VN composite: Molecular dynamics study

Journal of Alloys and Compounds 814 (2020) 152151

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Strain rate and temperature effects on the mechanical properties of TiN/VN composite: Molecular dynamics study Shoubing Ding*, Xinqiang Wang** School of Physics, Chongqing University, Chongqing, 401331, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 28 May 2019 Received in revised form 14 August 2019 Accepted 2 September 2019 Available online 13 September 2019

The second nearest-neighbor modified embedded-atom method (2NN MEAM) potential of TieVeN ternary system is developed based on the newly optimized interaction potentials of binary systems. The obtained potentials can excellently reproduce the structural, elastic and surface properties of the relevant systems. Then the effects of the strain rate and temperature on the mechanical properties of TiN/VN composite are studied by using the present potentials. It is found that strain rates have almost no influence on the Young's modulus of TiN/VN composite, but have a great influence on the inelastic properties. Whereas both the Young's modulus and the inelastic properties are sensitive to temperature. It is also found that the fracture of TiN/VN composite is a brittle fracture taking place in the VN layers. © 2019 Elsevier B.V. All rights reserved.

Keywords: TiN/VN composite 2NN MEAM potential Strain rate and temperature effects Mechanical properties MD simulation

1. Introduction Transition metal nitrides, such as TiN and VN, have attracted a lot of attention during the last decades because of their remarkable properties, such as high chemical and thermal stability, superior wear and oxidation resistance and high hardness [1e6]. The TiN/VN multilayered coating, which is the alternant structure with the TiN and VN layers of nanometer thickness, has been found that its hardness is much higher than that of the mononitride coatings [7]. To better understand the mechanical properties of TiN/VN multilayered coating, a number of theoretical and experimental efforts have been implemented [8e11]. However, it remains difficult to obtain sufficient information about the microstructure of TiN/VN, which is of significance for understanding the mechanism to enhance the hardness. Molecular dynamics (MD) simulation, as an atomic-level modeling technique, can serve as an effective approach to gain insights into the microstructure of the materials. Recently, this approach was used to investigate the influence of the applied strain rate and temperature on the mechanical properties of several materials [12e15]. For example, Fu et al. [14] investigated the effect

* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (S. Ding), [email protected] (X. Wang). https://doi.org/10.1016/j.jallcom.2019.152151 0925-8388/© 2019 Elsevier B.V. All rights reserved.

of strain rate on the tension and compression behavior of nanopolycrystalline VN, and found that the yield strain and yield stress increase with the increasing of strain rate. Liu et al. [15] performed a MD simulation to study the effect of temperature on the deformation and fracture behavior of Ti2AlN, and found that Ti2AlN changes from brittle to ductile with the increasing of temperature. Nevertheless, how the strain rate and temperature affect the mechanical behaviors of TiN/VN composite remains unknown. In all the MD simulations mentioned above, the second nearestneighbor modified embedded-atom method (2NN MEAM) potentials were used. This kind of potential is believed to be highly applicable for the alloys and composites. To investigate the effects of strain rate and temperature on the mechanical properties of TiN/ VN composite through MD simulation, the 2NN MEAM potential parameters for TieVeN ternary system are required, but not available up to now. These parameters can be determined in some way through those for the constituent unary (Ti, V, N) and binary (TieN, VeN, TieV) systems. The potential parameters for pure Ti [16], V [17] and N [18], and those for TieN [17] and VeN [17] binary systems are already available. Though the 2NN MEAM potential parameters for TieV binary system have been developed by Feng et al. [19], they are no accepted in this work to develop the TieVeN ternary potential parameters because the potential parameters for pure V used by Feng et al. are different from those used for VeN binary system [17]. So, before developing the potential parameters for TieVeN ternary system, the parameters for TieV binary

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system need to be determined first. The rest of this paper is organized as follows: The 2NN MEAM formalism and the simulation approach are given in the next section. In Section 3, the procedure of determining the potential parameters is briefly described, and the reliability of them is examined by comparing the fundamental physical properties of relevant materials with experimental and/or first-principles data available. In Section 4, the effects of strain rate and temperature on the mechanical properties of TiN/VN composite under uniaxial tension are studied by using the present interaction potentials. Finally, the results are summarized in Section 5.

2  1 1 Rij x2 þ y2 ¼ C 2

(6)

where x and y represent the coordinates of k with respect to the ellipse defined by the positions i, j, k. For each neighbor atom k, the value of parameter C can be calculated from relative distances among the three atoms, i, j and k, as follows:

  2  2 Xik þ Xkj  Xik  Xkj  1 C¼ 2  1  Xik  Xkj

(7)

2. Methodology 2.1. Interaction potential The 2NN MEAM interaction potentials have been widely applied to simulate the mechanical properties of materials. The detailed formalism of the 2NN MEAM can be found in literatures [16,20e22] and the main steps to determine the interaction potential of a binary or ternary system are given as follows. In the MEAM, the total energy of a system can be expressed as:

2 3 X X   1 4Fi ðri Þ þ E¼ S f R 5 2 jðsiÞ ij ij ij i

(1)

where Xik ¼ ðRik =Rij Þand Xki ¼ ðRkj =Rij Þ. The extent of screening is determined by the limiting values of Cmin and Cmax. Therefore, C < Cmin (Sij ¼ 0) and C > Cmax (Sij ¼ 1) mean that the interaction between atoms i and j is completely unscreened and screened, respectively. For a given reference structure, the value of the total energy per atom Eu ðRÞ can be estimated from the zero-temperature universal equation of state by Rose et al. [23]. The universal equation of state for materials is given in the following form:

  3 * Eu ðRÞ ¼  Ec 1 þ a* þ da* ea

(8)

where d is an adjustable parameter,





where Fi is the embedding function for the atom i embedded in a background electron densityri, fij ðRij Þ and Sij are the pair potential and the screening function between atom i and j with distance Rij. Since the functional formalism of the embedding function Fi has been given [21], the pair interactionfij ðRij Þcan be determined by Eq. (1). To calculate fij ðRij Þ, a reference structure of the system should be defined and its total energy per atom is expressed as a function of the nearest-neighbor distance. Then, fij ðRij Þ can be obtained based on the embedding energy and the total energy per atom. In the 2NN MEAM, the total energy per atom of the system in the reference structure can be given in the following form:

In Eqs (8) - (10), re, B, Ec and U are the nearest-neighbor distance, bulk modulus, cohesive energy and atomic volume of the equilibrium reference structure, respectively.

  Z Z2 Sij fðaRÞ Eu ðRÞ ¼ F r0 ðRÞ þ 1 fðRÞ þ 2 2

2.2. MD simulation

(2)

where Z1 and Z2 are the numbers of the first and second nearestneighbor atoms in the reference structure, respectively. a is the ratio of the second and first nearest-neighbor distances, and Sij is the many-body screening function, which reflects the influence of the neighbor atom k on the interaction between atom i and j, defined by the product of the screening factors, Sikj, duo to all the other neighbor atoms k:

Sij ¼

Y

Sikj

(3)

a* ¼ a

R 1 re

(9)

and

a¼



1 9BU 2 Ec

(10)

All MD simulations in this work are performed with the January 26, 2017 version of the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [24]. The radial cutoff distance is set to be 5.0 Å, which is larger than the second nearest-neighbor distance in the structures under consideration. The post-processing software OVITO [25] is used to visualize the evolution of the microstructure, and the center symmetry parameter (CSP) method [26] is employed to calculate the local lattice disorder and identify dislocations and stacking faults.

ksi;j

The screening factor Sikj is determined through the following formula:

 Sikj ¼ fc

C  Cmin Cmax  Cmin

 (4)

3.1. Determination and verification of interaction potential for TieV binary system

(5)

As mentioned in the introduction, the 2NN MEAM potential parameters for Ti, V, N unary and TieN, VeN binary systems are already available and only the parameters for TieV need to be redetermined here. According to the approach suggested in our previous work [17], the parameters for TieV are optimized in the reference structure of B2-type. The obtained results and all the other parameters for the constituent unary and binary systems

where fc is the smooth cutoff function defined as:

8 > <1 i2 h fc ¼ 1  ð1  xÞ4 > : 0 and

x1

9 > =

0x1 > ; x0

3. Determination of interaction potential for TieVeN ternary system

S. Ding, X. Wang / Journal of Alloys and Compounds 814 (2020) 152151

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Table 1 The 2NN MEAM potential parameters for pure Ti, V and N systems. The units of the cohesive energy Ec and the equilibrium nearest-neighbor distance re are eV and Å, respectively. All the other parameters are dimensionless.

a

Ti Vb Nc a b c

Ec

re

a

A

bð0Þ

bð1Þ

bð2Þ

bð3Þ

t ð1Þ

t ð2Þ

t ð3Þ

Cmin

Cmax

d

4.87 5.3 4.88

2.92 2.625 1.10

4.63 4.81 5.96

1.17 0.73 1.8

1.32 4.74 2.75

0.0 1.0 4.0

1.95 2.5 4.0

5.0 1.0 4.0

5.3 3.3 0.05

14.1 3.2 1.0

5.0 2.0 0.0

1.0 0.75 2.0

1.44 2.8 2.8

0.0 0.0 0.0

Ref. [16]. Ref. [17]. Ref. [18].

needed to develop the potential of TieVeN ternary system are presented in Table 1 and Table 2, respectively. As shown in Table 1, there are fourteen independent parameters for each pure element. Among them, Ec, re, a, and d appear in the universal equation of state. The decay length (bð0Þ ,bð1Þ ,bð2Þ ,bð3Þ ) and the weight factors (t ð1Þ ,t ð2Þ ,t ð3Þ ) are related to the electron density. The parameter A is associated with the embedding function, and the parameters Cmin and Cmax are responsible for many-body screening effect. For each binary system shown in Table 2, there are another thirteen parameters, Ec, re, a, d, Cmin(i-i-j), Cmin(j-j-i), Cmin(i-j-i), Cmin(j-i-j), Cmax(i-i-j), Cmax(j-j-i), Cmax(i-j-i), Cmax(j-i-j) and r0. Here, r0 is the ratio of .r0B and r0A (A-B¼TieN, VeN and TieV). In the process of optimizing the potential parameters for TieV system, the initial values of Ec, re and a of B2-type TiV are determined by the first-principles calculation using the Vienna ab initio simulation package (VASP) [27e29], and the elastic constants, with available experimental values [30], are applied to be the target property. To verify the reliability of the obtained potential parameters, the present MEAM lattice parameter, cohesive energy and elastic constants of B2-type TiV are compared with the experimental and/or other calculation results in Table 3. Though there are no experimental data of lattice parameter and cohesive energy available for comparison, the present MEAM values can be compared with the first-principles results and good agreement is reached. For the elastic constants, the comparison shows that both the present and previous MEAM values of C11 and C12 are very close to the experimental ones within an error of 1.8%, but the present MEAM value of C44 is much better than the previous MEAM one, with an error of 1.2% and 7.7%, respectively. This is usually considered to be a very significant improvement about the 2NN MEAM potential. As a consequence, the present MEAM results reach a better overall agreement with the experimental data than the previous MEAM ones, and from this point of view, the present potential parameters are believed to be more reliable.

Table 2 The 2NN MEAM interaction potential parameters for the binary systems. The units of Ec and re are the same as in Table 1, and all the other parameters are dimensionless. Parameter

TieN [17]

VeN [17]

TieV

Ec re

6.61 2.121 4.829 0.0 1.457 1.457 0.90 0.22 2.8 2.8 2.8 2.8 18

6.92 2.06 4.599 0.0 1.30 1.30 0.74 0.846 2.8 2.8 2.8 2.8 18

5.208 2.645 4.421 0.0 1.10 1.10 0.01 0.66 2.8 2.8 2.8 2.8 1

a

d Cmin (i-i-j) Cmin (j-j-i) Cmin (i-j-i) Cmin (j-i-j) Cmax (i-i-j) Cmax (j-j-i) Cmax (i-j-i) Cmax (j-i-j)

r0

Table 3 Comparison of the lattice parameter, cohesive energy and elastic constants of B2type TiV calculated by the present developed 2NN MEAM potentials with the experimental data and other calculation values. The units of the lattice parameter a, cohesive energy Ec and elastic constants are Å, eV and GPa, respectively. Structure

B2-type TiV

a b c d e

Ref. The Ref. Ref. Ref.

Property

a Ec C11 C12 C44

Exp.e

MEAM Present

Previous

3.06 5.208 167 108 41.8

3.08 5.085 168 108.9 38.1

a

e e 167.6 110 41.3

First-principles Presentb

Previousc

3.10 5.283 165.1 119.2 43.2

3.28 5.2076d 169.6 122.3 33.6

[19]. first-principles calculation performed in present work. [31]. [32]. [30].

Table 4 Comparison of the surface energies of B2-type TiV at 0 K calculated using the present 2NN MEAM potential with the first-principles calculation results and the previous MEAM potential ones. The unit of the surface energy is J/m2. Surface

Present MEAM

Firstprinciples

(001) (110) (111)

2.42 2.56 3.65

1.97 2.15 3.28

Previous MEAM [19] 2.88 2.44 2.65

To further evaluate the transferability of the present 2NN MEAM potential parameters, the surface energies of B2-type TiV at 0 K are calculated using LAMMPS and compared with those obtained by the first-principles calculation using VASP. The details of the method to calculate the surface energies can be found in our previous work [17]. As shown in Table 4, the present MEAM results agree well with the first-principles calculation ones, and the orientation dependency of surface energy is also reproduced. It should be mentioned that such a good agreement is difficult to be achieved by the previous MEAM potential. This comparison shows again that the present 2NN MEAM potentials are reliable. 3.2. Determination and verification of interaction potential for TieVeN ternary system According to the 2NN MEAM formalism for a ternary system, once the potential parameters for the constituent unary and binary systems are obtained, there are only six unknown parameters (three for Cmin (i-k-j) and the other three for Cmax (i-k-j)) left, which reflect the screening effect of the third element atom (k) on the interaction between two neighboring atoms (i and j). In the present case of TieVeN ternary system, these parameters are Cmin(TieVeN), Cmin(TieNeV), Cmin(VeTieN), Cmax(TieVeN), Cmax(TieNeV) and Cmax(VeTieN). Because of the difficulty in

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finding sufficient information to determine the parameters uniquely, the method to optimize the parameters for a binary system is usually cannot be applied to a ternary system. However, another approach to develop these parameters based on a kind of averaging concept has been proposed and widely used [33e35]. This approach simplifies the procedure of optimizing the parameters greatly and the six unknown parameters for TieVeN system can be calculated by the following formulae:

Cmin ðTi  V i2 h  NÞ ¼ 0:5ðCmin ðTi  V  TiÞÞ1=2 þ 0:5ðCmin ðN  V  NÞÞ1=2 (11) Cmin ðTi  N i2 h  VÞ ¼ 0:5ðCmin ðTi  N  TiÞÞ1=2 þ 0:5ðCmin ðV  N  VÞÞ1=2 (12) Cmin ðV  Ti i2 h  NÞ ¼ 0:5ðCmin ðV  Ti  VÞÞ1=2 þ 0:5ðCmin ðN  Ti  NÞÞ1=2 (13) Cmax ðTi  V i2 h  NÞ ¼ 0:5ðCmax ðTi  V  TiÞÞ1=2 þ 0:5ðCmax ðN  V  NÞÞ1=2 (14) Cmax ðTi  N i2 h  VÞ ¼ 0:5ðCmax ðTi  N  TiÞÞ1=2 þ 0:5ðCmax ðV  N  VÞÞ1=2 (15) Cmax ðV  Ti i2 h  NÞ ¼ 0:5ðCmax ðV  Ti  VÞÞ1=2 þ 0:5ðCmax ðN  Ti  NÞÞ1=2 (16) The values of all the parameters appearing on the right of Eqs (11)-(16) can be found in Table 2. The finally determined 2NN MEAM potential parameters for TieVeN ternary system are listed in Table 5. To evaluate the validity of the TieVeN ternary potential parameters, the lattice parameter and enthalpy of formation of FCC TixV1-xN solid solution changing with the atom concentration are calculated by LAMMPS. Since there is no any available information about these properties, the first-principles calculations for comparison are also performed by VASP. In both calculations above, the solid solutions are constructed by replacing part of Ti atoms in a

Table 5 The 2NN MEAM potential parameters for TieVeN ternary system. Parameter

TieVeN

Cmin(TieVeN) Cmin(TieNeV) Cmin(VeTieN) Cmax(TieVeN) Cmax(TieNeV) Cmax(VeTieN)

0.26 0.818 0.411 2.8 2.8 2.8

2  1  1 supercell of B1-type TiN with V atoms. The obtained results are compared in Fig. 1(a) and (b) for lattice parameter and enthalpy of formation, respectively. It can be seen that the present MEAM results are in good agreement with first-principles calculation ones. In order to further confirm the transferability of the TieVeN ternary potential parameters, the adhesion energies of the TiN/VN interface calculated are also compared with the first-principles calculation results in Table 6. It can be seen that the present MEAM results are consistent with first-principles calculation ones. 4. Results and discussion In MD simulations, the configuration of TiN/VN composite is constructed by TiN(100) and VN(100). The lattice parameters of the TiN(100) and VN(100) surfaces are 2.994 Å and 2.925 Å, respectively. The lattice mismatch is only 2.3%, indicating that the TiN(100)/VN(100) interface is a typical coherent interface. The dimension of the model is 6.4 nm  6.4 nm  10.6 nm in the x, y and z directions and the total number of atoms is 45000, as shown in Fig. 2. 4.1. Effect of strain rate on the mechanical properties of TiN/VN composite In MD simulations, the time scale is very small, thus the strain rate is much larger than that in experiments. To investigate the effect of strain rate on the mechanical properties of TiN/VN composite and find out a suitable strain rate for uniaxial quasi-static tensile simulations, several cases with different strain rates (1E9 s1, 5E9 s1, 1E10 s1, 5E10 s1 and 1E11 s1) in z direction at the temperature of 300 K are simulated using LAMMPS. Before applying the tension, the model is subjected to 20,000 steps of relaxation at 300 K to obtain a stable system. In this process, the isothermal-isobaric(NPT) ensemble [37] is used to keep the temperature constant and the pressures in x, y and z directions are adjusted to zero. During the tension process, the model is stretched in z direction under a given rate, while the pressures in x and y directions are kept at zero. Periodic boundary conditions are applied to all the three directions. Fig. 3 shows the stress (s)-strain (ε) curves of TiN/VN composite at different strain rates ranging from 1E9 s1 to 1E11 s1. It can be seen that the stress-strain curves almost coincide with each other and change linearly at the initial stage, indicating that the Young's modulus is less sensitive to strain rate. With the increasing of ε, the curves drop suddenly at the peak stress points, implying the occurrence of the failure. Unlike Young's modulus, the inelastic properties of the materials, such as the fracture strength and fracture strain are sensitive to strain rate. As shown in Fig. 3, both the fracture strength and fracture strain distinctly increase with the increasing of strain rate. This is because the smaller strain rate means that the time of relaxation and repartition for the local residual stress is longer, and more amount of energy is released to indemnify the deformation work and reduce the external energy for the further deformation. To further clarify the effect of strain rate on the mechanical properties of TiN/VN composite, the strain rate sensitivity parameter m is calculated by the following formula [14,38]:

m¼

vln s

(17)

·

vlnε ·

where s denotes the failure strength and ε represents the strain · rate. The relationship between ln sand lnε of TiN/VN composite is drawn in Fig. 4. It can be seen that the value of m is 0.01422 for 1E9

S. Ding, X. Wang / Journal of Alloys and Compounds 814 (2020) 152151

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Fig. 1. Comparisons of the MEAM and first-principles results for (a) the lattice parameter and (b) enthalpy of formation of FCC TixV1-xN solid solution changing with the atom concentration.

Table 6 The adhesion energies of the TiN/VN interface calculated by the present ternary potential, comparing with the first-principles calculation values. The unit of the adhesion energy is J/m2. Interface

(100) (110) (111) a b c

Present MEAM

3.696 5.788 6.858

First-principles Presenta

Yinb

Chenc

2.675 5.631 6.437

2.11 e 6.57

2.99 5.68 e

The first-principles calculation performed in present work. Ref. [10]. Ref. [36].

Fig. 3. Stress-strain curves of TiN/VN composite at 300 K at various strain rates.

4.2. Effect of temperature on the mechanical properties of TiN/VN composite In order to study the temperature effect on the mechanical properties of TiN/VN composite, the situations to a certain strain

Fig. 2. Atomic configuration of TiN/VN composite in X-Z plane. Blue, red and yellow dots represent Ti, V and N atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

s-1 <έ< 1E10 s-1 and 0.0492 for 1E10 s-1 <έ< 1E11 s-1. This indicates that when έ > 1E10 s1, the strain rate sensitivity increases a lot suddenly. Thus, considering both the accuracy and computational · efficiency, ε ¼ 1E10 s1 can be taken as a suitable choice for the uniaxial tension simulations.

Fig. 4. Dual logarithmic plot of failure stress versus strain rate for TiN/VN composite.

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rate (for example, 1E10 s1) but at different temperatures (300 K, 600 K, 900 K and 1200 K) are also simulated. Before applying the tension, the model is relaxed at each temperature in the same way as above. The stress-strain curves of TiN/VN composite at four different temperatures are shown in Fig. 5. It can be found that all stress-strain curves exhibit a linear increase when the applying strain is small (0ε  0.02), corresponding to the elastic deformation. Thereafter, with the increasing of ε, the model enters a plastic region and the stress increases nonlinearly until breaking. It is worth noting that the stresses drop suddenly at the limit strains of different temperatures and no obvious plastic deformation is observed during stretching. This indicates that TiN/VN composite undergoes a brittle fracture at all simulation temperatures. To clarify the effect of temperature on the mechanical properties of TiN/VN composite, the Young's modulus (E), fracture strength (sf), and fracture strain (εf) of TiN/VN composite at different temperatures are shown in Fig. 6. It can be seen that the Young's modulus and the fracture strength decrease, while the fracture strain increases with the increasing of temperature. When the temperature increases from 300 to 1200 K, the Young's modulus drops from 477 to 346 GPa and the fracture strength decreases from 22.20 to 18.97 GPa, with a reduction of 27.46% and 14.55%, respectively. This means that the Young's modulus is more sensitive to temperature than the fracture strength. To get more information about the effect of temperature on the deformation and failure behavior of TiN/VN composite, the atomic configurations of TiN/VN composite at 300 K and 1200 K and their evolution during the uniaxial tensile process are analyzed. In Figs. 7 and 8, the red dotted line represents the interface between the upper slab (TiN) and the lower slab (VN) of the model. Fig. 7 shows the atomic configurations of TiN/VN composite at 300 K. It can be seen that the defects start to concentrate at ε ¼ 0.062, corresponding to the overall peak stress in Fig. 5. With the increasing of ε, the micro-crack starts to occur at ε ¼ 0.076 (the ellipse area in Fig. 7(c)), and rapidly diffuses along (100) plane due to the accumulation of dislocations, resulting in that the stress drops more quickly. It can also be seen in Fig. 7(d) that the fracture surface is flat and perpendicular to the tensile direction, demonstrating that the failure behavior of TiN/VN composite is a typical brittle fracture at 300 K. The present result is in accordance with other MD simulations about the ceramic brittle fracture at low temperature [15,39]. As shown in Fig. 8, the situation of 1200 K is somewhat different from the beginning. A few of point defects can be observed in the

Fig. 6. The variation of Young's modulus (E), fracture strength (sf), and fracture strain (εf) with temperature.

initial atomic configuration of TiN/VN composite (Fig. 8 (a)). The micro-crack begins to appear at ε ¼ 0.090 (the ellipse area in Fig. 8(b)), corresponding to the overall peak stress of the curve at 1200 K in Fig. 5. Meanwhile, more kinds of dislocations are activated and they no longer accumulate only along (100) plane (Fig. 8 (c)). With the increasing of the number of dislocations (the square areas in Fig. 8(c)), the growth of the micro-crack near the upper interface is prevented by the nucleation of dislocations duo to the competition between the micro-crack and dislocations and new micro-cracks appear (the ellipse areas in Fig. 8(c)) and begin to propagate in the lower part of VN slab, resulting in that the fracture occurs near the lower interface. It is also found in Fig. 8 (d) that the fracture surface is no longer flat, implying that the plasticity of TiN/ VN composite is improved with the increasing of temperature, and the fracture gradually changes into a ductile fracture. By the way, to analyze the change of the fracture process with the increasing of temperature, the cases at 600 K and 900 K are also simulated but not shown here for the reason of conciseness. The results clearly show that the fracture surface moves gradually away from the upper interface with the increasing of temperature, and finally reach the lower interface at 1200 K. Besides, we also note that the fracture behavior takes place only in the VN layers, while the interface region and the TiN layers remain stable during the uniaxial tensile process, indicating that the dislocations can only nucleate in the softer phase of TiN/VN composite. The present result is consistent with the previous theoretical report [10], in which the fracture of TiN/VN(001) interface appears in the interfacial VN slab. 5. Summary

Fig. 5. Stress-strain curves for TiN/VN composite at four different temperatures.

We conduct molecular dynamic simulations to study the effects of strain rate and temperature on the mechanical properties of TiN/ VN composite under uniaxial tension. The 2NN MEAM interatomic potentials are selected for the simulations, and the potential

S. Ding, X. Wang / Journal of Alloys and Compounds 814 (2020) 152151

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Fig. 7. Atomistic representations of TiN/VN composite at 300 K under different strains. Atoms are color-coded according to center symmetry parameters (CSP) results. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 8. Atomistic representations of TiN/VN composite at 1200 K under different strains. Atoms are color-coded in the same way as in Fig. 7. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

parameters for TieVeN ternary system are developed based on the newly optimized interatomic potentials of binary systems. To validate the reliability of the present potential parameters, the various physical properties of the relevant materials are calculated by using the new potential parameters. The obtained results exhibit a good consistency with the theoretical calculation and/or experimental ones. The MD simulations reveal that strain rates have almost no effect on the Young's modulus of TiN/VN composite, but have a significant influence on the inelastic properties. However, both the Young's modulus and the inelastic properties are found to be sensitive to temperature. With the increasing of temperature, the Young's modulus and fracture strength decrease, but the fracture strain increases. It is also found that the fracture of TiN/VN composite is a brittle fracture taking place in the VN layers. These simulation results could be helpful to give a better understand for the hardening mechanism of multilayered coatings.

Acknowledgements The authors acknowledge the financial supports from the

National Natural Science Foundation of China (Grant nos. 11332013).

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