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Molecular Dynamics Simulation Study on the Effect of the Loading Direction on the Deformation Mechanism of Pearlite

  • Hadi Ghaffarian
  • Ali K. Taheri
  • Keonwook KangEmail author
  • Seunghwa RyuEmail author
Original Research

Abstract

Molecular dynamics simulations were carried out to study the effect of the loading direction on the deformation behavior of the pearlite structure with a Bagaryatsky orientation relationship at the ferrite-cementite interface. We found excellent ductility in the ferrite and pearlite nanocomposites along the \(\left[ {\bar{1}10} \right]_{f} ||\left[ {001} \right]_{c}\) loading direction, while a brittle behavior was observed along the \(\left[ {111} \right]_{f} ||\left[ {100} \right]_{c}\) loading direction because of the reduced number of activated slip systems. Additionally, we reveal that the ductility is improved by either increasing the temperature or reducing the interlamellar spacing.

Keywords

Molecular dynamics simulation Nanocomposite pearlite Loading direction Deformation mechanism 

Introduction

Pearlitic phase is a desired structure in high-strength steels because it offers a combination of strength and ductility [20]. Hence, it is important to understand the structural mechanisms and principles governing its plastic deformation and failure. Compared to ferrite, the pearlitic structure is a harder phase with higher strength because of the presence of cementite lamellae [27, 30]. It has been found that the fine pearlite with narrow ferrite (~ 100 nm) and cementite (~ 10 nm) lamellae shows higher ductility than coarse pearlite during plastic deformation [4, 22]. The coarse pearlite shows relatively nonhomogeneous deformation, presenting localized plastic strain in the slip bands, while the fine pearlite shows a more uniform strain distribution [2, 13]. Successful formation of nano-scale pearlite structure was observed during severe plastic deformation, such as steel wire drawing [5, 17]. The thickness of the nano-scale lamellae can be as fine as 10–20 and 1–2 nm for the ferrite and cementite lamellae, respectively [31]. However, the nature of deformation mechanism in pearlite as well as the formation of shear band in ferrite and its interaction with the cementite layer has remained unclear.

The mechanical properties of pearlite are expected to be affected by the loading direction based on the orthorhombic crystal structure of cementite. Umemoto et al. [27] reported that the deformed structure of a rolled pearlite sample is altered by changing the angle of the cementite lamellae with respect to the rolling direction. Izotov et al. [13] also reported that if the dislocation slip occurs along the ferrite lamella, deformation occurs without the participation of cementite. In comparison, if the deformation occurs across the ferrite lamellae, the cementite lamellae suppress slip development. However, the proposed mechanism by Izotov et al. [13] could be affected by the presence of individual ferrite grains, grain boundaries, other alloy elements, and the initial dislocation structures. These undesired conditions can be circumvented and the inherent properties can be modelled by employing atomistic simulations.

Molecular dynamics (MD) simulations offer a unique opportunity to investigate nano-scale material properties with the desired conditions. MD simulations have been widely employed to investigate the mechanical properties of nanocrystalline ferrite [6, 14]. In addition, MD simulation has been performed to investigate the origin of the brittle-to-ductile transition of nano-crystalline cementite [7], elucidate the effect of cementite size and temperature on the deformation behavior of pearlite [8], and characterize the structure of misfit dislocations and calculate the interface energies of various ferrite/cementite orientation relationships [16]. However, the present study is the first attempt to investigate the deformation behavior of the pearlite structure during tensile deformation.

In this study, we perform a series of tension tests of pearlite samples using MD simulations to study the mechanical properties of the pearlite structure. The purpose of this paper is to investigate the effect of the loading direction on the deformation behavior of pearlite at various temperatures and the pearlite lamellae size effect. Atomistic models of single crystal ferrite (Fe) and ferrite-cementite nanocomposite are constructed and subjected to tension tests with different loading directions. Our results show that the pearlite structure has an excellent ductility along the \(\left[ {\bar{1}10} \right]_{f} ||\left[ {001} \right]_{c}\) loading direction, while brittle behavior is observed along the \(\left[ {111} \right]_{f} ||\left[ {100} \right]_{c}\) loading direction because of the reduced number of activated slip systems. We also reveal that the ductility is improved by either increasing the temperature or reducing the interlamellar spacing.

Simulation Methods

Two pure ferrite samples and two ferrite-cementite nanocomposite samples with different longitudinal direction were prepared (as depicted in Fig. 1) to investigate the deformation behavior of pearlite during tension test. We chose \(x:[111]_{f} || [100]_{c}\),\(z:[\bar{1}10]_{f} || [001]_{c}\), and \(y:(11\bar{2})_{f} || (010)_{c}\) according to the Bagaryatsky [3] orientation relationship (with regard to the cementite lattice constants: a = 5.09 Å, b = 6.67 Å, and c = 4.47 Å). Figure 2 illustrates the details of atomic structures at ferrite-cementite interface and the atomic configuration of cementite unit cell with orthorhombic lattice structure. The x-aligned samples were 40 by 40 nm in the xy plane and 5 nm in the z axis, while the z-aligned samples were 50 by 50 nm in the yz plane and 5 nm in the x axis. For the nanocomposite ferrite-cementite samples, the width of the cementite layer was kept constant at 10 nm. Thus, the effective ferrite interlamellar spacing in Fig. 1 is 40 nm for each sample.
Fig. 1

Illustration of the pearlite nanocomposite models; a pure Fe under x-directional loading, b pearlite under x-directional loading, c pure Fe under z-directional loading, and d pearlite under z-directional loading with regard to the Bagaryatsky interface orientation relationship

Fig. 2

Atomic structure of ferrite-cementite interface along ax-direction and bz-direction, in Bagaryatsky orientation relationship. c A unit cell of cementite in orthorhombic lattice structure, containing 12 Fe atoms and 4 carbon atoms

The x- and z-aligned nanocomposite samples were composed of 750,000 and 1,000,000 atoms, respectively. We chose different unit cell numbers of Fe and cementite for constructing the samples to reduce in-plane misfit strain. Resultantly, 0.77% and 0.44% in-plane misfit strains were imposed at the ferrite-cementite interface of x-aligned pearlite along the x and z directions, respectively. For z-aligned pearlite, the imposed in-plane misfit strains were 1.56% and 0.17% along the x and z directions, respectively.

MD simulations were carried out using the parallel MD code, LAMMPS [21], with periodic boundary conditions (PBCs) in all dimensions at 100 K and 700 K. For each temperature, samples were annealed at 1000 K for 100 ps under zero pressure with the Nose–Hoover isobaric-isothermal (NPT) ensemble and then quenched to the objective temperature according to the approach of Vo et al. [28, 29]. Uniaxial tensile loading was applied to a maximum strain of 30% with a constant strain rate of 5 × 108 s−1 with PBC applied to all three directions. We increase the size of the simulation cell in the loading direction every 2 ps with a fixed strain increment (0.001) and remap the positions of atoms via affine transformation to match the box deformation. At each strain, only two lateral directions orthogonal to loading direction dimension were adjusted to maintain zero pressure via NPT ensemble. Accordingly, the cross-section of the simulation cell shrinks with the increase of tensile strain due to the Poisson’s effect. The recently developed interatomic potential of Fe–C by Liyanage et al. [18], which is based on a modified embedded atom method (MEAM), was used to describe the interatomic force. The atomic arrangements of the samples, including dislocations, were then visualized using centrosymmetry parameter [15]. The atomic shear strain distribution was also calculated using the method of Shimizu et al. [24].

Results and Discussion

Figure 3 shows the stress–strain curves for the nanocomposite ferrite and pearlite tensile tests at different temperatures and along different loading directions. The tensile stress increases with strain up to a certain peak stress and then suddenly drops for all conditions considered in this study. The peak stress point is attributed to the onset of plasticity, while it is amplified because of the higher strain rate imposed in the MD simulation and homogeneous dislocation nucleation due to the lack of initial dislocation network. However, the strength for z-aligned samples is smaller than that of x-aligned samples under the same conditions because of a higher Schmid factor along the z loading direction (the maximum values of the Schmid factor along the x and z loading directions are 0.31 and 0.47, respectively). Here, we consider the Schmid factor based on 48 slip systems in bcc crystal since the plasticity is initiated in the bcc ferrite crystal due to its relatively lower strength. The peak stress also decreases significantly as the temperature rises, showing a thermal softening effect. Our simulation results are different from the experimental results, in which ferritic and pearlitic steels show a yielding point at the beginning of the tensile curve and subsequent work hardening in the stress–strain plot [13]. These differences arise from the absence of initial dislocation density and grain boundaries in our MD simulation. Accordingly, the yield points are significantly overestimated compared to those of macroscale samples containing pre-existing defects, and thus they can be considered as the ideal yield strengths of ferrite and pearlite samples.
Fig. 3

Stress-strain plot of the nanocomposite ferrite and pearlite samples with different loading directions and temperatures

Dislocation nucleation has been observed for z-aligned samples at 100 K in Fig. 4, where the centrosymmetry parameter [15] was applied to screen out atoms on a non-perturbed bcc lattice site. Our simulations reveal that the onset of plasticity occurs with dislocation nucleation at the ferrite-cementite interface, while in pure Fe samples, it is associated with homogenous dislocation nucleation in the interior of ferrite at high stress. The ferrite-cementite interface becomes a preferential nucleation site because atoms in the vicinity of the interface possess higher strain energy. Similar results have been observed for z-aligned samples at 700 K and x-aligned samples at 100 K and 700 K.
Fig. 4

Dislocations evolution at the onset of plasticity of az-aligned nanocomposite pearlite and bz-aligned pure Fe at 100 K. Atoms are colored according to the centrosymmetry parameter values between 1 (blue) and 25 (red) with 14 neighbor atoms. Atoms on a perfect bcc lattice are not visualized

To understand the deformation behavior of pearlite, we present snapshots showing the dislocation evolution after 30% tensile strain in Fig. 5. After the onset of plasticity, dislocations, which are nucleated at the ferrite-cementite interface, glide toward the simulation cell boundaries. Because of the PBC in all dimensions, dislocation that leaves at one boundary enters again from the opposite side boundary and propagates toward the other interface side. However, different lattice structures across the ferrite-cementite interface and the low dislocation activity in cementite [11, 23] prevent the incoming dislocations from passing through the interface, and the dislocations are absorbed at the interface. The absorbed dislocations induce a shear deformation in the cementite layer. A similar result was observed during deformation of FCC/amorphous metallic glass nanolaminate [1].
Fig. 5

Dislocations evolution after 30% total tensile deformation of ax-aligned pure Fe, bx-aligned nanocomposite pearlite, cz-aligned pure Fe, and dz-aligned nanocomposite pearlite at 100 K and 700 K. Atoms are colored according to the centrosymmetry parameter values between 1 (blue) and 25 (red) with 14 neighbor atoms. Atoms on a perfect BCC lattice are not visualized. Gray color indicates crack regions that formed during tensile deformation. The crack tips are marked by black arrows in (a, b)

In contrast, in the x-aligned pure Fe sample, the formation of cracks along (114) and \((22\bar{1})\) planes without any significant dislocation activity is observed at all temperatures (Fig. 5a), which is not consistent with the experimental study on the brittle-to-ductile transition of single crystal ferrite, where the transition temperature is measured as approximately 130 K [26]. Such a severe overestimation of the brittle-to-ductile transition in MD simulations may be attributed to the difference of 10 orders of magnitude in the strain rate or the artificial confinement effects originating from the PBCs. Furthermore, cracks are also detected in x-aligned pearlite at 100 K, which leads to shearing of the cementite layer between the crack tips. However, for the same sample at 700 K (Fig. 5b), ductile deformation is pronounced with more dislocation traces where crack nucleation was completely suppressed.

Figure 5 also reveals the effect of the loading direction on the deformation behavior of ferrite and pearlite. While the localized deformation in ferrite and necking regions in the cementite layer are observed in x-aligned samples (Fig. 5a, b), we find a uniform dislocation distribution without any cracks in the z-aligned pure Fe sample (Fig. 5c) and uniform deformation of the cementite layer in the z-aligned pearlite sample (Fig. 5d). It is also interesting to note that deformation mechanism does not change in the z-aligned samples when the temperature increases to 700 K.

To further investigate the deformation mechanisms in detail, an atomic shear strain analysis was performed following the approach of Shimizu et al. [24]. Figure 6 presents atoms with shear strain higher than 0.3 in deformed samples after 30% total tensile deformation at 100 K and 700 K. We find that there is no significant slip trace in Fig. 6a because of the brittle behavior of the x-aligned pure Fe sample at all temperatures. The presence of the ferrite-cementite interface increases the slip traces because more frequent dislocation nucleation occurs at the interface in pearlite samples. However, the slip activities in Fig. 6b are not distributed at 100 K because of localized deformation at the crack tip. Therefore, only a thick shear band can be found in the cementite layer in the region between the crack tips. In other words, the cementite layer tends to be cut along the shear band due to the localized strain intensity. In contrast, increasing the temperature to 700 K increases the slip traces and shear bands in ferrite by the activation of new slip systems [12]. These shear bands propagate into the cementite layer, while cementite cutting is replaced by necking.
Fig. 6

Atomic shear strain distribution of Fe and C atoms after 30% total tensile deformation of ax-aligned pure Fe, bx-aligned nanocomposite pearlite, cz-aligned pure Fe, and dz-aligned nanocomposite pearlite at 100 K and 700 K. Only atoms with shear strain larger than 0.3 are visualized. Gray color indicates the crack region. The vertical dashed lines illustrate the original interface between ferrite and cementite, and the atoms in red experience a shear strain ≥ 1

A dramatically different mechanism is observed for the z-aligned samples in Fig. 6c, d. The slip traces are distributed uniformly in both ferrite and cementite. Furthermore, the shear band intensity (red points) in the z-aligned samples is smaller than that in the x-aligned samples, remarkably. This eventually forms a relatively uniform distribution of shear strain in the cementite layer without significant shear band formation. In other words, shear bands are only formed in the cementite layer if the shear band in ferrite is thick enough to penetrate the ferrite-cementite interface.

To describe the effect of the loading direction on the deformation mechanisms of pearlite, the Schmid factor (m) of possible slip systems in ferrite was calculated with respect to the \(x:[111]_{f}\) and \(z:[\bar{1}10]_{f}\) loading directions. By considering the main slip systems in ferrite (\(\left\{ {101} \right\}11\bar{1}\),\(\left\{ {112} \right\}11\bar{1}\), and \(\left\{ {123} \right\}11\bar{1}\)), we found 10 slip systems with m > 0.4 for z-aligned samples among the 48 possible slip systems in ferrite; however, for the x-aligned samples, all the slip systems have m < 0.31. The slip system with a lower Schmid factor requires a higher loading for the resolved shear stress to reach the Peierls stress [9] and for the material to show more brittle deformation behavior. Because of the reduced number of activated slip systems, non-uniform plastic deformation occurs in ferrite, which increases the probability of shear band formation by dislocation blocking at the ferrite-cementite interface. Inversely, the increased number of activated slip systems in z-aligned samples leads to more uniform deformation by strain distribution in the ferrite layer and cementite layer.

The loading direction also affects the deformation mechanism of cementite because of the anisotropic crystalline structure of cementite. Figure 7 shows the strain distribution in x-aligned and z-aligned pearlite at the onset of plasticity at 700 K. While the onset of plasticity begins in x-aligned pearlite with shear deformation in the ferrite phase (Fig. 7a) without any significant plastic deformation of the cementite layer, it is interesting to note that there is a fine uniform strain distribution in the cementite layer of z-aligned pearlite (Fig. 7c) before the onset of plasticity. In other words, the cementite layer along the x- and z-loading direction is stiffer and weaker than ferrite, respectively. Especially, the < 100 > {010} slip system is not activated in the cementite layer of nanocomposite pearlite because of the zero Schmid factor. However, Schmid factors of \(\left[ {1\bar{1}1} \right]\left( {110} \right)\) and \(\left[ {11\bar{1}} \right]\left( {011} \right)\) in cementite slip systems are non-zero in x-aligned and z-aligned pearlite, respectively. Experimental results show that these slip systems are activated in cementite [10]. On the other hand, the atomic density of the (011) plane is 25% greater than the (110) plane, indicating that the (011) plane is relatively easy slip plane in cementite. Resultantly, the activation energy for dislocation nucleation on the (011) slip plane could be less than that on the (110) plane. Therefore, the distributed plastic strain in the cementite layer of the z-aligned sample is attributed to a dislocation glide on the \(\left[ {11\bar{1}} \right]\left( {011} \right)\) slip system at the onset of plasticity, while the lack of strain in the cementite layer of the x-aligned sample is attributed to a higher activation energy of dislocation nucleation on the \(\left[ {1\bar{1}1} \right]\left( {110} \right)\) slip system.
Fig. 7

Atomic shear strain distribution of Fe and C atoms at the onset of plasticity at 700 K: a, c near the onset of plasticity in x-aligned and z-aligned pearlite, respectively, and b, d after the onset of plasticity in x-aligned and z-aligned pearlite, respectively. Only atoms with shear strain larger than 0.3 are shown. The vertical dashed lines illustrate the original interface between ferrite and cementite

To further study the deformation mechanisms of pearlite in detail, a series of analyses were performed on the deformed samples to calculate the length of the dislocation lines using the dislocation extraction algorithm (DXA) tool [25] and the percentage of highly strained atoms (atoms with shear strain more than 0.3). As observed in Fig. 8, the dislocation length and the percentage of highly strained atoms are very low for the x-aligned pure Fe sample at all temperatures because of the formation of cracks during tensile deformation. The presence of the cementite layer in x-aligned pearlite increases the fraction of highly strained atoms due to more dislocation nucleation at the interface, while the dislocation length is still short because of crack formation. However, increasing the temperature dramatically increases the percentage of highly strained atoms, while the dislocation length does not significantly change. For the z-aligned pure Fe sample, both the dislocation length and amount of highly strained atoms are large because of the more activated slip system along the z-loading direction. As for the x-aligned sample, the existence of the cementite layer in the z-aligned sample acts as a source for dislocation nucleation and dislocation absorption. Thus, compared to the z-aligned pure Fe sample, the fraction of highly straine d atoms in z-aligned pearlite is high while the dislocation length is significantly reduced. However, at elevated temperature, the larger amount of highly strained atoms and the shorter dislocation length indicate the activation of more slip systems and more dislocation absorption in z-aligned samples at higher temperatures.
Fig. 8

a Length of the dislocation lines in the nanocomposite samples at 100 K and 700 K calculated using the DXA tool; b percentage of atoms with a shear strain greater than 0.3 in the nanocomposite samples at 100 K and 700 K

Our findings are in good agreement with the experiments, whereby pearlite shows a different ductility by changing the angle between the cementite lamellae and loading direction. Umemoto et al. [27] reported successful bending in cementite lamellae that were perpendicular to the rolling direction, while cementite fragmentation and necking was observed in a pearlite grain with parallel lamellae with respect to the rolling direction. Inoue et al. [12] also reported different ductility and fracture mode of cementite lamellae elongated on different crystal orientation.

An important specific feature of pearlite deformation is the effect of ferrite interlamellar spacing on the dislocation evolution. Plastic deformation leads to the formation of a cellular dislocation structure in coarse pearlite. Such structural deformation is realized if the interlamellar spacing of ferrite becomes greater than the dislocation mean free path (MFP), defined as the MFP of dislocation up to its pinning by a stopper, cross slip, or annihilation [19]. Upon further development of the deformation, shear bands form and propagate into the cementite layer, which acts as a failure site. In fine pearlite, in which the interlamellar spacing is similar to or smaller than the MFP, the dislocation loops nucleate at the interface, pass through the ferrite layers, and are stopped at the opposite interface. In this case, the size effects manifest themselves most clearly, and no dislocation cellular structure is formed in ferrite [13, 31].

To evaluate the effect of lamellae size on the deformation behavior of pearlite, we repeated the tensile simulations by reducing the samples sizes by half while the thickness of the samples was maintained at 5 nm. Hence, the width of the effective ferrite lamellae is reduced to 20 nm, which is comparable to experimental data for drawn pearlitic wires as fine as 10–20 and 1–2 nm for the ferrite and cementite lamellae, respectively [31].

Figure 9 shows that the stress–strain curve is not significantly changed for x-aligned samples by reducing the interlamellar spacing while the yield points are moderately changed by less than 20% for z-aligned samples due to different volume fraction of cementite in large and small z-aligned pearlite (0.203 and 0.177, respectively), which is in agreement with experimental observations [13]. We found that the pearlite interlamellar spacing does not affect the z-aligned samples. However, a dramatically different dislocation distribution and shear band formation is demonstrated in the x-aligned pearlite samples (Fig. 10). As the interlamellar spacing is reduced, cementite cutting is replaced by cementite necking without any crack opening in ferrite during the tensile deformation at 100 K (Fig. 10a, compared to Fig. 5b). A more uniform strain distribution is observed in the ferrite layer (Fig. 10b), which finally reduces the strain intensity in the cementite shear bands. On other words, reducing the interlamellar spacing improves the ductility and effectively accommodates plastic deformation. Our results show that pearlite ductility is not affected by interlamellar spacing at high temperatures.
Fig. 9

Effect of interlamellar spacing on the stress–strain curves of ax-aligned and bz-aligned pearlite samples at different temperatures

Fig. 10

Deformation evolution after 30% total tensile deformation in reduced-size x-aligned nanocomposite pearlite. The length and width of the sample is half that of the sample in Fig. 1(b). a, c Dislocation evolution at 100 K and 700 K, respectively, under the same conditions as that in Fig. 5. b, d Atomic shear strain distribution of Fe and C atoms at 100 K and 700 K, respectively, under the same conditions as that in Fig. 6. Dashed lines illustrate cementite layers

Conclusion

In this work, we performed MD simulations to investigate the effect of the loading direction on the deformation behavior of pearlite at various temperatures and the effect of the lamellae size in pearlite. A lower flow stress was found along the z-loading direction and at higher temperature. We found a brittle behavior in ferrite and cementite cutting by localized deformation in pearlite under tensile loading along the \(\left[ {111} \right]_{f} ||\left[ {100} \right]_{c}\) direction. In contrast, pearlite and ferrite structures showed excellent ductility with uniform strain distribution without cementite cutting and necking under tensile loading along the \(\left[ {\bar{1}10} \right]_{f} ||\left[ {001} \right]_{c}\) direction. This uniform deformation is attributed to the higher Schmid factor of the activated slip systems in ferrite and higher atomic density of the (011) plane in cementite. Our analytical analysis revealed that the ferrite-cementite interface reduces the observed dislocations by dislocation annihilation and increases plastic strain by providing preferred dislocation nucleation sites. However, the pearlite ductility was improved by raising the temperature. In contrast, reducing the interlamellar spacing improved the pearlite ductility by reducing the strain intensity along the shear band and replacing cementite cutting with cementite necking under tensile loading along the \(\left[ {111} \right]_{f} ||\left[ {100} \right]_{c}\) direction.

Notes

Acknowledgements

H.G. and A.K.T. acknowledge the Research Board of Sharif University of Technology, Tehran, Iran, and the Iran National Science Foundation for financial support of the project. This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT & Future Planning (2016R1C1B2016484 and 2016R1C1B2011979).

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© Korean Multi-Scale Mechanics (KMSM) 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringKorea Advanced Institute of Science and Technology (KAIST)DaejeonRepublic of Korea
  2. 2.Department of Materials Science and EngineeringSharif University of TechnologyTehranIran
  3. 3.Department of Mechanical EngineeringYonsei UniversitySeoulRepublic of Korea

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