M-Value

M-Value

M-Value, Strain Rate Sensitivity

The strengthening of some metals changes with the speed at which they are tested. This strain-rate sensitivity is described by the exponent, m, in the modified power law equation:

 

where έ is the strain rate and m is the strain rate sensitivity.

To characterize the strain rate sensitivity, medium strain rate tests were conducted at strain rates ranging from 10-3/sec (commonly found in tensile tests) to 103/sec. For reference, 101/sec approximates the strain rate observed in a typical stamping. Both yield strength and tensile strength increase with increasing strain rate, as indicated Figures 1 and 2.

Figure 1: Influence of Strain Rate on Yield Strength

Figure 1: Influence of Strain Rate on Yield Strength.Y-1

 

Figure 2: Influence of Strain Rate on Tensile Strength

Figure 2: Influence of Strain Rate on Tensile Strength.Y-1

 

Up to a strain rate of 101/sec, both the YS and UTS only increased about 16-20 MPa per order of magnitude increase in strain rate. These increases are less than those measured for low strength steels. This means the YS and UTS values active in the sheet metal are somewhat greater than the reported quasi-static values traditionally reported. However, the change in YS and UTS from small changes in press strokes per minute are very small and are less than the changes experienced from one coil to another.

The change in n-value with increase in strain rate is shown in Figure 3. Steels with YS greater than 300 MPa have an almost constant n-value over the full strain rate range, although some variation from one strain rate to another is possible.

Figure 3: Influence of Strain Rate on n-value

Figure 3: Influence of Strain Rate on n-value.Y-1

 

Similar behavior was noted in another studyB-22 that included one TRIP steel and three DP steels. Here, DP1000 showed a 50% increase in yield strength when tested at 200/sec compared with conventional tensile test speeds. Strain rate has little influence on the elongation of AHSS at strain rates under 100/sec.

Relationship between strain rate and yield strength (left) and elongation (right)

Figure 4: Relationship between strain rate and yield strength (left) and elongation (right). Citation B-22, as reproduced in Citation D-44

 

Figure 5 shows the true stress-true strain curves for a processed Press Hardened Steel tested at different strain rates. The yield stress increases approximately five MPa for one order of magnitude increase in strain rate.

Figure 4: True stress-strain curves at different strain rates for 1mm thick Press Hardening Steel (PHS) after heat treatment and quenching.

Figure 5: True stress-strain curves at different strain rates for 1mm thick Press Hardening Steel (PHS) after heat treatment and quenching.V-1

 

The tensile and fracture response of different grades is a function of the strain rate and cannot be generalized from conventional tensile tests.  This has significant implications when it comes to predicting deformation behavior during the high speeds seen in automotive crash events.  See our page on high speed testing for more details.

Crash Management

Crash Management

In addition to enhanced formability, Advanced High-Strength Steels (AHSS) provide crash energy management benefits over their conventional High-Strength Steel (HSS) counterparts at similar strength levels.  Higher levels of work hardening and bake hardening at a given strength level contribute to this improvement in crash performance.

The energy required for plastically deforming a material (force times distance) has the same units as the area under the true stress-true strain curve.  This applies to all types of plastic deformation – from that which occurs during tensile testing, stamping, and crash.  The major difference between these is the speed at which the deformation takes place.

As an example, consider the press energy requirements of two grades by comparing the respective areas under their true stress – true strain curves.  The shape and magnitude of these curves are a function of the yield strength and work hardening behavior as characterized by the n-value when tested at conventional tensile testing speeds.    At the same yield strength, a grade with higher n-value will require greater press energy capability, as highlighted in Figure 1 which compares HSLA 350/450 and DP 350/600. For these specific tensile test results, there is approximately 30% greater area under the DP curve compared with the HSLA curve, suggesting that forming the DP grade requires 30% more energy than required to form a part using the HSLA grade.

Figure 1: True stress-strain curves for two materials with equal yield strength.T-3

Figure 1: True stress-strain curves for two materials with equal yield strength.T-3

 

The high degree of work hardening exhibited by DP and TRIP steels results in higher ultimate tensile strength than that exhibited by conventional HSS of similar yield strength. This provides for a larger area under the true stress-strain curve.  Similarly, when panels are formed from these grades, the work hardening during forming leads to higher in-panel strength than panels from HSS of comparable yield strength, further increasing the area under the stress-strain curve, ultimately resulting in greater absorption of crash energy.

Finally, the high work-hardening rate better distributes strain during crash deformation, providing for more stable, predictable axial crush that is crucial for maximizing energy absorption during a front or rear crash event.

Many AHSS are bake hardenable. The relatively large BH effect also increases the energy absorption capacity of these grades by further increasing the area under the stress-strain curve. The BH effect adds to the work hardening imparted by the forming operation. Conventional HSS do not exhibit a strong BH effect and therefore do not benefit from this strengthening mechanism.

Figure 2 illustrates the difference in energy absorption between DP and TRIP steels as a function of their yield strength determined at quasi-static tensile testing speeds.

Figure 2: Absorbed energy for square tube as function of quasi-static yield strength. T-2

Figure 2: Absorbed energy for square tube as function of quasi-static yield strength.T-2

 

Figure 3 shows calculated absorbed energy plotted against total elongation for a square tube component. The absorbed energy remains constant for the DP and TRIP steels but the increase in total elongation allows for formation into complex shapes.

Figure 3: Calculated absorbed energy for a square tube as a function of total elongation.T-2

Figure 3: Calculated absorbed energy for a square tube as a function of total elongation.T-2

 

For certain parts, conventional steels may have sufficient formability for stamping, yet lack the required ductility for the desired crash failure mode and will split prematurely rather than collapsing in a controlled manner. AHSS grades improve energy absorption by restoring a stable crush mode, permitting more material to absorb the crash energy.  The increased ductility of AHSS grades permit the use of higher strength steels with greater energy absorbing capacity in complex geometries that could not otherwise be formed from conventional HSS alloys.

Stable and predictable deformation during a crash event is key to optimizing the steel alloy selection. The ideal profile is a uniform folding pattern showing progressive buckling with no cracks (Figure 4).

Figure 4: Deformation after axial crushing.A-49

Figure 4: Deformation after axial crushing.A-49

 

Achieving crack-free folds is related to the local formability of the chosen alloy.  Insufficient bendability can lead to early failure (Figure 5).  Research to determine proper simulation inputs with physical testing for verification.

Figure 5: Three-point bend testing of two DP980 products having different folding and cracking behavior resulting from different microstructures and alloying approaches.B-12

Figure 5: Three-point bend testing of two DP980 products having different folding and cracking behavior resulting from different microstructures and alloying approaches.B-12

 

 

High Strain Rate Property Test Methods

for Steel and Competing Materials

Tensile testing occurs at speeds that are 1000x slower than typical automotive stamping rates. Furthermore, automotive stamping is done at speeds that are 100x to 1000x slower than crash events.  Stress-strain responses change with test speed – sometimes quite dramatically.

The m-value is one parameter to characterize this effect, since it is a measure of strain rate sensitivity.  Generally, steel has more favorable strain rate effect properties compared with aluminum, but this is also a function of alloy, test temperature, selected strain range, and test speed. L-20

These reasons form the background for the need to characterize the intermediate and high strain rate behavior of AHSS.

Crash Management

Twinning Induced Plasticity

TWinning Induced Plasticity (TWIP) steels have the highest strength-ductility combination of any steel used in automotive applications, with tensile strength typically exceeding 1000 MPa and elongation typically greater than 50%.

TWIP steels are alloyed with 12% to 30% manganese that causes the steel to be fully austenitic even at room temperature. Other common alloying additions include up to 3% silicon, up to 3% aluminum, and up to 1% carbon. Secondary alloying additions include chromium, copper, nitrogen, niobium, titanium, and/or vanadium.D-29 The high alloying levels and substantially greater levels of strength and ductility place these into the 2nd Generation of Advanced High Strength Steels. Furthermore, due to the density of the major alloying additions relative to iron, TWIP steels have a density which is about 5% lower than most other steels.

Calling this type of steel TWIP originates from the characteristic deformation mode known as twinning. Deformation twins produced during sheet forming leads to microstructural refinement and high values of the instantaneous hardening rate (n-value). The resultant twin boundaries act like grain boundaries and strengthen the steel. On either side of a twin boundary, atoms are located in mirror image positions as indicated in the schematic microstructure shown in Figure 1. Figure 2 highlights the microstructure of TWIP steel after annealing and after deformation.

Figure 1: Schematic of TWIP steel microstructure.

Figure 1: Schematic of TWIP steel microstructure.

 

Figure 2: TWIP steel in the annealed condition (left) and after deformation (right) showing deformation twins. The number of deformation twins increases with increasing strain.K-42

Figure 2: TWIP steel in the annealed condition (left) and after deformation (right) showing deformation twins. The number of deformation twins increases with increasing strain.K-42

 

EDDS or Interstitial-Free or Ultra-Low Carbon steels are different descriptions for the most formable lower-strength steel. Possible test results for this grade are 150 MPa yield strength, 300 MPa tensile strength, 22% to 25% uniform elongation, and 45% to 50% total elongation. In contrast, test results on TWIP steels may show 500 MPa yield strength, 1000 MPa tensile strength, 55% uniform elongation, and 60% total elongation.

The stress-strain curves for these two grades are compared in Figure 3. The TWIP curves show the manifestation of Dynamic Strain Aging (DSA), also known as the PLC effect, with more details to follow.

Figure 3: Uniaxial tensile stress-strain curves for an interstitial-free (IF) extra-deep-drawing steel and an austenitic Fe-18%Mn-0.6%C-1.5%Al TWIP steel. Curves are presented both terms of engineering (s,e) and true (σ,ε) stresses and strains, respectively.D-30

Figure 3: Uniaxial tensile stress-strain curves for an interstitial-free (IF) extra-deep-drawing steel and an austenitic Fe-18%Mn-0.6%C-1.5%Al TWIP steel. Curves are presented both terms of engineering (s,e) and true (σ,ε) stresses and strains, respectively.D-30

 

Figure 4 compares the results of bulge testing ferritic interstitial-free (IF) steel and austenitic Fe-18%Mn-0.6%C-1.5%Al TWIP steel. The TWIP steel is still undamaged at a dome height that is 31% larger than the IF steel dome height at failure.D-30

Figure 4: Comparison of dome testing between EDDS and TWIP.D-30

Figure 4: Comparison of dome testing between EDDS and TWIP.D-30

 

Excellent stretch formability is associated with high n-values. Shown in Figure 5 is a plot showing how the instantaneous n-value changes with applied strain. N-value increases to a value of 0.45 at an approximate true (logarithmic) strain of 0.2 and then remains relatively constant until an approximate true strain of 0.3 before increasing again. The high and uniform n-value delays necking and minimizes strain peaks. Twins continue to form at higher strains, leading to finer microstructural features and continued increases in n-value at higher strains.

Figure 5: Instantaneous n-value changes with applied strain. TWIP steels have high and uniform n-value leading to excellent stretch formability.C-30

Figure 5: Instantaneous n-value changes with applied strain. TWIP steels have high and uniform n-value leading to excellent stretch formability.C-30

 

A microstructural deformation phenomenon known as the Portevin-LeChatelier (PLC) effect occurs when deforming some TWIP steels to higher strain levels. The PLC effect is known by several other names as well, including jerky flow, discontinuous yielding, and dynamic strain aging (DSA).

The severity varies with alloy, strain rate, and deformation temperature. Figure 6 shows how DSA affects the appearance of the stress strain curve of two TWIP alloys.D-29 The primary difference in the alloy design is the curves on the right are for steel containing 1.5% aluminum, with the curves on the left for a steel without aluminum. The addition of aluminum delays the serrated flow until higher levels of strain. Note that both alloys have negative strain rate sensitivity.

 

Figure 6: Influence of aluminum additions on serrated flow in Fe-18%Mn-0.6%C TWIP (Al-free on the left) and Fe-18%Mn-0.6%C-1.5% Al TWIP (Al-added on the right).D-29

Figure 6: Influence of aluminum additions on serrated flow in Fe-18%Mn-0.6%C TWIP (Al-free on the left) and Fe-18%Mn-0.6%C-1.5% Al TWIP (Al-added on the right).D-29

 

The primary macroscopic manifestations of the Portevin-LeChatelier (PLC) effect areD-29:

  • negative strain rate sensitivity.
  • stress-strain curve showing serrated or jerky flow, indicating non-uniform deformation. Strain localization takes place in propagating or static deformation bands.
  • the strain rate within a localized band is typically one order of magnitude larger, while that outside the band is one order of magnitude lower, than the applied strain rate.
  • limited post-uniform elongation, meaning uniform elongation is just below total elongation. Said another way, fracture occurs soon after necking initiation.

The PLC effect leads to relatively poor sheared edge expansion, as measured in a hole expansion test. Figure 7 on the left highlights the crack initiation site in a sample of highly formable EDDS-IF steel, showing the classic necking appearance with extensive thinning prior to fracture. In contrast, note the absence of necking in the TWIP steel shown in the right image in Figure 7.D-29

Figure 7: Sheared edge ductility comparison between IF (left) and TWIP (right) steel. TWIP steels lack the sheared edge expansion capability of IF steels. D-29

Figure 7: Sheared edge ductility comparison between IF (left) and TWIP (right) steel. TWIP steels lack the sheared edge expansion capability of IF steels.D-29

 

The stress-strain curves of several TWIP grades are compared in Figure 8.

Figure 8: Engineering stress-strain curve for several TWIP Grades.P-30

Figure 8: Engineering stress-strain curve for several TWIP Grades.P-18

 

Complex-shaped parts requiring energy absorption capability are among the candidates for TWIP steel application, Figure 9.

Figure 9: Potential TWIP Steel Applications.N-24

Figure 9: Potential TWIP Steel Applications.N-24

 

Early automotive applications included the bumper beam of the 2011 Fiat Nuova Panda (Figure 10), resulting in a 28% weight savings and 22% cost savingsN-24 over the prior model which used a combination of PHS and DP steels.D-31

Figure 10: Transitioning to a TWIP Bumper Beam Resulted in Weight and Cost Savings in the 2011 Fiat Nuova Panda. N-24, D-31

Figure 10: Transitioning to a TWIP Bumper Beam Resulted in Weight and Cost Savings in the 2011 Fiat Nuova Panda. N-24, D-31

 

In the 2014 Jeep Renegade BU/520, a welded blank combination of 1.3 mm and 1.8 mm TWIP 450/950 (Figure 11) replaced a two-piece aluminum component, aiding front end stability while reducing weight in a vehicle marketed for off-road applications.D-31

Figure 11: A TWIP welded blank improved performance and lowered weight in the 2014 Jeep Renegade BU/520.D-31

Figure 11: A TWIP welded blank improved performance and lowered weight in the 2014 Jeep Renegade BU/520.D-31

 

Also in 2014, the Renault EOLAB concept car where the A-Pillar Lower and the Sill Side Outer were stamped from TWIP 980 steel.R-21 By 2014, GM Daewoo used TWIP grades for A-Pillar Lowers and Front Side Members, and Hyundai used TWIP steel in 16 underbody parts. Ssangyong and Renault Samsung Motors used TWIP for Rear Side Members.I-20

Other applications include shock absorber housings, floor cross-members, wheel disks and rims, wheelhouses, and door impact beams.

A consortium called TWIP4EU with members from steel producers, steel users, research centers, and simulation companies had the goal of developing a simulation framework to accurately model the complex deformation and forming behavior of TWIP steels. The targeted part prototype component was a backrest side member of a front seat, Figure 12. Results were published in 2015.H-58

Figure 12: TWIP4EU Prototype Component formed from TWIP Steel. H-58

Figure 12: TWIP4EU Prototype Component formed from TWIP Steel.H-58

 

In addition to a complex thermomechanical mill processing requirements and high alloying costs, producing TWIP grades is more complex than conventional grades. Contributing to the challenges of TWIP production is that steelmaking practices need to be adjusted to account for the types and amounts of alloying. For example, the typical ferromanganese grade used in the production of other grades has phosphorus levels detrimental to TWIP properties. In addition, high levels of manganese and aluminum may lead to forming MnO and Al2O3 oxides on the surface after annealing, which could influence zinc coating adhesion in a hot dip galvanizing line.D-29