Strengthening contributions of mechanical twinning and dislocations to the flow stress of 1.1C-12.5Mn steel at a strain rate of unity per second: Quantitative analysis

doi:10.21203/rs.3.rs-1499180/v1

Download PDF

Research Article

Strengthening contributions of mechanical twinning and dislocations to the flow stress of 1.1C-12.5Mn steel at a strain rate of unity per second: Quantitative analysis

https://doi.org/10.21203/rs.3.rs-1499180/v1

This work is licensed under a CC BY 4.0 License

Journal Publication

published 10 Jul, 2022

Read the published version in Journal of Materials Engineering and Performance →

Version 1

posted

You are reading this latest preprint version

The flow stress of high C-Mn austenitic 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 of 12.5Mn-1.1C steel. In this study, austenitic Hadfield steel (1.1 wt.% C and 12.5 wt.% Mn) was tensile tested at a strain rate of 10⁰ s^− 1. The lattice friction was estimated by the Hall-Petch relationship. DSA effect was neglected because of the high strain rate of deformation. Twin plates characteristics and dislocation densities were estimated quantitatively at different strain levels (11, 18, 25, 38, and 55%). The deformed twin plates were studied by optical and transmission electron microscopies. Dislocation densities were estimated by analyzing the X-ray diffraction patterns using Rietveld analyses. A linear approach was utilized to model the flow stress during the plastic deformation, and it is found that the linear model is consistent with the experimental results. During the early stages of the plastic deformation, the mechanical twinning was the dominant deformation mechanism, and it was more effective to the flow stress than the forest hardening due to the enhancement of the twin nucleation process. However, with increasing the strain level, the thicknesses of the twinned plates were increased rather than the initiation of new twin plates, resulting in a reduced contribution by the mechanical twinning to the flow stress. On the other hand, increasing the dislocation densities with an increase in the strain level was detected, which resulted in an enhanced contribution by forest hardening to the flow stress more than the mechanical twinning.

Austenitic steel

Flow stress

Deformation twins

Dislocation

Lattice friction

Due to the distinctive combination of the mechanical properties such as high strength, high toughness, high resistance to wear, a high strain-hardening rate in polycrystalline form, and heavy impact loads, Austenitic Hadfield steel is an excellent substrate of choice in various applications, i.e., excavators, railway crossings, crusher jaws, grinding mill liners, oil well drilling, impact hammers, bullet-proof helmets, and non-magnetic plates for electromagnets [1-4]. The standard austenitic Hadfield steel contains between 10–14% Mn and between 1.0–1.4% 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 to or martensitic structures and deformation twins [2, 5-7].

Hadfield steel has a low stacking fault energy (SFE, 23 mJ m^–2) [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% [5, 8]. Twins can cause a resistance to dislocation motion, and twin-twin interactions result in a high hardening rate [9, 10]. Four deformation mechanisms affect the mechanical properties of Hadfield steel including [2, 6, 11]: (i) lattice friction, (ii) dynamic strain ageing (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 [12, 13].

Firstly, the friction stress (lattice friction) or solid solution strengthening depends on the local atomic structure of the material, it occurs as a result of the fluctuations in the solute-dislocation interaction energy [14]. It can be calculated according to Hall-Petch relationship based on the yield strength of the austenitic structures with respect to the corresponding grain size [15, 16].

Secondly, dynamic strain aging (DSA), which 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 [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 [8]. The DSA's contribution to the stress response of Hadfield steel can be observed as serrated flow on the stress-strain curves.

Thirdly, regarding the mechanical twinning, prior studies revealed that twinning is the primary deformation mechanism at the beginning, and at initial stages of deformation for tensile loading of oriented Hadfield steel single crystals [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 [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 [6, 22, 23]. For example, Hutchinson and Ridley [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 ageing would decrease the mean free length of slip, leading to more dislocations being immobilised 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 [6]. However, Hutchinson and Ridley [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. [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 behaviour of high interstitial C-Mn steels, especially under high strain rate deformation.

The chemical composition of the utilized Hadfield steel is listed in table 1. The investigated microstructure showed only the FCC austenite phase with an average grain size of D of 65±15 μm using an Olympus GX-71 optical microscope. 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 25×6×1 mm³.

Table 1 The chemical composition of the investigated Hadfield steel.

Element	C	Mn	Si	P	S	Cr	Al	Fe
Wt.%	1.13	12.53	0.28	0.028	<0.001	0.14	0.006	Bal.

To obtain samples with different grain sizes (to calculate the lattice friction), the as-received Hadfield steel plates were cold rolled, then annealed at 1000 ^oC for 5 minutes to release the internal stresses, and subsequently quenched in water to keep a fully austenitic structure. The tension tests of the as-received specimens were accomplished at room temperature under a strain rate of 1 × 10⁰ s^-1 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 μm, 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 low incidence angle (3^o) via an ion beam polishing system (Gatan 691) operated at 3 KV for 20 minutes. 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 at between 40^o and 100^o with a rate of 2^o per minute.

3.1. 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 (σ_l), DSA behavior (σ_s), mechanically induced deformation twin plates (σ_t) and forest hardening resulting from dislocation storage (σ_d). We assume that σ_l, σ_s, σ_t and σ_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) [25, 26]:

$$\text{F}\text{S}= {{{\sigma }}_{\text{l}} +{\sigma }}_{\text{s}}+ {{\sigma }}_{\text{t}}+ {{\sigma }}_{\text{d}}$$

3.2. 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; then, from the Hall-Petch equation, the lattice friction can be calculated [15, 25, 27]. On the one hand, σ_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 [22, 27]. The yield strength is related to the grain size as expressed by Eq. (2):

$$YS= {{\sigma }}_{l}+ \frac{k}{\sqrt{D}}$$

where k is the strengthening coefficient.

3.3. Contribution of deformation twins

The mechanical twinning is a deformation mechanism that occurs in FCC structures with low SFE (18–35 mJ/m²) [28]. The SFE was estimated based on the thermodynamic model presented by Saeed-Akbari et al. [29], the SFE of Hadfield steel = 30 mJ/m². Moreover, Liu et al. [8] proved that twinning is the dominant deformation mechanism during the plastic deformation of Hadfield steel. The contribution of twins (σ_t) to the flow stress can be calculated according to Taylor’s formula as shown in Eq. (3) [25, 26, 30]:

$${{\sigma }}_{t}=\frac{M{\beta }\text{G}\text{b}}{L}$$

where G is the shear modulus, calculated according to the literature [31–33], being approximately equal to 75 GPa; M is the average Taylor factor, being approximately 3.06; β is a constant with a value of 0.3; and L represents the dislocation mean free path. L can be calculated by Eq. (4) as follows [25, 26, 30]:

$$\frac{1}{L}= \frac{1}{D}+ \frac{1}{t}$$

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 [34]:

$$\frac{1}{\text{t}}= \frac{\text{F}}{\text{e}\times \left(1-\text{F}\right)}$$

3.4. Contribution of dislocations

The XRD can be utilized to determine dislocation densities by estimating the broadening in the peaks profile [30, 35, 36]. The micro-strain ε and crystallite size d can be obtained by analysing the XRD patterns using Rietveld analyses performed by the MAUD programme [37]. The lattice constant a, crystallite sizes, and micro-strains could be estimated via the “size-strain” analysis in accordance to the Popa model [38]. The dislocation densities (ρ_d) could be determined according to Eq. (6) as follows [30, 36]:

$${{\rho }}_{d}=\frac{3\times \sqrt{2\pi } \times {(\epsilon }^{2}{)}^{0.5}}{d\times b}$$

Where b is the Burgers vector (b = a/(2)^0.5 for the FCC structure). The flow stress caused by the dislocation storage (σ_d) is calculated by the Taylor hardening model [6, 25, 39]. The forest hardening contributed by the dislocations can be described by Eq. (7) as follows:

$${\sigma }_{d}=Mb{\alpha }G\sqrt{{ {\rho }}_{d}}$$

where α is a constant with a value of 0.25.

4.1. Tension test and microstructure

Figure 1.a shows the true stress-strain curve of Hadfield steel at a strain rate of 10⁰ s^− 1 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 (dσ/dε). At the early stages of the deformation, the plateau appearing in the work hardening curve is associated with the nucleating of thin twins as discussed in the literature [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 [8]. However, the study of twin plates characteristics should be carried out by the TEM.

4.2. Temperature records

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 ^oC. Nevertheless, it increased to 54 ^oC at 25% strain, and to 89 ^oC at 38% strain; upon fracture, a temperature of 125 ^oC was recorded. In addition, as it was shown in Fig. 1.a, the serrations in the stress-strain 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; since that with the increase of the temperature, the diffusion of the interstitial C atoms is increased, as reported in the literature [40, 41].

4.3. Friction stress

Figures 3.a and 3.b show the microstructure of the Hadfield steel in the as-received condition and after cold rolling and subsequent heat-treatment. Clearly, the cold rolling of the Hadfield steel reduced the grain size from 65 ± 10 µm to 33 ± 6 µm. Figure 3.c shows the stress-strain curves of Hadfield steel with the two different grain sizes. The as-received Hadfield steel (with a grain size of 65 µm) presented a yield strength of 350 MPa, while the cold-rolled and heat-treated yield strength was 375 MPa. The lattice friction was calculated mathematically from Eq. (2) and found to equal 297 MPa.

4.4. Mechanical twinning

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 summarized in Table 2. The contribution of the mechanical twinning to the flow stress σ_t was calculated according to Eq. (3).

Table 2

The statistics of twins characteristics at different strain levels.
Strain level (%)	e (nm)	L (nm)	F (%)	σ_t (MPa)
11	30 ± 10	89.9	25 ± 3.5	195
18	45 ± 15	67.4	40 ± 7	261.6
25	60 ± 30	53	53 ± 4	335
38	90 ± 25	42.3	68 ± 8	416.7
Fracture	125 ± 40	35.2	78 ± 5	500.5

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 of 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 a nucleation of new twin boundaries. The increase of 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 [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 [6]. Consequently, this finding magnifies the contribution of forest hardening caused by dislocations.

4.5. Forest hardening

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 is an indicator of increasing dislocation densities [25].

Table 3 lists the lattice constant a, crystallite size d, micro-strain ε calculated by MAUD, average dislocation densities ρ_d, and flow stress contributed by forest hardening σ_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. [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.

Table 3

The values of lattice constant, crystallite size, micro-strain, dislocations densities, and forest hardening caused by dislocations at different strain levels.
Strain level (%)	a (nm)	d (A)	ε	ρ_d * 10¹⁴ (m^− 2)	σ_d (MPa)
0	0.3643	1014.8	0.00000156	0.0045	-
11	0.3624	692.2	0.000207	0.878	135.5
18	0.3624	472.1	0.00049	3.01	250.2
25	0.362	420	0.00072	5.17	314.4
38	0.3615	315.6	0.00098	9.14	437.2
Fracture	0.3615	205	0.001	14.1	544

5.1. 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 (Г), consequently hindering the nucleation of the twin boundaries [43]. In addition, the critical stress required to initiate twinning (σ_CT) can be calculated according to Eq. (8) as follows [43]:

$${\sigma }_{CT}=6.14 \times \frac{Г}{{b}_{p}}$$

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 [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^− 2 at 25^oC to 50 mJ.m^− 2 at 125 ^oC. 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^oC to 1200 MPa at 125 ^oC. 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 behaviour. 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 [39, 44, 45]:

$$\varDelta T= \frac{\beta }{\rho {C}_{p}} {\int }_{{\epsilon }_{1}}^{{\epsilon }_{2}}\sigma d\epsilon$$

where β represents the fraction of the mechanical energy which was converted into heat energy, ρ is density (7.8 g.cm^− 3), 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 stress–strain curves. By the integration of the area under the stress-strain plots at different strain levels, β was calculated. Figure 6.b exhibits the values of β at different strain levels. Clearly β increases with increasing strain level; consequently, the remaining mechanical energy (∆E) during the plastic deformation was decreased. ∆E can be calculated from Eq. 10 as follows:

∆E = ME × (1- β) (10)

Figure 6.b shows the remaining mechanical energy during the tensile testing at different strain levels. It is apparent that the ∆E decreases by 50% at a strain of 25%. By considering that all the ∆E 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 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 planar faults like SFs and/or twin plates because of increasing the temperature as found in the literature [41, 46–48], as well as it was evidenced recently that C-atoms are locally depleted at 25% strain during tensile testing of C-Mn steel under high strain rate deformation [49].

5.2. The contribution of deformation mechanisms to the flow stress

Figure 7 shows the stress-strain curve at the strain rate of 10⁰ s^− 1 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 [44], whereas it was suppressed during the initial stages of deformation.

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 [50, 51]. As it was 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 twin-growth 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 [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. and Saeed-Akbari et al. [39, 53]. 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 [54]. 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, enhance the strength and ductility as well as prevent premature failure due to dislocation accumulation on those thick twin plates.

Dislocation densities, twin volume fractions, and twin plate thicknesses increase with increasing strain level in Hadfield steel at a strain rate of 10⁰ s^− 1. 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, while 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 DSA effect.

Acknowledgement

The authors are grateful to the financial support of the National Key R&D Program of China (No. 2017YFB0703003), National Natural Science Foundation of China (Nos, 51831002 and 52071209).

Conflicts of interest

There is no conflicts of interest exist in the current study.

Availability of data and material

All the data generated during this study are included in this article.

M. Lindroos, G. Cailletaud, A. Laukkanen, V.-T. Kuokkala, Mater. Sci. Engineering: A 720, 145–159 (2018)
L. Zhang, P. Guo, G. Wang, S. Liu, J. Mater. Res. Technol. 9, 1500–1508 (2020)
M. Sabzi, M. Farzam, Mater. Res. Express 6, 1065c1062 (2019)
W.-S. Lee, T.-H. Chen, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 216, 971–982 (2002)
I. Karaman, H. Sehitoglu, K. Gall, Y.I. Chumlyakov, H. Maier, Acta Mater. 48, 1345–1359 (2000)
B. Hutchinson, N. Ridley, Scripta Mater. 55, 299–302 (2006)
F. Liu, B. Lv, F. Zhang, S. Yang, Mater. Lett. 65, 2333–2336 (2011)
F. Liu, Z. Yang, C. Zheng, F. Zhang, Scripta Mater. 66, 431–434 (2012)
P. Chowdhury, D. Canadinc, H. Sehitoglu, Mater. Sci. Engineering: R: Rep. 122, 1–28 (2017)
C. Efstathiou, H. Sehitoglu, Acta Mater. 58, 1479–1488 (2010)
M. Khedr, L. Wei, M. Na, L. Yu, J. Xuejun, JOM 71, 1338–1348 (2019)
I. Karaman, H. Sehitoglu, K. Gall, Y.I. Chumlyakov, Scripta Mater. 38, 1009–1015 (1998)
P. Adler, G. Olson, W. Owen, Metall. Mater. Trans. A 17, 1725–1737 (1986)
H. Chung, D.W. Kim, W.J. Cho, H.N. Han, Y. Ikeda, S. Ishibashi, F. Körmann, S.S. Sohn, J. Mater. Sci. Technol. 108, 270–280 (2022)
H.S. Oh, S.J. Kim, K. Odbadrakh, W.H. Ryu, K.N. Yoon, S. Mu, F. Körmann, Y. Ikeda, C.C. Tasan, D. Raabe, Nat. Commun. 10, 1–8 (2019)
B. Yin, F. Maresca, W. Curtin, Acta Mater. 188, 486–491 (2020)
D. Canadinc, C. Efstathiou, H. Sehitoglu, Scripta Mater. 59, 1103–1106 (2008)
E. Bayraktar, F.A. Khalid, C. Levaillant, J. Mater. Process. Technol. 147, 145–154 (2004)
I. Karaman, H. Sehitoglu, A. Beaudoin, Y.I. Chumlyakov, H. Maier, C. Tome, Acta Mater. 48, 2031–2047 (2000)
Y.I. Chumlyakov, I. Kireeva, H. Sehitoglu, E. Litvinova, E. Zaharova, N. Luzginova, Mater. Sci. Forum, 395–400, Trans Tech Publ
T. Mori, H. Fujita, Trans. Japan Inst. Met. 18, 17–24 (1977)
O. Bouaziz, S. Allain, C. Scott, P. Cugy, D. Barbier, Curr. Opin. Solid State Mater. Sci. 15, 141–168 (2011)
Z. He, N. Jia, H. Yan, Y. Shen, M. Zhu, X. Guan, X. Zhao, S. Jin, G. Sha, Y. Zhu, Int. J. Plast. 139, 102965 (2021)
W. Zhang, J. Wu, Y. Wen, J. Ye, N. Li, J. Mater. Sci. 45, 3433–3437 (2010)
Z. Liang, Y. Li, M. Huang, Scripta Mater. 112, 28–31 (2016)
K. Jeong, J.-E. Jin, Y.-S. Jung, S. Kang, Y.-K. Lee, Acta Mater. 61, 3399–3410 (2013)
R. Dalai, S. Das, K. Das, Int. J. Minerals Metall. Mater. 26, 64–75 (2019)
S. Allain, J.-P. Chateau, O. Bouaziz, S. Migot, N. Guelton, Mater. Sci. Engineering: A 387, 158–162 (2004)
A. Saeed-Akbari, J. Imlau, U. Prahl, W. Bleck, Metall. Mater. Trans. A 40, 3076–3090 (2009)
M. Khedr, W. Li, X. Zhu, P. Zhou, S. Gao, X. Jin, Mater. Sci. Engineering: A 712, 133–139 (2018)
D. Music, T. Takahashi, L. Vitos, C. Asker, I.A. Abrikosov, J.M. Schneider, Appl. Phys. Lett. 91, 191904 (2007)
T. Ungár, I. Dragomir, Á Révész, A. Borbély, J. Appl. Crystallogr. 32, 992–1002 (1999)
K. Benyelloul, H. Aourag, Comput. Mater. Sci. 67, 353–358 (2013)
J. Kim, Y. Estrin, H. Beladi, I. Timokhina, K.-G. Chin, S.-K. Kim, B.C. De Cooman, Metall. Mater. Trans. A 43, 479–490 (2012)
G. Williamson, W. Hall, Acta Metall. 1, 22–31 (1953)
R. Smallman, K. Westmacott, Phil. Mag. 2, 669–683 (1957)
P. Sahu, S. Shee, A. Hamada, L. Rovatti, T. Sahu, B. Mahato, S.G. Chowdhury, D. Porter, L. Karjalainen, Acta Mater. 60, 6907–6919 (2012)
N. Popa, J. Appl. Crystallogr. 31, 176–180 (1998)
Z. Liang, W. Huang, M. Huang, Mater. Sci. Engineering: A 628, 84–88 (2015)
B.C. De Cooman, Y. Estrin, S.K. Kim, Acta Mater. 142, 283–362 (2018)
J. Seol, J. Kim, S. Na, C. Park, H. Kim, Acta Mater. 131, 187–196 (2017)
Y. Zhu, Y. Xiang, K. Schulz, Scripta Mater. 116, 53–56 (2016)
S. Sato, E.-P. Kwon, M. Imafuku, K. Wagatsuma, S. Suzuki, Mater. Charact. 62, 781–788 (2011)
Z. Liang, Z. Luo, M. Huang, Int. J. Plast. 116, 192–202 (2019)
N. Li, Y. Wang, R.L. Peng, X. Sun, P.K. Liaw, G. Wu, L. Wang, H. Cai, Acta Mater. 59, 6369–6377 (2011)
T. Hickel, S. Sandlöbes, R.K. Marceau, A. Dick, I. Bleskov, J. Neugebauer, D. Raabe, Acta Mater. 75, 147–155 (2014)
S. Lu, R. Li, K. Kádas, H. Zhang, Y. Tian, S.K. Kwon, K. Kokko, Q.-M. Hu, S. Hertzman, L. Vitos, Acta Mater. 122, 72–81 (2017)
T. Byun, Acta Mater. 51, 3063–3071 (2003)
M. Khedr, W. Li, N. Min, W. Liu, X. Jin, Materials Science & Engineering A, MSA_143024 (2022)
H. Yang, Z. Zhang, Z. Zhang, Mater. Sci. Engineering: A 622, 184–188 (2015)
E. El-Danaf, S.R. Kalidindi, R.D. Doherty, Metall. Mater. Trans. A 30, 1223–1233 (1999)
C.C. Roth, D. Mohr, Int. J. Plast. 56, 19–44 (2014)
A. Saeed-Akbari, A. Mishra, J. Mayer, W. Bleck, Metall. Mater. Trans. A 43, 1705–1723 (2012)
Z. Luo, M. Huang, Scripta Mater. 142, 28–31 (2018)

Download PDF

Journal Publication

published 10 Jul, 2022

Read the published version in Journal of Materials Engineering and Performance →

Version 1

posted

You are reading this latest preprint version

Strengthening contributions of mechanical twinning and dislocations to the flow stress of 1.1C-12.5Mn steel at a strain rate of unity per second: Quantitative analysis

Status:

Journal Publication

Version 1

Abstract

Figures

1. Introduction

2. Materials And Methods

3. Mechanical Formulas

3.1. Linear approach to model the flow stress

3.2. lattice friction and DSA

3.3. Contribution of deformation twins

3.4. Contribution of dislocations

4. Results

4.1. Tension test and microstructure

4.2. Temperature records

4.3. Friction stress

4.4. Mechanical twinning

4.5. Forest hardening

5. Discussion

5.1. The relationship between temperature, SFE and twins characteristics

5.2. The contribution of deformation mechanisms to the flow stress

6. Conclusions

Declarations

References

Status:

Journal Publication

Version 1