Failure during Sheared Edge Stretching of Dual-Phase Steels

Failure during Sheared Edge Stretching of Dual-Phase Steels

B.S. LEVY, M. GIBBS, and C.J. VAN TYNE

The use of dual-phase steels has been limited in a number of applications, due to failure duringsheared edge stretching. Previous investigations have studied the properties of dual-phase steels,especially regarding the mechanical properties of the individual phases or constituents, thestrain partitioning to the microconstituents during loading, and the decohesion at the interfaceduring loading. On the basis of the literature review, a hypothesis is developed in which failurein sheared edge stretching is the result of a sequence of events. Cracking rst develops in thehard constituent, cracks grow in the interface between the hard constituent and ferrite, andrelative movement of ferrite relative to the hard constituent increases the rate of cracking. In thepresent study, a single steel was heat treated to produce dierent amounts of hard constituentwithin the ferrite matrix in order to better understand the behavior of dual-phase steels duringsheared edge stretching. The results of the study are consistent with the proposed hypothesis. Itwas found that in contrast to other studies, increased strength of the hard constituent retardscrack initiation. Crack growth increased with increasing surface area of hard constituentferriteinterfaces and increasing movement of ferrite relative to the hard constituent.

DOI: 10.1007/s11661-013-1718-7 The Minerals, Metals & Materials Society and ASM International 2013

I. INTRODUCTION

DUAL-PHASE sheet steels are being extensivelyused in automotive applications in order to reducevehicle mass, which can lead to better fuel economy andlower carbon emissions. One of the limitations informing these types of advanced high-strength steels(AHSSs) is the fracture that occurs when sheared edgesare stretched. A number of investigators have studiedaspects of this process. The results of these investiga-tions have identied conicting results on the factorsthat contribute to shear edge failures when shearededges of dual-phase steels are stretched. The intent ofthe present study is to provide insight on the importantsteps of the failure process in stretching sheared edges byevaluating a steel with a constant bulk carbon contentbut processed to dierent dual-phase microstructures.Analyzing the failure process during sheared edge

stretching must consider the literature on strength ofphases, fracture in the hard constituent, interfaceconditions, decohesion between phases, microstructuralmorphology, and the eect of shearing. The informationfrom the literature review provides the basis for theproposed failure sequence. The data from experimentalinvestigation in this study evaluate the factors thatcontribute to the failure as identied from the review ofthe literature.

A. Hard Constituent and Ferrite Strength

Krauss[1] has shown that the strength of martensite isdetermined by its carbon content and that Vickershardness is a linear function of carbon content, up tosomewhere between 0.3 and 0.5 pct carbon. Thereafter,the slope of the curve gradually decreases.McFarland[2,3] evaluated the stressstrain properties

of 100 pct martensite steels with carbon contentsranging from 0.06 to 0.25 pct. For carbon contentsranging between 0.09 and 0.15 pct, McFarland foundrapid strain hardening between the proportional limitand the 0.2 pct oset yield strength, followed by strain-hardening exponents (n-values) of 0.21/0.22, up to astrain of 0.03. Total elongation failure was ranging from3 to 4 pct, which indicates fairly low tensile ductility.In relating tensile strength to percent carbon,

McFarland[3] combined data from two separate experi-ments with data from Leslie et al., and a data set thatused results from Kurdjumov et al., and Aborn. Theequations from each regression were similar, and showedthat TS (in ksi) = 120+546 9 (wt pct C). These resultsexhibit excellent agreement with Hasegawa et al.[4] whodetermined that the tensile strength of a 0.052 pct C steelwith 100 pct martensite would be 1068 MPa.Huper et al.[5] evaluated a nominal 100 pct martensite

steel with 0.6 pct carbon. The reported eective stressstrain curve is r = 3560 (0.001+ ep)

0.21. The agreementwith the n-value from the McFarland study is excellent.Using the Huper et al. equation, the stress at strains of0.025 and 0.05 is respectively 1654 and 1906 MPa.Given the lower carbon content for the McFarland data,the two results exhibit excellent agreement.Data from Lee et al.[6] examine the dierence from

100 pct of a phase to a mixed microstructure. Lee et al.data show the strength of ferrite and martensite for twodual-phase steels. Steel A had a carbon content of

B.S. LEVY, President, is with the B.S. Levy Consultants Ltd, 1700E. 56th St., Suite 3705, Chicago, IL 60637. M. GIBBS, formerlyGraduate Student with the Department of Metallurgical and MaterialsEngineering, Colorado School of Mines, Golden, CO 80401, is nowEngineer with the ArcelorMittal, Burns Harbor, IN. C.J. VAN TYNE,FIERF Professor, is with the Department of Metallurgical andMaterials Engineering, Colorado School of Mines. Contact e-mail:[email protected]

Manuscript submitted December 11, 2012.Article published online April 10, 2013

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 44A, AUGUST 20133635

0.33 pct with 34 pct martensite and steel B had a carboncontent of 0.25 pct with 49 pct martensite. The eectivestress (in MPa) eective strain curves for martensite andferrite were determined to be as follows:

Steel A martensite: r 4679 0:001 ep 0:406

Steel B martensite: r 3976 0:001 ep 0:343

Steel A ferrite: r 891 0:002 ep 0:207

Steel B ferrite: r 874 0:002 ep 0:200

It can be seen that n value from the M G Leeet al. data is much larger than the n value from theMcFarland and Huper et al. data. The ferrite strength issimilar for steel A and steel B and the strengthcoecients (891 and 874 MPa) are much higher thanwould be expected for low carbon ferrite steel. Acomparison of the McFarland and Huper et al. datawith the M G Lee et al. data clearly shows that stressstrain properties of martensite and ferrite in a mixedmicrostructure are dierent from what is expected for100 pct of each of these phases.Allen and Levy[7] have shown that for a nominal

100 pct martensite steel with a yield strength of1200 MPa, an engineering tensile strength of1500 MPa, and a total elongation of 4.1 pct, it ispossible to draw a cup with a limiting drawing ratio(LDR) of 1.5. The equivalent strains for producing sucha cup are much larger than a total elongation of 4.1 pctin tensile deformation. The Allen and Levy results showthat the stress state from a macro view aects martensiteductility. If macro stress state aects ductility, then it islikely that stress state at the microconstituent levelshould also aect the ductility of a hard constituent witha dual-phase structure.

B. Deformation in Tensile Testing

While deformation in tensile testing is dierent fromthat in sheared edge stretching because of the largestrains imparted by shearing, the information obtainedfrom tensile deformation is still useful.Ballinger and Gladman[8] indicated that during plastic

deformation of dual-phase steel, ferrite supports largestrains, with martensite showing little deformation.Matlock et al.[9] also showed that ferrite accommodatesmost of the deformation in dual-phase steels. Incontrast, Ishigoru et al.[10] showed that with a largevolume fraction of ferrite, martensite exhibits signicantdeformation. The dierence in results between theseauthors is typical of other studies in the literature.Paul[11] showed that the form of plastic strain local-

ization is critical to understanding metallurgical dam-age. Kang et al.[12] showed that strain heterogeneityincreases when ferrite is surrounded by martensite. Sunet al.[13] showed that for martensite ranging from 15 to40 pct, failure is primarily governed by the instability

induced by phase inhomogeneity between the hard andsoft phases. In this case, the inuences of ferrite ductilityand microvoids in ferrite become relatively unimpor-tant. In another study, Sun et al.[14] developed a niteelement model using Abacus to show that plastic strainlocalization results from incompatible deformationbetween ferrite and martensite.Hasegawa et al.[15] suggested that increasing volume

fraction martensite enhances stress redistributionbetween ferrite and martensite. Minami et al.[16] showedthat martensite hardness aects deformation inhomoge-neity in dual-phase steels. In a subsequent study, Minamiet al.[17] also found that at strains of 7.2 and 13.7 pct,martensite deformation accounted for about 20 pct oftotal deformation, and that increasing strain particularlyincreases strain at the martensiteferrite interfaces.Shen et al.[18] found that, in general, ferrite deformed

immediately and to a much greater extent than thedeformation of martensite, and that, for dual-phasesteels with low volume fractions of martensite, there wasno measurable strain in martensite. At higher martensitevolume fractions, the shearing of martensiteferriteinterfaces extended into martensite islands. Fallihi[19]

found that decohesion is followed by martensite fractureat higher strains, and that as martensite volume fractionincreases there is more decohesion.The results of Paul,[11] Kang et al.,[12] Sun et al.,[13,14]

Hasegawa et al.,[15] Miami et al.,[16,17] Shen et al.,[18] andFallihi[19] show that while specic details vary, martens-ite deformation is possible and that stress concentrationon the constituent level as well as microstruc-tural morphology can aect the nature of martensitedeformation.Lee et al.[20] showed that applied stress is nonuni-

formly distributed because of second-phase particles;interface decohesion is inuenced by local stress con-centrations; and void nucleation usually occurs when theapplied stress on an interface exceeds the debondingresistance of the interface. S B Lee et al. also indicatedthat stress concentration on the microconstituent levelcan be higher than macro stress calculated from theexternal loading. While comparing void nucleationbetween tension and torsion, S B Lee et al. showed thatas a result of the stress state, void nucleation occurs athigher strains in torsion than in tension. The abovereferenced study by S B Lee et al. shows that both themacro stress and the micro stress aect the deformationand that micro stresses can be higher than macrostresses.In another study Lee et al.[21] also showed that a

damage accumulation function can be inferred from anormalized strain-hardening rate. The damage accumu-lation function is highly sensitive to steel microstructureand strength level. The second-phase volume fractionand particle size are believed to control damage accu-mulation, in conjunction with the matrix work harden-ing rate, which is the locally concentrated stress. Theinference from the current study is that relative defor-mation between ferrite and hard constituents aects thefailure process.Ahmed et al.[22] and Kunio et al.[23] showed that

martensite morphology aects the stress transfer

3636VOLUME 44A, AUGUST 2013 METALLURGICAL AND MATERIALS TRANSACTIONS A

between ferrite and martensite. Kunio et al. describedthe constraint due to martensite by a parameter: theboundary length of the martensite phase divided by thesum of the length of the martensite phase and the lengthof line of the ferrite grains less the length shared with themartensite. These results show that the hard constituent/ferrite interface aects failure.Kunio et al.[23] also found that connected martensite

islands increase martensite cracking. In subsequentadditional studies, Ahmed et al.[24,25] showed that voidsare due to the fracture of martensite or decohesion atferritemartensite interfaces. Gerbase et al.[26] showedthat voids occur by decohesion at ferritemartensiteinterfaces.Avramovic-Cingara et al.[27] showed that for uni-

formly distributed martensite, the major void nucleationwas at ferritemartensite interfaces at a local strain of atleast 0.15, with voids growing along ferrite grainboundaries. In contrast, with heavy centerline banding,martensite cracking was observed at a local strain of0.029.Kadkhodapour et al.[28] determined that void growth

occurs predominantly in the direct neighborhood ofmartensite islands due to the delamination of ferritemartensite interfaces. Kadkhodapour et al. also statedthat high strength ferritemartensite interfaces are resultof carbon diusion to ferrite during tempering, whichincreases interface strength.Erdgan[29] observed martensite cracking and void

formation at ferritemartensite and ferrite-inclusioninterfaces. Coarse martensite or martensite intercon-nected along ferrite grain boundaries resulted in moremartensite cracking than that of ne martensite.Szewczyk and Gurland[30] found that martensite yieldingoccurred at the uniform elongation strain and voidformation occurred at ferritemartensite interfaces.Uthaisangsuk et al.[31] found that the failure mecha-

nism depended on the microstructural constituents. Theinitial void nucleation occurred either by the de-bondingof martensite from ferrite, or by the cracking ofmartensite. Using simulation, they determined thatcracks initiated in martensite and then propagatedalong ferritemartensite interfaces.He et al.[32] determined that for a coarse dual-phase

microstructure consisting of elongated martensiteislands located entirely at ferrite grain boundaries ortriple points, martensite islands crack during the earlystages of deformation, and during necking voids areobserved at martensite ferrite interfaces. With very nelydispersed martensite islands located at ferrite grainboundaries or triple points, decohesion was observed atferritemartensite interfaces. In the latter case, voidgrowth and coalescence is much slower than for the steelwith the elongated martensite islands.Steinbrunner et al.[33] showed that void nucleation

occurs by three distinct processes: (1) decohesion atferritemartensite interfaces; (2) fracture of martensiteparticles; and (3) fracture between adjacent elongatedmartensite islands. The dominant mechanism for nucle-ation of voids is fracture of martensite islands at strainsas low as 0.05. However, void growth occurred primar-ily at ferritemartensite interfaces, which resulted from

strain gradients in the ferrite. Steinbrunner et al. alsoshowed that void nucleation in tensile deformation is aconsequence of microstructures in which signicantstrain gradients develop between ferrite and martensite.Ahmed et al.,[22,24,25] Kunio et al.,[23] Gerbase et al.,[26]

Avramovic-Cingara et al.,[27] Khadkhodapur et al.,[28]

Ergan,[29] Szewcyk and Gurland,[30] Uthaisangsuket al.,[31] He et al.,[32] and Steinbrunner et al.[33] showthat cracking can occur in martensite, at the interfacebetween ferrite and hard constituent, or some combina-tion of the two. Given the extent of these variousstudies, it is reasonable to believe that all the failurelocations are possible. Nonetheless, it would appear thatcracks in the hard constituent are likely to be animportant factor to the failure process.

C. Failure in Stretching Sheared Edges

Shearing and punching are deformation processesthat separate metal sheets by means of opposing toolsthat are oset by very small clearances. In a review ofthe literature on shearing and punching, Levy and VanTyne[34] showed that the shearing process is controlledby the geometry of the shearing tools and the thicknessof the work material. Thus, for a given geometry of theshear tooling and a constant thickness of the workmaterial, deformation caused by shearing is not aectedby material properties.Levy and Van Tyne[34] also showed that shearing is

characterized by high strain rate deformation in strainpaths close to pure shear to large true strains withadiabatic heating. It is also shown that there is a high-strain region up to 200 microns behind the sheared edgewhere signicant strain is accumulated, and whichultimately results in failure when the sheared edge isstretched. The region aected by shearing is identied asthe shear-aected zone, SAZ.[35]

Lee et al.[36] showed that cracks form in the SAZ rightbehind the shear face and then coalesce. In an idealsituation, deformation occurs by pure shear, but inactual cases, there are stress and strain gradients in theSAZ. It is known that deformation along a shear strainpath can impart signicant strain before failure. Citing aKorean doctoral thesis, S B Lee et al. showed that ferriteplus bainite microstructures exhibit the lowest strain-hardening rate and the highest hole expansion of thesteels studied. This result shows that strain-hardeningrate can describe the eect of a hard constituent failurein sheared edge stretching.Dalloz et al.[37] evaluated interrupted shearing at slow

speed with a clearance of 0.1 mm and no hold down.The interrupted shearing tests showed severe plasticdeformation and local cavitation at ferritemartensiteinterfaces at depths up to 200 microns from the shearface.Takahashi et al.[38] and Sudo et al.[39] showed that

ferritebainite steel has a better circumferential limitstrain than ferritemartensite steel. Sudo et al. attributedthe improved performance of bainite compared withmartensite because the ductility of bainite restrains voidinitiation at high strains. Sudo et al.[40] also showed thatas the volume fraction hard phase increases over a range


of 2.5 to 20 pct, circumferential limit strain markedlydecreases for ferritemartensite steels and moderatelydecreases for ferriteother hard-phase steels.The studies of Takahashi et al.[38] and Sudo et al.[39]

are consistent with the study of Lee et al.[36] because S BLee et al. show that dierences in strain-hardening ratecan be attributed to dierences in the hard constituent.This result indicates that the exact details of the hardconstituent microstructure in dual-phase steels are notalways necessary to evaluate failure in sheared edgestretching.Sudo et al.[40] also showed that for water-quenched

steels, as the martensite island size increased from 2 to 4microns, there was a substantial drop in the circumfer-ential limit strain. Thereafter, increasing martensiteisland size to 12 microns had little or no eect oncircumferential limit strain. These results could beconsistent with crack initiation within the martensiteislands where the initial increase island size makes iteasier to initiate a crack.Sudo et al.[40] determined that for ferritemartensite

steels, voids initiate by cracking in martensite islandsand by decohesion at ferritemartensite interfaces atabout 20 pct strain. For samples with ferrite, bainite,and martensite microstructures, voids are formed bydecohesion at ferritehard-phase interfaces at about25 pct strain.In studying damage in tensile tests, Lee et al.[36]

showed the importance of strain-hardening rate onmicrostructural damage that leads to failure. The greaterthe strain-hardening rate, the greater the deformation offerrite relative to a hard constituent. Increasing thestrain dierential between ferrite and a hard constituentincreases the rate of crack growth in the interface region.Since it is not possible to perform a tensile test on

material from the SAZ, Levy and Van Tyne[41] used thestrain-hardening rate at uniform elongation in a tensiletest as a measure of damage leading to failure in shearededge stretching. Data were taken from other studies.[4245]

It was found that circumferential limit strain increaseslinearly with decreasing strain-hardening rate at uniformelongation. The relationship applies to steels with arelatively soft ferrite and the following hard phases:angular or spherical carbides; pearlite; titanium carbo-nitride; bainite; and higher-carbon martensites. At thesame strain-hardening rate, it is found that an increasein ferrite strength, such as a recovery-annealed productand lower carbon martensite in dual-phase or TRIPsteels, resulted in improved circumferential limit strain.These results are consistent with the study of Leeet al.[36]

Based on the above results from the literature, atentative hypothesis for the failure sequence for shearededge stretching in dual-phase steels is proposed. Thishypothesis is that cracking initiates in the hard constit-uent with either a crack that may split a hard constituentisland or a crack at the hard constituent ferrite interface.Thereafter, a crack grows along hard constituentferriteinterfaces. Eventually, cracks at multiple hard constit-uentferrite boundaries link and failure ensues. Increas-ing the relative ow between ferrite and the hardconstituent increases the rate of crack growth.

D. Experimental Approach

The experimental approach in the current study wasdesigned to evaluate the hypothesis that crackinginitiates in the hard constituent and extends to the hardconstituentferrite interfaces where relative owbetween ferrite and the hard constituent is importantin determining the circumferential stain at failure. Theentire hypothesis cannot be evaluated from a singleexperiment. In the current study the experiments wereconducted on a steel with a single bulk carbon contentthat was heat treated to produce a hard constituent witha range of volume fractions.In evaluating the eect of microstructure on sheared

edge stretching, most studies use microstructure andtensile properties before shearing.[39,40,4550] Since theSAZ has signicantly dierent properties after shearing,sheared edge stretching performance should be evalu-ated using the properties of the SAZ that are within 200microns of the shear face.Since there is no phase transformation during shear-

ing, ferrite and hard constituent volume fractions andsize distributions remain unchanged. What, however,does change is that the ferrite grains and the hardconstituent islands are substantially elongated. Theincreased elongation increases the surface area offerritehard constituent interfaces. Shearing alsoincreases ferrite strength and has an undetermined eecton hard constituent strength.The current study examined ve dual-phase steels

with the same composition from the same coil. Four ofthe microstructures were produced by laboratory iso-thermal heat treatments on the cold rolled product. Theother steel microstructure was produced on a commer-cial hot-dip galvanizing line as a galvannealed steelproduct. Metallographic analysis and Vickers hardnessvalues were measured before and after shearing. Tensileproperties were determined before shearing. Theseproperties are used to examine structureproperty rela-tionships for sheared edge stretching.

II. EXPERIMENTAL PROCEDURE

A. Materials

Samples were taken from a single coil after coldrolling for use in isothermal annealing to vary dual-phase microstructures. The remainder of the coil wasused to produce hot-dip-galvannealed dual-phase steel.The full hard material was isothermally annealed in asalt pot and air-cooled to produce steels with four levelsof percent carbon in the hard constituent. The thicknessof the steel is 1 mm. Table I shows the chemicalcomposition of the steel.The percentage of carbon in the hard constituent is

determined by:

CM wt pct C in steel =VM 1where VM is the volume fraction of the hard constituent.The samples are identied by a code, where L

represents an isothermal laboratory heat treatment and


C represents the commercial hot-dip-galvannealed prod-uct. The number following the letter represents thevolume fraction hard constituent. Table II shows theisothermal annealing temperature, volume fraction hardconstituent, a description of the hard constituent, andpercentage of carbon in the hard constituent.

B. Metallography

Samples were examined using optical and scanningelectron microscopy. Etchants were selected to highlightmetallographic features, voids, and related metallurgicaldamage. Ferrite grain size and hard constituent island sizewere determined usingASTME112-96[51] for determiningsize in materials with a bimodal size distribution. Ferritegrain size (GF) or hard constituent island size (GM) wasdetermined from the following relationship:

Gd Vf=Na L=M 2where Gd is the average grain or island size, Vf is thevolume fraction of the phase or constituent of interest,Na is the number of intersections with either ferritegrains or hard constituent islands, L is the total length ofline, and M is the magnication.Volume fractions of ferrite and of hard constituent

were determined by the Abrams 3-circle interceptmethod with a line length of 500 mm. Intersections withwhole ferrite grains or hard constituent islands werecounted in accordance with ASTM E112-96.[51] Su-cient point counts were taken to insure an accuratedetermination of volume fraction.

C. Mechanical Testing

Tensile testing was done per ASTM E-8[52] using aspecimen width of 12.7 mm and a gauge length of12.7 mm. Tests were pulled at a constant engineeringstrain rate of 6 9 104 s1. Samples oriented longitudi-nally (L), transverse (T), and diagonal (D) to the rollingdirection were pulled, and the average tensile propertieswere determined from [L+T+2D]/4.

Plastic strain ratios (R-values) were determined usingASTM E-517.[53] R-values were determined at 10 pctelongation because of the limited ductility of thesematerials.Hardness on sample cross sections was determined

using Vickers hardness with a 100 gf load and a dwelltime of 10 s. The standard deviation of the hardnessmeasurements is 6 HV for samples tested beforeshearing. After shearing, the standard deviations arelarger. The increase in the standard deviation aftershearing is a result of the less homogenous microstruc-ture in the SAZ (i.e., within 200 microns of the shearededge).

D. Hole Expansion Limit

An initial circular hole was punched using a clearanceof 18 pct to produce a 19.15-mm hole. The punch speedwas not recorded, but was very rapid. A conventionalMarciniak die set with a 101.6-mm punch diameter wasused for expanding the initial hole. A good lubricantwas applied to the punch before testing. The force on thelock bead was sucient to prevent metal movement othe binder. Tests were run with the shear burr up at atest speed of 0.51 mm/s.Failure was determined visually with the aid of a

monitor screen. The failure criterion was that of eitherinitial fracture or a very deep neck. The increase in thediameter of the hole is the average of measurements at0/180, 45/225, 90/270, and 135/315 degrees around thehole. The approximate standard deviations of the holeexpansion ratio results range from 0.006 to 0.017.

III. RESULTS

A. Tensile Properties

Table III shows the average tensile properties of theve steels tested. Table III also shows that as volumefraction hard constituent increases, tensile strength

Table I. Chemical Analysis of Steel (in Weight Percent)

C Mn Si S Mo Al Ti V N

0.08 1.77 0.19 0.006 0.19 0.050 0.020 0.040 0.003

Table II. Annealing Temperature and Metallurgical Characteristics

MaterialAnnealing

Temperature (K)*

Volume FractionHard Constituent

(VM)Wt Pct C in

Hard Constituent (CM)Nature of

Hard Phase**

Size of HardConstituent,GM (lm)

Hard PhaseAspect Ratio

FerriteGrain Size,GF (lm)

L15 988 0.15 0.533 M 1.17 2.01 4.32C19 *** 0.19 0.421 M & B 1.84 2.24 4.55L24 1013 0.24 0.333 M 1.01 2.10 2.67L31 1038 0.31 0.258 M & B 1.21 2.04 2.53L38 1053 0.38 0.211 M & B 1.16 2.04 2.16

*Temperatures are 10 K.**M = martensite, B = bainite.***Hot-dip-galvannealed.


increases, with little or no increase in yield strength.Also, as volume fraction hard constituent increases,uniform elongation, total elongation, and n-valuedecrease. The volume fraction hard constituent doesnot aect the R-value.

B. Microstructure

Table II shows the laboratory annealing temperatureand selected metallurgical characteristics of the steels.As volume fraction hard constituent increases, itscarbon content decreases, which results in decreasingstrength. Also, for the isothermal heat treatments, amartensitebainite mixture is observed for the twohighest isothermal annealing temperatures.The heating cycle for the hot-dip-galvannealed steel,

C19, required about 300 s for the steel to reachapproximately 1093 K (820 C). The time at tempera-ture was at least 30 s. Cooling to room temperature tookabout 160 s with a hold and slight increase in temper-ature when the steel was in the zinc pot. The cooling ratewas somewhat faster after the sheet exited the zinc pot.The hot-dip-galvannealed steel exhibits a mixed mar-tensite bainite microstructure.The hard constituent aspect ratio for all ve steels and

the hard constituent island diameter for the fourisothermally annealed steels are similar. Ferrite grainsare relatively equiaxed before shearing. The hard con-stituent islands exhibit aspect ratios from 2.01 to 2.24.Figure 1 shows a typical microstructure after shearing,and indicates that the shearing process substantiallyelongates both the ferrite grains and hard constituentislands. On a qualitative basis, the elongation of theferrite grains appears to be equivalent to at least 60 pctcold reduction. A 60 pct cold reduction is equivalent toa true thickness strain of 0.92.Figure 2 shows the extent of voids and related

damage. While strain in shearing exceeds strain intensile deformation, it would seem that more micro-structural damage should be observed.For a single bulk carbon content, only one of the

following four variables is independent: (1) volumefraction hard constituent; (2) volume fraction ferrite; (3)percentage of carbon in hard constituent; and (4) isother-mal annealing temperature. Correlation analysis showsthat ferrite grain size is highly correlated with volumefraction martensite and circumferential strain at failure.These cross correlations are discussed in Section IVG.

Figure 3 shows a cross-sectional view of the SAZwhere it can be seen that the shearing process rotatesand elongates both ferrite grains and hard constituentislands. The extent of the elongation of the hardconstituent can be seen by comparing the aspect ratioof the hard constituent before shearing in Table II withthe metallographic evidence shown in Figure 3. Theincreased elongation of the hard constituent aftershearing indicates signicant deformation of the hardconstituent.As shown in Figure 3, voids were observed at ferrite

hard constituent interfaces in the burnish and fractureregions of the SAZ within 3 to 20 microns from theshear face for all the steels in the study. Within thelimitations of the metallographic work, the incidence ofvoids was similar for all ve steels.Figure 4 shows that cracks are sometimes observed at

hard constituentferrite interfaces. Figure 5 shows dec-ohesion at ferritehard constituent interfaces near thesurface of the shear face. Observations indicated thatvoids were more likely to form at martensiteferriteinterfaces than bainiteferrite interfaces. Also, crackswere occasionally observed at probable manganesesulde stringers that are parallel to the angle of grainrotation. These cracks intersect the shear face. Theimportance of these cracks to failure in sheared edgestretching is not known.

Table III. Mechanical Properties before Shearing

MaterialYield Strength

(MPa)Tensile Strength

(MPa)Uniform

Elongation (Pct)Total Elongation

(Pct)K-value(MPa) n-value* R-bar eC-limit

L15 391 581 22.0 28.7 977 0.19 0.83 0.336C19 346 624 17.6 26.4 986 0.16 0.88 0.365L24 333 712 16.0 22.7 1096 0.15 0.84 0.255L31 395 769 14.5 21.5 1154 0.14 0.83 0.231L38 383 756 14.9 21.3 1143 0.14 0.81 0.215

Tensile properties are average values calculated from (L+T +2D)/4.*These steels exhibit signicant variation in instantaneous n value. The results shown in the table are calculated from true stress of 425 MPa up to

the true stress at uniform elongation.

Fig. 1Typical microstructure after shearing. Sample L31.


C. Hardness

Table IV shows Vickers hardness values before andafter shearing. The after shearing Vickers hardnessvalues were determined from locations as close aspossible to the sheared edge. Given marked straingradients in the SAZ, it is not surprising that some of thestandard deviations for after shearing tests are greaterthan for before shearing tests. Considering the addedvariability of after shearing hardness values, the increasein Vickers hardness appears to be reasonably similar forall ve steels.Using a standard Vickers hardness table for steels,[54]

Vickers hardness and tensile strength can be related.

HV 0:3357 TS 18:581 3where HV is the Vickers hardness, TS is the tensilestrength in MPa, and the square of the correlationcoecient, R2, for this relationship is 0.997. To deter-mine tensile strength from HV values, the data areregressed again.

TS 2:97 HV 57:1 4

The valid range is: 125

expected. For calculating the adiabatic temperatureincrease, the average strain from shearing is used. Inestimating the adiabatic temperature increase, idealplastic stressstrain behavior is assumed, because muchof the deformation is for strains where there is very littlestrain hardening. The increase in adiabatic heat for thebulk is calculated using the approach of Dieter:[56]

DT 0:95WqCp 6where DT is the increase in temperature, W is the workper unit volume, q is density, and Cp is the specic heat.

The calculated adiabatic temperature increase in thefailure region of the SAZ increases with volume fractionhard constituentspecically, L15-306K, C19-308K,L24-343K, L31-361K, and L38-357K. While temperingis known to reduce the strength of hard constituents(particularly martensite), botha very short time attemperature and a rapid heat transfer to the bulksug-gest that adiabatic heating should not signicantly aectthe strength of the hard constituents or microstructuraldamage due to shearing.Microstructural examination of samples from after

shearing shows only modest void formation and crack

Fig. 3The shear-aected zone (SAZ) near the shear face; (a) Full cross section; (b) the burnish region to fracture region transition, with thearrows indicating the dierences in the general ow direction of the ferrite in the material near the burnish (upper) and fracture (lower) regions;(c) the middle of the fracture region, with the arrows indicating voids; and (d) the burr. Ferrite grains are elongated due to the strain imposed byshearing. Hard-phase islands aligned in the direction of ferrite elongation. Some hard-phase plasticity is observed. Sample L31.


growth. Given the calculated strain and the highlydeformed microstructure in the SAZ near the shear face,it is surprising that there is not more void formation andcrack growth.Lee[44] and Levy and Van Tyne[34] have shown that

shear deformation is a process that can achieve largestrains before fracture. Lee[44] has shown that for aDP590 steel void nucleation begins at a strain of 0.16 fortension and 0.60 for torsion. LeRoy and Embury[57]

have shown that the fracture strain of aluminum alloysis considerably greater in torsion than in tension.Given the high strains associated with shearing, the

extent of sheared edge stretching is surprising. Thesubstantial remaining ductility in stretching a shearededge would seem to be the result of minimum damage

that resulted from shear deformation. In subsequentstretching, the strain path will reach the failure limitsooner. Specically, there is a circumferential strainoset of 0.09 before the deformation follows a tensilestrain path[58].

B. Failure Hypothesis

The failure hypothesis developed from a review of theliterature suggests that there is a series of events thatultimately lead to failure in sheared edge stretching. Theinitial step is cracking across a hard constituent island orcrack initiation at the interface between the hardconstituent and ferrite. The cracks then grow alonghard constituentferrite interfaces. Furthermore,increases in the relative deformation of ferrite relative tothe hard constituent increases crack growth. Eventually,the cracks at ferritehard constituent interfaces link upand the macroscopic sheared edge cracking is observed.The independent variables needed to evaluate the

proposed failure hypothesis include the strength of thehard constituent; the strength dierence across the hardconstituentferrite interface; ferrite grain size, which forthe steels in the current study is a measure of the surfacearea of hard constituentferrite interface; and the strain-hardening exponent at uniform elongation before shear-ing. Since cracking in the hard constituent is part of the

Fig. 4A crack in the fracture region. The crack occurs where astring of inclusions meets the edge. The dashed oval shows the pene-tration depth of the crack into the sheet.

Fig. 5The fracture of hard constituent and voids at hard constituentferrite interfaces (a) low and (b) high magnications.

Table IV. Hardness before and after Shearing

Material Before (HV) After (HV)

L15 178 5 327 5C19 192 6 320 16L24 218 7 336 11L31 237 6 379 3L38 237 6 384 17


failure process, the eect of volume fraction hardconstituent is included in the analysis. The eect ofcross correlations between independent variables is alsoconsidered.

C. Strength of Hard Constituent

The strength of the hard constituent is dicult todetermine because (1) mechanical property data fromsamples of 100 pct of a single phase are limited, (2)in situ measurements are extremely dicult, and (3)stress concentrations on the micro level and microstruc-tural constraints can aect the strength and interactionsbetween individual constituents.The carbon content of the hard constituent was

calculated using Eq. [1]. A graph from Bain andPaxton[59] shows the relationship between Vickers hard-ness and carbon content of martensite. Points werepicked from the Bain and Paxton graph and regressed:

HVM b0 b1C b2C2 7where HVM (in kg/mm

2) is the hardness of martensite,b0 = 164.64, b1 = 2111.2, b2 = 1553.1, and C is thewt pct carbon. The regression has an R2 = 0.999.Since there is some bainite in the hard constituent of

several of the samples, the calculated Vickers hardness isan approximation. Nevertheless, the calculated hardnessof the hard constituent is still a useful approximation.The Vickers hardness for ferrite before shearing is

calculated using the law of mixtures.

HVF HVB VMHVM = 1 VM 8

where HVB is the bulk hardness of the steel, VM is thevolume fraction of the hard constituent, and HVM is thehardness of the hard constituent.The average calculated HVF before shearing is 61 9.

Since the carbon content of the ferrite for all ve steels isapproximately 0.004,[60] the calculated hardness seemsreasonable for very low carbon ferrite. Using Eqs. [7] and[8], the hardness ratio, hard constituent/ferrite beforeshearing can be calculated. Even if the hardness of theferrite is not exact, it is expected that its hardness shouldbe reasonably constant for all ve steels. Thus, changingthe ferrite hardness would aect the absolute values of thehardness ratios, but the relative values of the hardnessratios would still provide insight.After shearing, it is evident that ferrite strength should

increase substantially. The eect of shearing on thestrength of the hard constituents in a ferrite matrix is notknown. For the purpose of this analysis, it is assumedthat the strength of the hard constituent is not changed.The strain in ferrite in the SAZ has been shown to be

approximately 1.17. For convenience, a true strain ofone is used in each of the power law equations shown inTable III to determine the true stress in the ferrite.While the calculated true stress is not a tensile strength,it is considered a reasonable approximation of thetensile strength. Equation [3] is used to determine theVickers hardness for ferrite after shearing.Figure 6 shows the eect of the ratio of Vickers

hardness for the hard constituent to the Vickers hard-ness of ferrite before and after shearing on the truecircumferential strain at failure. The change in thecurves for before and after shearing in Figure 6 is theresult of an increase in ferrite strength. Since thehardness values of the ferrite before shearing and aftershearing are similar for each of the ve steels, Figure 6can be interpreted as the eect of the hard constituenton the true circumferential strain at failure.Figure 6 also shows that increased strength of the

hard constituent increases true circumferential limitstrain at failure. These results show that for the vesteels in the current study, increasing the strength of thehard constituent increases resistance to cracking in thehard constituent and/or at the hard constituentferriteinterface. Ishigoru et al.,[10] Kang et al.,[12] Minamiet al.,[16,17] Shen et al.,[18] Fallihi et al.,[19] Kunio et al.,[23]

Ahmed et al.,[24,25] Uthaisangsuk et al.,[31] and Heet al.[32] all indicate the importance of martensite in voidnucleation and crack growth.It can also be seen from Figure 6 that as the strength

dierential across the hard constituent/ferrite interfaceincreases, the true circumferential limit strain at failureincreases. The eect of both the strength dierential acrossthehard constituent/ferrite interfaceand the strengthof thehard constituent on the true circumferential limit strain atfailure are unexpected. Figure 6 also shows the pro-nounced eect of shearing on the value of the strengthdierential across the hard constituentferrite interface.

D. Interface Area

Table II shows that hard constituent island size isrelatively constant, while there is a range of ferrite grain

Table V. Comparison of Tensile Strength before and afterShearing

Material

BeforeAfter

Calculated# (MPa)

Actual(MPa)

Calculated# (MPa)

L15 585 581 1029C19 627 624 1009L24 706 712 1056L31 761 769 1184L38 761 756 1199

# Calculated from standard conversion.TS [MPa] = 2.97 HV+57.1.Applicable Range.125

size. Shearing elongates the ferrite grains, and to a lesserextent the hard constituent islands. This increasedelongation increases the interfacial surface area betweenferrite and the hard constituent.Since the ferrite grain elongation from shearing is

relatively similar for all ve steels, ferrite grain sizeremains a useful parameter for evaluating microstruc-ture after shearing. Despite being not fundamentallycorrect, ferrite grain size is a reasonable indicator of thesurface area of ferrite grains.Figure 7 shows a linear relationship between increas-

ing ferrite grain size and increasing circumferential limitstrain for all ve steels in the study. The results of aregression analysis are

eClimit a0 a1Gf 9where a1 = 0.076 0.016, a2 = 0.649 0.005, and Gfis ferrite grain size. The R2 value for the regression is0.98, with N = 5, and there is no systematic deviation.With a given volume fraction ferrite, as ferrite grain

size increases, the surface area of ferrite grains decreases.

Since the microstructures of the steels in the currentstudy show more examples of hard constituenthardconstituent interfaces than ferriteferrite interfaces, theright side of Eq. [9] is an approximation of the surfacearea of hard constituentferrite interface. Consequently,Figure 7 can be interpreted to show that the surface areaof hard constituentferrite interface area predicts truecircumferential limit strain at failure.Kunio et al.,[23] Gerbase et al.,[26] Avramovic-Cingara

et al.,[27] Kadhodapouret al.,[28] Erdgan,[29] andUthaisangsuket al.[31] all show the importance of hard constituentferrite interfaces in determining sheared edge stretchinglimits. It is most likely that as the area of hardconstituentferrite increases, crack length can increase,which accelerates the process of crack growth, cracklinkage, and ultimate failure. Alternatively, an increasedarea of hard constituentferrite interface increases theprobability of crack initiation at the hard constituentferrite interface.

E. Relative Movement of Ferrite Grains

Levy and Van Tyne[41] have shown that increasingstrain-hardening rate at a uniform elongation increasesthe local strain on the ferrite side of a hard constituentferrite interface. The basic logic is that on the micro-scopic scale, the greater the bulk strain-hardening rate,the greater the deformation of a soft phase relative to ahard phase. A greater deformation of ferrite relative to ahard constituent increases the likelihood of void initia-tion and crack growth that leads to failure.The strain-hardening rate at uniform elongation is the

engineering tensile strength expressed as a true stressvalue.[41] Table III provides the necessary data tocompute strain-hardening rate at uniform elongation.Figure 8 shows the eect of strain-hardening rate at

uniform elongation on the circumferential strain limit atfailure. For the isothermal heat treatments, the circum-ferential limit strain decreases linearly as the strain-hardening rate at uniform elongation increases. Since ahigher strain-hardening rate at uniform elongationdecreases the strain at which voids nucleate and cracksform, the sheared edge formability for these laboratory-heat-treated steels depends on the bulk mechanicalproperties.Figure 8 also shows that the hot-dip-galvannealed

steel, C19, exhibits an increased circumferential limitstrain, compared with the laboratory-annealed steels ata comparable value of the strain-hardening rate atuniform elongation. Levy and Van Tyne[41] have shownthat the eect of strain-hardening rate at uniformelongation depends on microstructure. Given the dier-ence in heat treatment, it is possible that C19 exhibitsmore bainite at the hard constituentferrite interface. Inthis case with more bainite at the interface, it isreasonable that for an equivalent amount of local strainat the hard constituentferrite interface, the interfaceshould be better able to withstand void formation andcrack growth than a martensiteferrite interface.

Ferrite Grain Size, GF (m)2.0 2.5 3.0 3.5 4.0 4.5 5.0Tr

ue C

ircum

fere

ntia

l Stra

in L

imir,

C-L

imit

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Uncertainty is 1 standard deviation

Fig. 7Relationship between eC-limit and ferrite grain size.

Hardness Ratio (Hard Constituent/Ferrite)0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Tr

ue C

ircum

fere

ntia

l Stra

in L

imit,

C-L

imit

0.10

0.15

0.20

0.25

0.30

0.35

0.40


After Shearing Before Shearing

Fig. 6Relationship between eC-limit and hardness ratio of constitu-entsbefore and after shearing.


F. Volume Fraction Hard Constituent

Limit true circumferential strain at failure is oftenplotted as a function of volume fraction hard constit-uent. Figure 9 shows that true limit circumferentialstrain at failure decreases as volume fraction hardconstituent with C19, exhibiting improved performancecompared with the laboratory heat-treated steels.While Hasegawa et al.[15] suggested that increasing

volume fraction martensite enhances the stress distribu-tion between ferrite and martensite; the explanationseems insucient to explain the results of the currentstudy. Supercially increasing volume fraction hardconstituent increases the probability of crack formationwithin the hard constituent or in hard constituent at theinterface with ferrite. However, the experimental resultsin the current study show the importance of thehardness of the hard constituent, which increases asvolume fraction hard constituent increases. Also, withrespect to the data in the current study, the hardconstituentferrite interface area does not increase withincreasing volume fraction hard constituent.

G. Correlation between Key Variables

Analyzing data that are highly cross correlated can bedicult. Table VII shows the cross correlations betweenkey independent variables and true circumferential limitstrain at failure. Based on fundamental considerations,cross correlation between percent carbon in the hardconstituent and its hardness is expected, and only thehardness of the hard constituent is used in the analysisof the experimental data. However, there are nofundamental considerations for hard constituent hard-ness, ferrite grain size, and strain-hardening rate atuniform elongation to be highly cross correlated.For a single bulk hardness and a limited number of

heat-treating conditions a high cross correlation can beintroduced between key independent variables. Thus,the analysis in the current study does not prove theproposed hypothesis describing the failure process forsheared edge stretching, but it can be concluded that theanalysis is consistent with the proposed failure hypoth-esis. Additional experimental study including sampleswith more bulk carbon contents, more varied heat-treatments, and a more detailed study of the hardconstituents is needed to denitively prove the proposedhypothesis.If a future experiment denitively proves the proposed

hypothesis, then the independent variables would still behighly cross correlated because a sequence of events isneeded to cause failure. Specically, hardness of thehard constituent aects its resistance to initial fracture;increased surface area of ferritehard constituent inter-face aects crack growth, which for the steels in thecurrent study is represented by ferrite grain size; andstrain-hardening rate at uniform elongation aectsrelative movement of ferrite grains relative to a hardconstituent, which increases crack growth. Given thesequence of events needed for failure, a high degreeof cross correlation for the causative variables isexpected.

V. CONCLUSIONS

For the steels used in the current study, analysis of theexperimental results is consistent with a failure process inwhich initial cracking is in or adjacent to the hardconstituent, crack growth occurs at the hard constituent

Table VII. Cross-Correlation Results for IndependentVariables

eC-limit VM CM GF HM dr/de

eC-limit 1VM 0.90 1CM 0.89 0.97 1GF 0.99 0.89 0.90 1HM 0.91 0.99 0.99 0.91 1dr/de 0.95 0.92 0.96 0.96 0.95 1

HM = Hardness of hard constituent.dr/de = Strain-hardening rate at uniform elongation.

Strain Hardening Rate at Uniform Elongation (MPa)700 750 800 850 900Tr

ue C

ircum

fere

ntia

l Stra

in L

imit,

C-L

imit

0.10

0.15

0.20

0.25

0.30

0.35

0.40


Fig. 8Relationship between eC-limit and strain-hardening rate atuniform elongation.

Volume Fraction Hard Constituent, VM0.10 0.15 0.20 0.25 0.30 0.35 0.40Tr

ue C

ircum

fere

ntia

l Stra

in L

imit,

C-L

imit

0.10

0.15

0.20

0.25

0.30

0.35

0.40

C19


Fig. 9Relationship between eC-limit and volume fraction-hardconstituent.


ferrite interface, and relative movement of ferriteincreases crack growth.Increased hardness in the hard constituent reduces

initial cracking.Increased surface area of hard constituentferrite

interface increases crack growth. For the steels used inthe current study, ferrite grain size provides an estimateof hard constituentferrite interface area.Increased strain-hardening rate at uniform elongation

increases ferrite movement relative to the hard constit-uent, which accelerates crack growth.Failure occurs in the shear-aected zone (SAZ) in a

region within about 200 microns from the sheared edge.True strain in the SAZ after shearing is about 1.2.Subsequent stretchability of this highly deformed regionis a consequence of the deformation being along a shearor a near shear strain path.

ACKNOWLEDGMENTS

Partial support for the current study from theAdvanced Steel Processing and Products ResearchCenter at Colorado School of Mines is gratefullyacknowledged.

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Copyright of Metallurgical & Materials Transactions. Part A is the property of SpringerScience & Business Media B.V. and its content may not be copied or emailed to multiple sitesor posted to a listserv without the copyright holder's express written permission. However,users may print, download, or email articles for individual use.

Failure during Sheared Edge Stretching of Dual-Phase SteelsAbstractIntroductionHard Constituent and Ferrite StrengthDeformation in Tensile TestingFailure in Stretching Sheared EdgesExperimental Approach

Experimental ProcedureMaterialsMetallographyMechanical TestingHole Expansion Limit

ResultsTensile PropertiesMicrostructureHardnessCircumferential Limit Strain

Discussion of ResultsDeformation in ShearingFailure HypothesisStrength of Hard ConstituentInterface AreaRelative Movement of Ferrite GrainsVolume Fraction Hard ConstituentCorrelation between Key Variables

ConclusionsAcknowledgmentsReferences

Failure during Sheared Edge Stretching of Dual-Phase Steels

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