{111} tilt grain boundaries as barriers for slip transfer in bcc Fe

{111}tilt grain boundaries as barriers for slip transfer in bcc Fe N. Kvashina,∗,N. Anentoa,D. Terentyevband A. Serraa aDept. Civil &Environmental Engineering, Universitat Politècnica de Catalunya, Barcelona, 08034, Spain bSCK·CEN, Nuclear Materials Science Institute, Boeretang 200, Mol, B-2400, Belgium ARTICLE INFO Keywords: Grain Boundary Strengthening Defect Interaction Dislocation Pile-ups Dislocation Interactions Molecular Dynamics ABSTRACT We have studied the interaction of an individual dislocation and a pile-up of dislocations with {111}tilt grain boundary in iron by means of atomistic simulations. The {111}tilt grain boundary, under externally applied stress, can change orientation by forming steps of three plane high thanks to shuffling of two atoms per Coincident Site Lattice (CSL) unit cell. When an individual crystal dislocation interacts with the GB, there is no transmission of the dislocation. Instead, we observe the formation of the same steps as found under the application of external stress. Depending on the orientation of the glide plane of the dislocation, two situations may occur. (i) If the glide plane perpendicular to the GB, the GB transforms into a stepped segment and a{112}twin boundary. (ii) For the other glide planes, the dislocation is absorbed by the GB and form a facet along the glide plane. Up on the interaction with a pile-up of dislocations, the stress concentration accumulated in the interaction region enhances the same reaction process, i.e. in (i) there is a penetration of one grain into the other with the dislocation in the tip of the intrusion bounded by the symmetric (112) and asymmetric stepped segment respectively. In (ii), the second dislocation is absorbed increasing the length of the facet. Based on the obtained results, one can conclude that {111}GB acts as a strong obstacle for gliding dislocations, does not allow a direct dislocation transmission, which makes a contrast with other types of h110iGBs (e.g. (112) and (332)). 1. Introduction The main mechanism behind plastic deformation of polycrystalline metals is the mobility of dislocations [1]. Any obstacle impeding or modifying its motion leads to a change in the mechanical response of the material. On early studies, Grain Boundaries (GBs) were considered, as a first approximation, as static obstacles for mobile dislocations [2]. The increasing understanding on the processes that occur at GBs at the atomic level shows that often the displacement of GB is not negligible and it affects the interaction with other defects. Thus, the sustainability of the macroscopic deformation is defined by two factors: (1) the propagation of dislocation-mediated slip through grains and (2) the activation of atomic processes that are intrinsic to the GBs. The former is ruled by the interactions of dislocations with the GBs [3,4] while the latter corresponds to the formation of GB dislocations (GBDs) that favour the shear-coupled GB migration [5], nucleation of dislocations [6]and nucleation of twins [7]. Any process to occur at atomic level at a GB is constrained by the atomic structure of both, the GB and the interacting defect [8] and also by the inter-atomic interactions, which are dependent on the material and the temperature. One atomic mechanism which participates in an efficient way at low temperature to the plastic deformation of metals is the shear-coupled GB migration (SCGBM), ∗Corresponding author [email protected] (N. Kvashin) as many experiments [9,10] and molecular dynamics simulations [11,12] have evidenced. Recent results in nano-crystalline materials [13], where GB migration is observed despite dislocation-mediated plasticity is negligible, reassure the significance of this mechanism. The essential element behind the SCGBM are glissile disconnections, namely, interfacial defects with both dislocation and step character, characterized by the Burgers vector (Bv) and the height of the step (b,h). We name these disconnections as elementary disconnections (EDisc) in the sense that, with (b,h) small, they are mobile and responsible for the displacement of the GB. Previous atomistic studies performed on several Tilt GBs in bcc-Fe [14–16] show in detail the key role played by EDisc on the GB migration and also on the interaction of the GBs with crystal dislocations. In real polycrystalline materials, GBs display a variety of structures, including both symmetric and general. If for some particular interfacial structure there are no glissile disconnections, the most relevant consequence would be the inability to activate the SCGBM mechanism. In this work we have investigated the interaction of a Σ3{111}h110itilt GB with single crystal dislocations and dislocation pile-ups (DPU) in bcc-Fe by means of a hybrid atomistic/discrete-dislocation model. The dichromatic pattern (DP) [8] presented in Fig. 1 shows the only EDisc that could be related to the SCGBM (identified as #4). As it is detailed in the Results Section, this EDisc does not appear involved on the reactions observed. This makes the {111}GB a suitable choice to investigate the plasticity mechanisms N. Kvashin, N. Anento, D. Terentyev, A. Serra: Preprint submitted to Elsevier Page 1 of 12 {111}tilt grain boundaries as barriers for slip transfer in bcc Fe / 2021 Figure 1: a) Dichromatic pattern of (111) GB. Black sites represent the lower grain, yellow sites the upper grain. Burgers vectors marked with numbers “1” and “2” are the Bv’s of crystal edge dislocations gliding on two different {112}planes. “3” is the Bv of a mixed dislocation gliding on a {110}plane, “4” is the Bv of a potential EDisc with the lowest possible step. b) Coincident-site Lattice for the (111) GB. The arrows indicate the motion of atoms necessary to create a step in the interface. in absence of EDisc, which will contribute to the understanding of the GB-dislocation interaction in bcc materials. In consistency with our previous works [14–16] we denote the GB dislocations that step the upper crystal along nplanes and the lower crystal along mplanes as bn/m. We extend this notation, for completeness, to the Bv of crystal dislocations in the upper crystal as bn/0. In this way, for any reaction considered, the values of n and mare conserved separately in the balance of Bv. The paper is structured as follows: in Section 2 there is a description of the simulation method while in Section 3 there are presented the most relevant findings on the interaction of the {111}GB with single dislocations and DPU. Finally, in Sections 4 and 5 we present the discussion and the main conclusions reached from the results obtained. 2. Methodology The interaction of 1/2h111idislocations with the Σ3{111}h110itilt GB in α-Fe has been studied by Molecular Dynamics (MD) simulations employing the parallel version of LAMMPS code [17]. In order to clarify the atomic level mechanisms, the interatomic interactions in iron were modelled by using the embeddedatom method potential by G. Ackland et al., fitted to reproduce properties of dislocation lines obtained from DFT [18]. The accuracy of the potential in the study of h110itilt GBs was checked in [19]. The MD simulation box consisted of a symmetric bcc bicrystal with an initially coherent symmetric tilt GB in the middle. The principal axes x,yand zof the upper crystal (λ) were oriented along the [1 -1 1], [-1 -1 0] and [1 -1 -2] directions, respectively, while for the lower crystal (µ) the orientation of the axes was mirror reflected. Approximate dimensions of the cell size were 120 ×4×120 lattice vectors along the corresponding directions with a total number of atoms ∼700000. Two different setups have been employed, the former to consider the interaction of the GB with a single dislocation (i) and the latter to simulate the interaction of the GB with a dislocation pile-up (DPU) (ii): (i) By using Atomsk software [20] we introduce a single 1/2h111idislocation on the upper crystal of the simulation box. For edge dislocations the glide planes are {112}type, while for mixed dislocations is {110}. An incremental shear strain is applied in order to move the dislocation to initiate the interaction with the interface. Periodic boundary conditions were imposed on the [-1 -1 0] tilt axis and [1 -1 2] axis along the GB, with fixed boundaries in the direction perpendicular to the interface. (ii) A hybrid atomistic/discrete dislocation model was applied [21]. This approach uses separate continuum and atomistic simulations that define mutual boundary conditions. The positions of continuum dislocations in the pile-up are defined as a function of an externally applied shear stress and the positions of any dislocation in the atomistic region held fixed at determined positions. This model has been used in fcc [22] and bcc [15] metals and a detailed description can be found in these studies. With respect to the loading conditions, the following parameters were fixed: the number of dislocations in a pile-up (15 units), the increment of the externally applied stress (∆σapp = 100 MPa) and the maximum of the externally applied stress (σapp,max = 5.5 GPa). In this model periodic boundary conditions were imposed only on the [-1 -1 0] tilt axis while on the [1 -1 2] axis and the direction perpendicular to the interface we used fixed boundaries. N. Kvashin, N. Anento, D. Terentyev, A. Serra: Preprint submitted to Elsevier Page 2 of 12 {111}tilt grain boundaries as barriers for slip transfer in bcc Fe / 2021 Figure 2: Interaction of the (111) GB with b3/0edge dislocations at 90◦. a) Dislocation is attached to the GB; b) start of steps formation; c) formation of a {112}twin. In all the simulations with both setups, the stress state of the system is recorded after each increment of strain and the open visualization tool OVITO [23] is used for visualization and analysis of the atomic configuration. To understand the particular mechanisms of dislocation-GB interaction, we varied the simulation temperature from 0 K (static simulations to find out the threshold to trigger the reaction) up to 900 K (to check the stability of the interfaces), thus enhancing or reducing the role played by thermal activation. There have been considered three different glide plane inclinations with respect to the GB to introduce the dislocations. These dislocations are identified in Fig. 1. The first corresponds to an edge dislocation tagged as #1, gliding at 90 degrees, named b3/0= 1 2[111]. The second one, tagged as #2, is another edge dislocation gliding at 19.47 degrees and named b1/0=1 2[111]. And the last one, tagged as #3 is a mixed dislocation gliding at 144.74 degrees and named b1/0=1 2[111]. For every glide plane inclination, it has been considered, in turn, two senses of the Bv, pointing away from the interface (denoted bn/0) and pointing towards the interface (denoted b−n/0). Finally, to assess the local evolution of stress state as a consequence of the GB-dislocation interactions, we have allocated several groups of atoms to record the forces and displacements during the simulation runs. These groups of atoms are placed in positions where they can provide relevant information on the reactions with the interface. They are indicated in Figs. 7, 9b & 10c (see also Fig. 2 in [15]). 3. Results In the present section, we describe the whole process of transformation undergone by both crystal dislocations and the interface when the former interacts with a{111}GB. The first subsection is focused on the case of a single dislocation, while on the second we show the results obtained from the interaction with a dislocation pile-up. The absence of glissile EDisc as a part of the reactions observed leads to a mechanism for coupling plastic deformation very different from the ones observed for other interfaces in bcc metals [14–16]. 3.1. Interaction of a single 1/2h111i dislocation with the (111) GB Previous studies on the interaction of single 1/2h111i dislocations with several STGBs with h110itilt axis in α-Fe [14,16] show that the former is spontaneously absorbed by the boundary followed with the formation of a GBD and the emission of one or several EDisc. Conversely, for the {111}GB we noticed that there is no absorption of the incident dislocation, independently of the glide plane, Bv orientation or dislocation character considered. On every possible case investigated the crystal dislocation stays attached to the GB keeping its Bv, the parameters defining each case only affect the final defects at the GB and the stresses at which the transformation takes place. In this section we present the results obtained for a range of temperatures going from 0 K up to 900 K. However, there are noticeable differences between the mechanisms observed at T = 0 K with those for T > 0 K, for that reason we have presented the results in two different subsections, one for static and another for dynamic calculations. 3.1.1. Static simulations The analysis of the results obtained from Molecular Statics (MS) on the interaction between a single dislocation and the GB shows exactly the same pattern irrespectively on the glide plane inclination, Bv orientation or character of the dislocation (edge or mixed) which can be described qualitatively as a three-steps process: N. Kvashin, N. Anento, D. Terentyev, A. Serra: Preprint submitted to Elsevier Page 3 of 12 {111}tilt grain boundaries as barriers for slip transfer in bcc Fe / 2021 Figure 3: Shear stress in the system vs strain applied for different incidence angles. The response of the pristine GB is included as reference. a) 90 degrees, b) 19.47 degrees and c) 144.74 degrees. 1. Attachment of the crystal dislocation to the GB without changes in its Bv. 2. Transformation of the defect (formation of several non-glissile steps and residual defect). 3. Accumulation of stresses at this region up to an eventual formation of a {112}twin attached to the GB. In the frames of Fig. 2 we can see the details on this process for the single dislocations on a glide plane forming an angle of 90 degrees with the GB. It starts moving from the attachment of the incident crystal dislocation to the GB (Fig. 2a) to the final formation of the {112}twin in the lower crystal (Fig. 2c) including the intermediate configurations where it can be noticed the formation of pure steps without dislocation character, that is, they are sessile. The only change with respect to other cases lies on the number of steps produced and the growth direction of the twin, which can expand towards the upper crystal or the lower crystal, depending on the sense of the Bv, i.e. the direction of the stress to be applied to trigger the reaction. The creation of these pure steps is shown on Fig. 1b. In this frame it is displayed the Coincidence Site Lattice (CSL) unit cell for this GB. The shuffles of two atoms inside this unit cell, indicated in the figure by the position and direction of the vertical arrows, leads to the appearance of steps on the boundary. This transformation of the interface is shear-induced, once a stress threshold is overcome, the motion of atoms takes place. The energy barrier of the transformation of the GB is 99 mJ/m2. Mrovec et al. [24] reported this mechanism of stress accommodation for the (111) GB in tungsten. The absence of EDisc in this interaction process prompted us to investigate the shear response of the pristine (111) GB. Our simulations show that shear coupled GB migration does not take place, as there is no production of EDisc. At 0 K the pure steps are formed on the GB interface at around 9 GPa of shear stress accommodated in the system. If a stress concentrator exists in the GB, the stress necessary to initiate transformations on the interface is smaller. The shear stresses averaged on all mobile atoms for all the cases considered are shown in Fig. 3. The results in Fig. 3 evidence that the presence of a dislocation attached to the GB allows to decrease the stress needed to initiate a reaction. From the 9 GPa in the pristine interface the values of shear stress are reduced to approximately 4 GPa in b−3/0case, to 6.3- 6.7 GPa in b1/0(mixed) and 6 GPa in b−1/0(edge). Therefore, the cases with the glide plane perpendicular to the GB are the most favoured ones, although, according to geometrical criteria, the GB should be transparent for the dislocations. All the big drops in the shear stress correspond to the formation of {112} twins. 3.1.2. Dynamic simulations At temperature T >0 K, the interface allows accommodation of stress by forming steps or irregular structures on the interface, as can be observed in Fig. 4. The shape of the GB far from the interaction region is no longer flat while on the local region of the boundary where the dislocation is attached there is no formation of {112}twins and the steps formed are higher (fig. 4c). This total absence of {112}twin formation indicates that stepping the interface is the preferred mechanism on this boundary for accommodation of plastic deformation. Unlike static simulations, the outcome of MD calculations shows to be sensitive to the glide plane inclination and Bv sense, so the results for each case are presented separately. In Fig. 4 it is displayed the evolution of the GB interacting with a b−3/0crystal dislocation at T = 300 K. Once the dislocation is attached to the interface as the stress increases it is formed a new interface: it grows a {112}interface (Fig. 4b) in a reaction quite similar to the initial split of the Bv shown on Fig. 2b. Applying temperature allows a better accommodation of the new interfacial structure, so that the formed defect is not a {112}twin, but a N. Kvashin, N. Anento, D. Terentyev, A. Serra: Preprint submitted to Elsevier Page 4 of 12 {111}tilt grain boundaries as barriers for slip transfer in bcc Fe / 2021 Figure 4: Interaction of the (111) GB with an edge dislocation b−3/0at T = 300 K. The dashed lines are a guide for the eye showing the position of the glide plane. pair of two interfaces: a {112}GB, coinciding with the initial glide plane of a dislocation, and an asymmetrical interface formed by steps created on (111) GB (fig. 4c). For the b3/0dislocations the process is similar although the change on the interface is less pronounced. In the case of edge dislocations gliding at 19.47 degrees applying temperature also leads to a formation of an asymmetrical interface. Once again, there is no formation of twins with re-emission of crystal dislocations and the interface is formed along the initial glide plane of the dislocation. There is a formation of a complementary interface to compensate the step height. As an example, Fig. 5 shows the two interfaces formed from the absorption of b1/0dislocation at T = 300 K. Finally, for the mixed dislocations gliding at 144.74 degrees, we have found that, irrespective to the screw component and Bv sense, the dislocation becomes attached to the interface but no reaction is observed. The main difference with edge dislocations is that no Figure 5: A GBD formed by the absorption of an edge b1/0at T = 300 K in iron. The picture shows two formed risers: one on the right (red circle) containing the absorbed dislocation and another one on the left (green circle) which is a ’complementary’ step. The dashed line is a guide for the eye showing the position of the glide plane. new interface is created as no risers or {112}GB formation takes place. Therefore, we can conclude that this attached mixed dislocation is not as effective as a stress concentrator as its counterparts for pure edge dislocations. The edge part of the Bv of this mixed dislocation is shorter than the Bv of b3/0and b1/0edge dislocations (0.5a0vs. 0.866a0). 3.2. Interaction of a pile-up of 1/2h111i dislocation with the (111) GB The analysis of the results from the interaction between the (111)[110] tilt grain boundary and a single dislocation has shown a mechanism leading to a local modification of the interface on the interaction region, based on the formation of steps. This mechanism is enhanced when T >0 K and the final outcome depends on the initial parameters of the simulation: temperature, glide plane inclination and Bv sense. In this subsection we present the results of our investigation on the interaction of the (111) GB with a pile-up of dislocations, considering the same set of cases described in subsection 3.1.2. There is a common element in all the simulations: the behaviour of the first dislocation of the pile-up is exactly the same as described for a single dislocation. The discrepancies between the different cases come from the influence of the remaining dislocations of the pile-up on the newly formed interface. Apart from the results obtained for each case investigated as a function of the temperature, we have included a subsection N. Kvashin, N. Anento, D. Terentyev, A. Serra: Preprint submitted to Elsevier Page 5 of 12 {111}tilt grain boundaries as barriers for slip transfer in bcc Fe / 2021 Figure 6: a), b), c) and d) Snapshots of MD simulation of a (111) GB interacting with a pile-up of b3/0dislocations at T = 300 K in Fe; e) and f) Idem for a pile-up of b−3/0dislocations. where it has been evaluated the stability of the new interfacial structures generated by the GB - pile-up interaction. 3.2.1. Pile-up of edge dislocations with Bv inclined 90 degrees The Burgers vectors of the edge dislocations of the pile-up are b3/0=1 2[111] and b−3/0=1 2[111]. In the same way observed for single dislocations, the outcome of the reactions involved with each dislocation is related by a mirror symmetry with respect to the glide plane of the disolocation, as shown in Fig. 6. The first dislocation is attached to the interface during all its transformation process. We have checked by using a Burgers circuit that the Bv stays the same as the initial crystal dislocation. We can conclude that this GB acts as a strong obstacle for dislocations, as the 2nd and the subsequent dislocations are unable to reach the boundary. The role played by these dislocations is to increase the local stress on the interaction region, triggering the reactions which modify progressively the shape of the boundary as it is displayed from Fig. 6a to Fig. 6d. Fig. 6a shows the full box and the region of the reaction after the first b3/0dislocation absorption while Fig. 6b shows in detail the interaction region with the second dislocation in the vicinity of the interface. The dislocation at the interface concentrates stresses coming from other dislocations leading to the formation of a new interface propagating into the lower grain. Figure 7: a) Snapshot of MD simulation of a (111) GB interacting with a pile-up of b3/0dislocations in Fe at T = 900 K. The figure shows the configuration with two interfaces created along with the propagation of crystal dislocations. b) Idem at T = 300 K. The dashed lines are guides for the eye indicating the glide plane. This new interface is the combination of a {112}GB parallel to the initial glide plane with a {110}/{001} facet, where the planes in the upper grain represent the sectors of {110}planes divided by steps along h110idirection. Figs. 6e & 6f show the formation of the equivalent structure for the pile-up of b−3/0 dislcoations which is approximately the mirror image of the formerly described b3/0. In Fig. 6d we can observe how the stress field of the second dislocation affects the {112}GB by inducing the creation of a glissile disconnection on this interface. As the applied stress increases up to 4.5 GPa no further reaction between the following pile-up dislocation and the interface was observed. The second dislocation continues its glide along with the propagation of the {112}interface, that does not increase in length. Instead, the upper grain extends into the lower by means of the formation of the new stepped facet. In order to investigate the effects of temperature on the interaction mechanism, we have studied the b3/0 case in Fe considering T = 900 K. The equivalent case at T = 300 K shows that the {112}GB of the new interface appears in the tensile region of the dislocations (right) while the {110}/{001}facet is on the compression region (left) as shown in Figs. 6d and 7b. However, at a higher temperature, even though the reaction is the same, we can observe a different outcome from the interaction indicating that the stress is accommodated differently. The new interface created (Fig. 7a) has a more symmetric shape: the {112}GB present at T = 300 K transforms into a {001}/{110} facet. We have analysed the stresses at the reaction site region: (1) close to the {112}GB and (2) close to the formed facet on the at T = 300 K and, similarly, close to two different facets at T = 900 K. The regions are shown on Fig. 7. The results are given in the Table I. There is also the formation of the {112}disconnection for b3/0dislocations case at T = 300 K. The shear stress before the reaction is in the (1) region - 350 MPa, in the (2) region - 340 MPa. The values obtained for the N. Kvashin, N. Anento, D. Terentyev, A. Serra: Preprint submitted to Elsevier Page 6 of 12 {111}tilt grain boundaries as barriers for slip transfer in bcc Fe / 2021 Table 1 Local stresses at the formation of the facets for the edge (b±3/0) in Fe. Shear is the local shear stress. Region (1) (2) Bv T (K) Shear (MPa) b3/0 300 570 570 900 1190 860 b−3/0 300 520 490 900 870 1000 stresses close to two different interfaces do not differ much, as can be seen on Fig. 7. We can summarize the interaction of a pile-up of b±3/0describing the reactions observed and the effect of temperature on their outcome. The first dislocation of the pile-up contacts the interface and remains attached without changing its Bv. As the {111}GB do not experience shear-coupled GB migration, there is another type of accommodation of applied stress – the formation of new interfaces where the upper crystal grows at the expenses of the lower crystal. The stress induced by the subsequent dislocations leads to the creation of a {112}GB on the tensile region and {110}/{001}type facets on the compression region. The {111}GB acts as a strong obstacle for this type of edge dislocations as no transmission is observed, even for a high level of stress (∼10 GPa). The temperature affects the final shape of the interface, the higher it is, the more favoured is the stepping mechanism responsible for the {110}/{001}type facets in front of the creation of the {112}GB along the former glide plane of the pile-up. 3.2.2. Reversibity of the new interfaces The {110}/{001}facets formed during the accommodation of plastic deformation are stable. If a reversed stress is applied, as in a cyclic deformation, the dislocations of the DPU move back, but the facet keeps unchanged. The first dislocation is not detached from the interface and when moving back it leads to the creation of a (112) twin that penetrates either the upper (λ) crystal if it is b3/0or the lower crystal (µ) if it is b−3/0. The creation of the EDisc responsible for the thickening of the twin are compensated by the creation of crystal dislocations that glide in the opposite direction of the twin. Inside the red circles in figure 8 there are two of the crystal dislocations created during the thickening of the twin. Notice that their glide planes are parallel but not coincident with the DPU. There is a balance in Bv and planes since three disconnections of the {112}twin boundary are equivalent to one 1/2h111icrystal dislocation and step the twin boundary one plane. The full cycle of MD simulations has been performed at T = 300 K and are divided in two parts: (1) Figure 8: Snapshots of MD simulation of a (111) GB interacting with pile-ups of the b3/0(a) and b−3/0(b) dislocations. The reversed sense strain is applied to the box with a newly formed interface. The figures show the evolution (left to right) of the interface along with the dislocations. Enclosed in a red circle there are the crystal dislocations emitted jointly with the creation of the {112}twin. A shear strain has been applied until reaching a level of 4 GPa of shear stress accumulated in the system. (2) The shear strain is then reversed up to the point where there is created a {112}twin on the interface, then the simulation is ended. In Fig. 8 there are displayed several snapshots showing the described evolution of the boundary along with the dislocations of the pile-up during the second part of the simulations for both Bv sense. The first configuration shown in Fig. 8a & 8b corresponds to the precise moment where the strain applied is reversed. On the remaining frames we can track the second and subsequent dislocations being gradually pulled away from the boundary until a {112}twin is created jointly with the emission of one or two crystal dislocations. For the b3/0dislocations, the twin is created towards the upper crystal while the extra dislocation is emitted into the lower crystal (is out of frame). And for the b−3/0dislocations the process is essentially mirrored: the twin is created towards the lower crystal and the emitted dislocations appear on the upper crystal (enclosed in red circle), following the ones from the pileup. The main conclusion from these results is that the process of growth of the new interfaces created from the interaction GB - pile-up is irreversible. 3.2.3. Pile-up of edge dislocations with Bv inclined 19.47 degrees For this glide plane inclination, the Burgers vectors of the incident edge dislocations of the pile-up are b1/0=1 2[111] and b−1/0=1 2[111]. In the same manner N. Kvashin, N. Anento, D. Terentyev, A. Serra: Preprint submitted to Elsevier Page 7 of 12 {111}tilt grain boundaries as barriers for slip transfer in bcc Fe / 2021 Figure 9: a), b), c), d) and e) Snapshots of MD simulation of a (111) GB interacting with a pile-up of b1/0dislocations at T = 300 K in Fe; f), g) and h) Idem for a pile-up of b−1/0 dislocations. The green circles indicate the position of the first absorbed dislocation. The dashed lines are guides for the eye indicating the glide plane. as observed for the b±3/0cases, no transmission takes place and the second and subsequent dislocations of the pile-up increase the local stress on the interaction region triggering the transformation of the interface. However, the low incidence angle leads to a very different interaction process with a substantial change in the final outcome, as it is reflected by comparing the frames of Fig. 9 (9e and 9h) with the equivalents in Fig. 6 (6d and 6f). The interaction process follows the same initial steps: the first dislocation of the pile-up reaches the GB and is not absorbed, it remains attached to the interface keeping its Bv. As the applied stress increases, this dislocation eventually gets absorbed forming a GBD with a Bv parallel to the interface. Figs. 9a and 9b show the configuration of the system once this first absorption has taken place for the b1/0case. As the stress continues increasing, several steps appear on the interface modifying its shape (Figs. 9c, 9d and 9e for b1/0) around the interaction region. Simultaneously, the second dislocation of the pile-up approaches to the GB and is finally absorbed, forming a riser (Fig. 9d). As the external stress keeps increasing, the evolution of the interface on the interaction region is different depending on the Bv direction, so let us detail it separately: (i) For the pile-up of b1/0we observe the formation and subsequent growth of a facet of {112}/{110} (+segments of {001}). Simultaneously, a second facet appears on the left of the interaction region (Fig. 9e) described as a facet of {110}/{112} (+segments of {110}). The length of the first formed facet ranges between 40 Å when its formed and 350 Å at the 6.5 GPa of stress applied. We noticed that during this process the mentioned GBD stays sessile and keeps the interface on the compression region of its vicinity flat as can be seen in Fig. 9c (red line). (ii) For the pile-up of b−1/0the GBD formed after the first absorption (green circle in Fig. 9f) has opposite sign and this conditions the ensuing interaction with the 2nd dislocation. The riser formed as a result of the second absorption (Fig. 9g) spreads and it splits into two risers with the same configuration as in b1/0case. The final configuration of the interface on the interaction region (Fig. 9h) is qualitatively a mirror image of the image in Fig. 9e, with a segment of pristine {111}GB between two facets, the main one being {112}/{110}(+segments of {001}), and the ’complementary’ one being {110}/{001}+{112} (irregular). We have investigated again the effect of temperature on the interaction mechanism comparing the displayed results with ones obtained applying a higher temperature (T = 900 K). For both Bv orientations we noticed that the main effect of temperature is on the way the deformation is accommodated and an additional dislocation is absorbed. The final structure of the interface is not as regular as observed at low temperatures and no flat regions can be found. In the same manner presented in subsection 3.2.1, we have measured the stresses at the reaction region when significant reactions take place (Fig. 9b). At T = 300 K the events are: initial absorption (I) second absorption (II) and formation of one step (III). At T = 900 K the events are the same, except for the (III) reaction, that is the third absorption. The reasults are given in the Table II. The difference between the values for b1/0and for b−1/0can be explained by the fact that the former stresses are accommodated mainly by the growth of the main riser, i.e. further propagation of initial dislocations, while for the latter stresses are accommodated by formation of irregularities (steps) along the whole interface. Comparing the values at different temperature, we can say that the higher the temperature the lower the stresses needed to trigger the reaction. As a summary of the results presented we can describe the interaction of a pile-up of b±1/0in a very different way than for b±3/0. Now, we observe the absorption of two or three dislocations of the pile-up, N. Kvashin, N. Anento, D. Terentyev, A. Serra: Preprint submitted to Elsevier Page 8 of 12 {111}tilt grain boundaries as barriers for slip transfer in bcc Fe / 2021 Table 2 Local stresses at the reaction region before the reactions for the edge (b±1/0) in Fe. Shear is the local shear stress. Reaction (I) (II) (III) Bv T (K) Shear (MPa) b1/0 300 830 1170 1320 900 820 980 1170 b−1/0 300 930 1550 1620 900 840 1160 980 Figure 10: Snapshots of MD simulation of a (111) GB interacting with a pile-up of mixed dislocations in Fe at T = 300 K. The configurations in a) and b) show the system after the absorption of the first dislocation in b1/0and b−1/0. Red line on a) indicates the facet of the formed riser. c) Configuration of the system after the absorption of the second dislocation for b−1/0. Dashed lines are guides for the eye indicating the glide plane. depending on the temperature. These absorption reactions lead to the formation of a riser (facet) modifying the shape of the interface. The effect of temperature changes the number of absorptions and the value of the stresses required to trigger the reactions, however, qualitatively the final outcome is very similar. 3.2.4. Pile-up of mixed dislocations with Bv inclined 144.74 degrees As it is detailed in Fig. 1, the mixed dislocations (identified as #3) interacting with the GB glide on a {110}plane. The Burgers vectors of the dislocations of the pile-up are b1/0=1 2[111] and b−1/0=1 2[111]. As we observed for the single dislocation case (subection Table 3 Local stresses at the reaction region before the reactions for the mixed (b±1/0) in Fe at T = 300 K. Shear is the local shear stress. Reaction (I) (II) (III) (IV) Bv Shear (MPa) b1/0390 - - 770 b−1/0300 630 600 600 Dynamic simulations), the screw component does not affect the interaction process and there is a noticeable similarity with the results obtained for b±1/0edge dislocations, although the smaller edge part (0.5a0vs. 0.866a0) of the Bv affects the number and the outcome of the reactions taking place. Once again, the sense of the Bv is relevant as the number of dislocations absorbed by the GB changes. In Fig. 10a it is shown the interaction region once the first b1/0dislocation of the pile-up has been absorbed by the interface. As in the previous cases, initially this dislocation is attached and is absorbed only when the local stress increases by the approaching of the second dislocation. Several steps appear in the interface along with a riser. However, this riser is smaller than for pure edge dislocation as can be seen indicated with a red line. As the stress increases the riser remains in the same position and does not grows while more steps appear on the interface to accommodate it. It seems that there is a repulsion between this riser and the second dislocation causing that no more dislocations are absorbed. Conversely, for the b−1/0case there is no repulsion between the GBD created on the first absorption and the second dislocation of the pile-up (Fig. 10b). Along with the motion of this dislocation towards the GB, as the external stress increases steps appear in the interface. Once the second dislocation is absorbed, it is formed a riser represented as a facet in Fig. 10c, equivalent to the one observed for edge dislocations: {110}/{112}(parts of {001}). After this absorption we observed the formation of several pure steps without dislocation character along the interface which interact with each other forming a step with h12/12 height on the right of the main riser (Fig. 11) leading to a better stress accommodation as can be seen from the comparison of the stress distributions in Fig. 10c (right frame) with the one in Fig. 11 (right frame). To complete the study we have measured the stresses at the interaction region where the relevant reactions take place (Fig. 10c). For the interaction with mixed dislocations we emphasize the following reactions: (I) the creation of the GBD after the first absorption; (II) the second absorption; (III) the creation of a ’complementary’ riser; (IV) the end of stress application. The reasults are given in the Table III. There is only one absorption for the b1/0, we can N. Kvashin, N. Anento, D. Terentyev, A. Serra: Preprint submitted to Elsevier Page 9 of 12