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Effects of solute segregation on surface properties of dilute Al-X (X = Li, Sn) alloys from first-principles calculations
Computational Materials Science 174 (2020) 109502
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Effects of solute segregation on surface properties of dilute Al-X (X = Li, Sn) alloys from first-principles calculations ⁎
T
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Z.P. Wanga,b,1, T.W. Fana,1, J.J. Lina, F. Liuc, B. Liuc, Q.H. Fangb, , D.C. Chena, , L. Mad, P.Y. Tangd a
School of Material Science and Energy Engineering, Foshan University, Foshan, Guangdong Province 528001, PR China State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, Hunan Province 410082, PR China c State Key Laboratory for Powder Metallurgy, Central South University, Changsha, Hunan Province 410083, PR China d Key Laboratory of New Electric Functional Materials of Guangxi Colleges and Universities, Nanning Normal University, Nanning, Guangxi Province 530023, PR China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Al alloys First-principles method Surface energy Nano-crack nucleation Solute atoms
Considering the interactions between solute atom (Li or Sn) and various surfaces, along with the ones between solute atoms in the surfaces, this work applies the first-principles method to investigate the influences of solute atoms on the surface energy of dilute Al alloys at room temperature, and further predicts the nano-crack nucleation along different surfaces. The statistical ordered surface configurations are depicted for ensuring the maximum surface concentrations of solute-atom segregations. The Gaussian-Like distribution (GLD) model is introduced to describe the distribution of solute atoms. Results indicate that the nano-crack nucleation may occur along the (110) surface in the region of dilute Li atom less than 0.016%, but along the (111) surface in the region of high concentration exceeding 0.016%. While Sn atom has a fairly stronger effect on reducing the surface energy than Li atom, especially in the (001) surface, suggesting that the nano-cracks are likely to nucleate along (001) surface under the action of Sn atom. This work provides a valuable guidance for theoretical and experimental study of the nano-crack nucleation in Al alloys.
1. Introduction Crack nucleation and propagation are the two main processes of material fatigue failure. With the emergence of the in-situ scanning electron microscopy/transmission electron microscopy (SEM/TEM) techniques, the fatigue crack nucleation and propagation processes have been successfully observed in many materials [1–5]. As a structural material, Aluminum (Al) alloys have been extensively used in many industrial areas, such as automotive, aerospace, electronics and 3D printing fields, which were intrinsically attributed to their superior properties, including light weight, high strength and good workability [6–9]. In Al alloys, the fatigue fracture is induced by crack nucleation and continuous propagation. Generally, the crack initiation occurs when the surface energy of materials is under the minimum energy of forming two free surfaces, which opens a window for further crack propagation, and the materials tend to the failure eventually under applied stress. Therefore, the study of crack nucleation is a rather significant work in Al alloys, directly affecting their fatigue performances. Recently, the vast investigations of crack nucleation have been conducted by means of the experimental and theoretical methods in Al
alloys, as well as the correlative nucleation mechanisms. By the in-situ SEM fatigue test, Chen et al. [10] and Yan et al. [11] have directly observed the fatigue crack initiation and propagation behavior in 2524 Al alloy, and investigated the effects of inclusions, grain boundaries (GBs) and grain orientations on the fatigue behavior, simultaneously, they found that fatigue cracks nucleated on the inclusion particles or interface between inclusion particles and matrix, including two mechanisms of crack propagation, such as shearing mechanism along slip bands and crack-linking mechanism ahead of crack tip. Babicheva et al. [12] investigated the cyclic behavior of Al bi-crystals with GB segregation of Co or Ti by applying the mode I cyclic loading perpendicular to GB plane, and the results found that GB segregations inhibited the formation of both perfect dislocations and twins in Al matrix, leading to decrease in ductility of the bi-crystals and intergranular crack propagation rate, but the alloying elements in GBs can improve the fatigue lifetime of the Al bi-crystals. Wang et al. [13] discovered that large pores in Al-Si alloy generated enough strain localization zones for crack initiation by combining 3D in-situ analysis and Finite Element Method (FEM) simulation. In addition, for nucleation and relaxation mechanisms in GBs, Wu et al. [14] found that the cracking occurred
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Corresponding authors. E-mail addresses: [email protected] (Q.H. Fang), [email protected] (D.C. Chen). 1 Co-first author. https://doi.org/10.1016/j.commatsci.2019.109502 Received 17 September 2019; Received in revised form 22 December 2019; Accepted 23 December 2019 0927-0256/ © 2019 Published by Elsevier B.V.
Computational Materials Science 174 (2020) 109502
Z.P. Wang, et al.
interaction energies are calculated when a solute atom (Li or Sn) is doped in the site from the surface layer (L1-layer) to fifth neighbor layer (L5-layer) away from the surface, respectively. Considering the shortrange order (SRO) effects on surface segregation [24,25], the interaction energies are approximately ignored when the relative site of solute atom exceeds the fifth neighbor layer. To calculate the surface energies at room temperature, we define the variable γs as the surface energy of Al metal, which denoted the minimum energy forming two free surfaces [26], and then it can be expressed as below:
preferentially on GBs, and the crack initiation occurred beyond the critical value of strength when the triple junction disclinations in GBs were unstable, and the cavity nucleation and local relaxation leading to some amorphization of GB structure were competing relaxation mechanisms during cracking process [15]. Meanwhile, many theoretical approaches have been widely applied to investigate the process of fatigue crack initiation, such as crystal plasticity finite element (CPFE) simulations [16,17], molecular dynamics (MD) simulations [18,19], variational phase-field models [20] and first-principles energy calculations [21–23], which provided an effective way to study the nanocrack nucleation and its mechanism from the atomic scale. To date, because of the limitations of experimental conditions, it is hard to measure the surface energies of Al metals or alloys, and then master their surface characteristics, especially for the nucleation process of nano-cracks. Thus, this work utilizes the first-principles method to investigate the impacts of solute atoms (Li, Sn) on the surface energy of Al alloys at room temperature, which are together decided by the interactions between solute atoms and surfaces, along with the ones between solute atoms in the surface, and the two key factors are of great significance in studying the nucleation process of nano-cracks. The statistical ordered surface configurations are used to determine the maximum surface concentrations of solute segregations to the surfaces. Simultaneously, the Gaussian-Like distribution (GLD) model is proposed for describing the distribution of solute atoms in Al alloys. Results show that the nano-crack nucleation may occur along the (110) surface in the region of dilute Li atom less than 0.016%, but turn into nucleation along the (111) surface in the region of high concentration exceeding 0.016%. While Sn atom has a fairly stronger effect on reducing the surface energy than Li atom, especially in the (001) surface, thus, the nano-cracks in the (001) surface are likely to nucleate under the action of Sn atom, which provides a valuable guidance for theoretical and experimental study of the nano-crack nucleation in Al alloys.
γs = [Esurf − Eperf ] [2S ]
(1)
where Eperf and Esurf indicate the total energies of perfect and surface supercells, respectively. S is the area of the corresponding supercell. Considering the interactions between solute atoms and surfaces, along with solute–solute interactions in the surfaces, we apply the following formula (2) to investigate the impacts of solute atoms on the surface energies γs - sol of Al alloys, which is further modified based on the works of Fan et al. [27] and Liu et al. [28]:
γs - sol = γs +
∑ cs−n (Eint - n + Eint - sol - Ni - n)
S′ (2)
n
where S′ is the area of unit cell for different crystal planes, and cs − n is the solute concentration in the n -th (n = L1~L5) plane in Fig. 1(a)-(c). Eint - n denotes the interaction energies between solute atoms (Li or Sn) and various surfaces, where the solute atoms are located in the n -th atomic plane. Eint - sol - Ni - n indicates the interaction energies between solute atoms of Ni -th neighbor in the n -th atomic plane, where the solute atoms are situated in different neighbor positions. Eint - n and Eint - sol - Ni - n can be calculated as follows [27,29]:
Eint − n = [Esurf
Eint 2. Theoretical model
- sol - Ni - n
- sol - n
− Eperf
- sol - Al]
= Esol - Ni - n − Esol - Nr
− [Esurf − Eperf ]
(3) (4)
-n
where Eperf - sol - Al is the total energy of perfect supercell doping a solute atom (Li or Sn) at room temperature, and Esurf - sol - n is that of corresponding surface supercell doping a solute atom (Li or Sn) in the n -th layer. Esol - Ni - n denotes the total energy of solute atom pairs of Ni -th neighbor in the n -th atomic plane of surface supercells, and Esol - Nr - n indicates the one of solute atom pairs of Nr -th referenced neighbor, which are directly obtained by first-principles energy calculations. Based on the Fermi-Dirac distribution (FDD) model [27,30,31], we further develop the GLD model to investigate the segregation behavior of solute atoms to the surface, which can better describe the characteristics of the completely random distribution of solute atoms in the matrix materials, and it can be expressed by the following formula:
In Al alloys with face-centered-cubic (FCC) crystal structure, we investigate the surface characteristics of (001) , (110) and (111) planes. As depicted in Fig. 1(a)-(c), we construct three surface supercells of 3 × 3 × 14, 3 × 3 × 14 and 3 × 3 × 12 for (001) , (110) and (111) atomic planes, respectively, containing a 12 Å vacuum gap. For investigating the interactions between solute atoms and surfaces, the
cs - n =
1 ⎧1 ⎡ E c0 ⎞ ⎤ + c0 ⎫ 1 − erf ⎛ int − n − ln ⎢ ⎬ 1 + c0 ⎨ 1 − c0 ⎠ ⎥ ⎝ KT ⎦ ⎭ ⎩2 ⎣ ⎜
⎟
(5)
where y = erf(x ) is the Gauss error function, K is the Boltzmann constant in physics, and c0 is the initial solute concentration at T = 300K in Al alloys. 3. Methodology This work applies the Vienna ab initio simulation package (VASP) to implement all energy calculations [32,33]. The projector–augmented wave (PAW) method is used to address the ion–electron interactions [34]. Generalized gradient approximation (GGA) of Perdew–Burke–Eruzerhof (PBE) is chosen as the exchange–correlation functional [35]. After strict convergence tests, the cutoff energy is set as 350 eV in all calculations. In calculating the interaction energies between solute atoms and surfaces, k-mesh Gamma-centered Monkhorst–Pack grids [36] in the Brillouin zone sampling are optimized as 5 × 5 × 1 for (001) , 4 × 5 × 1 for (110) and 5 × 5 × 1 for (111) plane, respectively, and the supercells are fully relaxed under fixing the volume instead of
Fig. 1. The schematic diagrams of (a) (001) , (b) (110) and (c) (111) surface supercells for calculating the interaction energies between solute atoms and various surfaces. 2
Computational Materials Science 174 (2020) 109502
Z.P. Wang, et al.
Fig. 2. The interaction energies between solute atoms and various surfaces versus different atomic layers from L1 to L5.
(a) (001)
the shape. However, for calculating the solute–solute interaction energies in each surface, k-grids are optimized as 3 × 3 × 2 for (001) , 2 × 3 × 2 for (110) and 3 × 3 × 2 for (111) plane, meanwhile, the atomic layers at the bottom, as well as the shape and volume of supercells, are fixed to ensure the same lattice constant as the matrix, and the other atoms are totally relaxed. In the light of the works of Touloukian et al. [37] and Liu et al. [38], the coefficient of cubical expansion is set as 1.014 based on the calculated results of phonon spectrum in Al alloys, which is used for simulating the environment at room temperature (T = 300 K ). The Hellmann–Feyman force acting on each atom is lower than 0.01 eV/Å, and the energy convergence criterion of all self-consistent calculations is selected as 10−6 eV/atom.
(b) (110)
N6 N4
N5
N4
N5
N3 N2 N0
N1 N0
N1
N3 N2
N6
(c) (111) N6 N5
4. Results and discussions
N4 N3 N2
Fig. 2 demonstrates the interaction energies between solute atoms and various surfaces, including (001) , (110) and (111) surfaces, where the solute atoms are separately located in the different atomic layers from L1 to L5. For (001) , (110) and (111) surfaces, the computational results exhibit that the value of interaction energies is negative when the solute atoms (Li or Sn) lie in the L1 surface layer, and the negative interaction energy in L1 layer is much smaller than those in the other atomic layers (L2 − L5), indicating that the solute atoms are more likely to segregate to the free surfaces with respect to L2 − L5 atomic layers. Moreover, the interaction energy of Sn atom in the L1 layer is much smaller than that of Li atom, suggesting that Sn atom has higher probability to segregate at the free surface of Al than Li atom. Similarly, as the solute atoms are segregated to the surface, we consider the SRO effects on the strong interactions between neighboring solute atoms, and then we build another three supercells of 6 × 6 × 4, 6 × 6 × 4 and 6 × 6 × 4 for (001) , (110) and (111) planes, respectively, along with the vacuum gap of 12 Å magnitude, which aims to calculate the interaction energies between solute atoms in the surfaces. As depicted in Fig. 3, when doped with a single solute atom (Li or Sn), we only consider the relative positions between solute atoms from the first neighbor to the sixth neighbor in each surface, namely, the interaction energies are approximatively neglected (Eint - sol - N 6 - n = 0 ) due to the SRO effects when the relative positions between solute atoms exceed the sixth neighbor (Nr = N 6), where N0 denotes the reference position between solute atoms, and N1 ~ N6 signify the relative positions between solute atoms from the first neighbor N1 to the sixth neighbor N6 with respect to N0, respectively. By VASP energy calculations, we have obtained the solute–solute interaction energies between various relative positions in (001) , (110) and (111) surfaces, including Li-Li and Sn-Sn atomic pairs, and they are described in Fig. 4, which are used to ensure the maximum surface concentration cmax of
N1
N0
Al atom N0 N1 N2 N3
N4 N5 N6
Fig. 3. The relative positions between solute atoms in various surfaces: (a) (001) surface; (b) (110) surface; (c) (111) surface. For convenience in description, N0 is defined as the reference position, and N1 ~ N6 denote the relative positions to N0, where N1 is defined as the first nearest neighbor position to N0, and so are the N2, …, N6 nearest neighbor positions. Herein, differently colored balls only stand for a single solute atom (Li or Sn) in various relative positions.
solute atomic segregations to the surfaces. To obtain the maximum surface concentration cmax of solute atomic segregations, as seen in Fig. 5, the statistical ordered surface configurations are drawn in the case of the maximum surface concentration cmax , which derives from the results of interaction energies between solute atoms in Fig. 4. For clearly explaining the derivation of statistical surface configurations in Fig. 5, we take Li solute atom for example in the (001) surface. When Li solute atoms are segregated to the (001) surface, Fig. 4(a) indicates that the lowest segregation energy between Li-Li solute atoms occurs in the relative position of the second neighbor N2, which results in preferentially occupying the N2 position in the 6 × 6 surface (see Fig. 5(a)). After the N2 positions of a red dotted line are filled, Li atoms with more segregations further occupy the N4 position due to its negative segregation energy, and then fill the N2 positions of another red dotted line, and so on, the statistical ordered surface configuration is finally obtained as shown in Fig. 5(a), and the same way is applied for getting the other surface configurations, and the yellow area is defined as a minimum repeating unit to calculate the maximum surface concentration cmax , and their values are listed in Table 1. 3
Computational Materials Science 174 (2020) 109502
Z.P. Wang, et al.
Fig. 4. The interaction energies between solute atoms with respect to various neighboring positions to N0.
(a) Li-(001)
(b) Li-(110)
(c) Li-(111)
(d) Sn-(001)
(e) Sn-(110)
(f) Sn-(111)
planes, thus, the functional relations between the total interaction energies and surface solute concentrations in the surfaces are still suitable for other atomic planes, like L2~L5 planes. In Fig. 6, the functional relations between the total interaction energies and surface solute concentrations cs are fitted to the third-order polynomial as follows:
ELi - (001) = −0.19477cs − 10.32203cs2 + 17.51055cs3
ELi - (110) = −0.07174cs −
Li
Sn
(001) (110) (111)
1/3 1/2 1/2
1/2 1/3 1/3
(6) (7) (8)
ESn - (001) = −0.05229cs − 7.88627cs2 + 6.36627cs3
(9)
0.03771cs2
+
0.14396cs3
ESn - (111) = 0.3825cs − 11.72068cs2 + 13.15843cs3
(10) (11)
To study the impacts of solute atoms on the nano-crack nucleation in Al alloys, we calculate the surface energy of various crystal planes as a function of solute concentration c0 by combining the Eqs. (1)–(11), as shown in Fig. 7. By VASP energy calculations at T = 300K , herein, the surface energies of Al metal are calculated as follows: γs - (001) = 0.907 J m2 , γs - (110) = 1.021 J m2 and γs - (111) = 0.812 J m2 . Meanwhile, the results in Fig. 7 indicate that with increasing the concentrations of solute atoms, the surface energies of Al alloys first keep unchangeable due to the fairly weak interaction in the case of small solute concentrations, and then decline rapidly, when the surface solute concentrations reach up to the maximum value cmax (see Fig. 5), the incremental solute atoms are no longer segregated to the surfaces, which is mainly caused by the strong interaction energies between solute atoms in the surfaces, thus, the surface energy remains unchanged at high solute concentrations. Furthermore, it is found that Sn atom has a fairly stronger effect on reducing the surface energy with respect to Li atom by comparing the results of Fig. 7(a) and (b), and Pogatscher et al. [39] also found in their studies that Sn additions of ~100 at.ppm can produce the rapid increase in hardness for Al alloys, indicating that the impacts of Sn additions are consistent. For Li solute atom in Fig. 7(a), when the solute concentration is less than 0.016%, small solute concentrations have a stronger effect on reducing the surface energy in (110) plane with respect to (001) and (111) planes, and the nano-cracks are more likely to tend to nucleate along the (110) plane, which may occur in the region of dilute Li atoms in AlLi alloys. However, with the concentration of Li atom exceeding 0.016%, the surface energy in (111) plane declines rapidly to 0.512 J m2 due to the strong interactions with (111) plane, which may force the nano-crack nucleation along the (111) plane, and it may take place in the region of high-concentration Li atoms, thus, Li atoms
Table 1 The maximum surface concentration cmax of solute atom (Li, Sn) segregations to various surfaces. Maximum surface concentration cmax
+
9.69872cs3
ELi - (111) = −1.24546cs − 4.6264cs2 − 2.13885cs3
ESn - (110) = 0.10602cs − Fig. 5. The statistical ordered surface configurations of solute atom (Li, Sn) segregations to various surfaces in the case of maximum surface concentration cmax . The yellow area is defined as a minimum repeating unit to calculate the is Al atom, and the red maximum surface concentration cmax (The blue ball ball is solute atom).
10.2761cs2
By combining the interaction energies between solute atoms in Fig. 4 and statistical ordered surface configurations in Fig. 5, we draw the schematic diagrams of the total interaction energies between solute atoms as a function of surface solute concentrations cs , as depicted in Fig. 6. These curves are obtained by the summation of interaction energies between corresponding solute atoms in the surfaces, and the surface configuration eventually reaches the lowest energy state with solute atom segregations to the surfaces, and an energy value of the curves in Fig. 6 corresponds to a certain surface configuration, as well as the corresponding surface solute concentration. In particular, when the surface solute concentration reaches up to the maximum value, solute atoms are no longer segregated to the corresponding surface, and then the total interaction energies between solute atoms keep unchangeable in the surfaces, forming the final surface configurations in Fig. 5. Since the interaction energies between solute atoms are approximately considered as identical in each plane, including L1~L5
4
Computational Materials Science 174 (2020) 109502
Z.P. Wang, et al.
Fig. 6. The total interaction energies between solute atoms in the surface with respect to the surface solute concentrations cs , (a) is the case of Li-Li solute atoms, and (b) is that of Sn-Sn solute atoms. cmax - (001) , cmax - (110) and cmax - (111) denote the maximum surface concentrations (see Table 1) of (001) , (110) and (111) surfaces, respectively.
higher probability to segregate at the free surface of Al than Li atom. (2) With the continuous segregations of solute atoms to the surface, the surface energies of Al alloys first keep unchangeable, and then decline rapidly in the case of surface solute concentrations lower than the maximum value cmax , and finally remains unchanged again since the surface solute concentration reaches its maximum, indicating that the high-concentration solute atoms (Li or Sn) promote the nano-crack nucleation. (3) For Li atom, small solute concentrations less than 0.016% have a stronger effect on decreasing the surface energy in (110) plane with respect to (001) and (111) planes, and the nano-crack nucleation may occur along the (110) plane in the region of dilute Li atoms. Li atom of high concentration exceeding 0.016% forces the nano-crack nucleation along the (111) plane. (4) Sn atom has a fairly stronger effect on reducing the surface energy than Li atom. Especially in the (001) plane, the surface energy drops rapidly in the case of a fairly low concentration, suggesting that the nano-cracks tend to nucleate along (001) plane under the action of Sn atom.
promote the nano-crack nucleation due to reducing the surface energies of each plane. Similarly, Sn atom has the stronger influences on reducing the surface energy than Li atom, as shown in Fig. 7(b), and the surface energy drops rapidly in the case of a fairly low concentration, especially in the (001) plane, suggesting that the nano-cracks tend to nucleate along (001) plane under the action of Sn atom compared with the (110) and (111) planes. 5. Conclusions In summary, this work utilizes the first-principles method to study the influences of solute atoms (Li, Sn) on the surface energy of Al alloys at room temperature, and further predicts the nano-crack nucleation along different surfaces. The interaction energies between solute atoms and various surfaces are calculated, and the statistical ordered surface configurations of solute atomic segregation to the surfaces are also drawn based on the interaction energies between solute atoms in the surfaces, which is used to ensure the maximum surface concentrations of solute atomic segregations. Herein, the GLD model is proposed for describing the distribution of solute atoms in Al alloys. The relevant conclusions are summarized as follows:
CRediT authorship contribution statement
(1) The solute atoms are more likely to segregate to the free surfaces with respect to the other atomic planes (L2 − L5), and Sn atom has
Z.P. Wang: Conceptualization, Methodology, Writing - original
Fig. 7. The surface energies as a function of solute concentration c0 with respect to Li (a) and Sn (b) solute atoms. 5
Computational Materials Science 174 (2020) 109502
Z.P. Wang, et al.
draft. T.W. Fan: Conceptualization, Data curation, Formal analysis. J.J. Lin: Formal analysis, Project administration. F. Liu: Project administration, Visualization. B. Liu: Resources, Visualization. Q.H. Fang: Funding acquisition, Supervision, Validation, Writing - review & editing. D.C. Chen: Investigation, Supervision, Validation. L. Ma: Data curation. P.Y. Tang: Software.
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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The authors would like to deeply appreciate the support from the National Natural Science Foundation of China (11572118, 11772122 and 51501060), the Hunan Provincial Science Fund for Distinguished Young Scholars (2015JJ1006), the National Key Research and Development Program of China (2016YFB0700300), the Key Project of Department of Education of Guangdong Province (2016GCZX008), Foshan University Scientific Research Project (CGG07257 and BGH206017), and the Hunan Provincial Innovation Foundation For Postgraduate (CX2017B085). This work was implemented in the Xiangqing Super Computational Platform (gg07026). Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.commatsci.2019.109502. References [1] Y. Shen, T.F. Morgeneyer, J. Garnier, L. Allais, L. Helfen, J. Crépin, Three-dimensional quantitative in situ study of crack initiation and propagation in AA6061 aluminum alloy sheets via synchrotron laminography and finite-element simulations, Acta Mater. 61 (2013) 2571–2582. [2] Y.B. Ju, M. Koyama, T. Sawaguchi, K. Tsuzaki, H. Noguchi, In situ microscopic observations of low-cycle fatigue-crack propagation in high-Mn austenitic alloys with deformation-induced ε-martensitic transformation, Acta Mater. 112 (2016) 326–336. [3] T.T. Nguyen, J. Yvonnet, M. Bornert, C. Chateau, Initiation and propagation of complex 3D networks of cracks in heterogeneous quasi-brittle materials: direct comparison between in situ testing-microCT experiments and phase field simulations, J. Mech. Phys. Solids 95 (2016) 320–350. [4] M. Seita, J.P. Hanson, S. Gradečak, M.J. Demkowicz, The dual role of coherent twin boundaries in hydrogen embrittlement, Nat. Commun. 6 (2015) 1–6. [5] Z. Tarzimoghadam, D. Ponge, J. Klöwer, D. Raabe, Hydrogen-assisted failure in Nibased superalloy 718 studied under in situ hydrogen charging: the role of localized deformation in crack propagation, Acta Mater. 128 (2017) 365–374. [6] G.S. Cole, A.M. Sherman, Light weight materials for automotive applications, Mater. Charact. 35 (1995) 3–9. [7] J.C. Williams, E.A. Starke Jr, Progress in structural materials for aerospace systems, Acta Mater. 51 (2003) 5775–5799. [8] J.H. Martin, B.D. Yahata, J.M. Hundley, J.A. Mayer, T.A. Schaedler, T.M. Pollock, 3D printing of high-strength aluminium alloys, Nature 549 (2017) 365–369. [9] S.S. Singh, E.Y. Guo, H.X. Xie, N. Chawla, Mechanical properties of intermetallic inclusions in Al 7075 alloys by micropillar compression, Intermetallics 62 (2015) 69–75. [10] Y.Q. Chen, S.P. Pan, M.Z. Zhou, D.Q. Yi, D.Z. Xu, Y.F. Xu, Effects of inclusions, grain boundaries and grain orientations on the fatigue crack initiation and propagation behavior of 2524–T3 Al alloy, Mater. Sci. Eng. A 580 (2013) 150–158.
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Effects of solute segregation on surface properties of dilute Al-X (X = Li, Sn) alloys from first-principles calculations ⁎
T
⁎
Z.P. Wanga,b,1, T.W. Fana,1, J.J. Lina, F. Liuc, B. Liuc, Q.H. Fangb, , D.C. Chena, , L. Mad, P.Y. Tangd a
School of Material Science and Energy Engineering, Foshan University, Foshan, Guangdong Province 528001, PR China State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, Hunan Province 410082, PR China c State Key Laboratory for Powder Metallurgy, Central South University, Changsha, Hunan Province 410083, PR China d Key Laboratory of New Electric Functional Materials of Guangxi Colleges and Universities, Nanning Normal University, Nanning, Guangxi Province 530023, PR China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Al alloys First-principles method Surface energy Nano-crack nucleation Solute atoms
Considering the interactions between solute atom (Li or Sn) and various surfaces, along with the ones between solute atoms in the surfaces, this work applies the first-principles method to investigate the influences of solute atoms on the surface energy of dilute Al alloys at room temperature, and further predicts the nano-crack nucleation along different surfaces. The statistical ordered surface configurations are depicted for ensuring the maximum surface concentrations of solute-atom segregations. The Gaussian-Like distribution (GLD) model is introduced to describe the distribution of solute atoms. Results indicate that the nano-crack nucleation may occur along the (110) surface in the region of dilute Li atom less than 0.016%, but along the (111) surface in the region of high concentration exceeding 0.016%. While Sn atom has a fairly stronger effect on reducing the surface energy than Li atom, especially in the (001) surface, suggesting that the nano-cracks are likely to nucleate along (001) surface under the action of Sn atom. This work provides a valuable guidance for theoretical and experimental study of the nano-crack nucleation in Al alloys.
1. Introduction Crack nucleation and propagation are the two main processes of material fatigue failure. With the emergence of the in-situ scanning electron microscopy/transmission electron microscopy (SEM/TEM) techniques, the fatigue crack nucleation and propagation processes have been successfully observed in many materials [1–5]. As a structural material, Aluminum (Al) alloys have been extensively used in many industrial areas, such as automotive, aerospace, electronics and 3D printing fields, which were intrinsically attributed to their superior properties, including light weight, high strength and good workability [6–9]. In Al alloys, the fatigue fracture is induced by crack nucleation and continuous propagation. Generally, the crack initiation occurs when the surface energy of materials is under the minimum energy of forming two free surfaces, which opens a window for further crack propagation, and the materials tend to the failure eventually under applied stress. Therefore, the study of crack nucleation is a rather significant work in Al alloys, directly affecting their fatigue performances. Recently, the vast investigations of crack nucleation have been conducted by means of the experimental and theoretical methods in Al
alloys, as well as the correlative nucleation mechanisms. By the in-situ SEM fatigue test, Chen et al. [10] and Yan et al. [11] have directly observed the fatigue crack initiation and propagation behavior in 2524 Al alloy, and investigated the effects of inclusions, grain boundaries (GBs) and grain orientations on the fatigue behavior, simultaneously, they found that fatigue cracks nucleated on the inclusion particles or interface between inclusion particles and matrix, including two mechanisms of crack propagation, such as shearing mechanism along slip bands and crack-linking mechanism ahead of crack tip. Babicheva et al. [12] investigated the cyclic behavior of Al bi-crystals with GB segregation of Co or Ti by applying the mode I cyclic loading perpendicular to GB plane, and the results found that GB segregations inhibited the formation of both perfect dislocations and twins in Al matrix, leading to decrease in ductility of the bi-crystals and intergranular crack propagation rate, but the alloying elements in GBs can improve the fatigue lifetime of the Al bi-crystals. Wang et al. [13] discovered that large pores in Al-Si alloy generated enough strain localization zones for crack initiation by combining 3D in-situ analysis and Finite Element Method (FEM) simulation. In addition, for nucleation and relaxation mechanisms in GBs, Wu et al. [14] found that the cracking occurred
⁎
Corresponding authors. E-mail addresses: [email protected] (Q.H. Fang), [email protected] (D.C. Chen). 1 Co-first author. https://doi.org/10.1016/j.commatsci.2019.109502 Received 17 September 2019; Received in revised form 22 December 2019; Accepted 23 December 2019 0927-0256/ © 2019 Published by Elsevier B.V.
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interaction energies are calculated when a solute atom (Li or Sn) is doped in the site from the surface layer (L1-layer) to fifth neighbor layer (L5-layer) away from the surface, respectively. Considering the shortrange order (SRO) effects on surface segregation [24,25], the interaction energies are approximately ignored when the relative site of solute atom exceeds the fifth neighbor layer. To calculate the surface energies at room temperature, we define the variable γs as the surface energy of Al metal, which denoted the minimum energy forming two free surfaces [26], and then it can be expressed as below:
preferentially on GBs, and the crack initiation occurred beyond the critical value of strength when the triple junction disclinations in GBs were unstable, and the cavity nucleation and local relaxation leading to some amorphization of GB structure were competing relaxation mechanisms during cracking process [15]. Meanwhile, many theoretical approaches have been widely applied to investigate the process of fatigue crack initiation, such as crystal plasticity finite element (CPFE) simulations [16,17], molecular dynamics (MD) simulations [18,19], variational phase-field models [20] and first-principles energy calculations [21–23], which provided an effective way to study the nanocrack nucleation and its mechanism from the atomic scale. To date, because of the limitations of experimental conditions, it is hard to measure the surface energies of Al metals or alloys, and then master their surface characteristics, especially for the nucleation process of nano-cracks. Thus, this work utilizes the first-principles method to investigate the impacts of solute atoms (Li, Sn) on the surface energy of Al alloys at room temperature, which are together decided by the interactions between solute atoms and surfaces, along with the ones between solute atoms in the surface, and the two key factors are of great significance in studying the nucleation process of nano-cracks. The statistical ordered surface configurations are used to determine the maximum surface concentrations of solute segregations to the surfaces. Simultaneously, the Gaussian-Like distribution (GLD) model is proposed for describing the distribution of solute atoms in Al alloys. Results show that the nano-crack nucleation may occur along the (110) surface in the region of dilute Li atom less than 0.016%, but turn into nucleation along the (111) surface in the region of high concentration exceeding 0.016%. While Sn atom has a fairly stronger effect on reducing the surface energy than Li atom, especially in the (001) surface, thus, the nano-cracks in the (001) surface are likely to nucleate under the action of Sn atom, which provides a valuable guidance for theoretical and experimental study of the nano-crack nucleation in Al alloys.
γs = [Esurf − Eperf ] [2S ]
(1)
where Eperf and Esurf indicate the total energies of perfect and surface supercells, respectively. S is the area of the corresponding supercell. Considering the interactions between solute atoms and surfaces, along with solute–solute interactions in the surfaces, we apply the following formula (2) to investigate the impacts of solute atoms on the surface energies γs - sol of Al alloys, which is further modified based on the works of Fan et al. [27] and Liu et al. [28]:
γs - sol = γs +
∑ cs−n (Eint - n + Eint - sol - Ni - n)
S′ (2)
n
where S′ is the area of unit cell for different crystal planes, and cs − n is the solute concentration in the n -th (n = L1~L5) plane in Fig. 1(a)-(c). Eint - n denotes the interaction energies between solute atoms (Li or Sn) and various surfaces, where the solute atoms are located in the n -th atomic plane. Eint - sol - Ni - n indicates the interaction energies between solute atoms of Ni -th neighbor in the n -th atomic plane, where the solute atoms are situated in different neighbor positions. Eint - n and Eint - sol - Ni - n can be calculated as follows [27,29]:
Eint − n = [Esurf
Eint 2. Theoretical model
- sol - Ni - n
- sol - n
− Eperf
- sol - Al]
= Esol - Ni - n − Esol - Nr
− [Esurf − Eperf ]
(3) (4)
-n
where Eperf - sol - Al is the total energy of perfect supercell doping a solute atom (Li or Sn) at room temperature, and Esurf - sol - n is that of corresponding surface supercell doping a solute atom (Li or Sn) in the n -th layer. Esol - Ni - n denotes the total energy of solute atom pairs of Ni -th neighbor in the n -th atomic plane of surface supercells, and Esol - Nr - n indicates the one of solute atom pairs of Nr -th referenced neighbor, which are directly obtained by first-principles energy calculations. Based on the Fermi-Dirac distribution (FDD) model [27,30,31], we further develop the GLD model to investigate the segregation behavior of solute atoms to the surface, which can better describe the characteristics of the completely random distribution of solute atoms in the matrix materials, and it can be expressed by the following formula:
In Al alloys with face-centered-cubic (FCC) crystal structure, we investigate the surface characteristics of (001) , (110) and (111) planes. As depicted in Fig. 1(a)-(c), we construct three surface supercells of 3 × 3 × 14, 3 × 3 × 14 and 3 × 3 × 12 for (001) , (110) and (111) atomic planes, respectively, containing a 12 Å vacuum gap. For investigating the interactions between solute atoms and surfaces, the
cs - n =
1 ⎧1 ⎡ E c0 ⎞ ⎤ + c0 ⎫ 1 − erf ⎛ int − n − ln ⎢ ⎬ 1 + c0 ⎨ 1 − c0 ⎠ ⎥ ⎝ KT ⎦ ⎭ ⎩2 ⎣ ⎜
⎟
(5)
where y = erf(x ) is the Gauss error function, K is the Boltzmann constant in physics, and c0 is the initial solute concentration at T = 300K in Al alloys. 3. Methodology This work applies the Vienna ab initio simulation package (VASP) to implement all energy calculations [32,33]. The projector–augmented wave (PAW) method is used to address the ion–electron interactions [34]. Generalized gradient approximation (GGA) of Perdew–Burke–Eruzerhof (PBE) is chosen as the exchange–correlation functional [35]. After strict convergence tests, the cutoff energy is set as 350 eV in all calculations. In calculating the interaction energies between solute atoms and surfaces, k-mesh Gamma-centered Monkhorst–Pack grids [36] in the Brillouin zone sampling are optimized as 5 × 5 × 1 for (001) , 4 × 5 × 1 for (110) and 5 × 5 × 1 for (111) plane, respectively, and the supercells are fully relaxed under fixing the volume instead of
Fig. 1. The schematic diagrams of (a) (001) , (b) (110) and (c) (111) surface supercells for calculating the interaction energies between solute atoms and various surfaces. 2
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Fig. 2. The interaction energies between solute atoms and various surfaces versus different atomic layers from L1 to L5.
(a) (001)
the shape. However, for calculating the solute–solute interaction energies in each surface, k-grids are optimized as 3 × 3 × 2 for (001) , 2 × 3 × 2 for (110) and 3 × 3 × 2 for (111) plane, meanwhile, the atomic layers at the bottom, as well as the shape and volume of supercells, are fixed to ensure the same lattice constant as the matrix, and the other atoms are totally relaxed. In the light of the works of Touloukian et al. [37] and Liu et al. [38], the coefficient of cubical expansion is set as 1.014 based on the calculated results of phonon spectrum in Al alloys, which is used for simulating the environment at room temperature (T = 300 K ). The Hellmann–Feyman force acting on each atom is lower than 0.01 eV/Å, and the energy convergence criterion of all self-consistent calculations is selected as 10−6 eV/atom.
(b) (110)
N6 N4
N5
N4
N5
N3 N2 N0
N1 N0
N1
N3 N2
N6
(c) (111) N6 N5
4. Results and discussions
N4 N3 N2
Fig. 2 demonstrates the interaction energies between solute atoms and various surfaces, including (001) , (110) and (111) surfaces, where the solute atoms are separately located in the different atomic layers from L1 to L5. For (001) , (110) and (111) surfaces, the computational results exhibit that the value of interaction energies is negative when the solute atoms (Li or Sn) lie in the L1 surface layer, and the negative interaction energy in L1 layer is much smaller than those in the other atomic layers (L2 − L5), indicating that the solute atoms are more likely to segregate to the free surfaces with respect to L2 − L5 atomic layers. Moreover, the interaction energy of Sn atom in the L1 layer is much smaller than that of Li atom, suggesting that Sn atom has higher probability to segregate at the free surface of Al than Li atom. Similarly, as the solute atoms are segregated to the surface, we consider the SRO effects on the strong interactions between neighboring solute atoms, and then we build another three supercells of 6 × 6 × 4, 6 × 6 × 4 and 6 × 6 × 4 for (001) , (110) and (111) planes, respectively, along with the vacuum gap of 12 Å magnitude, which aims to calculate the interaction energies between solute atoms in the surfaces. As depicted in Fig. 3, when doped with a single solute atom (Li or Sn), we only consider the relative positions between solute atoms from the first neighbor to the sixth neighbor in each surface, namely, the interaction energies are approximatively neglected (Eint - sol - N 6 - n = 0 ) due to the SRO effects when the relative positions between solute atoms exceed the sixth neighbor (Nr = N 6), where N0 denotes the reference position between solute atoms, and N1 ~ N6 signify the relative positions between solute atoms from the first neighbor N1 to the sixth neighbor N6 with respect to N0, respectively. By VASP energy calculations, we have obtained the solute–solute interaction energies between various relative positions in (001) , (110) and (111) surfaces, including Li-Li and Sn-Sn atomic pairs, and they are described in Fig. 4, which are used to ensure the maximum surface concentration cmax of
N1
N0
Al atom N0 N1 N2 N3
N4 N5 N6
Fig. 3. The relative positions between solute atoms in various surfaces: (a) (001) surface; (b) (110) surface; (c) (111) surface. For convenience in description, N0 is defined as the reference position, and N1 ~ N6 denote the relative positions to N0, where N1 is defined as the first nearest neighbor position to N0, and so are the N2, …, N6 nearest neighbor positions. Herein, differently colored balls only stand for a single solute atom (Li or Sn) in various relative positions.
solute atomic segregations to the surfaces. To obtain the maximum surface concentration cmax of solute atomic segregations, as seen in Fig. 5, the statistical ordered surface configurations are drawn in the case of the maximum surface concentration cmax , which derives from the results of interaction energies between solute atoms in Fig. 4. For clearly explaining the derivation of statistical surface configurations in Fig. 5, we take Li solute atom for example in the (001) surface. When Li solute atoms are segregated to the (001) surface, Fig. 4(a) indicates that the lowest segregation energy between Li-Li solute atoms occurs in the relative position of the second neighbor N2, which results in preferentially occupying the N2 position in the 6 × 6 surface (see Fig. 5(a)). After the N2 positions of a red dotted line are filled, Li atoms with more segregations further occupy the N4 position due to its negative segregation energy, and then fill the N2 positions of another red dotted line, and so on, the statistical ordered surface configuration is finally obtained as shown in Fig. 5(a), and the same way is applied for getting the other surface configurations, and the yellow area is defined as a minimum repeating unit to calculate the maximum surface concentration cmax , and their values are listed in Table 1. 3
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Fig. 4. The interaction energies between solute atoms with respect to various neighboring positions to N0.
(a) Li-(001)
(b) Li-(110)
(c) Li-(111)
(d) Sn-(001)
(e) Sn-(110)
(f) Sn-(111)
planes, thus, the functional relations between the total interaction energies and surface solute concentrations in the surfaces are still suitable for other atomic planes, like L2~L5 planes. In Fig. 6, the functional relations between the total interaction energies and surface solute concentrations cs are fitted to the third-order polynomial as follows:
ELi - (001) = −0.19477cs − 10.32203cs2 + 17.51055cs3
ELi - (110) = −0.07174cs −
Li
Sn
(001) (110) (111)
1/3 1/2 1/2
1/2 1/3 1/3
(6) (7) (8)
ESn - (001) = −0.05229cs − 7.88627cs2 + 6.36627cs3
(9)
0.03771cs2
+
0.14396cs3
ESn - (111) = 0.3825cs − 11.72068cs2 + 13.15843cs3
(10) (11)
To study the impacts of solute atoms on the nano-crack nucleation in Al alloys, we calculate the surface energy of various crystal planes as a function of solute concentration c0 by combining the Eqs. (1)–(11), as shown in Fig. 7. By VASP energy calculations at T = 300K , herein, the surface energies of Al metal are calculated as follows: γs - (001) = 0.907 J m2 , γs - (110) = 1.021 J m2 and γs - (111) = 0.812 J m2 . Meanwhile, the results in Fig. 7 indicate that with increasing the concentrations of solute atoms, the surface energies of Al alloys first keep unchangeable due to the fairly weak interaction in the case of small solute concentrations, and then decline rapidly, when the surface solute concentrations reach up to the maximum value cmax (see Fig. 5), the incremental solute atoms are no longer segregated to the surfaces, which is mainly caused by the strong interaction energies between solute atoms in the surfaces, thus, the surface energy remains unchanged at high solute concentrations. Furthermore, it is found that Sn atom has a fairly stronger effect on reducing the surface energy with respect to Li atom by comparing the results of Fig. 7(a) and (b), and Pogatscher et al. [39] also found in their studies that Sn additions of ~100 at.ppm can produce the rapid increase in hardness for Al alloys, indicating that the impacts of Sn additions are consistent. For Li solute atom in Fig. 7(a), when the solute concentration is less than 0.016%, small solute concentrations have a stronger effect on reducing the surface energy in (110) plane with respect to (001) and (111) planes, and the nano-cracks are more likely to tend to nucleate along the (110) plane, which may occur in the region of dilute Li atoms in AlLi alloys. However, with the concentration of Li atom exceeding 0.016%, the surface energy in (111) plane declines rapidly to 0.512 J m2 due to the strong interactions with (111) plane, which may force the nano-crack nucleation along the (111) plane, and it may take place in the region of high-concentration Li atoms, thus, Li atoms
Table 1 The maximum surface concentration cmax of solute atom (Li, Sn) segregations to various surfaces. Maximum surface concentration cmax
+
9.69872cs3
ELi - (111) = −1.24546cs − 4.6264cs2 − 2.13885cs3
ESn - (110) = 0.10602cs − Fig. 5. The statistical ordered surface configurations of solute atom (Li, Sn) segregations to various surfaces in the case of maximum surface concentration cmax . The yellow area is defined as a minimum repeating unit to calculate the is Al atom, and the red maximum surface concentration cmax (The blue ball ball is solute atom).
10.2761cs2
By combining the interaction energies between solute atoms in Fig. 4 and statistical ordered surface configurations in Fig. 5, we draw the schematic diagrams of the total interaction energies between solute atoms as a function of surface solute concentrations cs , as depicted in Fig. 6. These curves are obtained by the summation of interaction energies between corresponding solute atoms in the surfaces, and the surface configuration eventually reaches the lowest energy state with solute atom segregations to the surfaces, and an energy value of the curves in Fig. 6 corresponds to a certain surface configuration, as well as the corresponding surface solute concentration. In particular, when the surface solute concentration reaches up to the maximum value, solute atoms are no longer segregated to the corresponding surface, and then the total interaction energies between solute atoms keep unchangeable in the surfaces, forming the final surface configurations in Fig. 5. Since the interaction energies between solute atoms are approximately considered as identical in each plane, including L1~L5
4
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Fig. 6. The total interaction energies between solute atoms in the surface with respect to the surface solute concentrations cs , (a) is the case of Li-Li solute atoms, and (b) is that of Sn-Sn solute atoms. cmax - (001) , cmax - (110) and cmax - (111) denote the maximum surface concentrations (see Table 1) of (001) , (110) and (111) surfaces, respectively.
higher probability to segregate at the free surface of Al than Li atom. (2) With the continuous segregations of solute atoms to the surface, the surface energies of Al alloys first keep unchangeable, and then decline rapidly in the case of surface solute concentrations lower than the maximum value cmax , and finally remains unchanged again since the surface solute concentration reaches its maximum, indicating that the high-concentration solute atoms (Li or Sn) promote the nano-crack nucleation. (3) For Li atom, small solute concentrations less than 0.016% have a stronger effect on decreasing the surface energy in (110) plane with respect to (001) and (111) planes, and the nano-crack nucleation may occur along the (110) plane in the region of dilute Li atoms. Li atom of high concentration exceeding 0.016% forces the nano-crack nucleation along the (111) plane. (4) Sn atom has a fairly stronger effect on reducing the surface energy than Li atom. Especially in the (001) plane, the surface energy drops rapidly in the case of a fairly low concentration, suggesting that the nano-cracks tend to nucleate along (001) plane under the action of Sn atom.
promote the nano-crack nucleation due to reducing the surface energies of each plane. Similarly, Sn atom has the stronger influences on reducing the surface energy than Li atom, as shown in Fig. 7(b), and the surface energy drops rapidly in the case of a fairly low concentration, especially in the (001) plane, suggesting that the nano-cracks tend to nucleate along (001) plane under the action of Sn atom compared with the (110) and (111) planes. 5. Conclusions In summary, this work utilizes the first-principles method to study the influences of solute atoms (Li, Sn) on the surface energy of Al alloys at room temperature, and further predicts the nano-crack nucleation along different surfaces. The interaction energies between solute atoms and various surfaces are calculated, and the statistical ordered surface configurations of solute atomic segregation to the surfaces are also drawn based on the interaction energies between solute atoms in the surfaces, which is used to ensure the maximum surface concentrations of solute atomic segregations. Herein, the GLD model is proposed for describing the distribution of solute atoms in Al alloys. The relevant conclusions are summarized as follows:
CRediT authorship contribution statement
(1) The solute atoms are more likely to segregate to the free surfaces with respect to the other atomic planes (L2 − L5), and Sn atom has
Z.P. Wang: Conceptualization, Methodology, Writing - original
Fig. 7. The surface energies as a function of solute concentration c0 with respect to Li (a) and Sn (b) solute atoms. 5
Computational Materials Science 174 (2020) 109502
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draft. T.W. Fan: Conceptualization, Data curation, Formal analysis. J.J. Lin: Formal analysis, Project administration. F. Liu: Project administration, Visualization. B. Liu: Resources, Visualization. Q.H. Fang: Funding acquisition, Supervision, Validation, Writing - review & editing. D.C. Chen: Investigation, Supervision, Validation. L. Ma: Data curation. P.Y. Tang: Software.
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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The authors would like to deeply appreciate the support from the National Natural Science Foundation of China (11572118, 11772122 and 51501060), the Hunan Provincial Science Fund for Distinguished Young Scholars (2015JJ1006), the National Key Research and Development Program of China (2016YFB0700300), the Key Project of Department of Education of Guangdong Province (2016GCZX008), Foshan University Scientific Research Project (CGG07257 and BGH206017), and the Hunan Provincial Innovation Foundation For Postgraduate (CX2017B085). This work was implemented in the Xiangqing Super Computational Platform (gg07026). Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.commatsci.2019.109502. References [1] Y. Shen, T.F. Morgeneyer, J. Garnier, L. Allais, L. Helfen, J. Crépin, Three-dimensional quantitative in situ study of crack initiation and propagation in AA6061 aluminum alloy sheets via synchrotron laminography and finite-element simulations, Acta Mater. 61 (2013) 2571–2582. [2] Y.B. Ju, M. Koyama, T. Sawaguchi, K. Tsuzaki, H. Noguchi, In situ microscopic observations of low-cycle fatigue-crack propagation in high-Mn austenitic alloys with deformation-induced ε-martensitic transformation, Acta Mater. 112 (2016) 326–336. [3] T.T. Nguyen, J. Yvonnet, M. Bornert, C. Chateau, Initiation and propagation of complex 3D networks of cracks in heterogeneous quasi-brittle materials: direct comparison between in situ testing-microCT experiments and phase field simulations, J. Mech. Phys. Solids 95 (2016) 320–350. [4] M. Seita, J.P. Hanson, S. Gradečak, M.J. Demkowicz, The dual role of coherent twin boundaries in hydrogen embrittlement, Nat. Commun. 6 (2015) 1–6. [5] Z. Tarzimoghadam, D. Ponge, J. Klöwer, D. Raabe, Hydrogen-assisted failure in Nibased superalloy 718 studied under in situ hydrogen charging: the role of localized deformation in crack propagation, Acta Mater. 128 (2017) 365–374. [6] G.S. Cole, A.M. Sherman, Light weight materials for automotive applications, Mater. Charact. 35 (1995) 3–9. [7] J.C. Williams, E.A. Starke Jr, Progress in structural materials for aerospace systems, Acta Mater. 51 (2003) 5775–5799. [8] J.H. Martin, B.D. Yahata, J.M. Hundley, J.A. Mayer, T.A. Schaedler, T.M. Pollock, 3D printing of high-strength aluminium alloys, Nature 549 (2017) 365–369. [9] S.S. Singh, E.Y. Guo, H.X. Xie, N. Chawla, Mechanical properties of intermetallic inclusions in Al 7075 alloys by micropillar compression, Intermetallics 62 (2015) 69–75. [10] Y.Q. Chen, S.P. Pan, M.Z. Zhou, D.Q. Yi, D.Z. Xu, Y.F. Xu, Effects of inclusions, grain boundaries and grain orientations on the fatigue crack initiation and propagation behavior of 2524–T3 Al alloy, Mater. Sci. Eng. A 580 (2013) 150–158.
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