True Fracture Strain

True Fracture Strain

Formability, true fracture strain

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Fracture strain values derived from standard uniaxial tension tests can be used to evaluate automotive crashworthiness and forming behavior of aluminum alloys and Advanced High-Strength Steels (AHSS).Y-10, W-24, W-25, L-22, L-23, T-22, H-15, L-24  The true fracture strain (TFS) and similar concepts have emerged recently as intrinsic measures of local formability for AHSS. TFS is the true (logarithmic) strain associated with the “zero-gage-length” elongation at fracture (e0), where e0 is a conceptual engineering strain value based on an infinitesimal gage length in a tension test, where:

engineering strain with near-zero gauge length
Equation 1

and Ao and Af are the cross-section area before testing and the fracture area after testing, respectively (constant volume assumed).D-13  It follows that TFS is defined as:

true fracture strain definition
Equation 2

 

TFS is related to percent reduction of area at fracture (Z, %), where:

true fracture strain as function of Z
Equation 3


 

True Fracture Strain (TFS) Measurement Methods:

Fracture Area (Af)

Tensile test samples have a rectangular cross section before testing, indicated in the left image in Figure 1.  The right image shows an idealized tension test specimen fracture surface, where five thickness measurement locations are indicated: two at the edges (ta, te); one at the center (tc), and two at the quarter-width positions (tb, td). Measured approximately at mid-thickness, wf is the fracture width. The dashed outline indicates the original specimen cross-section before testing (to·wo = Ao), and a 10-sided polygon (decagon) approximates the projected fracture area (Af), where the corners of the polygon correspond width-wise to the five thickness measurement locations.

Figure 1: Schematic representation of a tension test specimen before testing (left) and after fracture (right) viewed along the tensile axis.

 

From the dimensions portrayed in Figure 1, four possible methods to determine Af are indicated in Table 1—three lineal methods and one areal method.H-17 Method A uses a single thickness measurement at mid-width. Alternatively, for Method A the minimum thickness (tmin) may be used in cases where tc ≠ tmin. Method B uses a weighted three-thickness average A-24 —also known as the ASTM parabolic method.H-14, H-16  Method C uses a five-thickness average. For Method D, Af is the area of the polygon depicted in the left image of Figure 1.

Table 1. Fracture Area Measurement Methods.H-17

Table 1. Fracture Area Measurement Methods.H-17 

 

Dimensional measurements may be made quickly and conveniently with a calibrated digital microscope equipped with focal stacking capability and linked to image analysis software. Note that tf, wf and Af are respectively: the projected thickness, the projected width, and the projected area of the fracture surface. That is, to accommodate irregular and angled fracture surface features, measurements are made with respect to a virtual plane normal to the tensile axis. Alternatively, lineal measurements may be made with a conventional microscope equipped with a dial indicator or measuring stage. In this case, continual manual refocusing may be necessary to ensure true projected dimensional measurements.  

Recently the effects of fracture area measurement method and tension test specimen type on fracture strain values were evaluated H-17. It was concluded that specimen type (i.e., width-to-thickness ratio) has a far greater impact on the consequent fracture strain value in contrast to that of measurement method. It was also advised that, when reporting fracture strain values derived from tension tests, the specimen type, the material thickness, and the fracture area measurement method be clearly indicated.

 

True Fracture Strain (TFS) Measurement Methods:

Fracture Types

Based solely on fracture appearance, various fracture types may be observed, with examples shown in Figure 2. H-17  The fracture type changes from Type 1 to Type 2 to Type 3 as the tension test specimen width-to-thickness ratio (wo/to) increases (left to right). Type 1 fracture is perpendicular to the tensile axis across the specimen width; Type 2 fracture is an irregular transition from Type 1 fracture to Type 3 fracture; and Type 3 fracture is aligned at an angle across the specimen width (~50-60° from the tensile axis).   

Figure 2: Various fracture types observed in uniaxial tension testing, from left to right: Type 1 fracture (wo/to = 4.5—ASTM Standard Sub-size specimen); Type 2 fracture (wo/to = 12.8—ASTM Standard specimen); and Type 3 fracture (wo/to = 16.8—JIS No. 5 Standard specimen); The original width-to-thickness ratio (wo/to) is measured within the gage section of the test specimen.  H-17

Figure 2: Various fracture types observed in uniaxial tension testing, from left to right: Type 1 fracture (wo/to = 4.5—ASTM Standard Sub-size specimen); Type 2 fracture (wo/to = 12.8—ASTM Standard specimen); and Type 3 fracture (wo/to = 16.8—JIS No. 5 Standard specimen); The original width-to-thickness ratio (wo/to) is measured within the gage section of the test specimen.H-17

 

A similar fracture orientation dependence on specimen width was reported for Dual Phase (DP) steels more than thirty years ago by researchers at the Colorado School of Mines.S-49  A 2018 publication W-23 confirmed this behavior for other AHSS types, and illustrated that the transitional behavior—in terms of critical width-to-thickness ratio—is material dependent.

Figure 3 shows example Type 1 and Type 3 fractures in cross-section at the mid-width position (corresponding to position tc in Figure 1). Type 1 fractures typically run at an angle through thickness (~50-55° from the tensile axis). While most Type 1 fractures resemble that shown in Figure 2 (left) and that shown in Figure 3a, occasional through-thickness chevron profiles and “cup and cone” W-23 type fractures have been observed for Type 1 fractures. Nevertheless, Type 1 fractures are roughly symmetric about a plane normal to the sheet surface at the mid-width position.

Figure 3. Examples of (a) Type 1 fracture, and (b) Type 3 fracture; Polished through-thickness cross-sections at the mid-width position; Tensile axis is horizontal.

Figure 3. Examples of (A) Type 1 fracture, and (B) Type 3 fracture; Polished through-thickness cross-sections at the mid-width position; Tensile axis is horizontal.

 

Type 3 fractures invariably show localized necking in through-thickness cross-section as in Figure 3b. Therefore, Type 3 fractures are roughly symmetric about a plane parallel to the sheet surface at the mid-thickness position. Type 2 fractures have both Type 1 and Type 3 characteristics at different positions across the width and thus have no overall plane of symmetry. Various degrees of damage (void formation) are observed in through-thickness cross-sections of fractured specimens— for example, Figure 3. Citation H-18 contains a detailed compendium with more information on this topic.

ElsewhereW-23, L-21 it was explained that the idealized fracture thickness profile—as depicted in the right image in Figure 1—is applicable only to smaller width-to-thickness ratios (thicker, hot-rolled materials or narrower gage sections). For thinner, cold-rolled materials, or for wider gage sections, there is often no clear fracture thickness minimum at the mid-width position. In fact, in some cases a fracture thickness maximum at mid-width has been observed. Furthermore, occasional mid-thickness delamination renders the volume-constancy assumption in question, with associated implications in Equation 1

 

True Fracture Strain (TFS):

Formability Classification and Rating System

In 2016 the foundation for a formability classification and rating system was introduced for AHSSH-14, where formability performance expectations are distinguished by the relationships between true fracture strain (TFS) and true uniform strain in a tension test. Such performance mapping concepts continue to be explored and modified by steelmakersH-16, W-23, L-21, D-12, W-22, V-5, R-6, S-48 by automakersH-18, H-19 and by international industry consortiums.G-20 Traditionally AHSS performance has been represented by the product of ultimate tensile strength and total elongation (UTS x TE) and relative position on the so-called “banana diagram” or Global Formability Diagram. While this conventional methodology discriminates behavioral extremes, much is lost regarding the nuances of local formability.

Intrinsic Formability Parameters

Widely considered an intrinsic measure of global formability, the true uniform strain (εu) is the logarithmic strain associated with uniform elongation (UE, %) in a uniaxial tension test, where:

true uniform strain
Equation 4

Example TFS and εu values are shown for a series of 980-class AHSS (980 MPa minimum tensile strength) in Figure 4H-14. In this analysis, TFS values ranged from less than 0.5 [DP 980 (LSi)] to more than 1.0 (CP 980), and εu values ranged from 0.05 (CP 980) to 0.15 (GEN3 980). The Third Generation AHSS materials (GEN3-type) have the largest εu values, and the Multi-Phase/Complex-Phase steels (MP/CP-type) have the largest TFS values. As a group the Dual Phase steels (DP-type) have intermediate εu values and a wide range of TFS values. As illustrated in Figure 4, TFS is far greater than εu. A similar disparity between fracture strain and uniform strain was shown in Citation D-14, and no consistent relationship between the two parameters was determined.

Figure 4: True uniform strain (εu) and true fracture strain (TFS) values for a series of 980-class advanced high-strength steels; Error bars show the range among three test specimens for each material..H-14

Figure 4: True uniform strain (εu) and true fracture strain (TFS) values for a series of 980-class AHSS; Error bars show the range among three test specimens for each material.H-14

 

The local/global strain ratio (L/GSR) and the formability index are key parameters to guide application-specific material selection and to help set targets for future AHSS grade developments.H-14, H-16 The L/GSR reflects the relative preponderance of local formability to global formability and is defined as:

local to global strain ratio definition
Equation 5


The L/GSR is useful in understanding relative intrinsic formability “character”. Materials with higher relative TFS values are naturally expected to perform better under flanging, edge stretching and tight-radius bending conditions [e.g., MP 980 (LCE) and CP 980 in Figure 4], while materials with higher relative uniform strain values (i.e., higher terminal n values) are better suited for stretch forming and are able to distribute strain more uniformly (e.g., GEN3 980 and GEN3 980-HY in Figure 4).

Furthermore, the formability index (F.I. in the formula) is defined as:

local to global strain ratio definition
Equation 6

This index represents an intermediate strain value between εu and TFS and provides a convenient measure of the overall formability expectation, where both local formability and global formability are considered.  As an example, Figure 5 shows an exponential relationship between F.I., and the limiting bend ratio (r/t) determined from 90° V-bend testing for the same series of 980-class AHSS represented in Figure 4.H-14  It was reasoned that in the early stages of deformation, global formability (εu) dictates the strain distribution around the punch nose, while fracture resistance is governed by local formability (TFS) in the latter stages of deformation.

Figure 5. Correlation between the limiting bend ratio (f) and the formability index (F.I.) for a series of 980-class advanced high-strength steels. A higher formability index corresponds to a lower (better) limiting bend ratio in 90° V-bend testing. H-14

Figure 5. Correlation between the limiting bend ratio (f) and the formability index (F.I.) for a series of 980-class AHSS. A higher formability index corresponds to a lower (better) limiting bend ratio in 90° V-bend testing.H-14

 

Local/Global Formability Map

Figure 6 illustrates the essential framework of the local/global formability map—known eponymously as the Hance diagram.H-14, D-12, G-20 Here, the dashed lines represent the boundaries between global character (L/GSR < 5), balanced character (5 < L/GSR < 10), and local character (L/GSR > 10). The continuous curves represent arbitrary iso-F.I. contours corresponding to the values indicated (in parentheses). The qualitative assessments (Poor through Excellent) indicated for each formability level are also arbitrary; however, these performance level monikers were chosen to reflect real-world experience. Portrayed in this way (in contrast to Figure 4, for example), the relationships between true fracture strain and true uniform strain are more discernable, and both the formability character and the formability level become apparent.

Figure 6: Essential framework of the local/global formability map concept. H-16

Figure 6: Essential framework of the local/global formability map concept.H-16

 

Case Study Using the Local/Global Formability MapH-15

The basic utility of the local/global formability map concept was demonstrated for an automotive seating system development program.H-15 In this case study, stamping trials were conducted with two 980-class AHSS (980 MPa minimum UTS designation):

  • 1.6mm 980DP(LSi): A classic Dual Phase (DP) ferrite/martensite steel with low silicon content (LSi), and 
  • 1.6mm 980MP(LCE)—a Multi-Phase (MP) steel with high yield strength and low carbon equivalent (LCE).

Basic formability parameters are summarized in Table 2 for the trial materials. Based solely on elongation values (UE, TE), one might have concluded that the formability of 980DP(LSi) would exceed that of 980MP(LCE).

Table 2. Formability Parameters for Two 980-Class AHSS.

Table 2. Formability Parameters for Two 980-Class AHSS.

 

However, the stamping trial results were counterintuitive and drastically different among the two trial materials. The 980DP(LSi) material exhibited severe edge-cracking in multiple locations, while the 980MP(LCE) material ran without issue. Both materials were free of necking-type failures as predicted by computer simulations (sufficient global formability). An example part overview is shown in Figure 7. Typical 980DP(LSi) edge cracks are shown in Figure 8 for a pierced/extruded hole (Location 1) and for a blanked/stretched perimetric edge (Location 2). Clearly, relative sheared-edge ductility may not simply be deduced from conventional tensile elongation values. 

Figure 7: Overview of a stamped automotive seating component [length ~ 480 mm (19 in.)]. H-15

Figure 7: Overview of a stamped automotive seating component [length ~ 480 mm (19 in.)].H-15

Figure 8: Close-up views of Location 1 (left) and Location 2 (right) identified in Figure 7 [material: 980DP(LSi)]; Location 1 is a pierced hole that was extruded during forming, and Location 2 is a blanked perimetric edge that was stretched during forming (underside with respect to Figure 7). H-15

Figure 8: Close-up views of Location 1 (left) and Location 2 (right) identified in Figure 7 [material: 980DP(LSi)]; Location 1 is a pierced hole that was extruded during forming, and Location 2 is a blanked perimetric edge that was stretched during forming (underside with respect to Figure 7).H-15

The local/global formability map coordinates of the 980DP(LSi) and 980MP(LCE) trial materials are shown in Figure 9. With reference to the framework described in Figure 6, 980DP(LSi) exhibits global/balanced character with an overall borderline rating of Fair/Good (F.I. = 0.20); while 980MP(LCE) has decidedly local character with an overall rating of Good (F.I. = 0.26). Furthermore, the TFS value of 980MP(LCE) is more than twice that of 980DP(LSi). 

Figure 9: Local/global formability map featuring three 980-class AHSS—980DP(LSi), a classic DP ferrite/martensite steel with low silicon content (LSi); 980MP(LCE), an MP steel with high yield strength and low carbon equivalent (LCE); and 980GEN3, a third generation AHSS. Image based on Citations H-15 and H-17.

Figure 9: Local/global formability map featuring three 980-class AHSS—980DP(LSi), a classic DP ferrite/martensite steel with low silicon content (LSi); 980MP(LCE), an MP steel with high yield strength and low carbon equivalent (LCE); and 980GEN3, a third generation AHSS. Image based on Citations H-15 and H-17.

 

As an independent confirmation of the local formability advantage of 980MP(LCE), the hole expansion ratio (HER, λ) is more than four times that of 980DP(LSi) (Table 2). A strong correlation between TFS and λ has been confirmed by several authors L-22 L-23  T-22  H-15 As the component featured in this case study is dominated by extremely challenging edge-stretching conditions, 980MP(LCE) is the clear wiser material selection. However, in applications with more demanding global formability requirements, other issues such as intolerable strain localization could arise, and a third generation AHSS might be the best choice. As an example, when contrasting 980GEN3 AHSS (third generation AHSS) to 980DP(LSi) in Figure 9, the intrinsic global and local formability parameters (εu and TFS), as well as the F.I, are approximately 50% greater.

 

True Fracture Strain (TFS): Alternatives to TFS

While the local/global formability map methodology was developed in the context of true fracture strain (TFS), there are other ways to represent intrinsic local formability (fracture resistance) with data derived from standard uniaxial tension tests. In the original conception (Hance diagram), true uniform strain (εu) and TFS are two points along a logarithmic strain continuum from zero to fracture, and the relationships between these values elegantly describe the formability character (local/global strain ratio) and the overall formability level (formability index). The “best” local formability parameter may be a matter of practicality or applicability, or simply a matter of preference. Each method has its strengths and weaknesses, and such fracture strain concepts continue to evolve. 

True Thinning Strain at Fracture  

The true fracture strain (TFS) value is an area-based measurement of fracture strain and thus reflects the tension test specimen width change as well as the thickness change, for better or for worse. Citation H-18 suggests that the true thinning strain at fracture (ε3f) is a more appropriate measure of local formability, where:

local to global strain ratio definition
Equation 7


and to and tf are the original thickness (before testing) and final thickness (after fracture). By convention ε3f is a positive value and represents the absolute value of the true thickness strain at fracture (a negative value). Furthermore, the post-uniform portion of the fracture strain may be isolated by subtracting the uniform component of thinning strain, where:

Post-uniform fracture strain definition
Equation 8

and εu and r are the true axial uniform strain and the plastic strain ratio (normal anisotropy) measured during the tension test, respectively. Post-uniform fracture strain components might be more relevant to materials with high uniform elongation values such as TWIP steels H-18. In a similar way, the post-uniform portion of the area-based TFS value may be expressed as:

Post-uniform TFS definition
Equation 9


Another study W-23 concluded that: (1) area-based fracture strain measurements such as TFS result in less experimental scatter when compared to thickness-based fracture strain measurements such as ε3f, and (2) area-based measurements show less dependence upon the method by which fracture strains are determined. It appears that a single thickness measurement may misrepresent the fracture strain and that a multiple-thickness (average thickness) or area measurement approach may be more stable.

Critical Fracture Strain

Perhaps a lesser-known and under-exploited representation of fracture strain is the so-called critical fracture strain value (CFS)—introduced in 1999 for aluminum alloys in Citation Y-10 and re-visited in 2007 in the context of High-Strength Steel in Citation W-24. In concept CFS is the estimated true thinning strain at fracture, where:

critical fracture strain definition
Equation 10


In determining CFS, only the engineering stress-strain data from a uniaxial tension test are needed—that is, no post-fracture area or thickness measurements are required: eu is the engineering uniform strain value (% uniform elongation/100); sf is the engineering fracture stress; and su is the ultimate tensile strength or UTS. Figure 10 shows an example engineering stress-strain curve for a 980-class AHSS, where the parameters relevant to CFS are marked. In this example, CFS = -ln[(1-0.07/2)·(787/1015)] = 0.29.

Figure 10: Example engineering stress-strain curve for a 980-class AHSS. Here, eu is the engineering uniform strain, su is the ultimate tensile strength (UTS), sf is the engineering fracture stress, CFS is the critical fracture strain, and ε3f is the true thinning strain at fracture. 

Figure 10: Example engineering stress-strain curve for a 980-class AHSS. Here, eu is the engineering uniform strain, su is the ultimate tensile strength (UTS), sf is the engineering fracture stress, CFS is the critical fracture strain, and ε3f is the true thinning strain at fracture.

 

True Fracture Strain (TFS):

Correlation to Hole Expansion Ratio

In a recent studyL-5, tensile properties (80 mm gage length) and hole expansion ratio were measure for AHSS with minimum tensile strength designations ranging from 600 to 1200 MPa, and thickness between 1 and 2 mm. No particular correlation was found between the hole expansion ratio and conventional tensile properties such as uniform elongation, total elongation, n-value, and so on.

The most promising relationship was found between the hole expansion ratio (converted to logarithmic strain) and the true thinning strain at fracture in tension. This relationship is illustrated in Figure 11 for total thinning strain (ε3f, Equation 7) on the left, and for post-uniform thinning strain (ε*3f, Equation 8) on the right. In both cases, better correlation is shown for transverse tension tests rather than for longitudinal tension tests (linear fit through the origin).

Figure 11: Hole expansion ratio (logarithmic strain) as a function of true thinning strain at fracture.   Left graph: total thinning strain (e3f); Right graph: post-uniform thinning strain (e*3f).L-5

Figure 11: Hole expansion ratio (logarithmic strain) as a function of true thinning strain at fracture.   Left graph: total thinning strain (ε3f); Right graph: post-uniform thinning strain (ε*3f).L-5

 

While the above correlations are good, the inherent scatter associated with the hole expansion test, fracture strain measurements, and other local formability parameters may limit applicability in a production environment. Furthermore, various factors affect hole expansion in production environments, including hole preparation technique, edge condition, and cutting clearance.

 
 

Standardization: VDA 238-110 for industrial applications of TTS (True Thickness Strain) and TFS (True Fracture Strain)


2023 saw the release of the first Industry standard method of using fracture surfaces from tested tensile bars to characterize local ductility. VDA 238-110V-25 covers industrial application of TTS (True Thickness Strain at fracture at minimum thickness) and TFS (True Fracture Strain from area reduction) to quantify local ductility based on the postmortem microscope analysis of the fracture surface of tensile test samples.

Shortly thereafter was the publicationL-72 of a detailed study evaluating the gauge repeatability and reproducibility (GRR) based on round-robin test results from 18 labs, spanning close to1500 tests of three AHSS grades: CR440Y780T-DH, CR780T980T-CP, and HR660Y760T-CP. Conclusions from this study include:

  • For the three grades evaluated, the greatest total variance of hole expansion results associated with punched holes
  • Measurement variance of TTS testing is comparable to that of elongation at breakage measurements, and substantially lower than seen in hole expansion testing.
  • For the two complex phase steels, TTS and TFS results are very similar, whereas in the high ductility dual phase (DH) grade, the TFS value is slightly higher than TTS. The larger TFS value may be related to the higher global ductility of the DH grade compared to the CP steels. TFS includes a contribution of both thickness and width reduction, leading to a comparatively high value, while TTS represents the thickness reduction. As such, TTS may be a more conservative, but more representative value of local formability material capability.H-18  In addition, characterizing TTS may be experimentally simpler than TFS.

The VDA 238-110 testV-25 is relatively recent, and is not as mature as tensile testing which has had a continually revised standard procedure for over 100 years [ASTM E8 was first issued in 1924].  Aspects of VDA 238-110 that may need to be addressed in future revisions include these observations from Citation L-75:

  • Tensile sample failure location – the minimum thickness at fracture may not be located at the sample center.
  • Cracks may form at the sample shoulders leading to premature failure – the validity of these results should be questioned.
  • Edge cracks starting normal to the tensile direction, typically without significant necking and an asymmetric fracture shape pattern, may not be a good measure of bulk local ductility.
  • The real fracture shape border may be best seen in three-dimensions rather than a 2-D representation. Otherwise, it is possible to produce false values for reduction of area and/or minimum thickness values.
  • There is ambiguity in the definition of thickness close to sample edges. Thickness is defined as the cross section of a vertical line with the sample fracture contourplot. If this line crosses “empty air” at the left/right outer edges of the broken tensile sample, then invalid readings may occur due to the definition.
  • When measuring broken surfaces, there is still some subjectivity in the measurement, especially on surfaces with high fracture angle.

 
 

 

Brandon Hance Thanks are given to Brandon Hance, Ph.D., who contributed the majority of this article.

 

 

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M-63

Citations

Citation:

M-63.  M. Milititsky, M. Garnett, C. Du, J. Wu, L. Zhang, P.J. Belanger, J.M. Prencipe, E.D. Bishop, “Variable Binder Force for Springback Management”,  International Conference on Advanced High-Strength Sheet Steels for Automotive Applications Proceedings, June 6-9, 2004, Association for Iron & Steel Technology.

Bake Hardenable

Bake Hardenable

AHSS, Conventional HSS, Steel Grades

BH Grades

Bake Hardenable (BH) steels grades are conventional High Strength Steels that exhibit a Bake Hardening Effect. BH steels exhibit an increase in yield strength after room-temperature stamping followed by processing through a thermal cycle comparable to the time-temperature profile used in paint curing (or baking) – approximately 170 °C for 20 minutes. Bake hardenability is characterized by determining the Bake Hardening Index.

Bake Hardenable steel grades have yield strength at shipment from the steel mills of 180 MPa to 300 MPa (approximately 25 ksi to 45 ksi). The grades at the lower strength levels are capable of being produced with a Class A surface finish and are used in applications where dent resistance is desired in thin sheet steel. Applications for the higher strength BH steels include structural parts where Class A surface is not required. The higher strength after forming and baking is the reason automakers might use these in body structure applications, potentially contributing to vehicle lightweighting efforts.

These grades work harden approximately 30 MPa when 2% strain is introduced, either from stamping or during a tensile test, which is similar to dent resistant IF-HS. In contrast to IF-HS, the paint-bake cycle after forming results in an additional yield strength increase. The minimum strength increase from baking is specified by some automakers as 20 MPa to 35 MPa, measured after applying a defined level of strain.

Higher yield strength directly improves the dent performance. Even though BH grades and their non bake hardening counterpart IF-HS grades may have similar yield strength and thickness after forming, bake hardenable steels will show superior dent resistance due to the increase in yield strength from the paint baking operation.

Ferrite is the main microstructural phase of BH steels. The strengthening from the paint bake cycle is due to the controlled amount of carbon remaining in solid solution (on the order of 25 ppm) when the steel leaves the production mill. At the baking temperatures after the part is formed, the dissolved carbon migrates to pin any free dislocations created from stamping. This increases the yield strength of the formed part for increased dent resistance. Formability does not suffer, since the strength increase occurs after stamping.

Most Advanced High Strength Steel (AHSS) grades also exhibit a Bake Hardening Effect, achieving yield strength increases of 40 MPa to 120 MPa from an appropriate thermal cycle. AHSS grades are not categorized with traditional bake hardenable steels, since their primary characteristics and applications are typically, but not exclusively, different. One exception are some Dual Phase (DP) steels available with a Class A surface, which are used as skin panels to combine excellent dent resistance with lightweighting benefits.

Some of the specifications describing uncoated Bake Hardenable (BH) steel are included below, with the grades typically listed in order of increasing minimum yield strength and ductility. Different specifications may exist which describe uncoated or coated, or steels of different strengths.

  • ASTM A1008M, with the terms BHS 26 [180], BHS 31 [210], BHS 35 [240], BHS 41 [280], BHS 44 [300]A-25
  • EN10268, with the terms HC180B, HC220B, HC260B, and HC300LAD-3
  • JIS G3135, with the term SPFC340HJ-3
  • JFS A2001, with the terms JSC270H, JSC340HJ-23
  • VDA239-100, with the terms CR180BH, CR210BH, CR240BH, and CR270BHV-3

 

Bake Hardening Effect

Bake Hardenable Steel Grades and most AHSS grades exhibit a Bake Hardening Effect, meaning that there is an increase in yield strength after room-temperature stamping followed by processing through a thermal cycle comparable to the time-temperature profile used in paint curing (or baking) – approximately 170 °C for 20 minutes.

The degree to which a sample is bake hardenable is characterized by the Bake Hardening Index.

In Bake Hardenable Steel Grades, solid solution hardening elements like phosphorus, manganese, and silicon are used to achieve the desired initial strength. For AHSS, the initial strength is determined by the balance and volume fraction of microstructural components like ferrite, bainite, retained austenite, and martensite. In both cases, a specifically engineered amount of dissolved carbon in the ferritic matrix causes an additional increase in the yield strength through controlled carbon aging during the paint-bake thermal cycle. The bake hardening process in AHSS grades is more complex, and results in substantially higher values of the Bake Hardening Index.

Figure 1 shows the work hardening and bake hardening increases for samples of three High-Strength steel grades having the same as-received yield strength prior to 2% pre-straining and baking. The HSLA steel shows little or no bake hardening, while AHSS such as DP and Transformation Induced Plasticity (TRIP) steels show a large positive bake hardening index. The DP steel also has significantly higher work hardening than HSLA or TRIP steel because of higher strain hardening at low strains. No aging behavior of AHSS has been observed due to storage of as-received coils or blanks over a significant length of time at normal room temperatures. Hence, significant mechanical property changes of shipped AHSS products during normal storage conditions are unlikely.

The higher bake hardening index (BHI) of AHSS grades DP 600 and TRIP 700 is also shown in Figure 2. While BHI is determined at a prestrain of 2%, this graph indicates that even higher levels of bake hardenability can be achieved with increasing strain. In a stamping where most areas have more than 2% strain, combining this higher bake hardenability with the increased work hardening that occurs with increasing strain results in a formed panel having a strength markedly higher than the incoming flat steel. This is beneficial for crash energy management.

Figure 1: Comparison of work hardening (WH) and bake hardening (BH) for TRIP, DP, and HSLA steels given a 2% prestrain. S1, K3

Figure 1: Comparison of work hardening (WH) and bake hardening (BH) for TRIP, DP, and HSLA steels given a 2% prestrain. S-1, K-3

 

Figure 2: Bake hardening responses of several HSS and AHSS products with varying pre-strain, reproduced from Figure 3 in Citation B-6. The bracketed numbers after each grade are references within the cited paper.

Figure 2: Bake hardening responses of several HSS and AHSS products with varying pre-strain, reproduced from Figure 3 in Citation B-6. The bracketed numbers after each grade are references within the cited paper.

 

Bake Hardenability of Exposed Quality Dual Phase Steels

Dent resistance is a function of the yield strength in the formed panel after it completes the paint baking cycle. Based on this premise, grades with higher bake hardenability, such as AHSS, should have substantially higher dent resistance. Application of AHSS grades to capitalize on improved dent resistance also requires their production at the desired thickness and width along with surface characteristics appropriate for Class A exposed quality panels. Some DP steels meet these tight requirements specified by the automotive industry.

A recent studyK-49 highlights this improved dent resistance. This work presents the experimental results and associated numerical investigation of the dent testing of DP270Y490T, a DP steel grade with 490 MPa minimum tensile strength. Tests performed to the SAE J2575 procedureS-7 measure the resultant dent depth after testing, so therefore smaller depths indicate improved performance. Compared with samples not processed through a bake hardening cycle, dent depth reductions occur with hotter and longer cycles, as shown in Figure 3. Increasing temperature plays a more significant role in dent depth reduction than increasing time. This work also reinforces that bake hardenability must be incorporated into simulation models in order to improve the accuracy of dent resistance predictions.

Figure 3: Dent resistance of DP270Y490T according to SAE J2575S-7* as a function of baking test conditions.K-49  Lower dent depth indicates better dent resistance.

Figure 3: Dent resistance of DP270Y490T according to SAE J2575S-7 as a function of baking test conditions.K-49 Lower dent depth indicates better dent resistance.

 

Bake Hardenability of 980 MPa and 1400 MPa Multi-Phase Steels with Different Prestrains

Citation X-5 evaluated the bake hardenability as a function of pre-strain on two steels having a microstructure of ferrite and martensite. The two steels are distinguished by their tensile strength:  Test steel 1# is a 980 MPa grade with a yield:tensile ratio of 80%, whereas test steel 2# is a 1400 MPa grade with a yield:tensile ratio of 85%.  See Table 1 for details.

Steel
ID #		 Thickness
(mm)		 Yield Strength
(MPa)		 Tensile Strength
(MPa)		 Elongation
(%)		 Elongation at Break
(%)
1# 1.5 832 1047 7 13.5
2# 1.4 1243 1455 4 7
Table 1: Mechanical Properties of Tested Steels. X-5

 

Conventional uniaxial tensile testing of a #5 JIS bar was used to apply prestrain and evaluate mechanical properties. After pre-straining, samples were tested by first bending coupons to 90°, followed by the conventional paint bake thermal cycle of 170 °C for 20 minutes except for the control samples which remained unbaked. In all cases, the bend line was parallel to the rolling direction.

In the absence of prestrain, no bake hardening was observed in the two steels, indicating that prestrain is a prerequisite for promoting bake hardening.

Increasing levels of prestrain did increase the bake hardening response, but only to a certain level, with the two steels having a different prestrain response. The lower strength Steel 1# reaches a maximum BH value of approximately 80 MPa at a prestrain of 2%, while the higher strength Steel 2# reaches a maximum BH value of approximately 160 MPa at a prestrain of 1%. See Figure 4.

Figure 4: Effect of prestrain on Bake Hardening of 980 MPa and 1400 MPa steels. X-5

Figure 4: Effect of prestrain on Bake Hardening of 980 MPa and 1400 MPa steels.X-5

 

The elongation to fracture response to increasing prestrain is found in Figure 5, which shows a continuous decrease in ductility.

Figure 5: Effect of prestrain on Elongation of 980 MPa and 1400 MPa steels. X-5

Figure 5: Effect of prestrain on Elongation of 980 MPa and 1400 MPa steels.X-5

 

Using these grades in production applications requires the formed product to be capable of withstanding additional damage if involved in a crash.  As such, some coupons bent to 90° were baked while others remained unbaked, and all were subsequently bent another 30°, producing a final bending angle of 60°. 

Baking has an adverse effect on the secondary bending performance of the 1400 MPa grade, which required a bend radius of 3 mm to avoid bend cracks in the baked condition. Without baking, a 2 mm radius was successfully bent.  In the 980 MPa grade, no cracking was found even with a 1 mm radius in either the unbaked and baked conditions.

 

Measuring The Bake Hardenability Index

Bake hardenability is characterized by determining the Bake Hardening Index, or BHI.

The Bake Hardening Index (BH2) is determined by taking a conventional tensile test sample and pulling it to 2% strain. This is known as a 2% pre-strain. The sample is then put into an oven for a thermal cycle designed to be typical of an automotive paint curing (paint baking) cycle: 170 °C for 20 minutes. The temperature and time may be different depending on the end-user specifications.

Some companies may specify BH0, which uses the same thermal cycle without the 2% pre-strain. BH5 or BH10 (5% or 10% pre-strain, respectively) may also be reported.

The experimental procedure and calculation of BH2 is standardized in EN 10325D-4 and JIS G 3135J-3, and is similarly described in several other specifications.

Figure 6 defines the measurement for work hardening (B minus A), unloading to C for baking, and reloading to yielding at D for measurement of bake hardening (D minus B).  Note that the bake hardening index shown here is measured up to the lower yield point, which is consistent with the EN 10325 definition.  JIS G 3135 prescribes the use of the upper yield point.

Figure 4: Measurement of work hardening index and bake hardening index.

Figure 6: Measurement of work hardening index and bake hardening index.  BHI is measured using the lower yield point in EN 10325D-4 and with the upper yield point in JIS G 3135J-3.

 

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M-Value

M-Value

Mechanical Properties

M-Value, Strain Rate Sensitivity

All metals strengthen as they are deformed through a process called work hardening. However, the degree of strengthening may change as a function of the speed at which they are tested. In these cases, when local necking starts, the strain rate in the necked area is different in the surrounding non-necking region.

With negative strain-rate sensitivity, as is the case with many aluminium alloys, the necked region is weaker than the surrounding area. Fracture occurs with very little additional strain after necking initiation.

With positive strain-rate sensitivity, the necked region is stronger than the surrounding area. This is the basis for many steel alloys having a total elongation to fracture that is nearly double that of uniform elongation.

This strain-rate sensitivity is described by the exponent, m, in the modified power law equation:

Holloman-Strain Rate Law
Equation 1

 
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.

Bake Hardenable

Crash Management

Crash Management, structural performance

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.