This content is based on Citation L-77.
All metals strengthen with increasing strain in a process referred to as work hardening, which is characterized by the n-value. As described in Equation 1, n-value is referred to as the strain hardening exponent in the Holloman equation:
Equation 1
where
σ is the true flow stress (the strength at the current level of strain),
K is a constant known as the Strength Coefficient, defined as the true strength at a true strain of 1,
ε is the applied strain in true strain units, and
n is the work hardening exponent
Depending on the grade, n-value may change with strain. Therefore, the range over which n-value is calculated must be reported.
For conventional steel grades, n-value remains basically constant after the strain exceeds the initial yield point. In grades like mild steels where uniform elongation is greater than 20%, n-value is usually determined between engineering strain in the range of 10 to 20%. In higher strength steels that have uniform elongation (Ag) less than 20%, n-value is calculated between 10% and uniform elongation.
In advanced high strength steels, however, the strain is distributed among several phases, especially for austenite-containing steel grades. Here, the degree of work hardening changes as deformation progresses. In these cases, instantaneous work hardening is used for analysis, Equation 2:
Equation 2
One method to compare the behavior of steel grades with different uniform elongation is to use the relative plastic strain, which is the ratio of the plastic strain to the plastic strain corresponding to uniform elongation. Figure 1 shows how instantaneous n-value changes as a function of plastic strain for several steel grades.
Figure 1: N-Value as a function of Relative Plastic Strain.L-77
For conventional steels shown in Figure 1a, n-value remains essentially constant after the strain exceeds the initial yield point. These are the only grades that were included in the studies to develop simple correlations between n-value and Forming Limit Curves in the 1960s and 1970s. Since other steel grades were not included in the correlation studies, it is not appropriate to use those equations to estimate the FLC in advanced grades.
Figure 1b compares the first generation of advanced high strength steels. At lower strains, DP980 has an extremely high n-value. Yet after reaching approximately 30% of uniform elongation (0.3 on the horizontal axis), DP980, CP980 and MS1180 all show a strong decreasing trend of n value with increasing strain.
Unlike the 1st Gen AHSS grades in Figure 1b, the 3rd Generation advanced high strength steel grades of QP980, QP1180 and DH980 (Figure 1c) are all influenced by the TRIP effect. The continuous decreasing trend of n value still exists, but the n-values are much higher.
Figure 1d highlights grades that have a large percentage of austenite in the microstructure. A pronounced TRIP effect in the Mn-TRIP980 leads to a sharp increase followed by a sharp decrease in the n value, while the n value of TWIP steels increases slowly to a very high value.
In summary, ferrite-based steels (mild steels and conventional high strength steels) have stable n values, multiphase 1st Generation AHSS grades show an overall decreasing trend in n-value, while 2nd Gen and 3rd Gen AHSS show complex n-value behavior from phase transformations and twinning mechanisms.
Experimental forming limit curves were generated for multiple grades of steel and are presented in Figure 2. FLC0 of 780 MPa to 1180 MPa 1st and 3rd Gen AHSS grades are all in the range of approximately 0.1 to 0.2.
Figure 2: Forming Limit Curves for multiple grades of steel.L-77
The forming limit curves of DP980 and QP980 are highlighted in Figure 3a, which shows very similar behavior between the two grades in terms of the FLC positioning. On the other hand, Figure 3b shows measurable differences in the limiting dome height (LDH) values at specimen widths from 20mm (specimen number 1) to 180mm (specimen number 9). The higher n-value of QP980 is likely responsible for improved performance in the LDH tests.Z-23
Figure 3: a) Forming limit curve and b) limiting dome height results of QP980 and DP980.Z-23 as reported in Citation L-77
Under the same die and stamping process conditions, QP980 and DP980 were used to produce reinforcing beam components with a production stamping process. After the drawing operation, QP980 did not split when formed to the final position, while DP980 cracked at two locations, noted in Figure 4a. Figure 4b shows the major strain levels at three locations are all lower on the stamping formed from QP980 than on that from DP980. This reinforces that QP980 has better formability, and better ability to distribute strains over a wider region of the panel.
Figure 4: Stamping results using QP980 and DP980. a) DP980 shows splits in two locations. b) Strains in QP980 are lower.L-77
For traditional grades, reviewing the forming limit curve to assess formability has been used successfully for decades. However, as shown above, the QP980 and DP980 grades studied have very similar FLCs (Figure 3a) but different stamping performance (Figure 4a).
This difference may be a result of the differences in the partitioning of strains between the multiple microstructural phases, the strain hardening evolution, and the impact of the TRIP effect present in different degrees in all advanced high strength steels.
Along with the complexities in forming behavior, the way forming behavior is assessed must evolve as well. One possible approach is described in Citation L-77, which proposes a new index describing the overall forming capability called the strain homogenization capability (SHC). At this time, however, there is no industry consensus on the best approach.