Strain Rate Effect on Tensile Behavior for a High Specific Strength Steel

Home , B (S-train), Specific strength, Strain partitioning, Strain rate

metals

Article Strain Rate Effect on Tensile Behavior for a High Speciﬁc Strength Steel: From Quasi-Static to Intermediate Strain Rates

Wei Wang 1,2, Yan Ma 1,2 ID , Muxin Yang 1, Ping Jiang 1, Fuping Yuan 1,2,* and Xiaolei Wu 1,2

1 State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, No. 15, North 4th Ring, West Road, Beijing 100190, China; [email protected] (W.W.); [email protected] (Y.M.); [email protected] (M.Y.); [email protected] (P.J.); [email protected] (X.W.) 2 School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100190, China * Correspondence: [email protected]; Tel.: +86-10-82544409; Fax: +86-10-82543977

Received: 6 December 2017; Accepted: 27 December 2017; Published: 29 December 2017

Abstract: The strain rate effect on the tensile behaviors of a high specific strength steel (HSSS) with dual-phase microstructure has been investigated. The yield strength, the ultimate strength and the tensile toughness were all observed to increase with increasing strain rates at the range of 0.0006 to 56/s, rendering this HSSS as an excellent candidate for an energy absorber in the automobile industry, since vehicle crushing often happens at intermediate strain rates. Back stress hardening has been found to play an important role for this HSSS due to load transfer and strain partitioning between two phases, and a higher strain rate could cause even higher strain partitioning in the softer austenite grains, delaying the deformation instability. Deformation twins are observed in the austenite grains at all strain rates to facilitate the uniform tensile deformation. The B2 phase (FeAl intermetallic compound) is less deformable at higher strain rates, resulting in easier brittle fracture in B2 particles, smaller dimple size and a higher density of phase interfaces in final fracture surfaces. Thus, more energy need be consumed during the final fracture for the experiments conducted at higher strain rates, resulting in better tensile toughness.

Keywords: high speciﬁc strength steel; strain rate effect; intermediate strain rates; strain partitioning; deformation twins

1. Introduction Metals and alloys with high strength and ductility are always desirable in applications for automobiles, aerospace and military defense. In recent decades, several design strategies have been proposed to reach such expectations, such as transformation-induced plasticity (TRIP) [1–3], twinning-induced plasticity (TWIP) steels [2–5], and dual-phase (DP) steels [6,7]. Recently, high specific strength steels (HSSS) with low density, achieved by adding Al (3–12 wt. %), have been widely studied due to their excellent mechanical properties, such as high specific yield strengths and large uniform elongations [8–19]. Most of these HSSS are based on Fe–Al–Mn–C alloy system (so called TRIPLEX steels), and consist of fcc austenite matrix, bcc ferrite matrix and finely dispersed κ-carbides

((Fe, Mn)3AlC. type) with nanometer size. More recently, a HSSS with chemical composition of Fe–16Mn–10Al–0.86C–5Ni (wt. %) has been developed [20]. This HSSS with a dual-phase microstructure and ultrafine grains was found to show excellent mechanical properties, such as high specific strength and large elongation (a combination of a specific yield strength of 200 MPa·g−1·cm3 and uniform elongation of 16%, which can hardly be achieved in other high-strength steels). Kim et al. [20] has attributed the outstanding mechanical properties of this HSSS to the precipitation strengthening by the brittle B2 intermetallic compound.

Metals 2018, 8, 11; doi:10.3390/met8010011 www.mdpi.com/journal/metals Metals 2018, 8, 11 2 of 14

In our previous work [21,22], the stress/strain partitioning between the constituent phases and the back-stress-induced strain hardening have been found to play an important role during the plastic deformation for this HSSS, since the B2 phase was found to be deformable. The HSSS can be considered as a perfect candidate for the advanced impact-tolerant structures in the automobile industry due to its excellent mechanical properties. It is widely accepted that the plastic flow behaviors and the corresponding deformation mechanisms are highly dependent on the loading rate for metals and alloys [23–40]. It is also well known that the observed resistance to plastic deformation is a rate-controlling process and can be affected by the strain rate [23–25,27,28]. The quasi-static tensile behaviors and the dynamic behaviors at high strain rates (~103/s) for TRIP steels, TWIP steels, DP steels and HSSS have been well characterized in previous research [1,2,20,41–50], while there is very limited experimental data on various steels at the intermediate strain rates (from 1 to 100/s) [51–55], which is an extremely important transition region in application of automobile industry, since vehicle crushing often happens in this strain rate range or within an even higher strain rate range. Thus, the potential applications for the HSSS in the automobile industry require a comprehensive understanding of deformation physics subjected to dynamic loading at intermediate strain rates. In the HSSS with dual-phase microstructure, the strain rate sensitivity (SRS) is quite different for the soft fcc γ-austenite and the hard B2 phase. Thus, the loading rate can affect the stress/strain partitioning between these two phases and the resultant flow behaviors for this HSSS. Moreover, the strain rate effect on the deformation mechanisms for both phases in the HSSS is still unknown. For this perspective, a series of uniaxial tensile tests over a wide range of strain rates (0.0006–56/s) have been conducted on this HSSS. The strain rate effect on the flow behaviors was studied, and the rate-related constitutive equation was obtained for this HSSS. Moreover, the corresponding deformation mechanisms were revealed by the subsequent microstructure observations.

2. Materials and Methods The HSSS (Fe–16.4Mn–9.9Al–0.86C–4.8Ni–0.008P–0.004S, wt. %) was produced using arc melting under protection of pure argon atmosphere, and the detailed procedures for preparing the hot-rolled (HR) strips can be found in our previous papers [21,22]. The HR strips with a thickness of 3.9 mm were annealed at 1000 ◦C for 1 h first, and then were cold rolled (CR) into a final thickness of 1.3 mm with a thickness reduction of 66%. The CR sheets were then annealed at 900 ◦C for 15 min, followed immediately by water quenching. Before and after tensile tests, the microstructures of the HSSS were characterized by electron back-scattered diffraction (EBSD) and transmission electron microscopy (TEM). For EBSD acquisition, a scanning area of 60 × 40 µm2 was chosen and a scanning step of 0.1 µm was used. The tensile fracture surfaces were also characterized by scanning electron microscopy (SEM). The detailed description of the sample preparation and the operating procedures for obtaining EBSD and TEM images can also be found in our previous papers [21,22]. Tensile tests at five different strain rates (0.0006, 0.05, 1.2, 3.6, 56/s) were conducted in the present study. Three experiments were conducted for each strain rate to check the repeatability. The quasi-static uniaxial tensile tests (strain rates of 0.0006, 0.05/s) were conducted using an MTS Landmark testing machine, and the dog-bone-shaped tensile specimens with a gauge length of 20 mm, a width of 4 mm and a thickness of 1.3 mm (with loading direction parallel to the rolling direction) were used (as shown in Figure1a). A 10 mm gauge extensometer was used in the quasi-static uniaxial tensile tests to measure the strain. The tests at intermediate strain rates were conducted using a servo-hydraulic high speed tensile testing machine (HTM5020, Zwick, Ulm, Germany). This high speed tensile testing machine has experimental capabilities for a maximum crosshead displacement of 350 mm, a maximum load of 50 kN and a maximum velocity of 20 m/s. The data synchronous acquisition is 1 MHz for the high speed tensile testing machine. The specimens for the tests at intermediate strain rates have a gauge length of 10 mm, a width of 5 mm and a thickness of 1.3 mm (with loading direction parallel to the rolling direction), and the schematic illustration for the specimens tested at intermediate strain rates is shown in Figure1b. A piezo-electric type load cell was used to measure the load during the Metals 2018, 8, 11 3 of 14

testsMetals at intermediate2018, 8, 11 strain rates. The dynamic strain measurement during the tests at intermediate3 of 14 strain rates was obtained using a non-contact full-ﬁeld strain measuring system (CSI Vic2D) base on (CSI Vic2D) base on the digital image correlation (DIC) method. A FASTCAMSA 5 high speed camera the digitalMetals 2018 image, 8, 11 correlation (DIC) method. A FASTCAMSA 5 high speed camera (Photron,3 of 14 Tokyo, Japan)(Photron, was used Tokyo, for Japan) DIC method, was used and for a DIC random method, application and a random of dots application by marking of pensdots wasby marking applied to the pens was applied to the sample surface for strain measurement. The whole gauge length was used sample(CSI surface Vic2D) for base strain on the measurement. digital image correlatio The wholen (DIC) gauge method. length A wasFASTCAMSA used for the5 high strain speed measurement camera for the strain measurement by DIC. The detailed description for the dynamic strain measurement can (Photron, Tokyo, Japan) was used for DIC method, and a random application of dots by marking bybe DIC. found The elsewhere detailed [51,52]. description for the dynamic strain measurement can be found elsewhere [51,52]. pens was applied to the sample surface for strain measurement. The whole gauge length was used for the strain measurement by DIC. The detailed description for the dynamic strain measurement can be found elsewhere [51,52].

FigureFigure 1. 1.(a ()a Shape) Shape and and dimensionsdimensions of of the the dog-bone-shaped dog-bone-shaped tensile tensile specimens specimens for quasi-static for quasi-static tests. tests. (b) Shape and dimensions of the dog-bone-shaped tensile specimens for tensile tests at intermediate (b) Shape and dimensions of the dog-bone-shaped tensile specimens for tensile tests at intermediate strain rate. strainFigure rate. 1. (a) Shape and dimensions of the dog-bone-shaped tensile specimens for quasi-static tests. 3. Results(b) Shapeand Discussions and dimensions of the dog-bone-shaped tensile specimens for tensile tests at intermediate 3. Resultsstrain and rate. Discussion The EBSD and TEM images for the microstructures of the HSSS before the tensile tests are shown in The3.Figure Results EBSD 2a,b, and and respectively. Discussions TEM images The corresponding for the microstructures indexed selected of the area HSSS diffraction before the pattern tensile for teststhe TEM are shown image is given in the inset of Figure 2b. After annealing at 900 °C for 15 min, two phases are clearly in Figure2Thea,b, EBSD respectively. and TEM Theimages corresponding for the microstructures indexed of selected the HSSS area before diffraction the tensile pattern tests are for shown the TEM visible, in which one is the fcc γ-austenite with equiaxed recrystalliz◦ed grains and the other is the B2 imagein isFigure given 2a,b, in therespectively. inset of Figure The corresponding2b. After annealing indexed selected at 900 areaC for diffraction 15 min, pattern two phases for the are TEM clearly phase (FeAl intermetallic compound) with both granular and lamellar shapes. The area fraction of B2 visible,image in which is given one in the is the inset fcc ofγ Figure-austenite 2b. After with annealing equiaxed at recrystallized 900 °C for 15 min, grains two and phases the are other clearly is the B2 phase is about 22%. From the TEM image, it can be seen that the B2 phase is much inclined to phasevisible, (FeAl in intermetallic which one is the compound) fcc γ-austenite with with both equiaxed granular recrystalliz and lamellared grains shapes. and the The other area is the fraction B2 of precipitate at either the grain boundaries or triple junctions of γ-austenite matrix. Both phases show B2 phasephase is (FeAl about intermetallic 22%. From compound) the TEM with image, both itgranular can be and seen lamellar that the shapes. B2 phase The area is muchfraction inclined of B2 to that they are nearly free of dislocation after annealing at 900 °C for 15 min, and annealing twins can phase is about 22%. From the TEM image, it can be seen that the B2 phase is much inclined to precipitatebe clearly at seen either in the the γ grain-austenite boundaries grain interiors. or triple Both junctions phases show of γ-austenite small grains, matrix. the average Both phases grain show precipitate at either the grain boundaries or triple junctions of◦ γ-austenite matrix. Both phases show thatsize they is about are nearly 1.65 μ freem for of the dislocation γ-austenite after phase annealing and is about at 900 0.77C μm for for 15 the min, B2 andphase. annealing twins can be that they are nearly free of dislocation after annealing at 900 °C for 15 min, and annealing twins can clearly seen in the γ-austenite grain interiors. Both phases show small grains, the average grain size is be clearly seen in the γ-austenite grain interiors. Both phases show small grains, the average grain about 1.65 µm for the γ-austenite phase and is about 0.77 µm for the B2 phase. size is about 1.65 μm for the γ-austenite phase and is about 0.77 μm for the B2 phase.

Figure 2. (a) Electron back-scattered diffraction (EBSD) phase image and grain morphology for the high specific strength steel (HSSS) after annealing at 900 °C for 15 min (The red color stands for γ- austenite phase, and the green color stands for B2 phase). (b) TEM image showing the microstructures Figure 2. (a) Electron back-scattered diffraction (EBSD) phase image and grain morphology for the Figureof γ-austenite 2. (a) Electron phase back-scatteredand B2 phase after diffraction annealing (EBSD) at 900 phase °C for image 15 min. and The grain indexed morphology selected forarea the high high specific strength steel (HSSS) after annealing ◦at 900 °C for 15 min (The red color stands for γ- speciﬁcdiffraction strength pattern steel for (HSSS) TEM im afterage annealingwith electron at 900beamC clos forely 15 parallel min (The to both red colorthe [011] standsγ and for [001]γ-austeniteB2 austenite phase, and the green color stands for B2 phase). (b) TEM image showing the microstructures phase,zone andaxes is the shown green in colorthe inset stands of Figure for B22b. phase). (b) TEM image showing the microstructures of of γ-austenite phase and B2 phase after annealing at 900 °C for 15 min. The indexed selected area γ-austenite phase and B2 phase after annealing at 900 ◦C for 15 min. The indexed selected area diffraction pattern for TEM image with electron beam closely parallel to both the [011]γ and [001]B2 diffractionzone axes pattern is shown for TEMin the imageinset of withFigure electron 2b. beam closely parallel to both the [011]γ and [001]B2 zone axes is shown in the inset of Figure2b.

Metals 2018, 8, 11 4 of 14 Metals 2018, 8, 11 4 of 14

The engineeringThe engineering stress–strain stress–strain curves curves and and the the true true stress–strain stress–strain curves curves for for the the HSSS HSSS at at various various strain rates arestrain displayed rates are in displayed Figure3 a,b,in Figure respectively. 3a,b, respec Thetively. Young’s The modulus Young’s ismodulus the same is forthe thesame experiments for the conductedexperiments at various conducted strain at rates. various The strain curves rates. of The the cu strainrves of hardening the strain hardening rate as a rate function as a function of the true of the true strain are shown in Figure 3c. It is observed that the yield strength and the flow stress strain are shown in Figure3c. It is observed that the yield strength and the flow stress increase with increase with increasing strain rate, while the uniform elongation decreases with increasing strain increasing strain rate, while the uniform elongation decreases with increasing strain rate. The positive rate. The positive strain rate sensitivity for the yield strength and the flow stress could be due to the strainfollowing rate sensitivity two aspects: for the(1) Higher yield strengthflow stress and is achiev the flowed at stresshigher couldstrain rate be duesince to higher the following strain rate two aspects:might (1) Higherdecelerate flow the stress dislocation is achieved annihilation; at higher (2) strainhigher rate strain since rate higher might strainincrease rate the might barriers decelerate of the dislocationdislocation annihilation; motion for the (2) higherthermal strain and ratemechanically might increase activated the plastic barriers deformations of dislocation [56]. motion The for the thermalmechanical and properties mechanically may activatedbe anisotropic plastic in other deformations directions due [56 ].to Thethe lamellar mechanical structure properties of some mayB2 be anisotropicgrains. in other directions due to the lamellar structure of some B2 grains.

FigureFigure 3. (a) 3. Engineering (a) Engineering stress–strain stress–strain curves curves for for the the HSSSHSSS at at various various strain strain rates; rates; (b) (Trueb) True stress–strain stress–strain curvescurves for the for HSSSthe HSSS at at various various strain strain rates; (c ()c Strain) Strain hardening hardening rate a rate function a function of true strain of true for strain the HSSS for the at various strain rates; (d) Yield strength and flow stresses at various true strains as a function of true HSSS at various strain rates; (d) Yield strength and flow stresses at various true strains as a function of strain rates in double logarithmic coordinates for the HSSS. The insets of Figure 3a show good true strain rates in double logarithmic coordinates for the HSSS. The insets of Figure3a show good repeatability for both tests conducted at quasi-static strain rates and intermediate strain rates. repeatability for both tests conducted at quasi-static strain rates and intermediate strain rates. It is interesting to note that all the stress–strain curves at various strain rates show non- Itcontinuous is interesting yielding. to note A thatconcave all thesegment stress–strain over a range curves of atstrains various is observed strain rates for all show the non-continuousstress-strain yielding.curves A at concave various segment strain rates, over and a rangethe stress–str of strainsain curves is observed show fordifferent all the yielding stress-strain behaviors curves at at variousvarious strain strain rates, rates. and At the lower stress–strain strain rates, curves a transient show deformation different yielding stage is behaviors observed without at various yield strain drop, while at higher strain rates, a yield-peak with yield drop shows up first, followed by a transient rates. At lower strain rates, a transient deformation stage is observed without yield drop, while at deformation stage. As observed in Figure 3b for the strain hardening rate vs. true strain curves, the higher strain rates, a yield-peak with yield drop shows up first, followed by a transient deformation hardening rate drops rapidly first after yielding, even drops to below zero for the curves with yield stage.drop As observedat higher strain in Figure rates,3 followedb for the by strain an up-t hardeningurn to reach rate its maximum, vs. true strain and then curves, decreases the hardeningslowly rate dropsuntil the rapidly necking first point. after In our yielding, previous even paper drops [21], such to below a transient zero deformation for the curves stage with has been yield found drop at higherto strainbe caused rates, by followedthe back stress by an hardening up-turn due to reach to the itsdeformation maximum, incompatibility and then decreases between different slowly until the neckingphases over point. a strain In our regime previous corresponding paper [21 to], the such elasto-plastic a transient transition deformation stage. Similar stage has behavior been in found to be causedthe hardening by the rate back has stress also been hardening found recently due to in the the deformationother heterogeneous incompatibility materials, such between as gradient different phasesstructure over a strain[57,58], regime heterogeneous corresponding lamella to structure the elasto-plastic [59] and multilayer transition laminates stage. Similar [60]. behaviorDuring the in the hardening rate has also been found recently in the other heterogeneous materials, such as gradient structure [57,58], heterogeneous lamella structure [59] and multilayer laminates [60]. During the plastic deformation of this HSSS, load transfer and strain partitioning between two phases will occur since Metals 2018, 8, 11 5 of 14 Metals 2018, 8, 11 5 of 14 plastic deformation of this HSSS, load transfer and strain partitioning between two phases will occur since the softer fcc austenite phase are easier to deform than the harder B2 phase. Thus, the softer fcc theaustenite softer fccgrains austenite should phase carry are hi easiergher plastic to deform strain than and the lower harder flow B2 phase. stress Thus,during the the softer plastic fcc austenitedeformation. grains The should strain carry rate hardening higher plastic behaviors strain and and lower the SRS flow for stress the two during phases the in plastic this HSSS deformation. should Thebe quite strain different, rate hardening which definitely behaviors will and affect the SRSthe magnitude for the two of phases the strain in thisredistribution HSSS should between be quite the different,two phases. which This definitely effect of strain will affect rate theon the magnitude strain partitioning of the strain between redistribution two phases between will the be twoshown phases. and Thisdiscussed effect ofin strainthe following rate on thesections. strain partitioning between two phases will be shown and discussed in the followingThe SRS sections.of flow stress can be defined as The SRS of flow stress can be defined as ∂ σ = ln m ()∂ ln σ T ,ε (1) m = ( ∂ln.ε) (1) ∂ ln ε T, ε σ ε ε where . ,  , , T are true stress, true strain rate, true strain and applied temperature, whererespectively.σ, ε, ε ,TheT are yield true strength, stress, truethe true strain flow rate, stresses true strainat true and strains applied of 5%, temperature, 10%, 15% and respectively. 20% have Theplotted yield in strength,Figure 3d the as a true function flow stressesof true strain at true rate strains in double of 5%, logarithmic 10%, 15% coordinates, and 20% have and plotted then the in Figureaverage3d SRS as a ( functionm ) for this of true HSSS strain has ratebeen in calculated double logarithmic to be about coordinates, 0.0087. and then the average SRS (m) forThe this well-known HSSS has beenLudwik’s calculated equation to be [61] about can 0.0087. generally be used to describe the strain hardening behaviorsThe well-known of materials Ludwik’s and the strain equation hardening [61] can exponent generally (n be) can used be toobtained describe from the this strain equation: hardening behaviors of materials and the strain hardening exponent (n) can be obtained from this equation: σσ=+ εn 0 K (2) n σ = σ0 + Kε (2) σ where 0 is the yield strength, and K is the strength coefficient. The uniform elongation, the total where σ is the yield strength, and K is the strength coefficient. The uniform elongation, the total elongation0 and the strain hardening exponent as a function of strain rate are displayed in Figure 4a elongation and the strain hardening exponent as a function of strain rate are displayed in Figure4a for for this HSSS. The uniform elongation and the strain hardening exponent are observed to decrease this HSSS. The uniform elongation and the strain hardening exponent are observed to decrease with with increasing strain rate, while the total elongation remains similar at all strain rates. It is well increasing strain rate, while the total elongation remains similar at all strain rates. It is well known known that the specific energy absorption under tension can be obtained by integrating the that the specific energy absorption under tension can be obtained by integrating the engineering stress engineering stress over the engineering strain: over the engineering strain: Z Wd= σε Wss =  σeeedεe (3)(3)

FigureFigure 4.4. (a(a)) Uniform Uniform elongation, elongation, total total elongation elongation and and strain strain hardening hardening exponent exponent as a functionas a function of strain of ratestrain for rate the for HSSS; the (HSSS;b) Speciﬁc (b) Specific energy energy absorption absorption as a function as a functi of engineeringon of engineering strain atstrain various at various strain rates;strain (crates;) Speciﬁc (c) Specific energy energy absorption absorption as a function as a function of strain of rate strain at various rate at engineeringvarious engineering strains; (d strains;) Yield strength,(d) Yield ultimatestrength, strength ultimate and strength tensile and toughness tensile toughness as a function as a of functi strainon rate. of strain rate.

Metals 2018, 8, 11 6 of 14

Thus, the specific energy absorption as a function of engineering strain at various strain rates is plotted in Figure4b, the specific energy absorption as a function of strain rate at various engineering strains is displayed in Figure4c. It is clearly seen that the specific energy absorption increases with increasing strain rate at various engineering strains due to the positive SRS for this HSSS. The product of the ultimate strength and the total elongation can generally be considered as tensile toughness for materials [53]. Then, the yield strength, the ultimate strength and the tensile toughness are plotted as a function of strain rate in Figure4d. It should be noted that the error bars for the standard deviation have been provided in Figure4a,d, since three specimens were tested for each data point. Thus, the yield strength, the ultimate strength and the tensile toughness are all observed to increase with increasing strain rate, which indicates both higher strength and higher toughness under tension at higher strain rates. The larger specific energy absorption at higher strain rates is mainly due to the higher flow stress and the similar fracture elongation. It is well known that excellent candidates for energy absorbers require materials that are (i) capable of keeping a high value of the yield strength upon deformation, and (ii) able to absorb more energy up to fracture [30,32]. In addition to the high specific yield strength and the large uniform elongation under quasi-static conditions for this HSSS when compared to the other dual phase steels [11,14,16–19], the simultaneously improved strength and the improved tensile toughness at the intermediate strain rates are very appropriate for the application of this HSSS in the automotive industry to enhance safety during a vehicle crash since the applied strain rate range for vehicle crushing is generally between 1 and 100/s (intermediate strain rates) [51–55] or even higher. It is well known that the strain and the strain rate have strong influences on the flow stress of metals and alloys [24–28]. A computational model, known as the Johnson-Cook (J-C) model, has been presented for describing all effects of strain hardening, strain rate hardening and thermal softening on the flow stress. This model has been used for different materials including TRIP steels [62] and high strength dual phase steels recently [63,64]. This model is quite useful due to its simple expression for engineering applications, and the von Mises flow stress can be expressed as three uncoupled terms as following: n . ∗ ∗m σ = [A + Bε p][1 + C ln ε ][1 − T ] (4) . ∗ . . . where ε p is the true plastic strain, ε = ε/ε0 is the normalized strain rate with respect to ε0 = 0.0006 /s, ∗ ∗ and T is the homologous temperature define as T = (T − Troom)/(Tmelt − Troom). A, B, C, n, m are five material parameters, which need to be determined by fitting the experimental curves. The first term of Equation (4) represents the strain hardening term (usually known as Ludwik equation), which can be determined by the true stress–true strain curve for the test at strain rate of 0.0006/s (as shown in Figure5a). The second term of Equation (4) represents the strain rate hardening term, and parameter C is the strain-rate sensitivity. The third term of Equation (4) represents the thermal softening term, which is not within the consideration of the current study. In order to determine parameter C, the true flow stresses at four true plastic strains (ε p = 0.05, 0.1, 0.15, 0.2) were plotted against the logarithmic normalized strain rate in Figure5b. The fitting parameters for these experimental data at four true plastic strains were demonstrated as four solid lines in Figure5b, and an average value of parameter C was obtained to be 0.0084 from these four fitting lines. Thus, the J-C model for the flow stress without considering the thermal softening effect can be written as:

0.991 . ∗ σ = [1.155 + 2.326ε p ][1 + 0.0084 ln ε ] (5)

In Equation (5), the constants A (1.155) and B (2.326) have unit of GPa. Based on Equation (5), the hardening J-C model was found to have good agreement with the experimental data for the true stress-true plastic strain curves at various strain rates, as shown in Figure5c. The maximum possible temperature rise (assuming adiabatic condition) during the plastic tensile deformation can be estimated as ∆T = η R σdε , where ρ is the mass density, C is the heat capacity, η is the Taylor–Quinnery ρCv p v coefﬁcient for plastic work converted to heat (commonly η = 0.85), ε p is the plastic strain, and σ is the Metals 2018, 8, 11 7 of 14 η Δ=Tdσε ρ C η estimated as ρ  p , where is the mass density, v is the heat capacity, is the Cv η = 0.85 ε MetalsTaylor–Quinnery2018, 8, 11 coefficient for plastic work converted to heat (commonly ), p is7 ofthe 14

σ ρ 3 plastic strain, and is the tensile flow stress. For this HSSS, is 6.8 g/cm and Cv can be 3 tensileapproximately flow stress. taken For as this 540 HSSS, J/kg ρ[65].is 6.8 Thus, g/cm Equationand Cv can(5) becan approximately be used to well taken describe as 540 J/kgthe flow [65]. Thus,behaviors Equation of this (5) HSSS can be up used to strain to well rate describe of 56/s the since flow the behaviors possible of temperature this HSSS up rise to strainby the rate dissipated of 56/s sinceplastic the work possible in the temperature specimen is rise less by than the 80 dissipated °C (calculation plastic based work inon theabove specimen equation) is less for than the test 80 ◦ atC (calculationstrain rate of based 56/s. Moreover, on above equation)the application for the of test this at HSSS strain at rateeven of higher 56/s. strain Moreover, rates therequires application in-depth of thisstudy HSSS on atthe even relation higher between strain rates the requirestemperature in-depth and studythe flow on thestress relation in the between future thework temperature since the andadiabatic the flow temperature stress in therise future during work high since strain the rate adiabatic tension temperature is inevitable rise and during the thermal high strain softening rate tensionshould be is inevitableconsidered. and the thermal softening should be considered.

Figure 5.5. ((aa)) ExperimentalExperimental datadata forfor truetrue stress–truestress–true plasticplastic strainstrain curvecurve atat strainstrain raterate ofof 0.0006/s 0.0006/s andand thethe ﬁttingfitting curvecurve ofof thethe J-CJ-C model;model; ((b)) TrueTrue ﬂowflow stressstress asas aa functionfunction ofof logarithmiclogarithmic normalizednormalized strainstrain raterate atat variousvarious truetrue plastic plastic strains; strains; (c ()c Comparison) Comparison for for true true stress-true stress-true plastic plastic strain strain curves curves between between the experimentalthe experimental data data and and the J-Cthe model.J-C model.

In our recent paper [66], significant phase transformation from fcc austenite phase to B2 phase In our recent paper [66], signiﬁcant phase transformation from fcc austenite phase to B2 phase by by diffusional transformation has been observed to facilitate the superplasticity during the tensile diffusional transformation has been observed to facilitate the superplasticity during the tensile testing testing under temperature of 973 K for this HSSS. The high temperature (973 K) can facilitate the under temperature of 973 K for this HSSS. The high temperature (973 K) can facilitate the diffusional diffusional behaviors of the elements and the diffusional transformation. The EBSD phase behaviors of the elements and the diffusional transformation. The EBSD phase distributions after distributions after tensile tests at various strain rates under room temperature are displayed in Figure tensile tests at various strain rates under room temperature are displayed in Figure6a–e, and the 6a–e, and the volume fraction of B2 phase after tensile testing as a function of the applied tensile volume fraction of B2 phase after tensile testing as a function of the applied tensile strain rate is shown strain rate is shown in Figure 6f. As indicated, the volume fractions of B2 phase after tensile tests at in Figure6f. As indicated, the volume fractions of B2 phase after tensile tests at various strain rates various strain rates (~22%) are very similar to that of the untested sample (~22%), indicating that no (~22%) are very similar to that of the untested sample (~22%), indicating that no phase transformation phase transformation is observed at all strain rates. These observations indicate that the fcc austenite is observed at all strain rates. These observations indicate that the fcc austenite phase is relatively phase is relatively stable under room temperature even at intermediate strain rates since the stable under room temperature even at intermediate strain rates since the diffusional transformation diffusional transformation cannot occur at these stresses and strain rates without the assistance of cannot occur at these stresses and strain rates without the assistance of high temperature. Thus, the high temperature. Thus, the plastic deformation during tensile tests at various strain rates under plastic deformation during tensile tests at various strain rates under room temperature should be room temperature should be accommodated by the deformation twins and the dislocation behaviors accommodated by the deformation twins and the dislocation behaviors in both phases, which will be in both phases, which will be illustrated by TEM observations later. illustrated by TEM observations later.

Metals 2018, 8, 11 8 of 14 Metals 2018, 8, 11 8 of 14

Figure 6. EBSDEBSD phase phase distributions distributions after after testing testing at at strain strain rate rate of of (a ()a 0.0006/s;) 0.0006/s; (b) ( b0.05/s;) 0.05/s; (c) 1.2/s; (c) 1.2/s; (d) 3.6/s;(d) 3.6/s; (e) 56/s. (e) 56/s. The red The color red color stands stands for γ for-austeniteγ-austenite phase, phase, and andthe green the green color color stands stands for B2 for phase. B2 phase. (f) The(f) The volume volume fraction fraction of B2 of B2phase phase after after tensile tensile testing testing versus versus the the applied applied tensile tensile strain strain rate. rate.

In this HSSS, the γ-austenite phase is softer than the B2 phase, thus the strain partitioning makes In this HSSS, the γ-austenite phase is softer than the B2 phase, thus the strain partitioning makes the γ-austenite grains to bear larger amount of plastic strains. The back stress hardening has been the γ-austenite grains to bear larger amount of plastic strains. The back stress hardening has been found to play an important role for the tensile ductility in this HSSS due to the load transfer and the found to play an important role for the tensile ductility in this HSSS due to the load transfer and strain partitioning between two phases [21]. This strain partitioning is measured by the aspect ratio the strain partitioning between two phases [21]. This strain partitioning is measured by the aspect changes before and after tensile tests at two different strain rates (0.0006 and 56/s) for this HSSS. The ratio changes before and after tensile tests at two different strain rates (0.0006 and 56/s) for this HSSS. grain morphologies for γ-austenite grains before tensile tests are displayed in Figure 7a, while the The grain morphologies for γ-austenite grains before tensile tests are displayed in Figure7a, while grain morphologies for γ-austenite grains after tensile tests at two strain rates (0.0006 and 56/s) are the grain morphologies for γ-austenite grains after tensile tests at two strain rates (0.0006 and 56/s) shown in Figure 7b,c (the tensile direction is along the horizontal direction). The corresponding are shown in Figure7b,c (the tensile direction is along the horizontal direction). The corresponding aspect ratio information before and after tensile tests is displayed in Figure 7d–f. In these figures, l aspect ratio information before and after tensile tests is displayed in Figureα 7d–f. In these ﬁgures, andl and ww indicate indicate the average spacing spacing in in axial axial and and transverse transverse directions, directions, α is is thethe averageaverage aspect ratio defineddeﬁned by by α ==llw/w/ . In. In Figure Figure7b,c, 7b,c, the the EBSD EBSD images images correspond correspond to to the the true true uniform uniform tensile tensile strainsstrains of 28.1% and 20.9% (as (as shown in in Figure 33b),b), respectively.respectively. AsAs indicated,indicated, mostmost ofof thethe initial,initial, relativelyrelatively equi-axed γ-austenite-austenite grains grains now now become strongly elon elongatedgated along the tensile direction. Then, the mean true strain in the γ-austenite grains grains can can be be estimated, an andd the details for the derivation of the formulaformula and and the the calculation calculation method method can can be be found found in in our our previous previous paper paper [59]. [59]. Basically, Basically, by assuming assuming thethe volume volume is is constant during the plastic deformatio deformation,n, the the tensile true strain is estimated based on thethe aspect aspect ratio ratio change after the tensile deformation. Then, Then, the the mean mean true true tensile tensile strains strains experienced experienced by the γ-austenite-austenite grains during the uniform tensile loading atat thethe strainstrain ratesrates ofof 0.00060.0006 andand 56/s56/s can can be estimated to to be be 31.5% 31.5% and and 24.0%, 24.0%, respectively. respectively. Ba Basedsed on the rule of mixture, the mean true tensile strains experienced experienced by by the the B2 B2 phase during the uniform tensile loading at at the strain rates of 0.0006 and 56/s can can be be calculated calculated to to be be 16.0% 16.0% and and 9.9%, 9.9%, respectively. respectively. Then, Then, the the ratio ratio of strains between fcc austenite phase phase and and B2 B2 phase phase at at the the strain strain rate rate of of0.0006/s 0.0006/s is estimated is estimated to be to about be about 1.97, 1.97,while while the ratio the ofratio strains of strains between between fcc austenite fcc austenite phase phase and B2 and phase B2 phaseat the atstrain the strainrate of rate 56/s of is 56/s estimated is estimated to be about to be 2.42.about The 2.42. data The for data strain for strain partitioning partitioning between between two twophases phases at attwo two different different strain strain rates rates can can be summarized in in Table Table 11.. ItIt isis observedobserved thatthat thethe softersofter fccfcc austeniteaustenite grainsgrains eveneven bearbear aa higherhigher fractionfraction of true tensile strain at higher strain rate rates.s. It It is is well known that the SRS for the fcc γ-austenite and thethe hard hard B2 phase should be qu quiteite different. It It is is highly highly possible possible that that the the SRS SRS of the fcc γ-austenite-austenite is is higher than that of thethe B2B2 phase,phase, makingmaking the the fcc fccγ γ-austenite-austenite to to accommodate accommodate more more fraction fraction of of strain strain at athigher higher strain strain rates. rates. It It is is well well accepted accepted that that the the tensile tensile elongationelongation isis generallygenerally muchmuch smaller at high strain rates due to the adiabatic temperature rise under dynamic loading loading [23,27,28], [23,27,28], while the total tensile elongation is similar at all strain rates in the present study, which could be due to the fact that

Metals 2018, 8, 11 9 of 14

Metals 2018, 8, 11 9 of 14 tensile elongation is similar at all strain rates in the present study, which could be due to the fact that the softer fcc γ-austenite grains with high deformation ability bear more fraction of strain, which delays the deformation instability and the crack initiationinitiation forfor thethe B2B2 phasephase andand thethe phasephase interfaces.interfaces.

Figure 7.7. EBSDEBSD images images and and grain grain morphologies morphologies of γ of-austenite γ-austenite phase phase for (a )for untested (a) untested sample; sample; (b) sample (b) aftersample testing after attesting strain at rate strain of 0.0006/s; rate of 0.0006/s; (c) sample (c) aftersample testing after attesting strain at rate strain of 56/s. rate of The 56/s. EBSD The images EBSD correspondimages correspond to the true to uniformthe true tensileuniform strains tensile of 28.1%strains (Figure of 28.1%7a) (Figure and 20.9% 7a) (Figure and 20.9%7b). Histograms(Figure 7b). showingHistograms the showing statistics the of thestatistics grain sizeof the distribution grain size anddistribution aspect ratio and measurementsaspect ratio measurements for: (d) untested for: sample;(d) untested (e) sample sample; after (e) sample testing atafter strain testing rate at of strain 0.0006/s; rate ( fof) sample0.0006/s; after (f) sample testing atafter strain testing rate at of strain 56/s. rate of 56/s. Table 1. Summary of data for strain partitioning between two phases at two different strain rates. Table 1. Summary of data for strain partitioning between two phases at two different strain rates. Uniform Elongation Fraction of Strain Fraction of Strain Ratio of Strains Strain Rates (/s) Uniform Elongationεγ εB Fraction of Strain Fraction of Strain Ratio of Strains (ε ) 2 (f εγ/εu) (f ε /ε ) (ε /ε ) u ε ε γ B2 B2 u γ B2 Strain Rates (/s) γ B ( ε ) 2 ( fγγεε/ ) ( f εε/ ) ( εγ / ε ) 0.0006 28.1%u 31.5% 16.0% 87.4%u B22Bu 12.6%B2 1.97 560.0006 20.9%28.1% 24.0%31.5% 16.0% 9.9% 87.4% 89.6% 12.6% 10.4% 1.97 2.42 56 20.9% 24.0% 9.9% 89.6% 10.4% 2.42 In order to illustrate the strain rate effect on the strain partitioning and the deformation mechanisms,In order theto TEMillustrate images the forstrain the samplesrate effect after on testingthe strain at strain partitioning rates of 0.0006/sand the anddeformation 56/s are displayedmechanisms, in Figurethe TEM8. As images indicated, for the a highsamples density after of te deformationsting at strain twins rates (even of 0.0006/s occasional and multiple 56/s are twins,displayed marked in Figure by primary 8. As indicated, twins as ﬁrst a high and density secondary of deformation twins as second) twins and (even dislocations occasional in themultiple grain interiorstwins, marked of fcc by austenite primary phase twins areas first observed and second at bothary lowtwins and as second) high strain and rates.dislocations The fcc in austenitethe grain grainsinteriors are ofobserved fcc austenite to be phase stretched are observed to true at strains both low of 31.5% and high and strain 24.0% rates. at strain The ratesfcc austenite of 0.0006 grains and 56/s,are observed and these to be high stretched plastic to deformations true strains of are 31.5% expected and 24.0% to increase at strain the rates dislocation of 0.0006 density and 56/s, and and the deformationthese high plastic twins deformations in the grain interiorsare expected of fcc to austenite increase grains.the dislocation These formed density twin and boundaries the deformation (TBs) bytwins deformation in the grain twins interiors are effective of fcc obstacles austenite to thegrains. motion These of dislocationsformed twin and boundaries can accumulate (TBs) theby pile-updeformation of dislocations twins are neareffective TBs (asobstacles indicated to the in Figuremotion8), of which dislocations could provide and can great accumulate resistance the to pile- the furtherup of dislocations dislocation near motion TBs and (as thusindicated the strong in Figure strain 8), hardening which could for provide sustaining great uniform resistance elongation to the asfurther suggested dislocation by previous motion researchand thus [the4]. strong Dislocations strain hardening are also observed for sustaining in the B2uniform grains elongation after tensile as testing,suggested indicating by previous that theresearch B2 phase [4]. are Dislocations plastically are deformable also observed and the in dislocations the B2 grains can after be stored tensile in thetesting, B2 grains. indicating As indicated, that the B2 high phase density are plastically of dislocations deformable are also and observed the dislocations to accumulate can be around stored the in B2the particlesB2 grains. and As these indicated, high densityhigh density of dislocations of dislocations at the are phase also interfaces observed will to accumulate ensure the continuousaround the strainsB2 particles at the and phase these interfaces high density to accommodate of dislocations the at strainthe phase gradient interfaces between will theensure two the phases continuous and to elevatestrains at the the back phase stress interfaces [21]. to accommodate the strain gradient between the two phases and to elevate the back stress [21].

Metals 2018, 8, 11 10 of 14 Metals 2018, 8, 11 10 of 14

Metals 2018, 8, 11 10 of 14

FigureFigure 8. TEM 8. TEM images images for for (a) (a sample) sample after after testing testing atat strain rate rate of of 0.0006/s; 0.0006/s; (b) (sampleb) sample after after testing testing at at strain rate of 56/s. strain rate of 56/s. FigureThe SEM 8. TEM images images of forfinal (a )fracture sample aftersurfaces testing for at th straine tensile rate of tests 0.0006/s; at various (b) sample strain after rates testing are atshown Thein Figurestrain SEM 9.rate images The of 56/s.tensile of final fracture fracture at various surfaces strain for therates tensile is observed tests atto variousbe ductile strain with rates dimples. are shownThe in Figureaverage9. The dimple tensile size fracture is estimated at various to be strain 3.22, 2.96, rates 1.63, is observed 1.44, 1.37 to μm be for ductile the tensile with tests dimples. at strain The rates average The SEM images of final fracture surfaces for the tensile tests at various strain rates are shown dimpleof 0.0006, size is 0.05, estimated 1.2, 3.6, to 56/s be based 3.22, 2.96,on the 1.63, SEM 1.44, images. 1.37 Theseµm for dimples the tensile appear tests to be at formed strain by rates pulling of 0.0006, in Figure 9. The tensile fracture at various strain rates is observed to be ductile with dimples. The the B2 grains out from the fcc austenite matrix or fracturing the B2 particle during the tensile loading. 0.05,average 1.2, 3.6, dimple 56/s size based is estimated on the SEM to be images.3.22, 2.96, These1.63, 1.44, dimples 1.37 μm appear for the totensile be formed tests at strain by pulling rates the As indicated earlier, the B2 phase is less deformable at higher strain rates, which result in easier brittle B2 grainsof 0.0006, out 0.05, from 1.2, the 3.6, fcc 56/s austenite based on matrix the SEM or images. fracturing These the dimples B2 particle appear duringto be formed the tensileby pulling loading. fracture in B2 particles and smaller dimple size at the final fracture surface. Thus, the size of B2 As indicatedthe B2 grains earlier, out from the B2 the phase fcc austenite is less deformablematrix or fracturing at higher the strainB2 particle rates, du whichring the result tensile in loading. easier brittle particles will be smaller and the density of the phase interfaces will be higher at the final fracture As indicated earlier, the B2 phase is less deformable at higher strain rates, which result in easier brittle fracturesurfaces, in B2 and particles more energy and smalleris needed dimple to consume size for at th thee final final fracture fracture at higher surface. strain Thus, rates due the to size the of B2 fracture in B2 particles and smaller dimple size at the final fracture surface. Thus, the size of B2 particlesfracturing will beof B2 smaller phase during and the the density tensile deformation of the phase at interfaceshigher strain will rates. be These higher observations at the final could fracture particles will be smaller and the density of the phase interfaces will be higher at the final fracture surfaces,also andprovide more the energy origin isfor needed the higher to consume energy abso forrption the final during fracture the tensile at higher deformation strain rates at higher due to the surfaces, and more energy is needed to consume for the final fracture at higher strain rates due to the fracturingstrain ofrates, B2 as phase shown during in Figure the tensile4. deformation at higher strain rates. These observations could fracturing of B2 phase during the tensile deformation at higher strain rates. These observations could also provide the origin for the higher energy absorption during the tensile deformation at higher strain also provide the origin for the higher energy absorption during the tensile deformation at higher rates,strain as shown rates, as in shown Figure in4. Figure 4.

Figure 9. SEM images of the fracture surfaces for the tensile tests at various strain rates: (a) 0.0006/s; (b) 0.05/s; (c) 1.2/s; (d) 3.6/s; (e) 56/s.

Figure Figure 9. SEM 9. SEM images images of of the the fracture fracture surfaces surfaces forfor th thee tensile tensile tests tests at atvarious various strain strain rates: rates: (a) 0.0006/s; (a) 0.0006/s; (b) 0.05/s; (c) 1.2/s; (d) 3.6/s; (e) 56/s. ( b) 0.05/s; (c) 1.2/s; (d) 3.6/s; (e) 56/s.

Metals 2018, 8, 11 11 of 14

4. Conclusions The tensile behaviors of the HSSS with ultrafine grains and dual-phase microstructure were investigated over a wide range of strain rates from 0.0006 to 56/s in the present study, and the main findings are summarized as follows: (1) This HSSS shows excellent tensile properties at the strain rate range of 0.0006 to 56/s. The uniform elongation and the strain hardening exponent are observed to decrease slightly with increasing strain rate for this HSSS, while it is observed that the yield strength, the ultimate tensile strength and the tensile toughness all increase with increasing strain rate at the strain rate range from 0.0006 to 56/s, rendering this HSSS as an excellent candidate for energy absorber in automobile industry. (2) The Johnson-Cook model can be used to well describe the strain hardening behaviors and the strain rate effect for this HSSS, and the final constitutive relation has the form of 0.991 . ∗ σ = [1.155 + 2.326ε p ][1 + 0.0084 ln ε ] and has a good agreement with experimental results. (3) At lower strain rates, a transient strain hardening behavior is observed without yield drop, while at higher strain rates a yield-peak with yield drop shows up first, followed by a transient deformation stage. Such a transient deformation stage has been found to be caused by the back stress hardening due to the load transfer and strain partitioning between two phases, and the softer fcc austenite grains even bear more fraction of true tensile strain to delay the deformation instability at higher strain rates. No phase transformation is observed at all strain rates. The deformation twins are observed in the fcc austenite grains at all strain rates, facilitating the uniform tensile deformation. (4) The dimple size is observed to be smaller and the density of phase interfaces is found to be higher at final fracture surfaces, and thus more energy need be consumed during the final fracture for the experiments conducted at higher strain rates, resulting in better tensile toughness at higher strain rates. This higher density of the phase interfaces can be attributed to the easier brittle fracture in B2 particles since the B2 phase is less deformable at higher strain rates. The present results should provide insights for better understanding the deformation physics of this HSSS and provide design strategy for achieving better mechanical properties for impact-tolerant applications in automobile industry. In future work, the compressive properties of this HSSS at various strain rates should also be investigated for better understanding in applications as energy absorbers.

Acknowledgments: This work was supported by National Key R&D Program of China [Grant number 2017YFA0204402]; NSFC [Grant numbers 11672313, 11472286, 11572328, 51701228, and 51601204]; and the Strategic Priority Research Program of the Chinese Academy of Sciences [Grant number XDB22040503]. The authors would like to thank Yang Liu from Northeastern University (China) for helping to conduct the mechanical testing. Author Contributions: Fuping Yuan and Xiaolei Wu conceived and designed the experiments; Muxin Yang provided the materials; Wei Wang performed the mechanical testing; Wei Wang, Yan Ma and Ping Jiang conducted the microstructure characterization; Fuping Yuan and Wei Wang wrote the paper. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Fischer, F.D.; Reisner, G.; Werner, E.; Tanaka, K.; Cailletaud, G.; Antretter, T. A new view on transformation induced plasticity (TRIP). Int. J. Plast. 2000, 16, 723–748. [CrossRef] 2. Grässel, O.; Krüger, L.; Frommeyer, G.; Meyer, L.W. High strength Fe–Mn–(Al, Si) TRIP/TWIP steels development-properties-application. Int. J. Plast. 2000, 16, 1391–1409. [CrossRef] 3. Frommeyer, G.; Brüx, U.; Neumann, P. Supra-ductile and high-strength manganese-TRIP/TWIP steels for high energy absorption purposes. ISIJ Int. 2003, 43, 438–446. [CrossRef] 4. Bouaziz, O.; Allain, S.; Scott, C. Effect of grain and twin boundaries on the hardening mechanisms of twinning-induced plasticity steels. Scr. Mater. 2008, 58, 484–487. [CrossRef] 5. Kang, S.; Jung, Y.S.; Jun, J.H.; Lee, Y.K. Effects of recrystallization annealing temperature on carbide precipitation, microstructure, and mechanical properties in Fe–18Mn–0.6C–1.5Al TWIP steel. Mater. Sci. Eng. A 2010, 527, 745–751. [CrossRef] Metals 2018, 8, 11 12 of 14

6. Son, Y.I.; Lee, Y.K.; Park, K.T.; Lee, C.S.; Shin, D.H. Ultrafine grained ferrite-martensite dual phase steels fabricated via equal channel angular pressing: Microstructure and tensile properties. Acta Mater. 2005, 53, 3125–3134. [CrossRef] 7. Calcagnotto, M.; Adachi, Y.; Ponge, D.; Raabe, D. Deformation and fracture mechanisms in fine-and ultrafine-grained ferrite/martensite dual-phase steels and the effect of aging. Acta Mater. 2011, 59, 658–670. [CrossRef] 8. Jiang, S.H.; Wang, H.; Wu, Y.; Liu, X.J.; Chen, H.H.; Yao, M.J.; Gault, B.; Ponge, D.; Raabe, D.; Hirata, A.; et al. Ultrastrong steel via minimal lattice misfit and high-density nanoprecipitation. Nature 2017, 544, 460–464. [CrossRef][PubMed] 9. Raabe, D.; Springer, H.; Gutierrez-Urrutia, I.; Roters, F.; Bausch, M.; Seol, J.B.; Koyama, K.; Choi, P.P.; Tsuzaki, K. Alloy design, combinatorial synthesis, and microstructure-property relations for low-density Fe–Mn–Al–C austenitic steels. JOM 2014, 66, 1845–1856. [CrossRef] 10. Raabe, D.; Tasan, C.C.; Springer, H.; Bausch, M. From high-entropy alloys to high-entropy steels. Steel Res. Int. 2015, 86, 1127–1138. [CrossRef] 11. Frommeyer, G.; Bruex, U. Microstructures and mechanical properties of high strength Fe–Mn–Al–C light-weight TRIPLEX steels. Steel Res. Int. 2006, 77, 627–633. [CrossRef] 12. Rana, R.; Lahaye, C.; Ray, R.K. Overview of lightweight ferrous materials: Strategies and promises. JOM 2014, 66, 1734–1746. [CrossRef] 13. Kim, H.; Suh, D.W.; Kim, N.J. Fe–Al–Mn–C lightweight structural alloys: A review on the microstructures and mechanical properties. Sci. Technol. Adv. Mater. 2013, 14, 014205. [CrossRef][PubMed] 14. Sohn, S.S.; Song, H.; Suh, B.C.; Kwak, J.H.; Lee, B.J.; Kim, N.J.; Lee, S. Novel ultra-high-strength (ferrite + austenite) duplex lightweight steels achieved by fine dislocation substructures (Taylor lattices), grain refinement, and partial recrystallization. Acta Mater. 2015, 96, 301–310. [CrossRef] 15. Gutierrez-Urrutia, I.; Raabe, D. Multistage strain hardening through dislocation substructure and twinning in a high strength and ductile weight-reduced Fe–Mn–Al–C steel. Acta Mater. 2012, 60, 5791–5802. [CrossRef] 16. Gutierrez-Urrutia, I.; Raabe, D. Influence of Al content and precipitation state on the mechanical behavior of austenitic high-Mn low-density steels. Scr. Mater. 2013, 68, 343–347. [CrossRef] 17. Yoo, J.D.; Hwang, S.W.; Park, K.T. Factors influencing the tensile behavior of a Fe–28Mn–9Al–0.8C steel. Mater. Sci. Eng. A 2009, 508, 234–240. [CrossRef] 18. Hwang, S.W.; Ji, J.H.; Lee, E.G.; Park, K.T. Tensile deformation of a duplex Fe–20Mn–9Al–0.6C steel having the reduced specific weight. Mater. Sci. Eng. A 2011, 528, 5196–5203. [CrossRef] 19. Wu, Z.Q.; Ding, H.; An, X.H.; Han, D.; Liao, X.Z. Influence of Al content on the strain-hardening behavior of aged low density Fe–Mn–Al–C steels with high Al content. Mater. Sci. Eng. A 2015, 639, 187–191. [CrossRef] 20. Kim, S.H.; Kim, H.; Kim, N.J. Brittle intermetallic compound makes ultrastrong low-density steel with large ductility. Nature 2015, 518, 77–79. [CrossRef][PubMed] 21. Yang, M.X.; Yuan, F.P.; Xie, Q.G.; Wang, Y.D.; Ma, E.; Wu, X.L. Strain hardening in Fe–16Mn–10Al–0.86C–5Ni high specific strength steel. Acta Mater. 2016, 109, 213–222. [CrossRef] 22. Wang, W.; Zhang, H.S.; Yang, M.X.; Jiang, P.; Yuan, F.P.; Wu, X.L. Shock and spall behaviors of a high specific strength steel: Effects of impact stress and microstructure. J. Appl. Phys. 2017, 121, 135901. [CrossRef] 23. Nemat-Nasser, S.; Guo, W.G. Thermomechanical response of DH-36 structural steel over a wide range of strain rates and temperatures. Mech. Mater. 2003, 35, 1023–1047. [CrossRef] 24. Mishra, A.; Martin, M.; Thadhani, N.N.; Kad, B.K.; Kenik, E.A.; Meyers, M.A. High-strain-rate response of ultra-fine-grained copper. Acta Mater. 2008, 56, 2770–2783. [CrossRef] 25. Wei, Q. Strain rate effects in the ultrafine grain and nanocrystalline regimes—Influence on some constitutive responses. J. Mater. Sci. 2007, 42, 1709–1727. [CrossRef] 26. Subhash, G. The constitutive behavior of refractory-metals as a function of strain-rate. JOM 1995, 5, 55–58. [CrossRef] 27. Suo, T.; Li, Y.L.; Zhao, F.; Fan, X.L.; Guo, W.G. Compressive behavior and rate-controlling mechanisms of ultrafine grained copper over wide temperature and strain rate ranges. Mech. Mater. 2013, 61, 1–10. [CrossRef] 28. Suo, T.; Chen, Y.Z.; Li, Y.L.; Wang, C.X.; Fan, X.L. Strain rate sensitivity and deformation kinetics of ECAPed aluminum over a wide range of strain rates. Mater. Sci. Eng. A 2013, 560, 545–551. [CrossRef] Metals 2018, 8, 11 13 of 14

29. Wei, Q.; Kecskes, L.; Jiao, T.; Hartwig, K.T.; Ramesh, K.T.; Ma, E. Adiabatic shear banding in ultrafine-grained Fe processed by severe plastic deformation. Acta Mater. 2004, 52, 1859–1869. [CrossRef] 30. Xue, Q.; Gray, G.T., III; Henrie, B.L.; Maloy, S.A.; Chen, S.R. Influence of shock prestraining on the formation of shear localization in 304 stainless steel. Metall. Mater. Trans. A 2005, 36, 1471–1486. [CrossRef] 31. Yang, Y.; Jiang, F.; Zhou, B.M.; Li, X.M.; Zheng, H.G.; Zhang, Q.M. Microstructural characterization and evolution mechanism of adiabatic shear band in a near beta-Ti alloy. Mater. Sci. Eng. A 2011, 528, 2787–2794. [CrossRef] 32. Yuan, F.P.; Jiang, P.; Wu, X.L. Annealing effect on the evolution of adiabatic shear band under dynamic shear loading in ultra-fine-grained iron. Int. J. Impact Eng. 2012, 50, 1–8. [CrossRef] 33. Yuan, F.P.; Bian, X.D.; Jiang, P.; Yang, M.X.; Wu, X.L. Dynamic shear response and evolution mechanisms of adiabatic shear band in an ultrafine-grained austenite-ferrite duplex steel. Mech. Mater. 2015, 89, 47–58. [CrossRef] 34. Yuan, F.P.; Chen, P.; Feng, Y.P.; Jiang, P.; Wu, X.L. Strain hardening behaviors and strain rate sensitivity of gradient-grained Fe under compression over a wide range of strain rates. Mech. Mater. 2016, 95, 71–82. [CrossRef] 35. Singh, N.K.; Cadoni, E.; Singha, M.K.; Gupta, N.K. Dynamic tensile behavior of multi phase high yield strength steel. Mater. Des. 2011, 32, 5091–5098. [CrossRef] 36. Xiong, R.G.; Fu, R.Y.; Su, Y.; Li, Q.; Wei, X.C.; Li, L. Tensile Properties of TWIP Steel at High Strain Rate. J. Iron Steel Res. Int. 2009, 16, 81–86. [CrossRef] 37. Boyce, B.L.; Dilmore, M.F. The dynamic tensile behavior of tough, ultrahigh-strength steels at strain-rates from 0.0002 s−1 to 200 s−1. Int. J. Impact Eng. 2009, 36, 263–271. [CrossRef] 38. Cadoni, E.; Singh, N.K.; Forni, D.; Singha, M.K.; Gupta, N.K. Strain rate effects on the mechanical behavior of two Dual Phase steels in tension. Eur. Phys. J. Spec. Top. 2016, 225, 409–421. [CrossRef] 39. Geiger, M.; Merklein, M.; Kaupper, M. Investigation of the mechanical behaviour of advanced high strength steels under various loading conditions. Int. J. Mater. Form. 2008, 1, 225–228. [CrossRef] 40. Yu, H.D.; Guo, Y.J.; Lai, X.M. Rate-dependent behavior and constitutive model of DP600 steel at strain rate from 10−4 to 103 s−1. Mater. Des. 2009, 30, 2501–2505. [CrossRef] 41. Das, A.; Tarafder, S. Experimental investigation on martensitic transformation and fracture morphologies of austenitic stainless steel. Int. J. Plast. 2009, 25, 2222–2247. [CrossRef] 42. Lee, S.; Estrin, Y.; De Cooman, B. Effect of the strain rate on the TRIP–TWIP transition in austenitic Fe-12 pct Mn-0.6 pct C TWIP steel. Mater. Trans. A 2014, 45, 717–730. [CrossRef] 43. Zaera, R.; Rodríguez-Martínez, J.A.; Vadillo, G.; Fernández-Sáez, J. Dynamic necking in materials with strain induced martensitic transformation. J. Mech. Phys. Solids 2014, 64, 316–337. [CrossRef] 44. Gu, Z.W.; Jin, X.G.; Gao, G.Q. Shock response of stainless steel at high temperature. J. Mater. Sci. 2000, 35, 2347–2351. [CrossRef] 45. Gray, G.T., III; Livescu, V.; Rigg, P.A.; Trujillo, C.P.; Cady, C.M.; Chen, S.R.; Carpenter, J.S.; Lienert, T.J.; Fensin, S. Structure/property (constitutive and dynamic strength/damage) characterization of additively manufactured 316L SS. EPJ Web Conf. 2015, 94, 02006. [CrossRef] 46. Savinykh, A.S.; Garkushin, G.V.; Razorenov, S.V.; Wolf, S.; Kruger, L. Influence of the temperature-induced martensitic-austenitic transformation on the strength properties of high-alloy steels under dynamic loading. Combust. Explos. Shock Waves 2015, 51, 124–129. [CrossRef] 47. Tarigopula, V.; Hopperstad, O.S.; Langseth, M.; Clausen, A.H.; Hild, F. A study of localization in dual-phase high-strength steels under dynamic loading using digital image correlation and FE analysis. Int. J. Solids Struct. 2008, 45, 601–619. [CrossRef] 48. Wang, W.R.; Li, M.; He, C.W.; Wei, X.C.; Wang, D.Z.; Du, H.B. Experimental study on high strain rate behavior of high strength 600–1000 MPa dual phase steels and 1200 MPa fully martensitic steels. Mater. Des. 2013, 47, 510–521. [CrossRef] 49. Qin, J.G.; Chen, R.; Wen, X.J.; Lin, Y.L.; Liang, M.Z.; Lu, F.Y. Mechanical behaviour of dual-phase high-strength steel under high strain rate tensile loading. Mater. Sci. Eng. A 2013, 586, 62–70. [CrossRef] 50. Moćko,W.; Brodecki, A.; Kruszka, L. Mechanical response of dual phase steel at quasi-static and dynamic tensile loadings after initial fatigue loading. Mech. Mater. 2016, 92, 18–27. [CrossRef] 51. Dong, D.Y.; Liu, Y.; Yang, Y.L.; Li, J.F.; Ma, M.; Jiang, T. Microstructure and dynamic tensile behavior of DP600 dual phase steel joint by laser welding. Mater. Sci. Eng. A 2014, 594, 17–25. [CrossRef] Metals 2018, 8, 11 14 of 14

52. Liu, Y.; Dong, D.Y.; Wang, L.; Chu, X.; Wang, P.F.; Jin, M.M. Strain rate dependent deformation and failure behavior of laser welded DP780 steel joint under dynamic tensile loading. Mater. Sci. Eng. A 2015, 627, 296–305. [CrossRef] 53. Meyers, M.A. Dynamic Behavior of Materials; John Wiley & Sons: Hoboken, NJ, USA, 1994. 54. Xu, S.Q.; Ruan, D.; Beynon, J.H.; Rong, Y.H. Dynamic tensile behaviour of TWIP steel under intermediate strain rate loading. Mater. Sci. Eng. A 2013, 573, 132–140. [CrossRef] 55. Oliver, S.; Jones, T.B.; Fourlaris, G. Dual phase versus TRIP strip steels: Comparison of dynamic properties for automotive crash performance. Mater. Sci. Technol. 2007, 23, 423–431. [CrossRef] 56. Huh, H.; Kim, S.B.; Song, J.H.; Lim, J.H. Dynamic tensile characteristics of TRIP-type and DP-type steel sheets for an auto-body. Int. J. Mech. Sci. 2008, 50, 918–931. [CrossRef] 57. Wu, X.L.; Jiang, P.; Chen, L.; Yuan, F.P.; Zhu, Y.T. Extraordinary strain hardening by gradient structure. Proc. Natl. Acad. Sci. USA 2014, 111, 7197–7201. [CrossRef][PubMed] 58. Yang, M.X.; Pan, Y.; Yuan, F.P.; Zhu, Y.T.; Wu, X.L. Back stress strengthening and strain hardening in gradient structure. Mater. Res. Lett. 2016, 4, 141–151. [CrossRef] 59. Wu, X.L.; Yang, M.X.; Yuan, F.P.; Wu, G.L.; Wei, Y.J.; Huang, X.X.; Zhu, Y.T. Heterogeneous lamella structure Unites ultrafine-grain strength with coarse grain ductility. Proc. Natl. Acad. Sci. USA 2015, 112, 14501–14505. [CrossRef][PubMed] 60. Ma, X.L.; Huang, C.X.; Moering, J.; Ruppert, M.; Höppel, H.W.; Göken, M.; Narayan, J.; Zhu, Y.T. Mechanical properties of copper/bronze laminates: Role of interfaces. Acta Mater. 2016, 116, 43–52. [CrossRef] 61. Sung, J.H.; Kim, J.H.; Wagoner, R.H. A plastic constitutive equation incorporating strain, strain-rate, and temperature. Int. J. Plast. 2010, 26, 1746–1771. [CrossRef] 62. Van Slycken, J.; Verleysen, P.; Degrieck, J.; Bouquerel, J. Constitutive equations for multiphase TRIP steels at high rates of strain. J. Phys. IV 2006, 134, 69–74. [CrossRef] 63. Vedantam, K.; Bajaj, D.; Brar, N.S.; Hill, S. Johnson-Cook strength models for mild and DP 590 steels. AIP Conf. Proc. 2006, 845, 775–778. 64. Roth, C.C.; Mohr, D. Effect of strain rate on ductile fracture initiation in advanced high strength steel sheets: Experiments and modeling. Int. J. Plast. 2014, 56, 19–44. [CrossRef] 65. Pehlke, R.D.; Jeyarajan, A.; Wada, H. Summary of Thermal Properties for Casting Alloys and Mold Materials; University of Michigan: Ann Arbor, MI, USA, 1982. 66. Wang, W.; Yang, M.X.; Yan, D.S.; Jiang, P.; Yuan, F.P.; Wu, X.L. Deformation mechanisms for superplastic behaviors in a dual-phase high specific strength steel with ultrafine grains. Mater. Sci. Eng. A 2017, 702, 133–141. [CrossRef]

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).