaded hat channel test (S-20, E-4).

Based on an evaluation of different combinations of factors-flaking, powdering, frictional resistance, and instability in subsequent stampings (die buildup and panel damage) – various authors propose different types of galvanized steel as being the best for formability.

Another type of coating failure is galling. Apparently galling begins when interface pressure exceeds some limit (M-2). However, once galling is initiated, the friction coefficient tends to decrease during sliding as built up particles on the tool surface become coarser and cause fewer contact points. A thicker galvanized coating tends towards higher galling limit pressure, reducing the risk of galling. Likewise, large draw beads and die radii are beneficial since changes in the surface topography due to bending deformation are small.

4.4.5 SUMMARY

One theme is constant in all the papers reviewed – formability has many definitions, many modes, and many different types of failure. The coated steels have an added variable (the coating) which adds yet another dimension to the already complex matrix of interactions. This complex interaction makes the coated steels less predictable from stamping to stamping and from laboratory to press shop. In addition, when the stamping has a zero safety factor, the coated steels are even more susceptible than uncoated steels to the prevailing forming parameters.

The only practical solution today is to model the galvanized steel in terms of the Forming System. The formability of coated steel is primarily dependent on the properties of the substrate and must be specified in the same manner as uncoated steel. The coating and lubricant combination must then be determined so as to provide metal flow patterns consistent with formability requirements of the stamping. This selection currently is guided by trial and error. Finally, the steel producer must user must implement steps to protect the more vulnerable coatings.

Figure 4.4-1 Two process cycles for producing hot-dipped galvanized steel compared to traditional method for producing uncoated, cold-rolled steel.

Figure 4.4-2 A variety of special processing options can be employed to improve the formability of hot-dipped galvanized steel (A-13).

Figure 4.4-3 The relative formability of the various galvanized steels encompasses the span of formability of uncoated cold-rolled steels (A-13).

Figure 4.4-4 Different forming modes can be simulated by different simulative tests.

Figure 4.4-5 Flaking Limit Strain Diagrams for various galvanized steels (S-43).

4.5 HIGHER STRENGTH STEELS

4.5.1 INTRODUCTION

Formability of higher strength steels, especially the HSLA variety, is simply an extension of the formability of low strength steels. The same analyses are applicable, the same rules apply, and the same predictions can be made. The primary difference is that the specific values of the formability parameters are generally lower.

Formability of higher strength steels depends on the material parameters reviewed in Sections 4.1 and 4.2. These include n, m, r, FLD, uniform elongation, and total elongation. The primary question to be asked for any higher strength steel is what the values of the formability parameters are when the minimum required yield (or tensile) strength has been achieved. These values will determine the relative formability of the steel under investigation compared to low strength steel, as well as compared to other higher strength steels which also meet the same strength requirements. In this respect, the composition/processing combinations used to obtain the required strength are important only as they influence the formability parameters. For example, a 60 ksi (415 MPa) yield strength steel can be obtained through grain size control, alloying elements, or by cold work. Evaluating the formability parameters of the final product will indicate that cold work is not the best method to obtain the necessary yield strength because the formability parameters will be substantially lower, and therefore not competitive, with respect to steels strengthened by other techniques. If the steel is simply to be used in a shallow box with little forming requirement, then cost plays the dominant role. However, in automotive stampings, the maximum formability usually is required. The decision then is made on the level of the formability parameters and the cost necessary to obtain them.

4.5.2 FORMABILITY PARAMETERS

4.5.2.1 Work Hardening Exponent

The relationship between yield strength and the work hardening exponent, n, is shown in figure 4.5-1. For yield strength less the 45 ksi (315 MPa), little n value change is noted with the possibility of a large scatter band. Above 45 ksi (315 MPa) yield strength, the n value decreases linearly. This curve is useful for estimating the n value for any steel which has “competitive formability”. Steels which have strengths created by cold work have n values which lie below the curve and are not competitive.

A German review of HSCR steels (K-2) contains a similar yield strength curve (Figure 4.5-2). The data here are below the middle line in Figure 4.5-1, indicating slightly lower n values for equal strengths.

Another German paper (W-25) reviews four other steels. The dual-phase steel falls in the right extension of the curve in Figure 4.5-2 and the rephosphorized steel falls in the existing curve. The mild steel was given two skin passes: 1.5 and 3.0 percent. The 1.5 percent skin passed sample had an n value of 0.18 versus a range of 0.22 to 0.24 from the curve in Figure 4.5-2 for equivalent yield strength. The 3.0 percent skin passed sample had an n value of 0.16 versus a range of 0.20 to 0.22. Thus, even small amounts of skin passing, beyond elimination of yield point elongation, can generate large reductions in n value.

A reduction of 0.05 in n value has a significant reduction in stretchability of the sheet metal. The n value versus yield strength curve is an excellent method of evaluating the expected stretchability of any given steel. In turn, the uniform elongation of steel sheet is directly related to its n value by the equation n = In (1+ uniform elongation) for steels which follow parabolic hardening.

4.5.2.2 Strain Rate Hardening

The post-uniform elongation can be related to the strain rate hardening exponent, m. The m value, in turn, is related to the strength of the steel; the m value decreases as the strength of the steel increases; this is shown in Figure 4.1-15 form reference S-9.

4.5.2.3 Total Elongation

Two major components of the total elongation are the uniform elongation (related to the n value) and the post-uniform elongation (related to the m value). Since both components decrease with increasing strength, the total elongation decreases with increasing strength (Figures 4.5-3 and 4.5-4). Figure 4.5-3 again shows the detrimental effect of achieving strength by cold work.

4.5.2.4 Plastic Anisotropy Ration

For most higher strength steels the plastic anisotropy ration, rm, is near unity. Typical data are shown in Figure 4.5-5. The rm values of micro-alloyed cold-rolled sheets ranges from 0.8 to 1.3. The rephosphorized steels (P275), on the other hand, have rm values ranging from 1.3 to 1.7; these steels have good deep-drawability and could effectively compete in formation of oil pans, inner door panels, etc.

4.5.2.5 Forming Limit Diagrams

The effect of work hardening (inverse effect of strength) on the Forming Limit Diagrams is shown in the FLD₀ nomograph shown in Figure 4.5-6. No effect is noted for n values greater than 0.21. This probably is related to the n value – yield strength effect noted previously in Figure 4.5-1, but no studies have been conducted in this area. For n values less than 0.21, the reduction in the FLD₀ with n value basically is a linear effect. The effect of sheet thickness in Figure 4.5-6 can be interpreted in two ways. First a 50 percent reduction in n reduces the FLD₀ by 50 percent. This same reduction holds for all sheet thicknesses. Therefore, it could be argued that sheet thickness does not affect the strength – FLD₀ relationship. However, in absolute terms, 50 percent of 60 strain percent is much greater than 50 percent of 30 strain percent. Therefore, in terms of absolute strain percent reductions, the thicker steels suffer a greater loss in FLD₀ as the strength increases.

The dual-phase steels have provided interesting studies. Thompson and Hobbs (T-10) showed that the FLD₀’s for dual-phase steels are no different from other steels when compared in terms of uniform elongation. Keeler (K-33) showed that the FLD of a dual-phase was similar to that of a 100 ksi (695 MPa) yield strength steel. Thus, at onset of localized necking depicted by the FLD, the n value at the necking strain (often called the terminal n) is the important n value. Thus, at necking, the dual-phase steel and the 100 ksi (605 MPa) yield strength are similar in resistance to localized necking; previous strain characteristics are not important.

4.5.3 SPRINGBACK

The standard rule of thumb is that springback increases with increasing yield strength. This rule generally is experimentally verified with a simple bend test. Most automotive panels are not so simply deformed (Section 8.3). For example, studies of an outer side sill showed springback increasing with increasing strength. However, the increase was completely overshadowed by the reduction in springback due to restriking (Figure 4.5-7). The springback characteristics of dual-phase steel have generated research interest, since this steel is both a low strength and high strength steel during its forming history. Nakagawa and Abe (N-2) report small springback for small bending curvature because of the low yield strength; large springback is reported for large curvature because of the high work hardenability.

4.5.4 FORMING EXPERIENCE

The literature contains few, well documented case histories on the relative formability of higher strength steels. The formability of higher strength steels is a complex interaction of all variables. One may be tempted to base formability analysis only on the reduction in the FLD. However, peak strain levels also need to be considered; for example, if the current safety factor is 20 strain percent, a higher strength steel which reduces the FLD by 10 strain percent will not maintain the desired safety factor of 10 strain percent. The reason is that the FLD is both lowered with increased strength and also the peak strain is increased with increased strength (Figure 4.508). Thus, both effects must be considered. This is why simple knowledge of the change in the FLD with strength is insufficient to predict how a higher strength steel will perform in a stamping currently made with low strength steel. Too many unknown parameters enter into the creation of the strain distribution to predict accurately the peak strain.

In one study (K-29), higher strength steels were placed in tooling designed for lower strength steel. The higher strength steel resisted deformation under the punch and transmitted a higher force to the material under the binder. This higher force overcame binder restraint forces and permitted more metal flow from the binder. This reduced the level of stretch required under the punch necessary to create the stamping depth. The higher strength steel could withstand less stretch under the punch, but in effect, the higher strength steel compensated for this stretch reduction by pulling relatively more metal from the binder area.

The increased strength of the steel sheet reduces the amount of stretch which can be induced in the center of automotive body panels. For this reason Asai et al (A-23) recommend that higher strength autobody panels for formed with stretch draw forming instead of conventional double-acting draw dies. This can increase the strain level by 50 to 100 percent of the normal level. The dent resistance for the stretch draw panels will be raised about 10 percent. Of course, the strain window for the higher strength steel is smaller and the stretch forming operation must be carefully controlled not to exceed allowable stretch limits.

Similar process changes were recommended by Wollrab and Streidl (W-24); they encouraged increased blankholder forces or larger blanks to prevent wrinkling and surface deflections with higher strength steels. The higher pressures could result in increased tool wear, however. Similar results were found by Sato et al (S-7) who documented their work in Figure 4.5.9. However, as the strength of the steel increases, the ability to induce center panel straining by increased blank holder force is diminished.

Press shop experience forming an intrusion beam from a 140 ksi (1000 MPa) tensile strength steel showed that while the maximum forming height is normally low for this steel, two drawing stages gave almost the same results as with mild steel formed under identical conditions (M-29). In this case the first stage forming was done with a large punch radius and the second with a small radius.

A formability study done on higher strength, cold-rolled, sheet steels with a 58 ksi (400 MPa) tensile strength concluded that is was impossible to improve all properties to the level of mild steel sheets (S-18). Therefore, the applicability of specific higher strength steels should be considered with respect to the deformation mode of the intended application. The characteristics of the six steels studied are portrayed in a “Formability Balance” as shown in Figure 4.5-10.

4.5.5 SUMMARY

Generalized statements concerning the formability of higher strength steels sometimes are misleading or even incorrect. In terms of stretching, the work hardening exponent of the steel decreases with an increase in yield strength of the steel. This decrease is not a discontinuous loss of stretchability but is a gradual decrease well defined in the literature. On the other hand, the normal plastic anisotropy ratio is a function of steel processing and is independent of the yield strength per se.

Sometimes the change in formability limits caused by different material properties is offset by a change in deformation over the tooling. Flow patterns usually will change because of the different material properties. The net deformation change, therefore, for higher strength steel may be more favorable than for lower strength steel.

Springback in a pure bending configuration increases with increasing yield strength of the steel. However, deformation sequences are possible which will eliminate all the springback. In terms of formability, higher strength steels should be categorized as having different forming characteristics – with no connotations attached as to whether these characteristics are “good” or “bad”. On this basis, the tooling can be designed and turned to accommodate these different characteristics to produce satisfactory stamping.

Figure 4.5-1 A linear relationship exists between yield strength and n value for steels with a yield strength greater than 45 ksi (315 MPa) (K-29).

Figure 4.5-2 Relationship between n value and yield strength (K-2).

Figure 4.5-3 The total elongation for a given yield strength depends upon the strengthening mechanism (K-55).

Figure 4.5-4 Relationship between total elongation after fracture and yield strength of cold rolled steels for a series of German steels (K-2).

Figure 4.5-5 Distribution of n_mm values for cold-rolled steels. Both parameters are determined by the processing used to produce the steel and are not related to each other (K-2).

Figure 4.5-6 The combined relationship of FLD₀, sheet thickness, and work hardening exponent (n) for low carbon steel (K-29).

Figure 4.5-7 Effect of yield strength, blankholder, and restrike on the springback on two automotive components (Y-1).

Figure 4.5-8 Strain distributions for four HSLA steels measured on the wing radius of an automotive bumper (A-12, N-7, K-33).

Figure 4.5-9 Relationship between yield strength of the steel and the equivalent strain in the center of the panel (S-7).

Figure 4.5-10 Formability balance for six steels shows wide formability differences depending on mode of deformation (S-18).