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Anisotropic deformation behaviors of amorphous-crystalline nanolaminates investigated via molecular dynamics simulations
Accepted Manuscript Anisotropic deformation behaviors of amorphous-crystalline nanolaminates investigated via molecular dynamics simulations Dan Zhao, Shunbo Wang, Bo Zhu, Lijia Li, Hongwei Zhao PII:
S0925-8388(19)30608-5
DOI:
https://doi.org/10.1016/j.jallcom.2019.02.162
Reference:
JALCOM 49594
To appear in:
Journal of Alloys and Compounds
Received Date: 10 November 2018 Revised Date:
29 January 2019
Accepted Date: 12 February 2019
Please cite this article as: D. Zhao, S. Wang, B. Zhu, L. Li, H. Zhao, Anisotropic deformation behaviors of amorphous-crystalline nanolaminates investigated via molecular dynamics simulations, Journal of Alloys and Compounds (2019), doi: https://doi.org/10.1016/j.jallcom.2019.02.162. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Anisotropic Deformation Behaviors of Amorphous-Crystalline Nanolaminates Investigated via Molecular Dynamics Simulations Dan Zhao, Shunbo Wang, Bo Zhu, Lijia Li, Hongwei Zhao* School of Mechanical and Aerospace Engineering, Jilin University, Changchun, Jilin 130022, China *Corresponding author. E-mail address: [email protected] (H. Zhao).
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Abstract: Amorphous-crystalline nanolaminates (ACNLs) composed of CuZr metallic glass layers and single crystal copper layers were constructed, and the anisotropy of the material deformation behaviors were investigated by conducting shear loadings on the ACNL sample in parallel deforming and serial deforming directions using molecular dynamics method. In parallel deforming mode, the yielding of the material was mainly triggered by generation of dislocations and slips in crystalline layer, and both crystalline and amorphous phases participated in the subsequent plastic deforming. In serial deforming mode, the results showed that the yielding and plastic deforming of the material was induced by shear localization of amorphous layers only. Amorphous-crystalline interfaces (ACIs) served as stress resistance weakness and dislocations breeding cradle in the former deforming mode while a strong connection of two phases in the later deforming mode. Furthermore, the increasing of crystalline layer thickness would promote the material shear modulus and shear strength in both deformation modes. The promotions and incentives varied and had dependence on the coupled deforming mechanisms. For the serial deforming mode, the shear moduli obtained from our simulations fitted the predicted ones from rule-of-mixture very well, while in the parallel deforming mode, the simulated shear moduli were much higher than predicted ones, which could be explained with the size effect induced by reduction of crystalline layer thickness surround with ACIs. Keywords: Amorphous-crystalline interfaces; Molecular dynamics simulation; Anisotropic deformation behaviors; Nanolaminates
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1. Introduction Metallic glasses (MGs) are well known for their excellent mechanical properties, e.g. high strength, high elastic modulus and high hardness [1], yet limited by the shear banding deformation mode, they are easily encountered with catastrophically failure. In a brittle MG, the generation of one major shear band usually localizes and induces uneven deformation, and finally develops as local fracture, which is responsible for the failure of brittle MGs [4]-[6]. This brittle deformation mechanism hinders the application of MGs in micro mechanical systems, thus should be avoid when employed as structural materials. Since the success in preparing bulk metallic glasses (BMGs), lots of researchers have been working on improving the fracture ductility of BMGs, and several methods have been developed to improve the plasticity of MGs by preventing localized shear bands formation. One method is tuning the heterogeneity of microstructure in the MG by controlling the component and preparation process, basing on the intrinsic heterogeneity of MGs [7]-[9]. Another effective method is introducing a second phase into the glass matrix with in-situ formation method or ex-situ assembling method either, usually ductile crystal phase. Lots of experimental works showed improvement of plasticity induced by the introduced second phase in the MG [10]-[12]. Hays et al. introduced ductile crystalline phase into V1 BMG matrix, and found a dramatic increase in plastic strain [10]. They concluded that the plasticity of the glass matrix 1
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composites could be enhanced from several aspects: the propagation of localized shear bands could be suppressed at the amorphous-crystalline interfaces (ACIs); the interface could also serve as trigger sites for multiple shear bands initiation; the dislocation and slip deformation of ductile crystalline phase also contributed to the total plasticity of the composites in a co-deformation process. With aid of sputtering deposition technique, Greer et al. constructed Amorphous-crystalline nanolaminates (ACNLs) by combining nanocrystalline Cu laminates and amorphous metallic laminates. They achieved improved homogeneous plasticity of MG without much loss of strength, and indicated the most coordinated strength and plasticity was size-dependent and the rule-of-mixtures could not describe variation of strength with alternated layer thickness [11]. In fact the existence of same elements in the MG matrix and crystalline phase makes the contribution of ACIs negligible. To find out the interfacial strength of the ACI, Huang fabricated the ACNL pillars with ACI inclined 45°to the pillar axis by focused ion beam machining, and applied a compression load to the pillar to achieve the interfacial shear stress [13]. They found the ACI strength was strong up to 1.3GPa, but still could not suppress the interfacial sliding. The above works, together with other research works have proved ACNL is a promising metallic material with both high strength and good toughness [14]-[15]. Molecular dynamics (MD) methods are developed to offer possibility for the investigation on MGs at atomic level. By simulating the atoms movements and tracking atoms trajectories, MD simulation can calculate the basic thermal information of a MG ensemble, including temperature, potential energy, as well as some derived information such as atomic stress, atomic strain, structure evolution and so on. Thus MD simulation method might be an effective tool to study the ACNL deformation behaviors. With aids of MD simulation method, lots of researchers have been working on revealing the deformation mode transition between amorphous layers and crystalline layers in ACNL, together with the role that ACI played during the deforming process [12], [16]-[18]. Wang et al. suggested ACI as a bond linking the dislocations in crystal and STZs in MG, wherein STZs would be triggered by dislocations when plasticity spread and crossed ACI [12]. Chen et al. put a pure shear deformation MD simulation on an ACNL model to investigate the ACI response under shear deformation. They found the interfacial sliding, together with the micro-sliding bands thickening were important contributors to the plasticity of the material [16]. Tensile simulations on ACNLs taken by Cheng et al. further revealed the bidirectional interaction mechanism between dislocations and STZ plasticity at the ACIs [17]. Besides, Cui found that the Shockley partial dislocation in crystal layer evolved at the ACIs contributed to strain hardening, and the hardening phenomenon was also affected by the crystal layer thickness [18]. Before the application of this promising composite material, it is worth noting that the ACNLs are actually anisotropic in material composition structure and crystalline phase orientation. The plasticity and deforming mechanism have a dependence on the deformation orientation. However, despite that lots of work had been done to investigate the ACNLs deformation behaviors in both experiments and simulations, little work have been done on the anisotropic plasticity of ACNLs. Our research work in this paper mainly investigate deforming mechanisms in two orthogonal deforming directions, and aims to find how dislocations in crystalline phase (C-phase) and STZs in amorphous phase (A-phase) will interact with each other in the two deforming mode, and what roles ACIs will play in the interactions. 2. Simulation methods 2
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MD simulations were performed by using Large-scale atomic/molecular massively parallel simulator (LAMMPS) code [19]. Embedded atom method (EAM) potential developed by Mendelev was employed to characterize the interactions between Cu atoms and Zr atoms in the whole sample [20]. The simulated ACNL structures are composed of amorphous layers (A-layers) and crystalline layers (C-layers). A cubic amorphous matrix was firstly constructed as Cu50Zr50 alloy. It was melted at 2500 K and equated for 1 ns with NPT ensemble, and then quenched to 100 K at cooling rate of 0.5 K/ps. The obtained amorphous cubic was replicated to a large matrix with three dimensions of 13.2 nm. The Cu crystalline layer with different thickness tc range from 2.64 nm to 10.56 nm was inserted into the middle of amorphous matrix, with crystalline layer ratio tc/d range from 0.2 to 0.8, and the ACIs are parallel to xz plane. Since this paper focuses on the material composition structure factors, the disturbance term crystalline orientation should be avoid, thus we chose the crystallographic orientations of Cu crystal set as [1 0 0] along x-axis, [0 1 0] along y-axis and [0 0 1] along z-axis. To get a more reasonable ACI structure, the constructed ACNLs were annealed at 900 K for 1 ns and then cooled down to 100 K at a cooling rate of 0.5 K/ps with NPT ensemble. C-layers in the annealed sample were found to be single crystalline with nor line defects either surface defects inside, but only a few point defects, which can be hardly eliminated for the reason of non-zero temperature. Shear process are taken on the ACNL samples with periodic boundary condition applied in all directions. To investigate the anisotropic plasticity and deforming mechanism in different deformation modes, two orthogonal deforming directions are chosen, that the parallel deforming direction, which is along xz direction with non-deformed dimension along y-axis, named as P-direction as convenience; the serial deforming direction which is along xy direction with non-deformed dimension along z-axis, named as S-direction as convenience. The two shear models are present in Figure 1. The applied shear strain rate is 7.5×108/s, and the maximum strain is 0.23. The structural analysis during the whole simulation processing was performed with the open source OVITO software [21].
Figure 1 The shear directions in two deformation modes: (a) P-direction; (b) S-direction
3. Results and discussions 3.1 ACI structure During the annealing process, the atoms in A-layer and C-layer moved across the boundary driven by inter-diffusion, and then the layers diffused into each other and formed a special interface with several atoms thickness [22]. The regular ordered atomic structure in C- layer would gradually turn into less ordered structure, and finally became totally disordered ones when crossed the interface, thus we defined the intermediate structure as ACI of A-layer and C-layer. The structures in the two layers have great differences in atom compositions, potential energy and central symmetry, the parameters of ACI will lay on the transition state between the layers [22], 3
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thus we will discuss the structure of ACI from the above three aspects. Take the sample with tc/d of 0.5 as example. To determine the thickness of ACI layer, the whole sample was divided into slices along y-axis, and every slice is 0.06 nm. Figure 2 shows the average statistic atomic masses, potential energies and centrosymmetry parameters of the slices perpendicular to y-axis, wherein, all three parameters are found differing greatly in A-layer and C-layer, and the parameters have gradually transition between the two layers. Thus the transition layer with thickness of 0.6 nm was determined belong to ACI. The ACIs thicknesses in other samples with tc/d range from 0.2 to 0.8 were measured, and were found do not range much.
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Figure 2 The average atomic mass, potential energy and centrosymmetry parameter of every slice along y-axis In fact, the atoms in MGs are not totally disorderly distributed. They have locally specific topological structure in range of less than 1 nm, which is usually regarded as short range order (SRO) structure [24]. The SRO structures are regarded as clusters formed by some topologically related atoms. The Voronoi indices < i3,i4,i5,i6 > are usually used to describe the Voronoi polyhedral types, where ij represents the number of j-edge polygon in the polyhedral [25]. The center atoms with Voronoi indices <0,0,12,0>, together with their nearest-neighbor atoms, construct clusters with topological five-fold symmetry structure, are regarded as stable and solid-like SRO motif in the MGs, which is named as full icosahedra (FI) . The FIs in our MG model are extracted and the distribution along y-axis is shown in Figure 3. From the figure, it is found that the FI fraction in the A-layers has a variation around the original fraction in MG matrix, but it gradually descends when got close to the ACI. As the previous work indicated that the lack of FI structures meant poor resistance to shear stress during deformation [25] [26]. The descent part is regarded as the influenced area by the interface, and each layer is nearly 1nm thickness, which is thicker than expected in Figure 2.
Figure 3 the FI fraction of every slice along y-axis 4
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wherein, GP0 and GS0 represent the shear moduli along P-direction and S-direction respectively; tc and ta are the thicknesses of each C-layer and A-layer respectively; Gc is the shear modulus of crystalline copper along [001] direction, and Ga is the shear modulus of MG matrix. We obtained Gc and Ga by applying shear deformation on bulk monocrystalline copper and bulk CuZr MG at temperature of 100K, and the results were Gc=77.83 GPa and Ga=23.88 GPa, which fitted the previous work well [18],[26][27]. When tc/d=0.5, GP0 and GS0 can be obtained as GP0=50.86 GPa and GS0=36.55 GPa, theoretically. Figure 4 shows the stress-strain curves of ACNL-0.5 obtained from simulation at temperature of 100K. From the figure, the shear moduli can be obtained by fitting the elastic part using the offset criterion being 0.2%. The results show that the shear modulus along P-direction GP is 60.86 GPa, and that along S-direction GS is 36.82 GPa. The obtained GP is larger than theoretical prediction GP0; while GS is very close to GS0. Furthermore, the two curves have great disparities in the trend and shape with strain increasing. The strain-stress curve along P-direction has a clear and long elastic part and a sharp peak without plateau at strain of 0.09, and then turns into an abrupt stress drop till the stress falls to almost half of peak value. With the strain increasing, the stress has a phenomenon of recovery: at strain of 0.12, the stress rise again and reach a second stress peak; and it has another rising at strain of 0.2. For the strain-stress curve along S-direction, it has a relative blurry and short elastic part before the yield point, indicated plastic deformation began before the stress reaching the maximum at strain of 0.075. Subsequently, the stress has a relative smooth drop and becomes stable around 1.3 GPa with strain increasing. The disparities of two curves indicate different deformation mechanisms in the two modes, and the divergences of the shear moduli compared with theoretical ones also indicated that ACI might play different roles in the two modes. To further investigate the deformation mechanisms of ACNL-0.5 in the two modes, the Von Mises shear strain ηMises distribution in the whole sample were analyzed along the deformation process. Figure 4 (a)-(h) show the atomic strain distribution in different deforming stage of the two modes. In C-layer, the atoms with little atomic strain (ηMises<0.1) were deleted for the convenience to observe the plastic deforming part, which are composed of Shockley partial slips and full slips. Since the generations of full slips are composed of two partial slips, atoms in full slips would have higher atomic strain than partial slips. The threshold 0.1 is determined by analyze the atomic strain distribution frequency of HCP structures in plastic deformed crystal, and the atoms with atomic strain higher than 0.1 account for over 99%. In the P-direction deformation mode, neither dislocation in C-phase nor strain concentration in A-phase was detected before yielding. Once the deformation process exceeded elastic stage, partial dislocations generated in the 5
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copper layer, accompanied with stacking faults and slips, which formed large area of plastic deforming areas. Meanwhile, strain concentration was still not found in A-phase. With plastic deformation preceding, more slips proliferated in the crystalline region, while large shear strain area generated in the glass region and gradually gathered to form a localized shear transition area as a SB embryo. However, throughout the whole deformation process, no obvious SB formation was found in the glass region, which means dislocations and slips in C-phase dominated the plastic deformation of the ACNL in P-direction. In the S-direction deformation mode, no plastic deformation was found in C-phase all through the deforming process. Instead, the A-phase experienced sustained plastic deformation after yielding, and finally a highly localized area appeared near the ACI in the upper glass region. This indicates shear flow in glass dominated the plastic deformation of the ACNL in S-direction.
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Figure 4 the strain-stress curves of ACNL-0.5 along P-direction and S-direction, together with the atomic strain distribution in different deforming stage of the two modes. To analyze the participations of each layer on the plasticity of ACNL, the number of atoms with large shear strain was extracted during deforming process, the irreversible plasticity threshold in C-phase was determined as 0.1, while the one of A-phase was determined as 0.2 [28],[29]. Since Shockley partial dislocations dominated the plasticity of copper crystal, the total length of Shockley partial dislocations was also detected for reference. Figure 5 shows the dislocations and large strain atoms numbers variations in P-direction deforming mode, both C-phase and A-phase participated in the plasticity. The number of large strain atoms Nlsa in A-phase has relative steady increase and shows no sudden changes. While Nlsa in C-phase has a rapid growth at the beginning of plastic stage, and then reaches a relative slow growth stage, where two plateaus are found corresponding to the recovery stages in the stress-strain curve, meaning that no more slips generated during the recovery. In the corresponding stage, Shockley partial dislocation has a sudden drop at the beginning of recovery, and then keeps almost steady. It can be inferred that the 6
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recovery phenomenon has a relationship with structural evolution of C-phase. After the yielding of ACNL, the dislocations in C-phase begins to expand and proliferate, induces explosive growth of large strain atoms. When the dislocations glides near ACIs, some of them dissipates through ACIs, the C-phase reaches a temporary steady state similar with the initial elastic state, no more slips generate and the dislocations can only glide or dissipate under the applied shear pressure. Figure 6 shows the participants of each phase in plasticity of ACNL in S-direction. Only Nlsa in A-phase is shown, because no plastic deformation exists in C-phase during the whole deforming process, which means all the plasticity is resulted from A-phase plastic deformation. During the shear process in S-direction, the total deformation is a collaborative process of all layers enrolled, instead of uniform deformation of each layer. In addition, the shear direction is parallel to the layers interface, thus there exists a competition between the two phases. As we mentioned above, the defect free copper crystal has shear modulus of 77.83 GPa, which is much higher than that of MG. The disparity of shear modulus and strength between the two phases resulted that C-phase stayed an elastic state throughout the process, even when the glass entered plastic stage. The yielding strength of ACNL in S-direction is in fact decided by ACI cohesion and glass strength. Thus it is found that the maximum shear stress of ACNL in S-direction is much lower than that in P-direction. When it comes to the variation of Nlsa in A-phase, it is found that Nlsa has a very slow growth in the yielding stage. But when strain passed the maximum stress point, the growth speeded up till the stress drop to a lower state. In this period, we found the shear strain distribution became localized at the part near ACI, which would develop as the initialization of SB in Figure 4(h).
Figure 5 Shockley partial dislocations and large strain atoms statistics in C-phase and A-phase in the P-direction deforming mode
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Figure 6 Large strain atoms statistics in A-phase in the S-direction deforming mode 3.3 Roles of ACI in the two deformation modes To investigate the effects of ACIs during shear deformation process of ACNL, the ACNL sample was divided into slices along y-axis, and the atomic shear strain of every slice was calculated by average the atomic values in the slice. For the P-direction deformation mode, Figure 7 shows the averaged atomic shear strain ηave distributions in shear strain γ range from 0 to 0.1067. It is found that ηave in each slice has been increasing linearly in the elastic stage (γ<0.09), and it is higher in A-phase than that in C-phase, while the value of ηave in ACI is between the two and gradually decreases from glass side to crystal side. Once γ exceeds elastic range, ηave in C-phase has an abrupt increase and shows sharp fluctuations along y-axis. Meanwhile, it is observed that ηave in ACI exceeds other parts and small peaks appear. With the proceeding of shearing, ηave in the whole sample shows a leaping increasing, especially that the ACI suppressed the others by a large margin. This phenomenon interested us to analyze the atomic shear strain distribution in ACI layer, and thus we intercepted several sections in the ACI region to find out how the large strain atoms distributed in the layers. The range of ACI has been determined as -37 Å to -27 Å along y-axis according to Part 3.1. The sections (section I, II, III, IV) with y coordinate of -38 Å, -34 Å, -30 Å and -27 Å are selected, and the atomic strain snapshots of every section at γ=0.1067 are shown in Figure 8. Wherein, lines appears in section IV, which indicates the plasticity in crystal was resulted from slips; near the crystal part, strain concentration gradually becomes blurry at the corresponding positions, and in other area the shear strain has a general increasing; the strain localization lines gradually vanish with y coordinate decreases, and finally become localized sites with a few atoms, which would grow to a STZ with proceeding of shearing. The ACI is clearly responsible for mediating the shear banding in glass and slipping in crystal. In this deformation mode, the plasticity of ACNL can be described as a crystal to glass process as following. Shear stress concentrated on the uneven crystal boundary in ACI, which contributed to the breeding of dislocations in crystal, then the dislocations embryos quickly spread over the whole crystal and formed slipping lines in crystal. The slipping lines affected the localization of shear strains in ACI conversely, and finally when it came to the glass, STZ sites were activated by the large shear strain localizations in ACIs. 8
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Figure 7 The averaged atomic shear strain ηave distributions during P-direction deforming process
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Figure 8 The atomic strain snapshots in sections with y coordinate of -38 Å, -34 Å, -30 Å and -27 Å at γ=0.1067 For the S-direction deformation mode, Figure 9(a) shows the averaged atomic shear strain ηave distributions along y-axis (0<γ<0.0916). It is found that ηave in C-phase has no change with increasing of shear strain. The variations mainly happened in A-phase. Within the elastic range (γ<0.05), ηave increased at an almost linear speed. When it entered the yielding stage, ηave in glass firstly had a general increasing, and then localized to two peaks after the shear stress reaching maximum. In the following deforming process, peak I at y coordinate of 38Å grew into a shear band embryo in Figure 4(h). Although the shear banding site was very close to ACI, but since the localization only happened at one ACI, it cannot be deduced that ACIs are the weakness of the ACNL. In fact, the generation and deformation of ACNL was repeated three individual times in our simulations to exclude the inaccurate result induced by accidental factors. Three pictures in Figure 9(b) indicate that shear banding might happen at any position with enough collection of STZs. In contrast to Chen’s found [16], our results indicate the ACIs are strong interphase bonding C-phase and A-phase. Thus in the S-direction deformation mode, the plasticity of ACNL can be attributed by the generation and localization of STZs in glass. After the generation of an embryonic shear band, it needs enough space for its propagation and aging [30]. Thus the thickness of A-layer is important for totally formation of a mature shear band. We will discuss the effects of A-layer thickness on the formation of shear bands in Part 3.4.
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Figure 9 (a)The averaged atomic shear strain ηave distributions during S-direction deforming process; (b) the shear strain distributions of three individual samples at γ=0.1067; (c) the averaged atomic shear strain ηave distributions of three samples at γ=0.1067. When it comes to the diversities in the two deformation modes, it can be concluded that the origins of plasticity in ACIs would always find an easier way out. In S-direction, the shear direction was parallel to ACIs, and there was enough space for generation of a shear band, the residual strain relieved into the glass, offered opportunity for the gathering of STZs and relieving of elastic energies. The dislocations would never be triggered without enough energy collection near the crystal boundary. In P-direction, the individual formation of shear banding in glass cannot happen without crossing C-phase, thus energies at ACI kept accommodating when it was enough for triggering of dislocations in crystal [12]. And then with relieving of energies into crystal, there was not enough energy left to drive the generation and gathering of STZs, thus it became much difficult for the formation of shear bands in glass.
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3.4 Influence of crystalline layer ratio The thickness of C-layer was regarded have size effect on deformation modes and mechanical properties of ACNLs [31], thus we here presented several ACNLs with different C-layer thickness ratio range from 0.2 to 0.8. Figure 10 presents the stress-strain curves of all ACNLs in both P-direction and S-direction deforming modes. With increasing of C-layer thickness ratio, the shear moduli (curve slope in elastic stage) have an obvious increasing in both modes, indicating that ACNL has a higher shear modulus with larger ratio of C-phase generally. From Figure 10(a), it can be seen that the shear strength τmax had an increasing with thicker C-layer participated in ACNL. In the P-direction mode, the yielding of ACNL is mainly decided by C-phase, larger C-layer thickness would induce a larger τmax generally. We also noticed that not all the curves have the recovery phenomenon in plastic stage. For ACNL-0.2 (with C-layer thickness ratio of 0.2), the stress-strain curve shows a relative flat stage without obvious linearly recovery in its plastic segment. In this ACNL, the C-layer thickness was set as 2.6 nm initially. However, after the annealing treatment, the formation of ACI interphase invaded the crystal thickness about 1.3 nm, so the actual crystal thickness decreased to 1.3 nm. According the researching work by Cui et al. [18], Shockley partial dislocations needed space to dissipate into ACIs, when the thickness of crystal was less than the least width of dislocation, Shockley partial dislocations would stay and glide in crystal. As we mentioned in 3.2, the partial dislocation dissipation contributed to the recovery of shear stress. Without dissipation of dislocations in ACNL-0.2, the shear stress stayed a stable status since the plasticity began. Figure 10(b) demonstrated the stress-strain curves in S-direction mode. Similarly, all the curves showed relative smooth drops after yielding and stable stress in the plastic stage, indicating 10
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that the A-phase dominated plasticity in all ACNLs. With increasing of C-layer thickness ratio, the elastic stage showed a decreasing trend, together with a slight increasing of shear strength. Since C-phase did not participate in the plastic behavior, it will be seen that this tendency is related to thickness of A-layer, which means that thinner A-layer induced higher shear stress. Enough thickness is necessary for the generation of a shear band in A-layer. In an ACNL without sufficient A-layer thickness, there would be viscous and homogeneous flow instead of gathering of STZs [15]. We extracted the atomic shear strain distributions of A-phase atoms at a plastic strain of 0.2, which are shown in Figure 10(c). Meanwhile, to evaluate the localization degree of A-phase atoms, a localization parameter should be employed to verify formation of shear bands. A widely used localization parameter was defined as mean square error of atomic shear strains [26],[32],[33]. Considering A-layers might have different plastic deforming degree in different ACNLs, the global average atomic strain is evolved as a divisor to normalize the above localization parameter, thus:
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is the average atomic shear strain of all atoms in A-phase, N represents number Wherein, " #!# ! of atoms in A-phase, ψ indicates the deviation of atomic strain distribution from homogenous behavior. Larger ψ indicates more localized deformation behavior. The results for all ACNLs are shown in Figure 10(d). For ACNL-0.2, the atomic strain distribution curve and localization parameter is very close to that of glass, thus shear banding dominated in A-phase. With deceasing of A-phase layer thickness, there is a gradually transition from typical partial distribution to normal distribution in the atomic strain distribution curves, and the localization parameters also decreased. This trend indicates there is a gradually transition from highly localized shear banding to homogeneous flow with decreasing of glass thickness. In ACNL-0.7 and ACNL-0.8, without aggregation of these SRO weakness sites, the shear band propagation would be suppressed and the glass layer was more resistant to shear stress and induced higher strength. For the other ACNLs with thicker A-layer, the increasing of yield stress could be explained as the length-scale effect [34]. The decreasing of glass thickness induced increasing of viscosity of the shear band [15]. It would be more difficult for the aggregation of STZs and propagation of shear bands because of more viscous atoms flow.
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Figure 10 The stress-strain curves of ACNLs in (a) P-direction and (b) S-direction deforming modes; (c) the atomic shear strain distributions of atoms in A-phase at strain of 0.2; (d) localization parameters of ACNLs at strain of 0.2. The shear moduli of all ACNLs were extracted from the elastic deformation stage in both deformation modes, and the results were shown in Figure 11. The predicted shear modulus of every sample calculated by Eq. (1-2) were also presented for reference. It is found that all the shear moduli in S-direction fitted the predicted well, while the simulated shear moduli in P-direction were higher than predicted generally. To find out the factors that result this divergence, local shear modulus distributions were calculated with the stress tensor and strain tensor of every atom in the sample. The stress tensor for per-atoms was calculated with a virial theorem contributed by Thompson [35]. Since the virial stress obtained from LAMMPS was a stress*volume value, we calculated the true virial stress tensor by a divisor atomic volume obtained from Voronoi method. While the Green-Lagrangian strain tensor was obtained from, (4)
Thus the per-atom values of shear modulus were obtained through corresponding component of stress tensor and strain tensor in the P-direction. The averaged shear modulus was captured by the slicing method as described in 3.1. And the averaged local shear modulus Gave distributions along y-axis of all ACNLs at deformation strain of 0.03 were presented in Figure 12. It is found that Gave in C-phase was much higher than that obtained through a bulk single copper crystal shear simulation, and there was a general trend that the shear modulus of crystal increased with decreasing of crystal layer, expect for tc/d=0.2 (such a thin crystal layer cannot keep non-dislocation state during annealing and relaxing process). A recent work taken by Rohith et al. presented size effect of single copper crystal through MD tensile simulation [36]. They found that the Young’s modulus of <1 0 0> copper were greatly related to the cross-section width, that with increasing cross-section area, the Young’s modulus would decrease linearly, while it was not sensitive to the sample length. According to Rohith’s work, it can be deduced that size effect also 12
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exists in the shear deforming processes. Size effect on shear modulus explained the exceeding value than expected in Figure 11, and also revealed ACIs affected the elastic mechanical responses of ACNLs in an indirect way.
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Figure 11 The predicted and simulated shear moduli of ACNLs
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Figure 12 The averaged local shear modulus distributions along y-axis of the ACNLs at deformation strain of 0.03. 4. Conclusions In summary, the mechanical anisotropies of the ACNLs with different crystalline thickness ratios in parallel and serial deforming modes were investigated by conducting shear simulations. The differences of two deforming modes were reflected in yielding behaviors, the participations of two phases in plastic deformation, and the roles that ACIs played in the interaction of two phases. Some conclusions are drawn as following: (1) In parallel deforming mode, the yielding of ACNL was mainly triggered by generation of dislocations and slips in C-phase, and in the subsequent plastic deforming, both shear banding in A-phase and dislocations in C-phase contributed to the plasticity of materials. (2) In serial deforming mode, only A-phase participated in the yielding and plastic deforming of ACNL, the stress localization at ACIs released to the glass side and could not provide enough stress to trigger the dislocations. (3) ACIs served as stress resistance weakness and dislocations breeding cradle in the parallel deforming mode while a strong connection of two phases in the serial deforming mode. (4) With the increasing of C-layer ratio, shear moduli and maximum stress in two deformation modes both increased. The variation of shear moduli in serial deformation mode obeyed the rule-of-mixture and fitted the prediction well, while the shear moduli in parallel deformation modes had large excess compared with predicted ones, which mostly is attributed to the size effect of crystalline layer. 13
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There are other factors might affect the mechanical anisotropies of composites, including crystalline orientations, defects in crystalline layers (voids, dislocations, stacking faults and grain boundaries etc.), temperatures, deforming rates and so on, and they are the focus in our future researching. Acknowledge The authors would like to thank the High Performance Computing Center of Jilin University for access to the computing systems. This work was supported by the National Key R&D Program of China (Grant No. 2018YFF01012400), National Science and Technology Innovation Leading Academic (Ten Thousand Talent Program), Fund Guiding on Strategic Adjustment of Jilin Provincial Economic Structure Project (Grant No. 2014Z045), Major project of Jilin Province Science and Technology development plan (Grant No. 20150203014GX), Science and Technology Development Program of Jilin province (Grant No. 20180520072JH), the special fund project of Jilin provincial industrial innovation (Grant No. 2016C030), Jilin Provincial Middle and Young Scientific and Technological Innovation Talent and Team Project (Grant No. 20170519001JH), Project supported by Interdisciplinary Research Fund of Jilin University (Grant No. 10183201822), and Project (Grant No. 2017141) supported by Graduate Innovation Fund of Jilin University, . References [1] C.A. Schuh, T.C. Hufnagel, U. Ramamurty, Mechanical behavior of amorphous alloys, Acta Mater. 55 (2007) 4067-4109. [2] M. Chen, Mechanical Behavior of Metallic Glasses: Microscopic Understanding of Strength and Ductility, Annu. Rev. Mater. Res. 38 (2008) 445-469. [3] M.M. Trexler, N.N. Thadhani, Mechanical properties of bulk metallic glasses, Prog. Mater. Sci. 55 (2010) 759-839. [4] A.L. Greer, Y.Q. Cheng, E. Ma, Shear bands in metallic glasses, Mater. Sci. Eng. R Reports. 74 (2013) 71-132. [5] M.L. Falk, J.S. Langer, Deformation and failure of amorphous, solidlike materials, Annu. Rev. Conden. Ma. P. 2(1) (2010) 353-373. [6] B.A. Sun, W.H. Wang, The fracture of bulk metallic glasses, Prog. Mater. Sci. 74 (2015) 211-307. [7] E. Ma, J. Ding, Tailoring structural inhomogeneities in metallic glasses to enable tensile ductility at room temperature, Mater. Today. 19(10) (2016). [8] N. Wang, J. Ding, F. Yan, M. Asta, R.O. Ritchie, L. Li, Spatial correlation of elastic heterogeneity tunes the deformation behavior of metallic glasses, Npj Comput. Mater. 4(1) (2018) 19. [9] Y. Shi, J. Luo, F. Yuan, L. Huang, Intrinsic ductility of glassy solids, J. Appl. Phys. 115(4) (2014) 043528. [10] C.C. Hays, C.P. Kim, W.L. Johnson, Microstructure controlled shear band pattern formation and enhanced plasticity of bulk metallic glasses containing in situ formed ductile phase dendrite dispersions, Phys. Rev. Lett. 84 (2000) 2901. [11] J.Y. Kim, D. Jang, J.R. Greer, Nanolaminates utilizing size-dependent homogeneous plasticity of metallic glasses, Adv. Funct. Mater. 21 (2011) 4550-4554. [12] Y. Wang, J. Li, A. V. Hamza, T.W. Barbee, Ductile crystalline-amorphous nanolaminates, Proc. Natl. Acad. Sci. 104 (2007) 11155. [13] M.C. Liu, J.C. Huang, Y.T. Fong, S.P. Ju, X.H. Du, H.J. Pei, T.G. Nieh, Assessing the 14
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The anisotropies of ACNL were reflected in yielding and plasticity behaviors; ACI served as structural weakness and dislocations breeding cradle in P-direction; ACI served as strong connection of two phases in S-direction; The increase of tc/d would improve the ACNL shear moduli in both directions; C-layer thickness has size effect on the ACNL shear modulus in P-direction.
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DOI:
https://doi.org/10.1016/j.jallcom.2019.02.162
Reference:
JALCOM 49594
To appear in:
Journal of Alloys and Compounds
Received Date: 10 November 2018 Revised Date:
29 January 2019
Accepted Date: 12 February 2019
Please cite this article as: D. Zhao, S. Wang, B. Zhu, L. Li, H. Zhao, Anisotropic deformation behaviors of amorphous-crystalline nanolaminates investigated via molecular dynamics simulations, Journal of Alloys and Compounds (2019), doi: https://doi.org/10.1016/j.jallcom.2019.02.162. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Anisotropic Deformation Behaviors of Amorphous-Crystalline Nanolaminates Investigated via Molecular Dynamics Simulations Dan Zhao, Shunbo Wang, Bo Zhu, Lijia Li, Hongwei Zhao* School of Mechanical and Aerospace Engineering, Jilin University, Changchun, Jilin 130022, China *Corresponding author. E-mail address: [email protected] (H. Zhao).
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Abstract: Amorphous-crystalline nanolaminates (ACNLs) composed of CuZr metallic glass layers and single crystal copper layers were constructed, and the anisotropy of the material deformation behaviors were investigated by conducting shear loadings on the ACNL sample in parallel deforming and serial deforming directions using molecular dynamics method. In parallel deforming mode, the yielding of the material was mainly triggered by generation of dislocations and slips in crystalline layer, and both crystalline and amorphous phases participated in the subsequent plastic deforming. In serial deforming mode, the results showed that the yielding and plastic deforming of the material was induced by shear localization of amorphous layers only. Amorphous-crystalline interfaces (ACIs) served as stress resistance weakness and dislocations breeding cradle in the former deforming mode while a strong connection of two phases in the later deforming mode. Furthermore, the increasing of crystalline layer thickness would promote the material shear modulus and shear strength in both deformation modes. The promotions and incentives varied and had dependence on the coupled deforming mechanisms. For the serial deforming mode, the shear moduli obtained from our simulations fitted the predicted ones from rule-of-mixture very well, while in the parallel deforming mode, the simulated shear moduli were much higher than predicted ones, which could be explained with the size effect induced by reduction of crystalline layer thickness surround with ACIs. Keywords: Amorphous-crystalline interfaces; Molecular dynamics simulation; Anisotropic deformation behaviors; Nanolaminates
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1. Introduction Metallic glasses (MGs) are well known for their excellent mechanical properties, e.g. high strength, high elastic modulus and high hardness [1], yet limited by the shear banding deformation mode, they are easily encountered with catastrophically failure. In a brittle MG, the generation of one major shear band usually localizes and induces uneven deformation, and finally develops as local fracture, which is responsible for the failure of brittle MGs [4]-[6]. This brittle deformation mechanism hinders the application of MGs in micro mechanical systems, thus should be avoid when employed as structural materials. Since the success in preparing bulk metallic glasses (BMGs), lots of researchers have been working on improving the fracture ductility of BMGs, and several methods have been developed to improve the plasticity of MGs by preventing localized shear bands formation. One method is tuning the heterogeneity of microstructure in the MG by controlling the component and preparation process, basing on the intrinsic heterogeneity of MGs [7]-[9]. Another effective method is introducing a second phase into the glass matrix with in-situ formation method or ex-situ assembling method either, usually ductile crystal phase. Lots of experimental works showed improvement of plasticity induced by the introduced second phase in the MG [10]-[12]. Hays et al. introduced ductile crystalline phase into V1 BMG matrix, and found a dramatic increase in plastic strain [10]. They concluded that the plasticity of the glass matrix 1
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composites could be enhanced from several aspects: the propagation of localized shear bands could be suppressed at the amorphous-crystalline interfaces (ACIs); the interface could also serve as trigger sites for multiple shear bands initiation; the dislocation and slip deformation of ductile crystalline phase also contributed to the total plasticity of the composites in a co-deformation process. With aid of sputtering deposition technique, Greer et al. constructed Amorphous-crystalline nanolaminates (ACNLs) by combining nanocrystalline Cu laminates and amorphous metallic laminates. They achieved improved homogeneous plasticity of MG without much loss of strength, and indicated the most coordinated strength and plasticity was size-dependent and the rule-of-mixtures could not describe variation of strength with alternated layer thickness [11]. In fact the existence of same elements in the MG matrix and crystalline phase makes the contribution of ACIs negligible. To find out the interfacial strength of the ACI, Huang fabricated the ACNL pillars with ACI inclined 45°to the pillar axis by focused ion beam machining, and applied a compression load to the pillar to achieve the interfacial shear stress [13]. They found the ACI strength was strong up to 1.3GPa, but still could not suppress the interfacial sliding. The above works, together with other research works have proved ACNL is a promising metallic material with both high strength and good toughness [14]-[15]. Molecular dynamics (MD) methods are developed to offer possibility for the investigation on MGs at atomic level. By simulating the atoms movements and tracking atoms trajectories, MD simulation can calculate the basic thermal information of a MG ensemble, including temperature, potential energy, as well as some derived information such as atomic stress, atomic strain, structure evolution and so on. Thus MD simulation method might be an effective tool to study the ACNL deformation behaviors. With aids of MD simulation method, lots of researchers have been working on revealing the deformation mode transition between amorphous layers and crystalline layers in ACNL, together with the role that ACI played during the deforming process [12], [16]-[18]. Wang et al. suggested ACI as a bond linking the dislocations in crystal and STZs in MG, wherein STZs would be triggered by dislocations when plasticity spread and crossed ACI [12]. Chen et al. put a pure shear deformation MD simulation on an ACNL model to investigate the ACI response under shear deformation. They found the interfacial sliding, together with the micro-sliding bands thickening were important contributors to the plasticity of the material [16]. Tensile simulations on ACNLs taken by Cheng et al. further revealed the bidirectional interaction mechanism between dislocations and STZ plasticity at the ACIs [17]. Besides, Cui found that the Shockley partial dislocation in crystal layer evolved at the ACIs contributed to strain hardening, and the hardening phenomenon was also affected by the crystal layer thickness [18]. Before the application of this promising composite material, it is worth noting that the ACNLs are actually anisotropic in material composition structure and crystalline phase orientation. The plasticity and deforming mechanism have a dependence on the deformation orientation. However, despite that lots of work had been done to investigate the ACNLs deformation behaviors in both experiments and simulations, little work have been done on the anisotropic plasticity of ACNLs. Our research work in this paper mainly investigate deforming mechanisms in two orthogonal deforming directions, and aims to find how dislocations in crystalline phase (C-phase) and STZs in amorphous phase (A-phase) will interact with each other in the two deforming mode, and what roles ACIs will play in the interactions. 2. Simulation methods 2
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MD simulations were performed by using Large-scale atomic/molecular massively parallel simulator (LAMMPS) code [19]. Embedded atom method (EAM) potential developed by Mendelev was employed to characterize the interactions between Cu atoms and Zr atoms in the whole sample [20]. The simulated ACNL structures are composed of amorphous layers (A-layers) and crystalline layers (C-layers). A cubic amorphous matrix was firstly constructed as Cu50Zr50 alloy. It was melted at 2500 K and equated for 1 ns with NPT ensemble, and then quenched to 100 K at cooling rate of 0.5 K/ps. The obtained amorphous cubic was replicated to a large matrix with three dimensions of 13.2 nm. The Cu crystalline layer with different thickness tc range from 2.64 nm to 10.56 nm was inserted into the middle of amorphous matrix, with crystalline layer ratio tc/d range from 0.2 to 0.8, and the ACIs are parallel to xz plane. Since this paper focuses on the material composition structure factors, the disturbance term crystalline orientation should be avoid, thus we chose the crystallographic orientations of Cu crystal set as [1 0 0] along x-axis, [0 1 0] along y-axis and [0 0 1] along z-axis. To get a more reasonable ACI structure, the constructed ACNLs were annealed at 900 K for 1 ns and then cooled down to 100 K at a cooling rate of 0.5 K/ps with NPT ensemble. C-layers in the annealed sample were found to be single crystalline with nor line defects either surface defects inside, but only a few point defects, which can be hardly eliminated for the reason of non-zero temperature. Shear process are taken on the ACNL samples with periodic boundary condition applied in all directions. To investigate the anisotropic plasticity and deforming mechanism in different deformation modes, two orthogonal deforming directions are chosen, that the parallel deforming direction, which is along xz direction with non-deformed dimension along y-axis, named as P-direction as convenience; the serial deforming direction which is along xy direction with non-deformed dimension along z-axis, named as S-direction as convenience. The two shear models are present in Figure 1. The applied shear strain rate is 7.5×108/s, and the maximum strain is 0.23. The structural analysis during the whole simulation processing was performed with the open source OVITO software [21].
Figure 1 The shear directions in two deformation modes: (a) P-direction; (b) S-direction
3. Results and discussions 3.1 ACI structure During the annealing process, the atoms in A-layer and C-layer moved across the boundary driven by inter-diffusion, and then the layers diffused into each other and formed a special interface with several atoms thickness [22]. The regular ordered atomic structure in C- layer would gradually turn into less ordered structure, and finally became totally disordered ones when crossed the interface, thus we defined the intermediate structure as ACI of A-layer and C-layer. The structures in the two layers have great differences in atom compositions, potential energy and central symmetry, the parameters of ACI will lay on the transition state between the layers [22], 3
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thus we will discuss the structure of ACI from the above three aspects. Take the sample with tc/d of 0.5 as example. To determine the thickness of ACI layer, the whole sample was divided into slices along y-axis, and every slice is 0.06 nm. Figure 2 shows the average statistic atomic masses, potential energies and centrosymmetry parameters of the slices perpendicular to y-axis, wherein, all three parameters are found differing greatly in A-layer and C-layer, and the parameters have gradually transition between the two layers. Thus the transition layer with thickness of 0.6 nm was determined belong to ACI. The ACIs thicknesses in other samples with tc/d range from 0.2 to 0.8 were measured, and were found do not range much.
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Figure 2 The average atomic mass, potential energy and centrosymmetry parameter of every slice along y-axis In fact, the atoms in MGs are not totally disorderly distributed. They have locally specific topological structure in range of less than 1 nm, which is usually regarded as short range order (SRO) structure [24]. The SRO structures are regarded as clusters formed by some topologically related atoms. The Voronoi indices < i3,i4,i5,i6 > are usually used to describe the Voronoi polyhedral types, where ij represents the number of j-edge polygon in the polyhedral [25]. The center atoms with Voronoi indices <0,0,12,0>, together with their nearest-neighbor atoms, construct clusters with topological five-fold symmetry structure, are regarded as stable and solid-like SRO motif in the MGs, which is named as full icosahedra (FI) . The FIs in our MG model are extracted and the distribution along y-axis is shown in Figure 3. From the figure, it is found that the FI fraction in the A-layers has a variation around the original fraction in MG matrix, but it gradually descends when got close to the ACI. As the previous work indicated that the lack of FI structures meant poor resistance to shear stress during deformation [25] [26]. The descent part is regarded as the influenced area by the interface, and each layer is nearly 1nm thickness, which is thicker than expected in Figure 2.
Figure 3 the FI fraction of every slice along y-axis 4
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wherein, GP0 and GS0 represent the shear moduli along P-direction and S-direction respectively; tc and ta are the thicknesses of each C-layer and A-layer respectively; Gc is the shear modulus of crystalline copper along [001] direction, and Ga is the shear modulus of MG matrix. We obtained Gc and Ga by applying shear deformation on bulk monocrystalline copper and bulk CuZr MG at temperature of 100K, and the results were Gc=77.83 GPa and Ga=23.88 GPa, which fitted the previous work well [18],[26][27]. When tc/d=0.5, GP0 and GS0 can be obtained as GP0=50.86 GPa and GS0=36.55 GPa, theoretically. Figure 4 shows the stress-strain curves of ACNL-0.5 obtained from simulation at temperature of 100K. From the figure, the shear moduli can be obtained by fitting the elastic part using the offset criterion being 0.2%. The results show that the shear modulus along P-direction GP is 60.86 GPa, and that along S-direction GS is 36.82 GPa. The obtained GP is larger than theoretical prediction GP0; while GS is very close to GS0. Furthermore, the two curves have great disparities in the trend and shape with strain increasing. The strain-stress curve along P-direction has a clear and long elastic part and a sharp peak without plateau at strain of 0.09, and then turns into an abrupt stress drop till the stress falls to almost half of peak value. With the strain increasing, the stress has a phenomenon of recovery: at strain of 0.12, the stress rise again and reach a second stress peak; and it has another rising at strain of 0.2. For the strain-stress curve along S-direction, it has a relative blurry and short elastic part before the yield point, indicated plastic deformation began before the stress reaching the maximum at strain of 0.075. Subsequently, the stress has a relative smooth drop and becomes stable around 1.3 GPa with strain increasing. The disparities of two curves indicate different deformation mechanisms in the two modes, and the divergences of the shear moduli compared with theoretical ones also indicated that ACI might play different roles in the two modes. To further investigate the deformation mechanisms of ACNL-0.5 in the two modes, the Von Mises shear strain ηMises distribution in the whole sample were analyzed along the deformation process. Figure 4 (a)-(h) show the atomic strain distribution in different deforming stage of the two modes. In C-layer, the atoms with little atomic strain (ηMises<0.1) were deleted for the convenience to observe the plastic deforming part, which are composed of Shockley partial slips and full slips. Since the generations of full slips are composed of two partial slips, atoms in full slips would have higher atomic strain than partial slips. The threshold 0.1 is determined by analyze the atomic strain distribution frequency of HCP structures in plastic deformed crystal, and the atoms with atomic strain higher than 0.1 account for over 99%. In the P-direction deformation mode, neither dislocation in C-phase nor strain concentration in A-phase was detected before yielding. Once the deformation process exceeded elastic stage, partial dislocations generated in the 5
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copper layer, accompanied with stacking faults and slips, which formed large area of plastic deforming areas. Meanwhile, strain concentration was still not found in A-phase. With plastic deformation preceding, more slips proliferated in the crystalline region, while large shear strain area generated in the glass region and gradually gathered to form a localized shear transition area as a SB embryo. However, throughout the whole deformation process, no obvious SB formation was found in the glass region, which means dislocations and slips in C-phase dominated the plastic deformation of the ACNL in P-direction. In the S-direction deformation mode, no plastic deformation was found in C-phase all through the deforming process. Instead, the A-phase experienced sustained plastic deformation after yielding, and finally a highly localized area appeared near the ACI in the upper glass region. This indicates shear flow in glass dominated the plastic deformation of the ACNL in S-direction.
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Figure 4 the strain-stress curves of ACNL-0.5 along P-direction and S-direction, together with the atomic strain distribution in different deforming stage of the two modes. To analyze the participations of each layer on the plasticity of ACNL, the number of atoms with large shear strain was extracted during deforming process, the irreversible plasticity threshold in C-phase was determined as 0.1, while the one of A-phase was determined as 0.2 [28],[29]. Since Shockley partial dislocations dominated the plasticity of copper crystal, the total length of Shockley partial dislocations was also detected for reference. Figure 5 shows the dislocations and large strain atoms numbers variations in P-direction deforming mode, both C-phase and A-phase participated in the plasticity. The number of large strain atoms Nlsa in A-phase has relative steady increase and shows no sudden changes. While Nlsa in C-phase has a rapid growth at the beginning of plastic stage, and then reaches a relative slow growth stage, where two plateaus are found corresponding to the recovery stages in the stress-strain curve, meaning that no more slips generated during the recovery. In the corresponding stage, Shockley partial dislocation has a sudden drop at the beginning of recovery, and then keeps almost steady. It can be inferred that the 6
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recovery phenomenon has a relationship with structural evolution of C-phase. After the yielding of ACNL, the dislocations in C-phase begins to expand and proliferate, induces explosive growth of large strain atoms. When the dislocations glides near ACIs, some of them dissipates through ACIs, the C-phase reaches a temporary steady state similar with the initial elastic state, no more slips generate and the dislocations can only glide or dissipate under the applied shear pressure. Figure 6 shows the participants of each phase in plasticity of ACNL in S-direction. Only Nlsa in A-phase is shown, because no plastic deformation exists in C-phase during the whole deforming process, which means all the plasticity is resulted from A-phase plastic deformation. During the shear process in S-direction, the total deformation is a collaborative process of all layers enrolled, instead of uniform deformation of each layer. In addition, the shear direction is parallel to the layers interface, thus there exists a competition between the two phases. As we mentioned above, the defect free copper crystal has shear modulus of 77.83 GPa, which is much higher than that of MG. The disparity of shear modulus and strength between the two phases resulted that C-phase stayed an elastic state throughout the process, even when the glass entered plastic stage. The yielding strength of ACNL in S-direction is in fact decided by ACI cohesion and glass strength. Thus it is found that the maximum shear stress of ACNL in S-direction is much lower than that in P-direction. When it comes to the variation of Nlsa in A-phase, it is found that Nlsa has a very slow growth in the yielding stage. But when strain passed the maximum stress point, the growth speeded up till the stress drop to a lower state. In this period, we found the shear strain distribution became localized at the part near ACI, which would develop as the initialization of SB in Figure 4(h).
Figure 5 Shockley partial dislocations and large strain atoms statistics in C-phase and A-phase in the P-direction deforming mode
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Figure 6 Large strain atoms statistics in A-phase in the S-direction deforming mode 3.3 Roles of ACI in the two deformation modes To investigate the effects of ACIs during shear deformation process of ACNL, the ACNL sample was divided into slices along y-axis, and the atomic shear strain of every slice was calculated by average the atomic values in the slice. For the P-direction deformation mode, Figure 7 shows the averaged atomic shear strain ηave distributions in shear strain γ range from 0 to 0.1067. It is found that ηave in each slice has been increasing linearly in the elastic stage (γ<0.09), and it is higher in A-phase than that in C-phase, while the value of ηave in ACI is between the two and gradually decreases from glass side to crystal side. Once γ exceeds elastic range, ηave in C-phase has an abrupt increase and shows sharp fluctuations along y-axis. Meanwhile, it is observed that ηave in ACI exceeds other parts and small peaks appear. With the proceeding of shearing, ηave in the whole sample shows a leaping increasing, especially that the ACI suppressed the others by a large margin. This phenomenon interested us to analyze the atomic shear strain distribution in ACI layer, and thus we intercepted several sections in the ACI region to find out how the large strain atoms distributed in the layers. The range of ACI has been determined as -37 Å to -27 Å along y-axis according to Part 3.1. The sections (section I, II, III, IV) with y coordinate of -38 Å, -34 Å, -30 Å and -27 Å are selected, and the atomic strain snapshots of every section at γ=0.1067 are shown in Figure 8. Wherein, lines appears in section IV, which indicates the plasticity in crystal was resulted from slips; near the crystal part, strain concentration gradually becomes blurry at the corresponding positions, and in other area the shear strain has a general increasing; the strain localization lines gradually vanish with y coordinate decreases, and finally become localized sites with a few atoms, which would grow to a STZ with proceeding of shearing. The ACI is clearly responsible for mediating the shear banding in glass and slipping in crystal. In this deformation mode, the plasticity of ACNL can be described as a crystal to glass process as following. Shear stress concentrated on the uneven crystal boundary in ACI, which contributed to the breeding of dislocations in crystal, then the dislocations embryos quickly spread over the whole crystal and formed slipping lines in crystal. The slipping lines affected the localization of shear strains in ACI conversely, and finally when it came to the glass, STZ sites were activated by the large shear strain localizations in ACIs. 8
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Figure 7 The averaged atomic shear strain ηave distributions during P-direction deforming process
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Figure 8 The atomic strain snapshots in sections with y coordinate of -38 Å, -34 Å, -30 Å and -27 Å at γ=0.1067 For the S-direction deformation mode, Figure 9(a) shows the averaged atomic shear strain ηave distributions along y-axis (0<γ<0.0916). It is found that ηave in C-phase has no change with increasing of shear strain. The variations mainly happened in A-phase. Within the elastic range (γ<0.05), ηave increased at an almost linear speed. When it entered the yielding stage, ηave in glass firstly had a general increasing, and then localized to two peaks after the shear stress reaching maximum. In the following deforming process, peak I at y coordinate of 38Å grew into a shear band embryo in Figure 4(h). Although the shear banding site was very close to ACI, but since the localization only happened at one ACI, it cannot be deduced that ACIs are the weakness of the ACNL. In fact, the generation and deformation of ACNL was repeated three individual times in our simulations to exclude the inaccurate result induced by accidental factors. Three pictures in Figure 9(b) indicate that shear banding might happen at any position with enough collection of STZs. In contrast to Chen’s found [16], our results indicate the ACIs are strong interphase bonding C-phase and A-phase. Thus in the S-direction deformation mode, the plasticity of ACNL can be attributed by the generation and localization of STZs in glass. After the generation of an embryonic shear band, it needs enough space for its propagation and aging [30]. Thus the thickness of A-layer is important for totally formation of a mature shear band. We will discuss the effects of A-layer thickness on the formation of shear bands in Part 3.4.
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Figure 9 (a)The averaged atomic shear strain ηave distributions during S-direction deforming process; (b) the shear strain distributions of three individual samples at γ=0.1067; (c) the averaged atomic shear strain ηave distributions of three samples at γ=0.1067. When it comes to the diversities in the two deformation modes, it can be concluded that the origins of plasticity in ACIs would always find an easier way out. In S-direction, the shear direction was parallel to ACIs, and there was enough space for generation of a shear band, the residual strain relieved into the glass, offered opportunity for the gathering of STZs and relieving of elastic energies. The dislocations would never be triggered without enough energy collection near the crystal boundary. In P-direction, the individual formation of shear banding in glass cannot happen without crossing C-phase, thus energies at ACI kept accommodating when it was enough for triggering of dislocations in crystal [12]. And then with relieving of energies into crystal, there was not enough energy left to drive the generation and gathering of STZs, thus it became much difficult for the formation of shear bands in glass.
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3.4 Influence of crystalline layer ratio The thickness of C-layer was regarded have size effect on deformation modes and mechanical properties of ACNLs [31], thus we here presented several ACNLs with different C-layer thickness ratio range from 0.2 to 0.8. Figure 10 presents the stress-strain curves of all ACNLs in both P-direction and S-direction deforming modes. With increasing of C-layer thickness ratio, the shear moduli (curve slope in elastic stage) have an obvious increasing in both modes, indicating that ACNL has a higher shear modulus with larger ratio of C-phase generally. From Figure 10(a), it can be seen that the shear strength τmax had an increasing with thicker C-layer participated in ACNL. In the P-direction mode, the yielding of ACNL is mainly decided by C-phase, larger C-layer thickness would induce a larger τmax generally. We also noticed that not all the curves have the recovery phenomenon in plastic stage. For ACNL-0.2 (with C-layer thickness ratio of 0.2), the stress-strain curve shows a relative flat stage without obvious linearly recovery in its plastic segment. In this ACNL, the C-layer thickness was set as 2.6 nm initially. However, after the annealing treatment, the formation of ACI interphase invaded the crystal thickness about 1.3 nm, so the actual crystal thickness decreased to 1.3 nm. According the researching work by Cui et al. [18], Shockley partial dislocations needed space to dissipate into ACIs, when the thickness of crystal was less than the least width of dislocation, Shockley partial dislocations would stay and glide in crystal. As we mentioned in 3.2, the partial dislocation dissipation contributed to the recovery of shear stress. Without dissipation of dislocations in ACNL-0.2, the shear stress stayed a stable status since the plasticity began. Figure 10(b) demonstrated the stress-strain curves in S-direction mode. Similarly, all the curves showed relative smooth drops after yielding and stable stress in the plastic stage, indicating 10
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that the A-phase dominated plasticity in all ACNLs. With increasing of C-layer thickness ratio, the elastic stage showed a decreasing trend, together with a slight increasing of shear strength. Since C-phase did not participate in the plastic behavior, it will be seen that this tendency is related to thickness of A-layer, which means that thinner A-layer induced higher shear stress. Enough thickness is necessary for the generation of a shear band in A-layer. In an ACNL without sufficient A-layer thickness, there would be viscous and homogeneous flow instead of gathering of STZs [15]. We extracted the atomic shear strain distributions of A-phase atoms at a plastic strain of 0.2, which are shown in Figure 10(c). Meanwhile, to evaluate the localization degree of A-phase atoms, a localization parameter should be employed to verify formation of shear bands. A widely used localization parameter was defined as mean square error of atomic shear strains [26],[32],[33]. Considering A-layers might have different plastic deforming degree in different ACNLs, the global average atomic strain is evolved as a divisor to normalize the above localization parameter, thus:
= ∑ ( − 1) ,
(3)
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is the average atomic shear strain of all atoms in A-phase, N represents number Wherein, " #!# ! of atoms in A-phase, ψ indicates the deviation of atomic strain distribution from homogenous behavior. Larger ψ indicates more localized deformation behavior. The results for all ACNLs are shown in Figure 10(d). For ACNL-0.2, the atomic strain distribution curve and localization parameter is very close to that of glass, thus shear banding dominated in A-phase. With deceasing of A-phase layer thickness, there is a gradually transition from typical partial distribution to normal distribution in the atomic strain distribution curves, and the localization parameters also decreased. This trend indicates there is a gradually transition from highly localized shear banding to homogeneous flow with decreasing of glass thickness. In ACNL-0.7 and ACNL-0.8, without aggregation of these SRO weakness sites, the shear band propagation would be suppressed and the glass layer was more resistant to shear stress and induced higher strength. For the other ACNLs with thicker A-layer, the increasing of yield stress could be explained as the length-scale effect [34]. The decreasing of glass thickness induced increasing of viscosity of the shear band [15]. It would be more difficult for the aggregation of STZs and propagation of shear bands because of more viscous atoms flow.
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Figure 10 The stress-strain curves of ACNLs in (a) P-direction and (b) S-direction deforming modes; (c) the atomic shear strain distributions of atoms in A-phase at strain of 0.2; (d) localization parameters of ACNLs at strain of 0.2. The shear moduli of all ACNLs were extracted from the elastic deformation stage in both deformation modes, and the results were shown in Figure 11. The predicted shear modulus of every sample calculated by Eq. (1-2) were also presented for reference. It is found that all the shear moduli in S-direction fitted the predicted well, while the simulated shear moduli in P-direction were higher than predicted generally. To find out the factors that result this divergence, local shear modulus distributions were calculated with the stress tensor and strain tensor of every atom in the sample. The stress tensor for per-atoms was calculated with a virial theorem contributed by Thompson [35]. Since the virial stress obtained from LAMMPS was a stress*volume value, we calculated the true virial stress tensor by a divisor atomic volume obtained from Voronoi method. While the Green-Lagrangian strain tensor was obtained from, (4)
Thus the per-atom values of shear modulus were obtained through corresponding component of stress tensor and strain tensor in the P-direction. The averaged shear modulus was captured by the slicing method as described in 3.1. And the averaged local shear modulus Gave distributions along y-axis of all ACNLs at deformation strain of 0.03 were presented in Figure 12. It is found that Gave in C-phase was much higher than that obtained through a bulk single copper crystal shear simulation, and there was a general trend that the shear modulus of crystal increased with decreasing of crystal layer, expect for tc/d=0.2 (such a thin crystal layer cannot keep non-dislocation state during annealing and relaxing process). A recent work taken by Rohith et al. presented size effect of single copper crystal through MD tensile simulation [36]. They found that the Young’s modulus of <1 0 0> copper were greatly related to the cross-section width, that with increasing cross-section area, the Young’s modulus would decrease linearly, while it was not sensitive to the sample length. According to Rohith’s work, it can be deduced that size effect also 12
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exists in the shear deforming processes. Size effect on shear modulus explained the exceeding value than expected in Figure 11, and also revealed ACIs affected the elastic mechanical responses of ACNLs in an indirect way.
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Figure 11 The predicted and simulated shear moduli of ACNLs
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Figure 12 The averaged local shear modulus distributions along y-axis of the ACNLs at deformation strain of 0.03. 4. Conclusions In summary, the mechanical anisotropies of the ACNLs with different crystalline thickness ratios in parallel and serial deforming modes were investigated by conducting shear simulations. The differences of two deforming modes were reflected in yielding behaviors, the participations of two phases in plastic deformation, and the roles that ACIs played in the interaction of two phases. Some conclusions are drawn as following: (1) In parallel deforming mode, the yielding of ACNL was mainly triggered by generation of dislocations and slips in C-phase, and in the subsequent plastic deforming, both shear banding in A-phase and dislocations in C-phase contributed to the plasticity of materials. (2) In serial deforming mode, only A-phase participated in the yielding and plastic deforming of ACNL, the stress localization at ACIs released to the glass side and could not provide enough stress to trigger the dislocations. (3) ACIs served as stress resistance weakness and dislocations breeding cradle in the parallel deforming mode while a strong connection of two phases in the serial deforming mode. (4) With the increasing of C-layer ratio, shear moduli and maximum stress in two deformation modes both increased. The variation of shear moduli in serial deformation mode obeyed the rule-of-mixture and fitted the prediction well, while the shear moduli in parallel deformation modes had large excess compared with predicted ones, which mostly is attributed to the size effect of crystalline layer. 13
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There are other factors might affect the mechanical anisotropies of composites, including crystalline orientations, defects in crystalline layers (voids, dislocations, stacking faults and grain boundaries etc.), temperatures, deforming rates and so on, and they are the focus in our future researching. Acknowledge The authors would like to thank the High Performance Computing Center of Jilin University for access to the computing systems. This work was supported by the National Key R&D Program of China (Grant No. 2018YFF01012400), National Science and Technology Innovation Leading Academic (Ten Thousand Talent Program), Fund Guiding on Strategic Adjustment of Jilin Provincial Economic Structure Project (Grant No. 2014Z045), Major project of Jilin Province Science and Technology development plan (Grant No. 20150203014GX), Science and Technology Development Program of Jilin province (Grant No. 20180520072JH), the special fund project of Jilin provincial industrial innovation (Grant No. 2016C030), Jilin Provincial Middle and Young Scientific and Technological Innovation Talent and Team Project (Grant No. 20170519001JH), Project supported by Interdisciplinary Research Fund of Jilin University (Grant No. 10183201822), and Project (Grant No. 2017141) supported by Graduate Innovation Fund of Jilin University, . References [1] C.A. Schuh, T.C. Hufnagel, U. Ramamurty, Mechanical behavior of amorphous alloys, Acta Mater. 55 (2007) 4067-4109. [2] M. Chen, Mechanical Behavior of Metallic Glasses: Microscopic Understanding of Strength and Ductility, Annu. Rev. Mater. Res. 38 (2008) 445-469. [3] M.M. Trexler, N.N. Thadhani, Mechanical properties of bulk metallic glasses, Prog. Mater. Sci. 55 (2010) 759-839. [4] A.L. Greer, Y.Q. Cheng, E. Ma, Shear bands in metallic glasses, Mater. Sci. Eng. R Reports. 74 (2013) 71-132. [5] M.L. Falk, J.S. Langer, Deformation and failure of amorphous, solidlike materials, Annu. Rev. Conden. Ma. P. 2(1) (2010) 353-373. [6] B.A. Sun, W.H. Wang, The fracture of bulk metallic glasses, Prog. Mater. Sci. 74 (2015) 211-307. [7] E. Ma, J. Ding, Tailoring structural inhomogeneities in metallic glasses to enable tensile ductility at room temperature, Mater. Today. 19(10) (2016). [8] N. Wang, J. Ding, F. Yan, M. Asta, R.O. Ritchie, L. Li, Spatial correlation of elastic heterogeneity tunes the deformation behavior of metallic glasses, Npj Comput. Mater. 4(1) (2018) 19. [9] Y. Shi, J. Luo, F. Yuan, L. Huang, Intrinsic ductility of glassy solids, J. Appl. Phys. 115(4) (2014) 043528. [10] C.C. Hays, C.P. Kim, W.L. Johnson, Microstructure controlled shear band pattern formation and enhanced plasticity of bulk metallic glasses containing in situ formed ductile phase dendrite dispersions, Phys. Rev. Lett. 84 (2000) 2901. [11] J.Y. Kim, D. Jang, J.R. Greer, Nanolaminates utilizing size-dependent homogeneous plasticity of metallic glasses, Adv. Funct. Mater. 21 (2011) 4550-4554. [12] Y. Wang, J. Li, A. V. Hamza, T.W. Barbee, Ductile crystalline-amorphous nanolaminates, Proc. Natl. Acad. Sci. 104 (2007) 11155. [13] M.C. Liu, J.C. Huang, Y.T. Fong, S.P. Ju, X.H. Du, H.J. Pei, T.G. Nieh, Assessing the 14
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The anisotropies of ACNL were reflected in yielding and plasticity behaviors; ACI served as structural weakness and dislocations breeding cradle in P-direction; ACI served as strong connection of two phases in S-direction; The increase of tc/d would improve the ACNL shear moduli in both directions; C-layer thickness has size effect on the ACNL shear modulus in P-direction.
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