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Materials Science & Engineering A

journal homepage: www.elsevier.com/locate/msea

Deformation mode and strain path dependence of martensite phasetransformation in a medium manganese TRIP steel

Wei Wua, Yu-Wei Wanga,⁎, Panagiotis Makrygiannisa, Feng Zhua, Grant A. Thomasb,Louis G. Hector, Jr.c,⁎⁎, Xiaohua Hud, Xin Sune, Yang Renf

a AK Steel Research and Innovation, AK Steel Corporation, Dearborn, MI 48120, USAbAK Steel Research and Innovation, AK Steel Corporation, Middletown, OH 45005, USAcGM Global Technical Center, General Motors Corporation, Warren, MI 48092, USAd Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352, USAeOak Ridge National Laboratory, Oak Ridge, TN, 37930, USAf X-ray Science Division, Argonne National Laboratory, Argonne, IL 60439, USA

A R T I C L E I N F O

Keywords:Deformation modesMartensite phase transformationNon-linear strain path

A B S T R A C T

The martensite phase transformation dependence upon deformation modes and strain paths in a mediummanganese (10 wt%) TRIP steel stamped into a T-shape panel was quantified through combination of 3D digitalimage correlation and synchrotron X-ray diffraction. The T-shape emulates a portion of a common anti-intrusioncomponent. The stamping speed was kept intentionally slow (1 mm/s) so as to avoid excessive heat generation.The steel, which belongs to the third generation advanced high strength steel (3GAHSS) family, was chosen fortwo reasons: (1) it is two-phase, i.e. austenite and ferrite, with martensite resulting from deformation-inducedphase transformation; (2) the 66 vol.% initial retained austenite volume fraction (RAVF) enabled a thoroughexamination of the martensite phase transformation at large deformation levels without exhaustion. Strain fieldswere coupled with measured RAVF values of small specimens extracted from specific locations on a formed T-shape panel. This enabled an exploration of the effects of linear, bilinear, and non-linear strain paths as well asdeformation modes such as tension, plane strain, biaxial tension, and equibiaxial tension. Results suggest asignificant martensite phase transformation dependence on deformation mode and strain path in the absence offracture and when martensite phase transformation is unaffected by heat generated during forming. In general,the uniaxial and biaxial tension deformation modes facilitate the martensite phase transformation, while thesmallest amount of martensite phase transformation occurs under plane strain. Some discussion as to furtherapplication of the experimental methods detailed in this study to other 3GAHSS and the effects of fracture onmartensite phase transformation is provided.

1. Introduction

The third generation advanced high strength steels (3GAHSS) offercombinations of strength and ductility that are potentially favorable forautomotive component forming. Their macroscopic-scale mechanicalproperties, as represented by an advanced high strength steel (AHSS)tensile strength-ductility chart [1], are typically intermediate to thoseof the high strength/lower ductility first generation advanced highstrength steels (1GAHSS), and the high strength/high ductility secondgeneration advanced high strength steels (2GAHSS) [2]. As-received3GAHSS microstructures are multiphase and may consist of combina-tions of body-centered cubic (BCC) ferrite, face-centered cubic (FCC)

austenite, and body-centered tetragonal (BCT) martensite phases pro-duced from sophisticated alloying and heat treatment schemes. Theferrite (α) phase controls ductility, while strength is enhanced bymartensite (α′) as well as bainitic ferrite. A common deformation me-chanism in many 3GAHSS is the transformation induced plasticity(TRIP) [3] effect, i.e., the diffusionless shear transformation of me-tastable retained austenite (γ or RA) to new martensite (also BCT) withplastic straining [3]. The combination of phases and the martensitictransformation of austenite enhances the work hardening rate andimproves strength and ductility thereby delaying fracture: this isespecially favorable for automotive applications. In some cases, theaustenite to martensite transformation may occur via an intermediate

https://doi.org/10.1016/j.msea.2017.11.008Received 7 September 2017; Received in revised form 2 November 2017; Accepted 3 November 2017

⁎ Correspondence to: Research and Innovation, Advanced Engineering, AK Steel Corporation, 14661 Rotunda Dr., Dearborn, MI 48120, USA.⁎⁎ Correspondence to: GM Global Technical Center, General Motors Corporation, 30470 Harley Earl Blvd, Warren, MI 48092, USA.E-mail addresses: Yu-Wei.Wang@aksteel.com (Y.-W. Wang), Louis.Hector@gm.com (L.G. Hector, Jr).

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step through ε-martensite, the non-magnetic, HCP form of martensite,[4]. Subsequent transformation of ε-martensite to α′-martensite at in-tersections of shear bands has been experimentally confirmed in theliterature [5,6].

The 3GAHSS are also distinct from the first generation (1GAHSS)TRIP steels [1] by virtue of a higher retained austenite (γ or RA) volumefraction (RAVF) and Mn content [e.g. 3–12 weight percentage (wt%)].The 3GAHSS alloying typically differs from that of the low stackingfault, twinning induced plasticity (TWIP) steels, which are 2GAHSS,wherein Mn content can range from 15 to 25 wt% [7,8] and austenite isstable against transformation. Steels that exhibit both the TRIP andTWIP effects with 15–25 wt% Mn have also been identified [9,10]. Inaddition to the TWIP and TRIP effects, dislocation glide [11] also oc-curs, with one mechanism predominating over others within a specifictemperature range.

Examples of 3GAHSS are Medium Mn (~ 3–12 wt% Mn) TRIP steels[12], TRIP steels with a bainitic ferrite matrix (TBF steels) [13], andTRIP steels subject to a quenching and partitioning (Q&P) heat treat-ment (also known as QP steels with ~ 3 wt% Mn) [14]. Of these ma-terials, the Medium Mn TRIP steels, in which austenite is stabilizedthrough enrichment with Mn, have recently received considerable at-tention in the literature since they are produced through intercriticalannealing in the ferrite–austenite region, a processing route that mightbe somewhat simpler than Q&P [10,15], for example. In addition, theyprovide strengths and ductilities well within the range of 3GAHSS.Therefore, there is still considerable interest in understanding the mi-crostructure evolution during alloy processing and the effect of micro-structure on component manufacturing and performance [16–18]. ATBF microstructure results from cooling to just above the martensitestart temperature thereby allowing bainitic ferrite to form with C par-titioning to the remaining austenite. Although there are different var-iants of Q&P, the essential approach is heating to a temperature abovethe austenitization temperature, which can be followed by an im-mediate quench to a temperature between the martensite start andfinish temperatures. Carbon mobility and subsequent carbon enrich-ment of austenite occurs during a final partitioning step which en-hances austenite stability. The size and morphology of austenite issomewhat varied in QP steel. Xiong et al. [19] found that film-like(< 1.0 µm) and blocky (≥ 1.0 µm) austenite in a Fe-0.22C-1.4Si-1.8Mn(wt%) TRIP steel subject to a Q&P heat treatment transformed at dif-ferent tensile strains. In general, the RAVF decreases with increasingplastic strain and can be measured with a variety of methods includingsynchrotron X-ray diffraction [20,21] (or high energy X-ray diffraction,HEXRD), neutron diffraction [22] and additional techniques such asthose detailed by Jacques et al. [23].

The mechanical stability of austenite is dependent upon tempera-ture [24] and strain rate [25–27], deformation mode [28–30], strainpath [31,32], chemistry (e.g. carbon concentration), and morphology(e.g. film or blocky) [19]. Previous research reported in the literaturehas largely focused on measuring retained austenite transformation(e.g. RAVF or RAVF vs. strain) in AHSS almost exclusively for quasi-static, uniaxial tension under different thermal conditions[12,20,33–40]. Diffraction techniques have been successfully employedto investigate deformation mechanisms in uniaxial and cyclic loadingconditions [41–47]. There are, however, some notable exceptionswhere austenite transformation under deformation modes other thantension have been explored. For example, Yan et al. [48] measuredRAVF vs. effective strain in a 0.21C–1.5Si–1.0Mn TRIP steel subject tothree different deformation modes, viz., uniaxial tension, biaxial andplane strain deformation. Martensite phase transformation, measuredwith an X-ray diffractometer technique using Cr Kα radiation [49], wasfastest under plane strain deformation which the authors concluded wasthe most favorable deformation mode. Iwamoto et al. [28] employed anX-ray diffractometer with a Mo Kα X-ray source measuring martensitephase transformation in various TRIP steels. For small strains, a sig-nificant volume of martensite was noted under compression. However,

this changed at higher strains with tension giving the greater volume ofmartensite. Choi et al. [50] developed a microstructure-based finiteelement model to investigate deformation and failure of a commercialFe-0.18C-1.62Si-1.75Mn (wt%) TRIP800 alloy. They predicted the mostrapid transformation of austenite to occur under equi-biaxial stretching,while transformation was slowest under shear. Gnäupel-Herold andCreuziger [22] employed neutron diffraction to measure austenitetransformation in commercial TRIP590, TRIP700 and TRIP780 steelsunder uniaxial tension, biaxial and plane strain deformation. With acombined neutron diffraction and digital image correlation (DIC)technique, Jacques et al. [51] reported that faster austenite transfor-mation rates corresponding to higher hardening at smaller strains oc-curred at stress states between uniaxial and equi-biaxial tension for twoTRIP steels.

At present, no attempts to quantify the dependence of local RAVF ondeformation mode and strain path in a stamped, 3GAHSS componentcould be located in the literature. This data is critical as it is the firststep towards quantitatively linking local ductility, strength and fracturemechanism to 3GAHSS component performance under complex loadingpaths. Such linkages will be required not only for alloy developmentand material selection but also for the development of mechanism-based material constitutive models for finite element simulations. Thereare in fact very few studies in the literature that attempt to link RAVF tolocal properties in a formed (e.g. room temperature stamped) AHSScomponent. For example, Kobayashi et al. noted that stretch flange-ability is dependent, in part, on the martensite phase transformation inTRIP steel and the associated relaxation of local stresses [52]. Sugimotoand Srivastava observed that superior impact toughness of TRIP steels isdependent upon RAVF [53]. Lacroix et al. [54] found that tearing re-sistance of TRIP-assisted steels is improved with higher austenite me-chanical stability. In their study of a 0.1C–1.5Si–1.5Mn–0.5Cu TRIP-assisted steel, Lee et al. [55] attempted to connect retained austenitestability and formability and found better formability in specimens withgreater austenite stability.

In this paper, RAVF variations with deformation mode and strainpath were measured at specific positions around a T-shaped panelstamped from a two-phase, medium Mn (10 wt%) TRIP steel with alarge (~ 66%) initial austenite volume fraction. The panel emulates aportion of a common automotive stamping. The positions chosen formeasurement were subject to different deformation modes and strainpaths as verified with a three-camera DIC technique used to measurethe major and minor strains during forming. The forming speed wassufficiently slow so as not to inhibit martensite phase transformationthrough excessive heat generation thereby enabling measurement ofdata in the limit of room temperature deformation. This is a critical firststep for assessment of material constitutive models for componentforming and performance. Following DIC measurement of the formedpanel, small specimens were extracted from the specific positions forRAVF measurements using high-energy synchrotron X-ray diffraction atthe Advanced Photon Source (APS), Argonne National Laboratory(ANL). Representative results that show the deformation and strainpath dependence of RAVF are presented in a plot of major vs. minorstrain (or “forming limit diagram space”) with the corresponding valueof local RAVF decrease in the formed panel. The results provided acomprehensive examination of deformation-induced martensite phasetransformation under various strain paths, ranging from tension tobiaxial.

2. Materials and experimental procedures

2.1. Med. Mn (10 wt%) TRIP steel

A Medium Manganese (Fe-0.15C-10Mn-1.5Al-0.2Si, wt%)) TRIPsteel, hereinafter referred to as Med. Mn (10 wt%) TRIP, with me-chanical properties within the 3GAHSS family, was developed for thisstudy. No coating was applied to the material. Tensile properties over a

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range of nominal strain rates are detailed in Supplementary AppendixA. Processing involved intercritical batch annealing at 600–700 °C for96 h. According to Gibbs et al. [12], this facilitates enrichment of re-tained austenite with both C and Mn. The material was then hot rolledin billet form and then cold rolled into 1500 mm long strips each with anominal 1.1 mm thickness and 200 mm width. The chemical composi-tion in weight percentage is listed in Table 1. The as-manufacturedmaterial contains ~66% retained austenite by volume fraction with thebalance ferrite. The large initial volume fraction was deemed suitablefor the present study since focus was on deformation mode and strainpath dependence of martensite phase transformation in a 3GAHSSformed panel. Hence, it was unlikely that retained austenite would becompletely exhausted at positions selected for RAVF measurement onthe final formed panel. A field emission SEM image of the as-manu-factured microstructure is exhibited in Fig. 1 showing the ferrite andaustenite phases. The average grain size of the Med. Mn (10 wt%) TRIPwas approximately 2 µm.

2.2. Stamping die set

The laboratory T-shape stamping die set shown in Fig. 2(a) wasdesigned to generate deformation modes (e.g. biaxial tension, uniaxialtension, and plane strain,) and strain paths (i.e. linear, bi-linear, andnon-linear) in a stamped panel for subsequent strain and RAVF mea-surements at discrete locations. Stamping of a flat Med. Mn (10 wt%)TRIP steel blank produced a shell structure with a T-shaped profilehaving a maximum 25 mm stamping depth. The T-shape geometrymimics a section of a generic b-pillar (i.e. the rocker end) which is ananti-intrusion component in vehicle body structures. The die set is in-tegrated into an Interlaken S225 hydraulic press, which contains twoactuators that enable double action: a blank holder actuator and astamping actuator. Each actuator has a maximum 350 mm displace-ment operating within a speed range of 0.01–25 mm/s. For all stamp-ings in the present study, a 1 mm/s actuator speed was used. This speedwas sufficiently slow so that martensite phase transformation was notsuppressed by excessive heat generation and strain rate effects can alsobe avoided (see Supplementary Appendix A) [56]. The maximum forcewas 1000 kN for each actuator. No lubricant was applied in the currentstudy during forming.

The T-shape die set includes an upper die, shown in Fig. 2(b), and alower binder and lower punch, shown in Fig. 2(c). The die cavity depthis adjustable from 17 to 25 mm using shims. A step bead, shown inFig. 2(c), was added to control material flow as the blank is clampedbetween the upper die and the lower binder. Since material along thetop of the T-shape, which is flat, accumulates minimal strain duringstamping, a center pocket was added to the upper die along with amatching recession in the lower punch, shown in Fig. 2(b) and (c). Thecenter pocket follows a square profile with rounded corners. Its depthcan be adjusted with shims to induce various deformation modes, strainpaths, and strain gradients along the center pocket. When the T-shapedie is fully closed, the gap between the die cavity and punch is 1.4 mm,which allows a maximum blank thickness of 1.2 mm for testing. Aftermaterial flow control is established upon application of the binder load,the clamped blank is subsequently formed by the lower punch until a T-shape shell structure results. In multiple tests, the selected stampingparameters were such that no cracking or necking was noted in any ofthe formed Med. Mn (10 wt%) TRIP steel panels in this study.

2.3. Blank geometry

T-shaped panels were stamped from the trapezoid blank geometrydisplayed in Fig. 3(a). The blank thickness in the current study was1.1 mm. Each blank was cut from strips of the Med. Mn (10 wt%) TRIPsteel using wire electrical discharge machining (wEDM). The taperedend of each blank was aligned with the “T” end of the lower punchshown in Fig. 2(c) prior to stamping. Fig. 3(b) shows a fully formed T-shaped panel. This adopts the lower punch geometry shown in Fig. 3(b)with a top surface containing the imprint of the center pocket, a flangeregion along the lower binder, and a vertical wall connecting the two.

2.4. Strain measurement

A custom, three-dimensional (3D) digital image correlation (DIC)system was applied to compute the strain distributions from measureddisplacement fields of the T-shape panels formed from blanks of Med.Mn (10 wt%) TRIP steel under incremental stamping, as shown inFig. 4(a). The stereoscopic configuration of a three-camera system wasattached to the Interlaken press, as shown in Fig. 4(a), which is speci-fically designed for forming limit and hole expansion measurements(not considered in this study). The resolution of each CCD camera is2452 × 2056 pixel2 and each generates an HDF5 data file. Three AlliedVision Stingray CCD cameras, each with a 5 Megapixel resolution andmaximum 9 fps framing rate, were positioned such that the field of viewin adjacent cameras overlapped to enable imaging of the entire surfaceof a T-shaped panel as shown in Fig. 3(b). Each used a 50 mm lens. Allblanks were cleaned with a combination of acetone and ethyl alcohol. ADIC contrast pattern, consisting of a thin layer of flat white paint fol-lowed by flat black paint droplets, was applied to one surface of eachblank. A representative contrast pattern is shown in Fig. 3(b). The blackdroplets were applied randomly, such that the nominal diameter ofeach droplet did not exceed ~ 25% of the chosen pixel subset size inDIC post-processing of strains. This pattern also enabled suitable con-trol of glare. The three cameras were then calibrated with a standard.Additional details behind the multi-camera DIC technique for strainmeasurement used in this study are in Refs. [57–59].

Since the T-shape die is a close-die test, strain evolution duringforming was measured ex situ under incremental stamping. Here, re-ference images of the contrast pattern on the blank surface from each of

Table 1Chemical composition in weight percentage (wt%) of Med. Mn (10 wt%) TRIP steel.

Elements Mn C Al Si Sn P S Co Cr Fe

wt% 9.76 0.16 1.37 0.19 0.003 0.002 0.0018 <0.002 <0.002 Balance

A = Austenite (γ) and F = Ferrite (α)

F

A

A

2 μm

F

F

A

AT

AT

Fig. 1. Field emission SEM image of the as-received Med. Mn (10 wt%) TRIP steel [twophase, ferrite (F) and retained austenite (A)] with approximately 2 µm grain size. Someannealing twins (AT) were observed in the austenite grains which are indicative of a lowstacking fault energy.

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the three cameras were first recorded at a designated location tominimize the rigid movement of the T-shape panel. The forming processwas interrupted every 1 mm of forming depth, with the T-shape panelthen removed from the die. An image from each of the three cameraswas then recorded for strain measurement at the corresponding formingdepth on the evolving T-shape shell structure surface relative to theinitial blank with the DIC cameras. This process, which required re-positioning the T-shaped panel in the same designated location as wererecorded a few images of the blank surface prior to forming, was con-tinued until the maximum 25 mm forming depth was achieved. A ty-pical loading curve for a Med. Mn (10 wt%) TRIP steel T-shape panelduring incremental forming is shown Fig. 4(b).

Once forming was completed, true major and minor strain dis-tributions on a T-shape panel were parsed in a post-processing stepfrom the collected images using the DANTEC DYNAMICS ISTRA 4Dcommercial software [60]. The true major and minor strains from DICmeasurements are the principal strains in the sheet metal plane. For theDIC data analysis process, an optimal set of parameters was selected,

with a pixel subset or facet size of 41 pixels, grid point spacing of 9pixels, and a 3D residuum of 0.4 pixel, to achieve high quality straindata with a limited error bar. A custom computer program was devel-oped to further analyze the image data using the Igor Pro software [61].This enabled calculation of the thickness and effective strain distribu-tions as well as the ratio of minor to major strain distribution for de-termination of deformation mode. Based on the assumption of constantvolume, the thickness strain was calculated from the major and minorprincipal strains with,

= − +ε ε ε( )3 1 2 (1)

where ε1, ε2, and ε3 are major, minor, and thickness strains, respec-tively. The DIC measurement technique was validated by comparing thecomputed thickness strains against thickness strains measured on aMed. Mn (10 wt%) TRIP T-shape panel with an ultrasonic technique[62,63]. The ultrasonic technique has an accuracy of ~ 1.0 µm. Thedifference of the thickness measurement between the DIC and ultra-sonic technique was approximately 1% [64]. In addition, the von Miseseffective strain was calculated to quantify the total plastic deformation

Upper Die

Lower Punch

Lower Binder

Center Pocket

(a)

(b)

(c)

50 mm

20 mm

20 mm

Fig. 2. (a) The T-shaped stamping die set in thedouble-action Interlaken press. (b) Close-up view ofthe upper die showing the center pocket region. (c)Close-up view of the lower punch showing the centerpocket region, vertical wall, lower binder, and stepbead.

Fig. 3. (a) Blank geometry (denoted by the solidblack boundary). All dimensions in mm. The rollingdirection is denoted by RD. The top of the T-shape isformed from the 200 mm end, while the bottom ofthe T-shape is formed from the 90 mm end. (b) Theouter surface of a T-shape stamping formed to themaximum 25 mm depth with a DIC contrast patternconsisting of black spray paint droplets on top of thewhite spray paint applied to the blank.

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of a material point with

= − + − + −ε ε ε ε ε ε ε23

(( ) ( ) ( ) )eff 1 22

1 32

2 32 1 2/

(2)

To determine the deformation modes in a T-shape panel, the ratio ofminor to major strain, R1 (= ε2 / ε1), was calculated in a customizedprogram using the Igor software at selected forming depths [65]. Ingeneral, R1 = – 0.5 for uniaxial tension; R1 = 0 for plane strain; R1 = 1for balanced or equibiaxial tension [66].

2.5. RAVF measurement

The small specimens for RAVF measurement, each approximately6 mm × 6 mm, were extracted with wEDM at 24 selected locationsaround the perimeter of a fully formed Med. Mn (10 wt%) TRIP panel.These locations were chosen to examine as broad a range of deforma-tion modes and strain paths as possible. Some of the specimens had asmall degree of curvature but this did not affect the RAVF measure-ments. Specimens were not extracted from the lower portion of thevertical walls that connect with the flange region (noted by the lowerbinder in Fig. 2(c)) of a T-shaped stamping. These locations weredeemed unsuitable for measurement since the DIC contrast pattern waspartially worn off from the walls during stamping thereby precludingstrain measurements. The corresponding major and minor strains wereextracted from the whole field DIC strain maps in the center of eachextracted specimen. In the present paper, only 10 of the 24 extractedspecimens were analyzed in detail since these were associated withrelevant deformation modes and strain paths in stamping. The RAVF foreach specimen was measured from integrated intensity plots computedfrom Debye rings generated by the high-energy synchrotron X-raybeamline 11-ID-C at APS, ANL. The 500 µm × 500 µm synchrotron X-ray beam size, with energy and wavelength (λ) of 105 keV and0.01165 nm, respectively, provided a volumetric measurement since itpenetrated the entire specimen thickness. During the 8 s exposure time,multiple images of the Debye rings from a given specimen were re-corded by a PerkinElmer 2D detector and then summed. This gave asignificantly improved statistical measurement of the Med. Mn (10 wt%) TRIP microstructure relative to Cu Kα X-ray diffraction (for ex-ample) with which penetration depths are limited (e.g. several microns)because of much lower beam energies (8–17 keV). To avoid possiblemachining effects on the microstructure around its edges, each spe-cimen was positioned such that the monochromatic synchrotron X-raybeam impinged its center, corresponding to the DIC strain measure-ment. This was confirmed with a green laser that followed the samepath as the X-ray beam to a specimen surface. Ancillary tests in whichthe beam location was moved along a circumference at a radius of

several millimeters from the center of several specimens revealed nosubstantive differences in measured RAVF relative to the center loca-tion. Hence the centrally-positioned location was deemed re-presentative of the RAVF within the entire specimen. Additional detailson the diffraction measurements and extraction of RAVF are in Ref.[67] and Appendix B.

3. Results and discussion

The results considered in this section are indicative of those fromancillary tests that were conducted to determine the consistency of themeasurement techniques for strain and RAVF from panel to panel. Theanalysis of one panel follows, and the corresponding results were de-termined to be representative of results from 5 T-shape panels producedin this study using the same stamping parameters and instrumentation.No scuffing marks or other features indicative of friction effects werenoted on any of the panels. Each Med. Mn (10 wt%) TRIP steel T-shapepanel was deformed to the full 25 mm depth allowed by the die setwithout fracture/splitting.

3.1. Strain fields from 3D DIC

Determination of locations along the T-shape panel at which RAVFwas to be measured was preceded by a careful investigation of strainfield development during forming. Fig. 5(a)-(i) are DIC-generatedcontour maps of major, minor, and thickness true strain fields measuredduring forming of a Med. Mn (10 wt%) TRIP steel panel at 5 mm[Fig. 5(a), (d), and (g)], 15 mm [Fig. 5(b), (e), and (h)], and 25 mm[Fig. 5(c), (f), and (i)] depths. The surface of the panel on which strainfields were generated follows that of the punch shape shown inFig. 2(c). Six locations around the perimeter of the panel are labeled inFig. 5(c), (f), and (i), viz. i – vi. Locations i and ii represent the left andright (rounded) corners at the bottom (or vertical portion) of the T-shape. Locations, iii and iv denote the lower (rounded) corners of theupper portion (or horizontal portion) of the T-shape, while iv and vdenote the upper corners of the upper portion of the T-shape. Asstamping progressed from 5 mm to 15 mm, and then to 25 mm, peakmajor and minor strain fields accumulated at these six locations, asexpected. Maximum major and minor strains at i – vi achieved values of0.25 and 0.07, respectively. The flat surface of the panel [denoted bythe dark blue surrounded by a lighter outline of the T-shape inFig. 5(a)] accumulated negligible strains indicating minimal deforma-tion relative to the rounded corners. When the T-shape panel wasstamped to the maximum 25 mm forming depth allowed by the die set[see Fig. 2(c)], an impression of the center pocket in the upper dieappeared which generated a small strain gradient in that location on the

Fig. 4. (a) Image of the three-camera digital image correlation system affixed above the Interlaken press. (b) Load-displacement curves from interrupted forming (1 mm depth per step) ofT-shaped stampings.

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panel, see Fig. 5(c), (f), and (i). Small tensile major and minor strainsand compressive thickness strains initially accumulated at locations i –vi at the 5 mm forming depth, as shown in Fig. 5(a), (d), and (g), re-spectively. At the 15 mm forming depth, strains concentrated at theselocations. In addition, tensile minor and compressive thickness strainsaccumulated in the center pocket region at the 25 mm forming depth.Note that the white spots along the region where the lower radius meetsthe flange are regions where the DIC contrast pattern was rubbed offduring stamping. These regions are especially notable in Fig. 5(b) and(h). This region was removed from consideration in Fig. 5(c), (f), and(i). Compressive minor strains were observed at locations vii and viii inFig. 5(e) at 15 mm forming depth. The compressive minor strains atlocation vii and viii became concentrated when the panel was furtherstamped to the maximum 25 mm forming depth in Fig. 5(f).

Effective strain field (εeff ) contour maps at the 5 mm, 15 mm, and25 mm forming depths are shown in Fig. 6(a)-(c), respectively. Eachcontour map was computed using DIC-generated strains in Eq. (2). Peakvalues of the effective strain field appear at all rounded corners, asexpected, which are denoted by labels i – vi in Fig. 6(c). This is con-sistent with the strain fields shown in Fig. 5. Very small effective strainsare relatively evenly distributed around the upper radius along thehorizontal portion of the Med. Mn (10 wt%) TRIP steel T-shape panel atthe 5 mm forming depth in Fig. 6(a). When the forming depth reached15 mm, the effective strain around the upper radius increased withstrain concentrations at locations i – vi in Fig. 6(b). When the T-shape

panel was further stamped to the maximum (and final) 25 mm formingdepth, severe strain concentrations appear at locations i – vi as denotedin Fig. 6(c). Moreover, a non-negligible effective strain concentrationappears in the center pocket region in Fig. 6(c).

Deformation mode contours of the T-shape panel calculated as R1 =ε2 / ε1, where ε2 and ε1 are the true minor and major strain fields,respectively, from DIC, are shown in Fig. 6(d)-(f) for forming depths of5, 15, and 25 mm, respectively. Colors in the key to the right of Fig. 6(f)denote the range of deformation modes. The values of R1 = – 0.5, 0,and 1 represent uniaxial tension, plane strain, and equibiaxial tension,respectively. For example, Fig. 6(d) shows that at the 5 mm formingdepth, the locations i – vi underwent plane strain deformation due topure bending, while material around the upper radius of the horizontalportion of the T-shape panel deformed under a biaxial tension de-formation mode (light yellow). Alternatively, material at locations i – viin Fig. 6(e) and (f) was subject to biaxial tension deformation close tothe equibiaxial tension deformation mode as indicated by the red/whitecontours of R1. A similar observation holds for material in the curvedregions between the upper and lower portions of the T-shape. Locationsvii and viii at the 15 and 25 mm forming depths deformed under auniaxial tension deformation mode. Material at the center of the pocketwas subject to biaxial tension. At the 25 mm forming depth, R1 variesfrom – 0.5 (uniaxial tension) to 1 (equibiaxial) for material within thecenter pocket region in Fig. 6(f), suggesting the activation of a range ofvarious deformation modes at that location. The pure shear

Fig. 5. Major (a)-(c), minor (d)-(f), and calculated thickness [Eq. (1), (g)-(i)] true strain fields, at 5, 15, and 20 mm forming depths, respectively, on the outer surface of a Med. Mn (10 wt%) TRIP T-shape panel. As expected, peak strain accumulation occurs at the corners of the T-shape denoted by i-vi in (c), (f), and (i). Compressive minor strains were observed at wereobserved at vii and viii marked on (e). Note that the white regions are indicative of artifacts from the DIC measurement due to loss of the contrast pattern during stamping. These artifactsin no way affected the strains used to investigate RAVF dependence on deformation mode and strain path.

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deformation mode was not observed at any point on the panel with the3D DIC measurement method.

3.2. Deformation modes and strain paths

The DIC experimental results were further analyzed by examiningthe relationship between true major and minor strains along varioussection lines at different locations on the T-shape panel. The chosensection lines are shown in Fig. 7(a), as the black segments A-A′, B-B′, C-C′, and D-D′. Segment A-A′, which is 50.6 mm long, runs through thecenter of the center pocket of the T-shape panel at 25 mm formingdepth. The corresponding major and minor strain distributions areshown, respectively, in Fig. 7(b) and (c). The horizontal axis inFig. 7(b)-(c) is displayed in terms of data points from DIC measure-ments. For segment A-A′, 140 data points are plotted representing atotal length of 50.6 mm, with the center position of the center pocketbeing at 25.3 mm from point A. The maximum true major and minorstrains accumulated just outside of the center of the pocket. Hence,positions 1, 2, and 3 which correspond to 27.1 mm (position 1 denotedby the red arrow on segment A-A′), 28.9 mm (position 2 denoted by thegreen arrow on segment A-A′), and 31.4 mm (position 3 denoted by theblack arrow on segment A-A′), were selected to further investigate thedeformation modes and strain paths in the pocket. Fig. 7(d) is a plot ofmajor vs. minor strain at positions 1, 2, and 3 on segment A-A′. Specificdeformation modes and associated strain paths are denoted by thegreen dashed line (pure shear), the blue dashed line (pure uniaxialtension), and the purple dashed line (pure equibiaxial tension).Fig. 7(d) shows that material at position 1 was subject to a biaxialtension mode, material at position 2 was subject to a plane strain de-formation mode, while material at position 3 was subject to a uniaxialtension mode. Deformation at positions 1 and 3 followed linear strainpaths, while deformation at position 2 followed a non-linear strainpath. Fig. 7(e) shows that material on section line B-B′ in Fig. 7(a),which is 24.2 mm in length, was subject primarily to plane strain de-formation following a linear strain path associated with pure bending.Fig. 7(f) shows the evolution of deformation and strain path along

section line C-C′ in Fig. 7(a), which was 23.9 mm in length. Here,material at some points was under uniaxial tension deformation fol-lowing a linear strain path. However, deformation of material at otherpoints along line C-C′ ranged from uniaxial tension to plane strain withnon-linear strain paths. Fig. 7(g) shows that material along line D-D′,which is 39.0 mm in length, was subject to biaxial deformation withnon-linear strain paths as indicated.

3.3. RAVF measurement results

Results in Section 3.2 guided the selection of those positions on theT-shaped panel from which specimens were extracted for RAVF mea-surements using high-energy synchrotron X-ray diffraction. Of the 24specimens extracted for RAVF measurement, those at the 10 numberedlocations shown in Fig. 8(a) from the fully formed T-shaped panel werechosen as representative of all relevant deformation modes and strainpaths. Consequently, there was no need to extract specimens from thepocket region for RAVF measurement which was formed late in thestamping process. The ten locations are numbered in Fig. 8(a) (startingfrom the lower left of the bottom of the T-shape as follows: 9, 8, 2, 3,12, 14, 20, 21, 23, and 24). Fig. 8(b) shows locations 2,3, and 12 at thebottom of the T-shape. Fig. 8(c) shows locations 8 and 9, while Fig. 8(d)shows locations 14 (along the curved section of the T-shape) and 20 and21. Fig. 8(e) shows locations 23 and 24 extracted from the head of theT-shape.

The RAVF decrease relative to the initial RAVF value of 66 vol% ateach of the 10 locations detailed in Fig. 8 are superimposed on a plot oftrue major and minor strains (i.e. forming limit diagram space) in Fig. 9along with the corresponding strain path. Again, specific deformationmodes are denoted by the green dashed line (pure shear), the bluedashed line (uniaxial tension), and the purple dashed line (equibiaxialtension). The RAVF decrease was calculated from

∆ = −RAVF RAVF RAVF RAVF( )/0 1 0 (3)

where ∆RAVF , RAVF0, and RAVF1 are the RAVF decrease, initial RAVF,and RAVF in the fully formed T-shape panel, respectively. The relative

Fig. 6. (a)-(c) The calculated εeff field [Eq. (2)] at the 5, 15, and 25 mm forming depths on the T-shape panel, respectively. This information calls out the locations of peak strainaccumulation during stamping. (d)-(f) The deformation mode distribution in terms of calculated R1 = ε2 / ε1 contours at the 5, 15, and 25 mm forming depths. The values of R1 = −0.5,0, and 1 represent uniaxial tension, plane strain, and equibiaxial tension deformation modes, respectively. (For interpretation of the references to color in this figure, the reader is referredto the web version of this article).

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size of ∆RAVF at any one of the 10 locations in Fig. 9 is proportional tothe diameter of the corresponding filled circle in the color contour keyin Fig. 9. The larger the diameter of a filled circle, the larger the cor-responding ∆RAVF in the fully formed T-shape panel. A curved dottedline runs through each circle. This line has the same color of the circlethrough which it runs and it denotes a constant effective strain, εeff ,computed with Eq. (2). The εeff value for each ∆RAVF is marked alongthe right edge of the effective strain line in Fig. 9. For example, the εeffat location 8 with a ∆RAVF = 59% is 0.510 with a green color. In fact,the largest ∆RAVF and εeff was measured at location 8 where materialwas subject to biaxial deformation according to Fig. 9. At location 20,however, the strain level is smaller, with εeff = 0.133, but the corre-sponding ∆RAVF of 53% is significant. Hence, martensite phasetransformation is especially sensitive to both the biaxial and tensile

deformation modes during forming of the Med. Mn (10 wt%) TRIP steelT-shape panel. In addition, the strain path corresponding to location 20is linear, while that corresponding to location 8 is non-linear. Only an11% ∆RAVF is noted at location 14 with very small strains, whichexperienced a plane strain deformation mode under pure bending.Notice that at location 12, the 47% ∆RAVF is large but the strain pathwas linear in a nearly balanced biaxial tension deformation mode withrelatively small strains. Linear strain paths are associated only withdeformation at locations 3 and 12 in the biaxial range of strains. Whilethe range of effective strains for locations 2, 9, 21, and 23 is limited to0.301 ≤ εeff ≤ 0.357 under biaxial deformation, the correspondingvalues of ∆RAVF are different and range from 32% at location 1–47%at location 23. A 29% change in RAVF is noted at location 24 in thebiaxial deformation range.

Fig. 7. (a) The major strain distribution in Fig. 5(c) at the 25 mm forming depth with segments A-A′ (50.6 mm), B-B′ (24.2 mm), C-C′(23.9 mm), and D-D′ (39.0 mm) called out on the T-shape panel. The arrows denote points along segment A-A′ within the pocket region of the stamping considered in (b)-(d). The true major (b) and minor (c) strain distributions from DICalong segment A-A′ in (a) in terms of data points (50.6 mm= 140 data points) at the 25 mm forming depth. The dashed lines denote shear (green), uniaxial tension (blue), and equibiaxialtension (purple). (d) The evolution of deformation modes and strain paths for locations 1, 2, and 3 marked on segment A-A′ in (a). (e)-(g) Strain path and deformation mode evolution forB-B′, C-C′, and D-D′ segments at selected locations, respectively, during forming. The deformation mode along B-B′ is primarily plane strain. Deformation modes along C-C′ change fromnon-equibiaxial at small strains, to plane strain to tension at the largest strains. Deformation modes along segment D-D′ are initially equibiaxial tension at the smallest strains and thennon-equibiaxial tension at the largest strains. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

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3.4. ∆RAVF dependence on deformation mode and strain path

Specific results extracted from Fig. 9 are investigated to provide amore in-depth examination of the martensite phase transformation inthe Med. Mn (10 wt%) TRIP steel during the entire stamping process tothe 25 mm limit of the die set. These focus on the following effects: 1)deformation mode under a linear strain path, 2) εeff level under linearand bilinear strain paths, 3) εeff level under different bilinear strainpaths, and 4) linear vs. nonlinear strain paths. Each effect is examinedin terms of true major vs. minor strain plots that identify ∆RAVF valuesand associated strain paths at selected locations in Fig. 9.

3.4.1. Deformation mode under a linear strain pathFig. 10 considers ∆RAVF values under the three main deformation

modes, viz., tension, plane strain, and biaxial tension. These modes

were chosen since they each follow a linear strain path as shown inFig. 10 and their εeff values fall within the narrowest range of0.079–0.133 for all ∆RAVF values having linear strain paths. The lar-gest ∆RAVF of 53% occurred under uniaxial tension. Alternatively,∆RAVF is smallest under plane strain deformation since only an 11%change was noted, while ∆RAVF = 19% occurred under a biaxialtension mode which is intermediate to changes occurring under theother two deformation modes. Of the three deformation modes con-sidered in Fig. 10, a greater amount of austenite transformed to mar-tensite under uniaxial tension following a linear strain path under thenarrowest range of εeff .

3.4.2. εeff level under linear and bilinear strain pathsValues of ∆RAVF , following linear and bilinear strain paths, are

considered in Fig. 11. For each strain path, the largest range of εeff

Fig. 8. (a) Fig. 5(c) (major true strain contours from DIC) with the 10 of the 24 locations at which RAVF was measured with synchrotron X-ray diffraction denoted. Moving clockwisearound the bottom of the T: (b) Locations 2, 3, and 12, (c) Locations 8 and 9, (d) Locations 14, 20 and 21, (e) Locations 23 and 24.

Fig. 9. Variation ΔRAVF [relative to the initial 66% RAVF, see Eq.(3)] with major and minor true strains at the 10 locations iden-tified in Fig. 8(a). The larger the diameter of a colored circle is,the greater is the measured RAVF decrease. The dashed (straight)lines denote shear (green), uniaxial tension (blue), and equi-biaxial tension (purple) deformation modes. Dotted (curved) linesdenote calculated εeff [see Eq. (2)] levels using DIC-measured truestrains. Each is associated with a specific RAVF decrease. (Forinterpretation of the references to color in this figure legend, thereader is referred to the web version of this article).

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values is considered for the compared ∆RAVF values. In Fig. 11(a),locations 3 and 12 in Fig. 8(a) are considered. The ∆RAVF varied from19% (location 3) to 47% (location 12), when εeff increased from 0.113to 0.169, respectively, following linear strain paths under biaxial ten-sion – both are quite close to equibiaxial tension. Fig. 11(a) seems tosuggest that the higher the value of εeff , the more austenite transformsto martensite. In Fig. 11(b),∆RAVF = 47% is also achieved at (location23) with εeff = 0.350 under biaxial tension with a bilinear strain path.However, ∆RAVF = 19% at the companion point in Fig. 11(b) for lo-cation 3 with a linear strain path at εeff = 0.113. Comparison of the dataassociated with ∆RAVF = 47% in Fig. 11(a) and (b), leads to an in-teresting observation about the effect of strain path on ∆RAVF . A largeεeff = 0.35 was required to achieve ∆RAVF = 47% at location 23Fig. 11(b) under a bilinear strain path. Yet the much lower value of εeff= 0.169 was required to achieve the same ∆RAVF with a linear strainpath at location 12 in Fig. 11(a). This suggests that the biaxial tensiondeformation mode following a linear strain path to ∆RAVF = 47% was

more effective at martensite phase transformation since a lower εeff wasrequired to achieve the same∆RAVF as was achieved under the bilinearmode at location 23 in Fig. 11(b).

3.4.3. εeff level under different bilinear strain pathsBilinear strain paths in Fig. 9 occurred in one of two ways: (i) with a

rapid increase in ε1 (major strain) followed by a slower increase in ε1,(ii) a slower initial increase in ε1 followed by a rapid increase in ε1.Different bilinear strain paths are called out in Fig. 12(a) and (b). The∆RAVF values associated with locations 2 and 24 in Fig. 12(a), 32%and 29%, respectively, are similar. Both follow (i), and their bilinearstrain paths are nearly coincident resulting in εeff levels of 0.193 (po-sition 24) and 0.338 (position 2). They suggest that most of the aus-tenite transformation occurred below εeff = 0.193 with only minimaltransformation occurring with additional strain under a similar bilinearstrain path associated with location 2. A larger disparity between∆RAVF values occurred between the two locations considered inFig. 12(b), viz. 59% at location 8 and 47% at location 23. Both follow(ii). Here, the εeff increased from 0.350 (position 23) to 0.510 (position8). Fig. 12(b) suggests that the majority of martensite phase transfor-mation occurred below εeff = 0.350. Comparison of the data inFig. 12(a) and (b) suggests that martensite phase transformationreaches the largest ∆RAVF under a biaxial tension deformation modefollowing a bilinear strain path, characterized by a slower initial in-crease in ε1 followed by a rapid increase in ε1. Moreover, positions onthe T-shaped stamping (see Fig. 8(a)) such as 2, 8, 23 and 24 were likelyto accumulate the highest εeff .

3.4.4. Linear vs. nonlinear strain pathsA bilinear stain path is associated with location 2 in Fig. 13(a), i.e. a

plane strain deformation mode followed by biaxial tension (case (i)considered in Section 3.4.3). Alternatively, material at position 21 ex-perienced a non-linear strain path. Interestingly, the ∆RAVF, the minorstrain, and the εeff values at locations 2 and 21 are very similar, withonly the strain path (i.e. linear vs. non-linear) being the notable dif-ference. Alternatively, three bilinear strain paths leading to ∆RAVFvalues of 32%, 43%, and 47% are shown in Fig. 13(b). These are: planestrain followed by biaxial tension (location 2, ∆RAVF = 32%), biaxialtension (location 9, ∆RAVF = 43%) characterized by a rapid increasein ε1 followed by a slower increase in ε1, and (nearly) equibiaxial ten-sion followed by a biaxial tension (location 23, ∆RAVF = 47%) mode.The εeff values at locations 2, 9, and 23 in Fig. 13(b) are nearly the

Fig. 10. Effect of deformation modes on ΔRAVF [see Eq. (3)] under linear strain paths.The dashed (straight) lines denote shear (green), uniaxial tension (blue), and equibiaxialtension (purple) deformation modes. Dotted (curved) lines denote calculated εeff [see Eq.(2)] levels using DIC-measured true strains. Each is associated with a specific RAVF. (Forinterpretation of the references to color in this figure legend, the reader is referred to theweb version of this article).

Fig. 11. The εeff level effect on ΔRAVF [see Eq. (3)] under linear (a) and bilinear (b) strain paths. The dashed (straight) lines denote shear (green), uniaxial tension (blue), and equibiaxialtension (purple) deformation modes. Dotted (curved) lines denote calculated εeff [see Eq. (2)] levels using DIC-measured true strains. Each is associated with a specific ΔRAVF. (Forinterpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

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same, i.e. 0.338, 0.357, and 0.350, respectively. In addition, the∆RAVF values are similar at locations 9 and 23 i.e. 43% and 47%,respectively, while that at location 2 is smallest (32%). A comparison ofFig. 13(a) and (b) suggests that austenite transformation to martensiteunder a biaxial tension deformation mode is more sensitive to changesin the true minor strain, ε2, rather than the true major strain, ε1, sincethere are only very minimal differences in εeff levels at the end ofstamping. Moreover, when ε2 levels were comparable at two locations,such as 2 and 21 in Fig. 13(a), similar ∆RAVF values resulted, irre-spective of the strain path (i.e. linear or bilinear). At the highest ε2values, such as occurred at locations 9 and 23 in Fig. 13(b), ∆RAVFsignificantly increased relative to other strain paths and deformationmodes considered in Fig. 13.

4. Summary remarks

In this paper, state-of-the-art experimental methodologies werecombined to determine the influence of deformation modes and strainpaths on martensitic transformation during stamping of Med. Mn (10 wt%) TRIP steel panels. The panel geometry was designed to emulate a

portion of generic b-pillar. This study was motivated by the need forexperimental data to assess material constitutive models in finite ele-ment simulations of Gen. 3 steel stamping processes and componentperformance as well as to guide Gen. 3 steel material selection andimplementation. An experimental Med. Mn (10 wt%) TRIP steel sheetmaterial, with an initial RAVF value of 66%, was stamped in a la-boratory die set at 1 mm/s. Stamping did not produce heating to thepoint where the martensite phase transformation was affected. This isan idealization of most automotive stamping processes in which noheating is intentionally applied either to the blank or the stampingtools. It is a useful first step that will enable CAE modeling to simplifythe stamping processing conditions by eliminating the temperaturedependence of the martensite phase transformation. Strain measure-ment was accomplished with a three-camera DIC technique usingcustom post-processing software. Retained austenite volume fractionwas measured with synchrotron X-ray diffraction at locations in a se-lected panel (from a set of 5) wherein material undergoes uniaxial,plane strain, and biaxial tension deformation modes following linear,bi-linear, and non-linear strain paths. The greatest decrease in RAVFoccurred under biaxial tension modes each following a bilinear strain

Fig. 12. (a) and (b) The εeff level effect on ΔRAVF [see Eq. (3)] under different bilinear strain paths. The dashed (straight) lines denote shear (green), uniaxial tension (blue), andequibiaxial tension (purple) deformation modes. Dotted (curved) lines denote calculated εeff [see Eq. (2)] levels using DIC-measured true strains. Each is associated with a specific ΔRAVF.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

Fig. 13. (a) and (b) The strain path effect on ΔRAVF [see Eq. (3)]. The dashed (straight) lines denote shear (green), uniaxial tension (blue), and equibiaxial tension (purple) deformationmodes. Dotted (curved) lines denote calculated εeff [see Eq. (2)] levels using DIC-measured true strains. Each is associated with a specific ΔRAVF. (For interpretation of the references tocolor in this figure legend, the reader is referred to the web version of this article).

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path. Alternatively, the smallest decrease in RAVF occurred under aplane strain deformation mode following a linear strain path.

These results suggest some interesting possibilities for achievingdesired levels of local RAVF in a stamped Med. Mn (10 wt%) TRIP partwith a given initial RAVF. The first possibility is matching of the steelwith a stamping process wherein a specific deformation and strain pathpredominate. If a higher level of retained austenite is desired in astamped part, a stamping process wherein plane strain under purebending may be of interest. The second possibility resides with locally“adjusting” deformation modes and strain paths in the stamped part byadjusting an existing die geometry to achieve desired local levels ofretained austenite and martensite. For example, if a higher level oftransformation induced martensite is desired for strength, then perhapsa local geometry change in a die that switches the deformation modefrom plane strain to biaxial deformation may be desirable given thatsuch a change does not significantly affect part functionality. Thesepossibilities warrant further investigation.

The measurements detailed in this study should be repeated forMed. Mn TRIP steels with different Mn wt% and corresponding heattreatments (e.g. batch annealed vs. continuous anneal). The tensile flowproperties of these materials are likely to differ from those detailed inSupplementary Appendix A for the Med. Mn (10 wt%) TRIP steel, whichwas the subject of the present study. This suggests that measured RAVFvalues from the different deformation modes and strain paths in T-shape panels are likely to differ in magnitude from the values in thispaper. The effect of heat generation at stamping speeds in excess of thatchosen for this study (1 mm/s) should be explored along with mea-surement of RAVF values at selected forming depths, rather than only inthe final stamped part. Both will require expansion and enhancementsof the existing experimental methodology. The effect of edge fractureon martensite phase transformation during T-shape stamping is espe-cially intriguing. This can be explored with the experimental methodsused in this study but starting with a blank containing strategicallypositioned holes. Accurate measurement of RAVF in the vicinity of theholes both before and after they are generated in the blank is required.This will address the influence of the specific machining/punchingtechnique on austenite to martensite phase transformation in the blankmaterial prior to stamping. Once this is done, the combined 3D DIC andhigh-energy synchrotron X-ray diffraction techniques can be used. Thepossibility of measuring RAVF in a T-stamping without having to cutout small specimens should be considered. While there is no evidence inthe literature of a residual stress effect on measured RAVF in Gen 3steels, a significant concern is the effect of texture on the initial RAVFmeasurement since the X-ray beam would not necessarily be positionedat normal incidence at all locations.

5. Conclusions

The main conclusions from this study are as follows:

(1) Stamping of Med. Mn. (10 wt%) TRIP steel into T-shape panels thatemulate the rocker-end of a generic b-pillar generated uniaxialtension, plane strain under pure bending, and biaxial tension de-formation modes following linear, bi-linear, and non-linear strainpaths.

(2) The variety of deformation modes and strain paths during stampingresulted in substantial variation in the ∆RAVF (11 – 59%) relativeto the initial RAVF of 66%. The greatest ∆RAVF (59%) occurredunder biaxial tension following a bi-linear strain path. The smallest∆RAVF (11%) occurred under plane strain following a linear strainpath.

(3) A dependence of martensite phase transformation on deformationmode was noted when a linear strain path is followed under similareffective strain levels. This can be gauged by the corresponding∆RAVF : uniaxial tension (53%)> biaxial tension (19%)>planestrain (11%).

(4) The lower εeff level associated with biaxial tension deformationmodes under linear strain paths renders the linear strain paths moreeffective at martensite phase transformation than bilinear strainpaths, which requires a higher εeff level.

(5) Martensite phase transformation reaches the largest ∆RAVF undera biaxial tension deformation mode following a bilinear strain pathcharacterized by a slower initial increase in ε1 followed by a rapidincrease in ε1.

(6) Martensite phase transformation under a biaxial-tension deforma-tion mode is more sensitive to changes in the tensile minor strain,ε2, rather than the tensile major strain, ε1. This is supported by theobservation that there are only very minimal differences in εeff le-vels at the end of stamping.

(7) For a Med. Mn. (10 wt%) TRIP steel with a known initial RAVF, theresults of this study suggest the possibility that martensite trans-formation can be manipulated to better control formability,strength, and ductility in stamped parts via one of the two meansbelow:(a) Selecting a steel that is better suited to stamping wherein a

specific deformation mode and strain path predominate.(b) Locally manipulating deformation modes and strain paths by

modifying an existing die geometry to achieve a desired level ofretained austenite in a stamped part.

Acknowledgements

The synchrotron X-ray diffraction work was conducted at theAdvanced Photon Source, a U.S. Department of Energy (DOE) Office ofScience User Facility operated for the DOE Office of Science by ArgonneNational Laboratory under Contract No. DE-AC02-06CH11357. Thesupport of Mr. R. Spence of Argonne Beam Line 11-I-DC during allphases of the synchrotron study is gratefully acknowledged. R. Alturkand C.M. Enloe assisted with measurement of the Med. Mn (10 wt%)TRIP tensile flow properties detailed in Appendix A. W.W., YW.W., P.M., F. Z., and G.A.T. acknowledge the support of the AK Steel Cor-poration. This material is based upon work supported by the Depart-ment of Energy National Energy Technology Laboratory under AwardNumber No. DE-EE0005976. This report was prepared as an account ofwork sponsored by an agency of the United States Government. Neitherthe United States Government nor any agency thereof, nor any of theiremployees, makes any warranty, express or implied, or assumes anylegal liability or responsibility for the accuracy, completeness, or use-fulness of any information, apparatus, product, or process disclosed, orrepresents that its use would not infringe privately owned rights. Re-ference herein to any specific commercial product, process, or serviceby trade name, trademark, manufacturer, or otherwise does not ne-cessarily constitute or imply its endorsement, recommendation, or fa-voring by the United States Government or any agency thereof. Theviews and opinions of authors expressed herein do not necessarily stateor reflect those of the United States Government or any agency thereof.Such support does not constitute an endorsement by the Department ofEnergy of the work or the views expressed herein.

Supplementary materials

Appendix A. and B. associated with this article can be found in theonline version at http://dx.doi.org/10.1016/j.msea.2017.11.008.

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