ABSTRACT KEYWORD. Keywords: brittle/ductile interface; tensile test; fracture; Ni/NiAl; Ni/Ni 3 Al. INTRODUCTION

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1 MOLECULAR DYNAMICS SIMULATIONS OF TENSILE TESTS AND INTERFACIAL FRACTURE IN NI/NIAL AND NI/NI 3 AL Siegfried Schmauder, Stephen Hocker, Priyank Kumar IMWF, University of Stuttgart, Pfaffenwaldring 32, D Stuttgart, Germany ABSTRACT Numerical tensile tests in the ductile/brittle systems Ni/Ni 3 Al and Ni/NiAl are performed using molecular dynamics simulations. It is shown that in both materials the interfaces have influence on strain induced material failure. Interfacial fracture was observed in the Ni/NiAl system whereas in Ni/Ni 3 Al defect nucleation eased by misfit dislocations is the occuring failure mechanism. KEYWORD Keywords: brittle/ductile interface; tensile test; fracture; Ni/NiAl; Ni/Ni 3 Al. INTRODUCTION Internal interfaces are known to have significant influence on the mechanical properties of extremely heterogeneous materials. The atomic length scale has usually to be involved for understanding the processes which lead to material failure. The aim of this work is to investigate the fracture and defect nucleation processes in uniaxial tensile tests with strain axis perpendicular to the interface. An atomistic view as given in molecular dynamics provides a realistic insight into these phenomena at the interfaces analyzed [1]. Because of the low ductility of the intermetallic alloys Ni 3 Al and B2-NiAl the systems Ni/Ni 3 Al and NiNi/B2-NiAl are model systems for brittle/ductile interfaces. They are chosen in this work due to the availablitiy of high accurate interatomic potentials between the atoms and phases involved [2, 3]. The system Al-Ni has been frequently investigated atomistically by Molecular Dynamics (MD) in the recent past for several reasons, such as surface tension in liquid Ni [4], liquid and amourphous Ni-Al alloys [5], melting of Ni 3 Al [6, 7], diffusion mechanisms in NiAl [8], surface roughnesses in Al [9], ordering kinetics in Ni 3 Al [10], investigation of Al and Ni thin film growth on Ni(111) surfaces [11], crystallization of (Ti-)Al amorphous alloys [12] and the calculation of P-T diagrams of Ni and Al using molecular dynamics simulations [13]. There are less papers available on fracture and damage simulations on the atomic scale in Ni-Al systems and none of them is related to interface related fracture. Molecular dynamics simulations are devoted to crack propagation phenomena in Ni [14, 15] and NiAl [16] monocrystals under mode I loading. Nanoimprinting phenomena including dislocation emission under the imprinting tool at different loading and unloading speed and increased temperatures were analyzed in order to understand nanoimprinting lithographic processes in different Cu-Ni alloys [17]. Finally, Ni/Cu(001) interfaces have been studied based on MD simulations in order to analyze epitaxial close atomic systems including anisotropy effects and interface strains [18]. In this work material failure due to uniaxial strain perpendicular to the interface is analyzed and compared in the systems Ni/Ni 3 Al and Ni/B2-NiAl. The influence of the specific interfaces is investigated by performing numerical MD tensile tests with Ni, NiAl and Ni 3 Al monocrystals.

2 COMPUTATIONAL DETAILS All simulations are carried out using the IMD code which is a very powerful molecular dynamics package [19]. It provides relaxation simulations as well as calculations in different ensembles. Additionally it can be used to calculate stress tensors and elastic constants from a relaxed configuration directly. The reliability of MD simulations crucially depends on the quality of the potentials used. We chose the so-called Embedded Atom Method (EAM) potentials [20, 21], which are better suited for metals and intermetallic compounds than pair potentials. They include an additional embedding term, taking the form where U i describes the energy of embedding atom i in a density n i, which is the sum of contributions ρ j from neighbours j at distances r ij. For Ni/NiAl the potential of Ludwig and Gumbsch [2] was used whereas for Ni/Ni 3 Al the potential of Mishin [3] was applied. The so chosen potentials give reasonable values for lattice parameters and elastic constants of the involved materials. A timestep of 2 fs was used for all calculations. Modelling tensile tests in structures with interfaces requires sufficiently relaxed structures with minimized residual stresses. This condition is achieved by relaxation of the initial structures with pressure adjustement. At each step, the pressure tensor of the sample is calculated, and the size of the simulation box is changed by a small amount in order to lower that pressure. Initial structures are generated by assembly of Ni and NiAl or Ni 3 Al using lattice constants of the relaxed structures. Axial pressure relaxation of these structures lowers the residual shear stresses to 20 GPa. Test calculations revealed that residual stresses in this range have negligible influence on the results. The dimensions of the so chosen samples (b x, b y, b z ) are about nm 3 containing about atoms. Dislocations and stacking faults are detected by applying common neighbour analysis [22]. In fcc-structures we observe three kinds of defects with this method. There are stacking faults consisting of {111} planes of atoms which have hcp structure. Another type of defects are atoms which have 12 nearest neighbours but do not posess fcc or hcp structure. Together with the third type of defects, which consists of atoms which do not have 12 nearest neighbours, these categories of local environments are used to visualize dislocations and stacking faults. TENSILE TESTS Numerical tensile tests at different temperatures were performed as follows. First an equilibration of the sample is achieved by performing a calculation of about steps in the npt ensemble. Thereafter tensile loading is done by stretching the sample. In each MD step the sample is stretched by a factor of uniaxially whereas the pressure in both perpendicular directions is kept zero by npt pressure control. Periodic boundary conditions are applied in all simulations. A. Ni, Ni 3 Al and NiAl monocrystals In the whole temperature range analyzed Ni and Ni 3 Al show ductility whereas NiAl is a brittle material. In Ni material failure occurs by the generation of stacking faults which are bordered by Shockley partials. At room temperature these stacking faults appear at strains of 11% at which the stress is 12 GPa. Tensile loading of Ni in the [001] direction leads to the appearance of stacking faults on all four possible {111} orientations.

3 In Ni 3 Al ductile failure was observed as well. However, the stress strain curves differ regarding the temperature dependence. Whereas the tensile strength of Ni decreases significantly with increasing temperature the tensile strength of Ni 3 Al ranges from 10 to 13 GPa in the whole temperature range analyzed. In contrary to the results for Ni the strain necessary for defect generation is about 8% in Ni 3 Al at all temperatures observed. In NiAl maximum strains and stresses reach higher values and material failure occurs by fracture. Tensile loading in [100] direction leads to cracking at a strain of 27% with a maximum stress of 22 GPa. Cracking occurs at the (100) and {110} planes of the crystal. B. Ni/NiAl Since B2-NiAl consists of periodic stackings of Ni and Al planes an {100} type interface to Ni can be Al oder Ni terminated. In our tensile tests we used a structure with each of these two interfaces. The obtained stress strain curves (Fig. 1a) show significant differences compared to those of the single crystal Ni and NiAl structures. Two effects occur whilst increasing strain: First the ductile material fails by the generation of stacking faults terminated by Shockley partials. Compared to the failure of the Ni single crystal this happens at lower strains and stresses in the bilayer structure with {100} interface, e.g. at 9% strain and 8.5 GPa stress at room temperature. These defects are generated at the Al-terminated interface and spread through the Ni-layer. Further increase of strain leads to a higher defect density whilst stresses are increasing again. All four possible orientations of the stacking faults occur. Finally, cracking at the Al-terminated interface occurs at strains of about 25% (Fig. 1b). (a) (b) Fig. 1: (a) Stress strain curves of Ni from tensile tests with potentials from [2] as a function of temperature with [001] tension axis. At all temperatures material failure which is observable by the first decrease of the stress in this figure occurs via dislocation nucleation. Stress strain curves of Ni obtained with potential from [3] look similar, but show a slightly increased tensile strength. (b) Final structure after tensile test of Ni/NiAl with (001) interface and [001] tension axis. The initial structure contains two interfaces differing in the termination layer of NiAl (Ni on top/bottom, Al in the middle of this structure). Cracking occured at the Al-terminated interface. In the Ni part of the structure, stacking faults are observable (dark grey atoms). Since material failure under strain is known to be dependent on initial defects as interfaces, vacancies or notches, further studies of the Ni/NiAl(001) interface system with regard to initial 3

4 notches were performed. An elliptic notch (semi-major in the interface plane: 0.4 nm, semiminor: 0.05 nm) was inserted at the interface by removal of atoms. Tensile tests with these initial structures showed that the tensile strength decreases from 9 GPa to 7 GPa. The cracking process is influenced by notches as well. As can be seen in Fig. 2 the strain at which cracking occurs decreases by 4% in the case of a notch at the Al-terminated interface. Fracture initiated by a notch at the Ni-terminated interface occurs at strains of about 25% as in the case of the Al-terminated interface without notches in the sample. However, it was observed that cracking occurs at the Ni-terminated interface with notch more preferably than at the Al-terminated interface without notch wheras cracking always occurs at the Alterminated interface in the case without notches. Fig. 2: Stress strain curves of Ni/NiAl samples with (001) interface orientation and [001] tension axis with an initial notch (at the Al- or Ni-terminated interface) compared to stress strain curves of the samples without notch. C. Ni/Ni 3 Al From the existence of cuboidal precipitations of Ni 3 Al in Ni it is known that a stable interface orientation of Ni/Ni 3 Al is of the Ni-terminated {100} type [3]. In our simulations we use a sample with two of these interfaces. The obtained stress strain curves (Fig. 3a) show a different temperature dependence than observed for the involved materials. In the whole temperature range observed the tensile strengths are between 4 and 6 GPa at strains of 3.7 to 5% which is significantly lower than the values of the Ni and Ni 3 Al monocrystals. Since the lattice constants of the Ni and Ni 3 Al are very close it is possible to perform tensile tests of Ni/Ni 3 Al without misfit dislocations as well. In this case the lattice constant of Ni 3 Al was used and therefore the Ni part of the structure was expanded by a factor of As can be seen in Fig. 3b the result of the tensile test differs significantly from the case with misfit dislocations. The tensile strength of 12 GPa is close to the values obtained for the Ni and Ni 3 Al monocrystals and as in Ni 3 Al material failure occurs at about 8% strain. The comparison to the case with misfit dislocations shows clearly that these defects ease the emission of stacking faults terminated by Shockley partials. The visualisation of the generated defects during tensile test with misfit dislocations (Fig. 4) reveals the process of defect nucleation. It is clearly visible that the stacking faults terminated by Shockley partials are nucleated at the misfit dislocations. At medium strain (4-6%) they spread exclusively into the more ductile Ni. Further increase of the strain leads to defect propagation in Ni 3 Al as well. Even at strains up to 40% no cracking at the interface is observable. For crack initiation an elliptic notch (semi-major in the interface plane: 4 nm, semi-minor: 0.5 nm) was inserted at the interface by removal of atoms. In contrary to the case of Ni/NiAl where cracking at the

5 more stable Ni-terminated interface was initiated by the notch we found no fracture in the case of Ni/Ni 3 Al. Ni/Ni 3 Al always shows ductile failure also in the tensile tests with notches. (a) (b) Fig. 3: (a) Stress strain curves of Ni/Ni 3 Al with Ni terminated (001) interfaces from tensile tests with [001] tension axis as a function of temperature. At all temperatures ductile failure by dislocation nucleation in Ni occurs at strains up to 6%. (b) Stress strain curve of a Ni/Ni 3 Al sample (Ni terminated (001) interfaces, tensile axis [001]) with misfit dislocations compared to the stress strain curve of a sample without misfit dislocations but expanded Ni part of the structure. The tensile strength is found to be significantly increased in the sample without misfit dislocations. Fig. 4: Structure during tensile test of Ni/Ni 3 Al with (001) interface and [001] tension axis. At 6% strain stacking faults (dark grey atoms) terminated by Shockley partials are emitted from the misfit dislocations (squares of light grey atoms) into the more ductile material. Tension axis: vertical. View: in direction of xy-xz-edge. CONCLUSIONS It was observed that in both brittle/ductile model systems the interfaces have influence on strain induced material failure. Basically we found that material failure occurs by the 5

6 generation of intrinsic stacking faults terminated by Shockley partials in the more ductile material. In the fcc/bcc structure Ni/NiAl the interface serves as nucleation plane for these defects. They are generated at the interface whereas they are most easily nucleated at Al terminated interfaces of the Ni/NiAl system. Cracking at the {100} type interface was observed at much higher strains than the strain necessary for defect generation. Even at high strains the fcc/fcc structure Ni/Ni 3 Al shows no cracking. At medium strains the ductile failure process is similar to Ni/NiAl regarding the type of defects emitted into Ni. However, the Shockley partials are not nucleated at the whole interface but they start growing from the misfit dislocations. Since misfit dislocations ease the emission of the described defects the tensile strength of Ni/Ni 3 Al with misfit dislocations is significantly decreased compared to the Ni/Ni 3 Al structure without misfit dislocations. In summary we found that the mechanical properties of the studied brittle/ductile interface systems differ significantly from those in each of the involved materials. The calculations presented show thus insight into the deformation and fracture behaviour of Ni/NiAl as well as the Ni/Ni 3 Al interfaces. Our work provides a starting point for molecular dynamics studies on the technologically very important metal/oxide-interface systems in which suitable potentials are presently under development [23]. ACKNOWLEDGEMENT The authors gratefully acknowledge the financial support by the Deutsche Forschungsgemeinschaft (DFG) via the project molecular dynamics simulation of the fracture of metal/ceramic interfaces within the collaborative research center 716 dynamic simulation of systems with large numbers of particles. REFERENCES [1] Kohlhoff, S., Schmauder, S., Gumbsch, P.: Coupled Atomistic-Continuum Calculations of Near Interface Cracking in Metal/Ceramic Composites" Metal-Ceramic Interfaces, Acta-Scripta Metallurgica Proceedings Series 4 (1990), pp [2] Ludwig, M., Gumbsch, P.: An empirical interatomic potential for B2 NiAl Modelling Simul. Mater. Sci. Eng 3 (1995), pp [3] Mishin, Y.: Atomistic modeling of the γ- and γ -phases of the Ni-Al system Acta Materialia 52 (2004), pp [4] Hou, H. Y., Chen, G. L., Chen, G., Shao, Y. L.: A molecular dynamics simulation on surface tension of liquid Ni and Cu Computational Materials Science 46 (2009), pp [5] Zhu, J.-B., Wang, S., Qiao, M.-H., Wang, W.-N., Fan, K.-N., First-principle molecular dynamics study of the structural and electronic properties of liquid and amorphous Ni Al alloys Journal of Non-Crystalline Solids 353 (2007), pp [6] Wang, R., Hou, H., Ni, X., Chen, G.: Molecular dynamics simulation of Ni 3 Al melting. Journal of University of Science and Technology Beijing 15 (2008) pp [7] Kohler, C. Kizler, P., Schmauder, S.: Atomistic simulation of the pinning of edge dislocations in Ni by Ni 3 Al precipitates Materials Science and Engineering A (2005), pp

7 [8] Bas, B. S. D., Farkas, D.: Molecular dynamics simulations of diffusion mechanisms in NiAl Acta Materialia 51 (2003), pp [9] Cheng, Y. Y., Lee, C. C.: Simulation of molecular dynamics associated with surface roughness on an Al thin film Surface & Coatings Technology 203 (2008), pp [10] Oramus, P., Massobrio, C., Kozlowski, M., Kozubski, R., Pierron-Bohnes, V., Cadeville, M., C.Pfeiler, W.: Ordering kinetics in Ni 3 Al by molecular dynamics Computational Materials Science 27 (2003) pp [11] Lee, S.-G.,Chung, Y.-C.: Atomic-level investigation of Al and Ni thin film growth on Ni(111) surface: Molecular dynamics simulation Applied Surface Science 253 (2007) pp [12] Shimono, M., Onodera, H.: Molecular dynamics study on formation and crystallization of Ti Al amorphous alloys Materials Science and Engineering A (2001) pp [13] Gurler, Y., Ozgen, S.: The calculations of P T diagrams of Ni and Al using molecular dynamics simulation Materials Letters 57 (2003), pp [14] Gumbsch, P., Zhou, S. J., Holian, B. L.: Molecular dynamics investigation of dynamic crack stability Phys. Rev. B. 55 (1997) pp [15] Karimi, M., Roarty, T., Kaplan, T.: Molecular dynamics simulations of crack propagation in Ni with defects Modelling Simul. Mater. Sci. Eng. 16 (2006), pp [16] Gumbsch, P.: Brittle fracture process modelled on the atomic scale Z. Metallkd. 87 (1996) pp [17] Fang, T.-H., Wu, C.-D., Chang, W.-J.: Molecular dynamics analysis of nanoimprinted Cu Ni alloys Applied Surface Science 253 (2007), pp [18] Jiménez-Sáez, J., Domíninguez-Vázquez, J., Pérez-Martín, A., Jiménez-Rodríguez, J.: A molecular dynamics study of Ni/Cu(001) interfaces. Nuclear Instruments and Methods in Physics Research B 193 (2002), pp [19] Mikula, R., Stadler, R. M. J., Trebin, H.-R.: IMD: A software package for molecular dynamics studies on parallel computers. Int. J. Mod. Phys. C 8 (1997), pp [20] Daw, M. S., Baskes, M. I.: Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals Phys. Rev. Lett. 50 (1983), pp [21] Daw, M. S., Baskes, M. I.: Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals Phys. Rev. B 29 (1984), pp [22] Clarke, A. S., Jónsson, H.: Structural changes accompanying densification of random hard-sphere packings Phys. Rev. E 47 (1993), pp [23] SFB 716, Project B.1, 7

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