Strengthening Contributions of Mechanical Twinning and Dislocations to the Flow Stress of Hadfield High-Manganese Steel: Quantitative Analysis

The flow stress of Hadfield steel is attributed to lattice friction, dynamic strain aging (DSA), mechanical twinning, and forest hardening. However, it has not been clarified yet which mechanism quantitatively contributes most to the work hardening. Here, an austenitic Hadfield steel containing 1.1 wt.% C and 12.5 wt.% Mn was studied, and tensile tests at a strain rate of 1 s−1 were performed to neglect the DSA effect. The lattice friction was estimated by the Hall–Petch relationship. Twin plates characteristics and dislocation densities were estimated quantitatively by TEM and XRD, at 11, 18, 25, 38, and 55% strain levels. A linear approach was utilized to model the flow stress. At 11 and 18% strain, the role of mechanical twinning dominated the work hardening by contributions to the flow stress with 195 and 261.6 MPa higher than the forest hardening contributions which recorded 135.5 and 250.2 MPa, respectively. With the strain level increase, the thicknesses of the twinned plates were increased from 30 to 125 nm at 11 and 55% strain, respectively, resulting in a reduced contribution by the mechanical twinning while a rising effect of dislocations was noticed at large strain levels (38 and 55%) recording contributions of forest hardening to the flow stress with 437.2 and 544 MPa higher than the mechanical twinning contributions which likewise recorded 416.7 and 500.5 MPa, respectively.


Introduction
Austenitic Hadfield steel is an excellent substrate of choice in various engineering applications due to the distinctive combination of its mechanical properties. This is because it has high strength, high toughness, high resistance to wear, high strain-hardening rate in a polycrystalline form, and under heavy impact loads. Hadfield steel is used in many industrial applications such as excavators, railway crossings, crusher jaws, grinding mill liners, oil well drilling, impact hammers, bullet-proof helmets, and non-magnetic plates for electromag-nets (Ref [1][2][3][4]. The standard austenitic Hadfield steel contains between 10 and 14% Mn and between 1.0 and 1.4% C, and it is completely austenitic in the normal quenched condition. Hadfield steel has a superior work hardening ability compared to other carbon steels. This exceptional work hardening capacity is ascribed to the transformation of c to a or e martensitic structures and deformation twins ( Ref 2,[5][6][7]. Hadfield steel has a low stacking fault energy (SFE, $23-35 mJ m -2 ) ( Ref 5), which induces the formation of deformation twins. It is reported that twinning is activated in polycrystalline Hadfield steel, especially at strains of the order of 5-10% ( Ref 5,8). Twin boundaries resist dislocation motion, while twin-twin interactions result in a high hardening rate (Ref 9,10). Four deformation mechanisms affect the mechanical properties of Hadfield steel including (Ref 2, 6, 11): (i) lattice friction, (ii) dynamic strain aging (DSA), (iii) mechanical twinning, and (iv) dislocation accumulations. However, it is challenging in polycrystalline Hadfield steel to experimentally identify the contribution of each deformation mechanism as all four mechanisms are generally active, and due to grain boundary effects ( Ref 12,13).
Firstly, the friction stress (lattice friction) or solid solution strengthening depends on the local atomic structure of the material, and it occurs as a result of the fluctuations in the solute-dislocation interaction energy ( Ref 14). It can be calculated according to the Hall-Petch relationship based on the yield strength of the austenitic structures with respect to the corresponding grain size ( Ref 15,16).
Secondly, dynamic strain aging (DSA) is associated with the repeated dynamic interactions of moving dislocations with diffusing interstitial solute atoms after yielding. DSA is supposed to accelerate the work hardening rate of Hadfield steel, leading to a high uniform elongation and ultimate tensile strength ( Ref 17,18). DSA appears under low strain rates conditions because of the sufficient time available for the interstitial atoms to interact with dislocations, which results in locking/unlocking of dislocation movements. However, DSA can be suppressed by increasing the strain rate during tension tests (Ref 8). The DSA's contribution to the stress response of Hadfield steel can be observed as a serrated flow on the stressstrain curves.
Thirdly, regarding the mechanical twinning, prior studies revealed that twinning is the primary deformation mechanism at the beginning, and at the initial stages of deformation for tensile loading of h111i oriented Hadfield steel single crystals ( Ref 5,10,12,19,20). There is evidence from an earlier study on Cu single crystals that activation of primary twinning alone could lessen the hardening rate. However, the rate of hardening increases when primary twins interact with secondary twins (Ref 21).
Eventually, in terms of dislocation accumulations, some low SFE FCC alloys, as well as TWIP steels, have been shown to develop a high density of dislocations ( Ref 6,22,23). For example, Hutchinson and Ridley (Ref 6) revealed that the observed dislocation density of deformed Hadfield steel is one order of magnitude more than that of pure FCC metals, possibly because of interactions between the dislocations and manganese-carbon atomic dipoles. It is expected that dynamic aging would decrease the mean free length of slip, leading to more dislocations being immobilized in the crystal after a given strain. Furthermore, the interaction could impede dynamic recovery, hence decreasing the rate of dislocation annihilation. As a result, work hardening is predicted to rise (Ref 6). However, Hutchinson and Ridley (Ref 6) reported that the high work hardening rate at true strains above about 0.15 is mostly due to mechanical twinning, which can contribute almost twice as much as the effect of dislocation accumulation, whereas Zhang et al. (Ref 24) reported that the work hardening of Hadfield steel mostly caused by dislocation interactions during the initial stages of deformation, while the initiation of twin plates led to an unusual hardening at the final stages of the deformation under low strain rate conditions. The study advances expressively from the literature survey that research studies are still needed to investigate the contributions of the deformation mechanisms to the work hardening of the Hadfield steel under high strain rates. Therefore, the present study aims to quantitatively evaluate the contribution of deformation twins and dislocation accumulations to the flow stress of Hadfield steel at a strain rate of unity per second. Such analysis can provide more details about the plastic behavior of high interstitial C-Mn steels, especially under high strain rate deformation.

Materials and Methods
A commercial hot-rolled Hadfield steel obtained from Baosteel company was investigated. The chemical composition of the utilized Hadfield steel is listed in Table 1. Specimens for optical microstructure were ground by different grades of Si-C sandpapers up to #2000 grade, then the ground specimens were polished by diamond paste for 5 min, and finally the polished specimens were etched by Nital (2% nitric acid, 98% ethanol) for 10 s. The investigated microstructure showed only the FCC austenite phase with an average grain size (D) of 65±15 lm using an Olympus GX-71 optical microscope. Three samples for tension tests were experimented based on the ASTM standard (E 8M-03) with the long axes parallel to the rolling direction and having gauge dimensions of 25 9 6 9 1 mm 3 .
To obtain samples with different grain sizes (to calculate the lattice friction), the as-received Hadfield steel plates were cold rolled (with 30% area reduction), and then the cold-rolled sheets with thicknesses of approximately 1.2 ± 0.15 mm were annealed at 1000°C for 5 min to release the internal stresses and subsequently quenched in water to keep a fully austenitic structure. More details about this flash annealing were discussed in the literature ( Ref 11). The tension tests of the asreceived specimens were accomplished at room temperature under a strain rate of 1 s À1 by a Zwick (Z100) universal testing machine. The temperatures during the tension tests were recorded by an Optris infrared temperature measurement camera.
After the tension test, thin circular foils with a diameter of 3 mm for transmission electron microscopy (TEM) were selected within the gauge length near the fracture plane. The foils were polished down to 60 lm and then polished by twin jet using a sodium chromate melted in glacial acetic acid at 100 V. Finally, the foils were additionally thinned at a low incidence angle (3°) via an ion beam polishing system (Gatan 691) operated at 3 KV for 20 min. Twins were studied by a transmission electron microscope (TEM) with a JEM 2100F operated at 200 kV. The x-ray diffraction (XRD) was performed using a RIGAKU ULTIMAIV operating at 40 kV and 30 mA using a copper tube between 40 and 100°with a rate of 2°per minute.

Linear Approach to Model the Flow Stress
The flow stress of Hadfield steel (which does not contain precipitates) implies the contributions from the lattice friction or solid solution hardening (r l ), DSA behavior (r s ), mechanically induced deformation twin plates (r t ), and forest hardening resulting from dislocation storage (r d ). We assume that r l , r s , r t , and r d contribute linearly to the flow stress. The following formula can be used to model the contributions of different deformation mechanisms to the flow stress (FS) (Ref 25,26):

Lattice Friction and DSA
On one hand, the lattice friction of Hadfield steel can be calculated by tensile testing of two specimens with different grain sizes at the same strain rate; then, from the Hall-Petch equation, the lattice friction can be calculated ( Ref 15,25,27). Therefore, quasistatic tensile tests at a strain rate of 10 À5 s À1 were performed to calculate the lattice friction. On the one hand, r s can be neglected as a result of using of high strain rates.
The yield strength (YS) of the cold-rolled and heat-treated samples was compared with that of the as-received steel to estimate the lattice friction of the Hadfield steel using the Hall-Petch relationship ( Ref 22,27). The yield strength is related to the grain size as expressed by Eq 2: where k is the strengthening coefficient.

Contribution of Deformation Twins
Mechanical twinning is a deformation mechanism that occurs in FCC structures with low SFE where G is the shear modulus, calculated according to the literature (Ref [31][32][33], being approximately equal to 75 GPa; M is the average Taylor factor, being approximately 3.06; b is a constant with a value of 0.3; and L represents the dislocation mean free path. L can be calculated by equation (4) where t is the mean spacing between twin plates, or in other words, it signifies the average width of the matrix lamellae represented between the twin plates. It is dependent on the average width of the twinned plates e and the twin volume fraction F, in which t can be calculated as follows (Ref 34):

Contribution of Dislocations
The XRD can be utilized to determine dislocation densities by estimating the broadening in the peaks profile ( Ref 30,35,36). The micro-strain e and crystallite size d can be obtained by analysing the XRD patterns using Rietveld analyses performed by the MAUD program (Ref 37). The lattice constant a, crystallite sizes, and micro-strains could be estimated via the ''size-strain'' analysis in accordance with the Popa model ( Ref 38). The dislocation densities (q d ) could be determined according to Eq 6 as follows (Ref 30,36): where b is the Burgers vector (b = a/(2) 0.5 for the FCC structure). The flow stress caused by the dislocation storage (r d ) is calculated by the Taylor hardening model ( Ref 6,25,39). The forest hardening contributed by the dislocations can be described by Eq 7 as follows: where a is a constant with a value of 0.25.

Tension Test and Microstructure
Figure 1(a) shows the true stress-strain curve of Hadfield steel at a strain rate of 10 0 s À1 and the corresponding work hardening rate. Clearly, the stress-strain curve exhibits serrations related to DSA after reaching 35% of the strain. On the other hand, the work hardening rate is defined as the change in stress over the change in the strain (dr/de). In the early stages of the deformation, the plateau appearing in the work hardening curve is associated with the nucleation of thin twin plates as discussed in the literature (Ref 6). Figure 1(b) shows the microstructure evolution of the Hadfield steel at different strain levels. Clearly, the deformation twin volume fractions increase with increasing of the strain due to the addition of thin twin boundaries and twin plates growth; this is consistent with the previous work reported by Liang and his colleagues (Ref 8). However, the study of twin plates characteristics should be carried out by the TEM. Figure 2 shows the temperature distribution records of the specimens during the tensile testing at different strain levels. Clearly, the temperatures of the specimens increased with increasing the strain level. The temperature was slightly increased at 18% strain recording 32°C. Nevertheless, it increased to 54°C at 25% strain and to 89°C at 38% strain; upon fracture, a temperature of 125°C was recorded. In addition, as it is shown in Fig. 1(a), the serrations in the stressstrain curve appeared at a strain of 35%, which is related to the activation of the DSA. We think that the appearance of the DSA is related to the increase in the temperature values; because with increasing the temperature, the diffusion of the interstitial C atoms is increased, as reported in the literature (Ref 40, 41).   friction was calculated mathematically from Eq 2 and found to equal 297 MPa. Furthermore, the serrations associated with DSA appeared at approximately $ 2% strain, while these serrations were suppressed until reaching $ 35% strain under a strain rate of 1 s À1 as shown in Fig. 1(a) Figure 4 shows the TEM results of the Hadfield steel at different strain levels (11,18,25, and 38%), and upon fracture. The evolution of deformation twins with increasing strain levels was confirmed by the selected area diffraction patterns along the [011] zone axis as shown in the insets of Fig. 4. The thicknesses of the twinned plates e and the volume fraction F were estimated and are summarized in Table 2. The contribution of the mechanical twinning to the flow stress r t was calculated according to Eq 3.

Mechanical Twinning
Clearly, the thicknesses and intensities of the twin plates increase with increasing strain, and consequently, the flow stress contributed by the mechanical twinning increases with the increase in the strain level. On the other hand, the increase in the twin volume fraction is mainly related to the twin growth associated with the increasing twins plate thicknesses. However, this increase in the twin volume fraction is not related to the nucleation of new twin boundaries. The increase in the twinned plate thicknesses with increasing strain levels is supposed to reduce the support of the mechanical twinning to the flow stress in comparison with twin plates initiation ( Ref 40). Moreover, because of decreasing the mean free path of dislocations L with increasing strain, the force required to push dislocations during the plastic deformation increases (Ref 6). Consequently, this finding magnifies the contribution of forest hardening caused by dislocations. Fig. 1 (a) The true stress-strain curve and the corresponding work hardening rate, (b) the evolution of deformation twins with increasing strain level recorded by OM. GBs refer to the grain boundaries, DTBs refers to the deformation twin boundaries Figure 5 shows the XRD patterns at different strain levels and the (111) diffraction peak profiles fitted by Pearson VII. On the one hand, only austenite peaks exist in the diffraction patterns, which confirms no phase transformation during the plastic deformation. On the other hand, the broadening in the peaks profiles increases with increasing strain level; moreover, it was reported that the broadenings in the peaks profiles measured by XRD are an indicator of increasing dislocation densities ( Ref 25). Table 3 lists the lattice constant a, crystallite size d, microstrain e calculated by MAUD, average dislocation densities q d , and flow stress contributed by forest hardening r d . An increasing strain level results in decreased crystallite sizes and increasing internal strains in the austenite matrix, which consequently increases the dislocation densities. Dislocation densities have been shown to rise in correlation with temperature, which is in line with the findings of Zhu et al. (Ref 42), who ascribed this to the increased slipping of planes at high temperatures. Since dislocation density increases with rising strain level, obviously, the forest hardening supplied by dislocation increases with increasing strain level.

The Relationship between Temperature, SFE, and Twins Characteristics
The SFE value is sensitive to the temperature, whereas the mechanical twinning is a SFE dependent. It was reported that increasing the temperature strongly increases the SFE (U), consequently hindering the nucleation of the twin boundaries ( Ref 43). In addition, the critical stress required to initiate twinning (r CT ) can be calculated according to Eq 8 as follows (Ref 43): where b p is the Burgers vector of a partial dislocation. The SFE values were calculated at different temperatures according to the thermodynamic models from the literature ( Ref 29). Figure 6(a) displays the effect of increasing the strain level on the temperature and the corresponding SFE values. The SFE was increased from 30 mJ m À2 at 25°C to 50 mJ m À2 at 125°C. This increase in the instantaneous SFE results in the initiation of fresh twins being eliminated because of the increased critical stress required to nucleate twins, which was increased from 720 MPa at 25°C to 1200 MPa at 125°C. However, the flow stress at fracture recorded more than 1400 MPa, whereas the addition of new thin twin plates was suppressed. It seems that the increase in the SFE value is not enough to explain this behavior. The loss of the mechanical energy can be attributed to its conversion into heat energy.
The temperature of the tension test specimens increased intensively when the strain level reached 25%. The temperature increase is related to the conversion of the mechanical energy into heat energy, and it can be calculated according to Eq 9 as follows ( Ref 39,44,45): where b represents the fraction of the mechanical energy which was converted into heat energy, q is density (7.8 g cm À3 ), C p is the typical specific heat capacity of steels (0.46 kJ), while the total mechanical energy generated (ME) during the tension test was obtained by integrating the area under the tensile stressstrain curves. By the integration of the area under the stressstrain plots at different strain levels, b was calculated. Figure 6(b) exhibits the values of b at different strain levels. Clearly b increases with increasing strain level; consequently, the remaining mechanical energy (DE) during the plastic deformation was decreased. DE can be calculated from Eq 10 as follows: Figure 6(b) shows the remaining mechanical energy during the tensile testing at different strain levels. It is apparent that the DE decreases by 50% at a strain of 25%. By considering that all the DE is consumed to initiate twin plates, it can be noticed that the ability to form fresh twin plates is restricted. As a consequence, twin growth is promoted rather than the formation of new twin plates. On the other hand, the widening of the twinned plates can be related to the C-atoms diffusion out of the  Figure 7 shows the stress-strain curve at the strain rate of 10 0 s À1 combined with the contributions of the lattice friction, mechanical twin plates, and forest hardening to the flow stress. It is apparent that mechanical twinning contributed to the flow stress of the Hadfield steel at a greater level than forest hardening during the early stages of plastic deformation. Moreover, there is a gap between the calculated flow stress and the actual stress-strain curve during the final stages of plastic deformation, which is attributed to the appearance of DSA at a strain of approximately 35% due to increasing in the temperature (Ref 44), whereas it was suppressed during the initial stages of deformation.

The Contribution of Deformation Mechanisms to the Flow Stress
It was reported that the flow stress of austenitic steels is enhanced because of the initiation of twins or due to the intersections of secondary and primary twin plates (Ref 50, 51). As it is shown in Fig. 4, it is clear that the nucleation of thin twin boundaries was enhanced during the early stages of plastic deformation (before temperature rise); this explains why mechanical twinning was more effective in terms of flow stress than dislocation accumulations. However, during the final stages of deformation, twin plates thickening was enhanced more so than the nucleation of new twins.
Currently, the twin plates volume fraction increase is attributed to the increased twin plate thicknesses. Nevertheless, increasing the widths of the twin plates is considered as a twingrowth event and not a twin-nucleation event (the addition of new twin boundaries), which does not enhance the work hardening rate, similar to the nucleation of fresh twins, because twin growth requires a much smaller driving force than that utilized during twin nucleation, as concluded in the literature ( Ref 11,52).
On the other hand, hindering of fresh twin nucleation at high strain levels is attributed to the increases in the SFE values associated with increasing of the temperature; this agrees with the results shown by Liang et al., Saeed-Akbari et al., and Hamada et al. (Ref 39,53,54). Thus, dislocation interactions contributed to a greater extent than the mechanical twinning during the final stages of the deformation because of the continuous increase in dislocation densities and the decrease in the dislocation mean free path. This finding refers to the important effect of dislocation interactions on controlling the work hardening behavior of TWIP steels at high temperatures and it agrees with the results reported by Luo and Huang (Ref 55). Furthermore, it is very important for future studies to   design ternary C-Mn-Fe alloys with controllable twin plates which can accommodate dislocations to initiate fresh twin plates instead of the enhancement of twin plate thickening. Consequently, this may enhance the strength and ductility as well as prevent premature failure associated with the dislocation accumulation on those thick twin plates.

Conclusions
Dislocation densities, twin volume fractions, and twin plate thicknesses increase with increasing strain level in Hadfield steel at a strain rate of 1 s À1 . On the one hand, because of the addition of thin twin plates, the contribution of the twinning mechanism to the flow stress was greater than the hardening contributed by dislocation interactions during the initial stages of the plastic deformation. On the other hand, during the final stages of the deformation, the forest hardening resulting from dislocation accumulations was more effective than the mechanical twinning because of the increasing dislocation densities. Since the temperature rise has hindered the initiation of twin plates, the growth of the twin plates was promoted. The proposed linear model showed a good agreement with the experimental values of the flow stress at the early stages of the plastic deformation. However, at the final stages of the deformation, the deviation between the model and the experimental flow stress values is related to the conversion of the mechanical energy into heat, which is associated with the temperature rise and the appearance of the DSA effect.