Initiation and Mechanisms of Plasticity in Bimetallic Al-Cu Composite

Abstract

We studied the shear deformation of a laminar Al-Cu composite with (100) and (110) interfaces with a shear perpendicular to the lamellae in comparison with pure single crystal Al and Cu at strain rates of 10⁹ s⁻¹ and 10⁸ s⁻¹ and different initial pressures in the range from −3 GPa to +50 GPa. The results of molecular dynamics (MD) for the plasticity initiation are generalized by means of an artificial neural network (ANN) trained by MD data for the (100) interface, and a rate sensitivity parameter identified using MD data for different strain rates. The ANN-based approach allows us to extrapolate MD data to much lower strain rates, which are more relevant for typical dynamic loadings. The considered problem is of interest as an example of the application of the developed ANN-based approach to bimetallic systems, whereas previously it was tested only for pure metals; in addition, Al-Cu composites are of practical interest for technology. The interface between metals reduces the shear strength of the composite in comparison with both pure metals. At an initial pressure below 10 GPa, the plasticity begins in the aluminum part of the composite, while at higher pressures, the plasticity of the copper part starts first. At a pressure above 40 GPa, a phase transition in the aluminum part governs the plasticity development. All this leads to a nonmonotonic pressure dependence of the critical shear stress of the Al-Cu composite in the case of (100) and (110) interfaces without misorientation. Misorientation decreases the critical stress of the nucleation of lattice dislocation and makes the pressure dependence of this stress monotonic. Deformation modes, with a defect-free copper part and a strain-accommodating aluminum part are observed in the MD and can be useful for technological applications related to deformable conducting materials.

1. Introduction

In comparison with pure metals, bimetallic systems reveal more complex behavior and a greater variety of mechanical properties. Among the possible combinations, aluminum–copper bimetallic composite can be treated as a model system composed of two well explored and widely used FCC metals, a combination of which can give new unexpected mechanical behavior. In addition to theoretical interest, this pair of metals also has practical applications. Copper has high thermal and electrical conductivity, whereas aluminum is cheaper, lighter and has an acceptable mechanical strength, especially in the form of alloys. Therefore, the application of aluminum–copper bimetallic composites is promising in aerospace and the automotive industry, as well as in the field of electrical engineering [1,2,3,4] for the replacement of pure copper parts. There are other possible applications; for example, the copper coating of carbon fibers enhances the mechanical properties of the fiber reinforced aluminum matrix composites [5]. Traditional fusion welding is not efficient for joining these two metals with different thermomechanical properties, but Al-Cu composites can be produced by several other methods. The possible production technologies of bulk composites include cold rolling [6,7], accumulative roll bonding [8], mechanical swaging [1], electromagnetic pulse welding with the Lorentz force as the driving force [2], friction stir welding [3,4,9,10] and explosive welding [11]. Finer structures can be produced by cold spraying [12,13,14]; molecular dynamics (MD) simulations show a good adhesion of copper particles to an aluminum substrate after high-speed collision [15,16]. The interface between two metals is prone to the formation of various intermetallic phases [6,7], which reduce electrical conductivity and mechanical strength [3,4]. Therefore, a decrease in the thickness of the intermetallic layer between metals is one of the technological goals in the production of Al-Cu composites [4,9], and recent works demonstrate a certain progress in this field [4]. All this motivates the study of Al-Cu bisystems with a clear interface, while the influence of intermetallic compounds at the interface can be revealed in future research.

At present, the plastic relaxation of materials provided by grain boundary (GB) processes is being actively studied using atomistic modeling, which allows one to reveal the detail of the GB-related mechanisms of plasticity. The authors of [17] used MD to consider the mechanical reaction of a system with a GB in aluminum under compression and tension. It was shown that compressive stress has an inhibiting effect on GB sliding, while the tensile stress has a facilitation effect on GB sliding. Paper [18] studied the impact of the structure of the symmetric tilt GB with various structural conjugations in copper on the stress of the nucleation of dislocations under tension. In paper [19], an estimate was obtained for the activation volume during the emission of dislocations by the grain boundaries of various FCC metals. The influence of the shear direction of a copper bicrystal on the mechanism of development of grain boundary plasticity was studied in [20]. It was established that, depending on the misorientation angle, the mechanism of GB plasticity changes from boundary migration to slip. In addition to studies of grain-boundary plasticity in pure metals, atomistic simulations are now appearing devoted to the study of the influence of atoms of the second element at the GB on grain-boundary processes. The authors of [21] studied the energy of Ni and Cu atoms at the symmetric tilt GB in Ag. In paper [22], the generation of dislocations at the GB under tension in pure aluminum and in the case of saturation of the boundary with magnesium atoms was studied using MD. It was shown that magnesium atoms on the boundary significantly stabilize the GB to the emission of dislocations.

Currently, MD studies on the influence of interfaces on the plasticity initiation and development in bimetallic systems is also attracting attention. Dislocation nucleation at the Cu-Ni bimetallic interface was explored in [23] by means of MD; the model was constructed by adjoining both crystals with the same crystallographic orientations. It was concluded that the critical yield stress of dislocation nucleation depends strongly on the external loadings, which vary the stacking fault energies. Atomistic detail of the initial stages of dislocation nucleation at the HCP/BCC interface was studied in [24] using the example of the Zr/Nb bimetallic system with three different mutual orientations of the lattices. MD simulations [25] for a Mg/Nb bimetallic composite revealed both dislocation nucleation at the interface and the HCP-to-BCC phase transition depending on the orientation of the HCP lattice of Mg relative to the interface. An MD study of the shock wave action on a multi-layer Cu-Ni composite was performed in [26] to explain the size effect in bimetal nanolaminates. In all the atomistic modeling works mentioned above, the grain boundaries were created as a simple contact between two perfect lattices, which we apply in our study to create the interface between Al and Cu.

In spite of a number of previous MD simulations on bicrystals and bimetallic interfaces in the literature, the plasticity properties of the Al-Cu interface are still insufficiently studied, especially in the conditions of complex loading, such as a combination of tension/compression and shear. In addition, the complex dependencies identified in MD require the development of theoretical methods for their description for use in a higher level modeling of plasticity. In this work, we study the initiation of plastic flow in an Al-Cu bimetallic laminar nanocomposite with an initially perfect crystal lattice within each metal. We consider simple shear perpendicular to the interface under different applied pressures in the range [−3 GPa, +50 GPa] by means of MD simulations. The shear deformation combined with compression or tension is relevant for both dynamic loading, including the action of shock waves and tensile waves, and quasistatic loading; however, pressure substantially effects the plasticity initiation in aluminum and copper separately [27,28,29]. The obtained data shows a complex interplay of the deformation processes in the aluminum and copper parts of the bimetallic system. Following our approach previously applied for pure metals [28,29], we use an artificial neural network (ANN) to approximate the thresholds of plasticity incipience as the function of pressure and the system composition (pure Al, pure Cu or bimetallic system). Thus, we verify that this ANN-based approach can be applied to more complex materials than pure metals. The strain rate dependence of the plasticity incipience is much more pronounced for a bimetallic system compared with pure metals, and we take this dependence into account by using the nucleation strain distance function proposed in our previous paper [29].

The organization of the paper is as follows. Section 2.1 describes the problem statement considered in the main MD simulations of the present work. Section 2.2 briefly introduces the ANN-based approach developed in our previous works for pure metals and applied here for the Al-Cu bimetallic system. Section 3.1 shows the general stress-strain response of the bimetallic system in comparison with pure metals. Section 3.2 presents an overview of plasticity mechanics for the case of the (100) interface in the Al-Cu system, whereas Section 3.3 considers both pure metals. Section 3.4 collects the results of the application of the ANN-based approach to describe the complex dependence of the dislocation nucleation threshold on the initial pressure and strain rate. In Section 3.5, we study the influence of the interface orientation and increased temperature on the plasticity of the Al-Cu composite. The obtained results are further discussed in Section 4 and concluded in Section 5.

2. Materials and Methods

2.1. MD Problem Statement

A bimetallic system consisting of aluminum and copper parts (see Figure 1) was chosen as the object of study. Both metals have perfect crystal lattices, which are oriented in accordance with the following lattice directions: [100] along the $x$-axis of the system, [010] along the $y$-axis, and [001] along the $z$-axis in most MD simulations. The consideration of perfect crystal lattices of both metals is substantiated by the fact that grain boundaries and interfaces are powerful sinks of dislocations and other defects in nanocrystalline materials. The dimensions of the system were 81 × 20 × 40 nm³. The aluminum and copper parts each occupied half of the system, so that the plane interface separating them was perpendicular to the $x$-axis and had a coordinate of 40.4 nm. The system contained 2,000,000 aluminum atoms and 2,809,856 copper atoms. The lattice parameter of aluminum was chosen to be 0.405 nm, and that of copper was 0.365 nm. Lattices of two metals were simply adjoined to form the interface as it is usually supposed in most MD simulations with bicrystals and bimetallic composites in the literature [17,18,19,20,21,22,23,24,25,26]. Two other orientations of the crystal lattices relative to the interface were also considered to study the effect of orientation as discussed in Section 3.5.

Molecular dynamics calculations were performed using the LAMMPS package [30]. Interactions of atoms were described with the ADP potential by Apostol and Mishin [31], which belongs to the angle-depended extension of the embedded atom model. This potential well reproduces elastic moduli, energies of pure metals, and their intermetallic phases. The MD study of the dislocation nucleation in aluminum [28] and copper [29] performed with the Al and Cu parts of this potential, respectively, showed that the calculated nucleation thresholds are close to that in the literature, including the results of ab initio DFT (density functional theory) calculations [27]. The room temperature isotherms calculated with this interatomic potential were verified for aluminum [32,33] and copper [34] by comparison with both the results of diamond anvil cell experiments [35] and DFT calculations [32,36]. Although MD results are sensitive to the quality of interatomic potential, all these previous comparisons evidenced the applicability of the potential [31] to the problem under consideration.

The temperature of the system was brought to 300 K within 0.2 ns. Pressures from −3 to +50 GPa were set as target pressures at the stage of bisystem relaxation. The subsequent stress relaxation of the system was carried out for 0.8 ns using a barostat and a thermostat, in addition to which the stress oscillations that arose in the system due to the different temperature dependences of the material elastic moduli were artificially suppressed in the system. Immediately after the system was brought to a given temperature, the difference between the ${\sigma }_{yy}$ and ${\sigma }_{zz}$ stress components in aluminum and copper reached 0.8 GPa, and the stresses themselves in the materials oscillated in an antiphase manner with an amplitude of 0.4 GPa. After stress relaxation, the difference between the stresses in the materials was about 0.05 GPa with an oscillation amplitude of about 0.025 GPa. After the system was relaxed to a target pressure, it was placed in the NVT ensemble at a temperature of 300 K. The system was subjected to a single shear deformation with a strain rate of 10⁹ or 10⁸ s⁻¹ using the “fix deform” command of LAMMPS, which rescales the coordinates of all atoms. The analysis of the lattice defect structure was carried out using the centrosymmetry parameter [37] and the dislocation extraction algorithm DXA [38]. The OVITO program [39] was applied for the visualization of the atomic configuration. The average stresses for the entire system were recorded, as well as the average stresses for the aluminum and copper parts of the system calculated by means of the virial theorem [40].

Additional calculations of shear deformation were made for aluminum and copper systems separately. Each of these systems contained either aluminum or copper as half of the bisystem. Preliminarily, each of the systems was brought to a target temperature and pressure within 0.05 ns using a thermostat and a barostat. In comparison with a bisystem, the relaxation time was much shorter, but it was quite sufficient, since in the case of a single system, there is no need to dampen stress fluctuations. Further, the system was subjected to a simple shear deformation with a strain rate of 10⁹ or 10⁸ s⁻¹.

2.2. ANN-Based Description

Let us consider the ANN-based approach proposed in our previous works [28,29] to approximate the MD data on the plasticity incipience. Let $C$ denote the composition of the material under consideration; put this variable as $C=0$ for the Al-Cu bimetallic system, $C=1$ for pure Al, and $C=2$ for pure Cu. MD simulations were performed for different initial pressures $P_0$, and the pairs of variables $\left\{C,P_0\right\}$ defined the deformation conditions. From MD, we know the threshold engineering strain ${\epsilon }_{\mathrm{n}0}$ of plasticity initiation during deformation at certain conditions with the reference strain rate ${\dot{\epsilon }}_0$. The nucleation strain distance function can be defined as follows [29]:

$$Q\left(C,P_0,\epsilon \right)=\epsilon -{\epsilon }_{\mathrm{n}0},$$

(1)

where $\epsilon$ is the current engineering strain. The function $Q$ is negative in the elastic domain and, at the reference strain rate ${\dot{\epsilon }}_0$, it becomes positive in the plastic domain.

The condition of plasticity initiation at other strain rate $\dot{\epsilon }$ can be expressed as follows [29]:

$$Q\left(C,P_0,{\epsilon }_{\mathrm{n}}\right)=\frac{k_{\mathrm{B}}T}{\mathrm{A}}\ln \left(\frac{\dot{\epsilon }}{{\dot{\epsilon }}_0}\right),$$

(2)

where $T$ is the temperature, $k_{\mathrm{B}}$ is the Boltzmann constant, and $\mathrm{A}$ is the absolute value of the derivative of the energy barrier of defect nucleation over strain. Equation (2) expresses the strain rate dependence of the threshold of plasticity incipience, and $\mathrm{A}$ can be treated as a model parameter with dimensionality of energy, which can be found [29] by comparison of two different strain rates. Here, we use MD data for the reference strain rate ${\dot{\epsilon }}_0={10}^9{\mathrm{s}}^{-1}$ to determine $Q$, while MD data for the lower strain rate ${10}^8{\mathrm{s}}^{-1}$ are used to identify parameter $\mathrm{A}$. Because of a difference in the plasticity mechanism of the Al-Cu bimetallic system at low and high pressures, we treat this parameter as a piecewise linear function of the initial pressure:

$$\mathrm{A}\left(P_0\right)=\left\{\begin{array}{c}{\mathrm{A}}_1,\mathrm{at}{P}_0\le 14\mathrm{GPa},\\ {\mathrm{A}}_2,\mathrm{at}{P}_0>14\mathrm{GPa},\end{array}\right.$$

(3)

where ${\mathrm{A}}_1$ and ${\mathrm{A}}_2$ are the rate sensitivity parameters for moderate pressures and high pressures, respectively.

Training of an artificial neural network (ANN) [41,42] is prone to be an efficient method to approximate MD results for both the nucleation strain distance function $Q$ and the stress-strain curves [29,32,33,34]. The deformation conditions and the current engineering strain of simple shear $\epsilon$ form the input vector of the ANN $\left\{C,P_0,\epsilon \right\}$. The nucleation strain distance function $Q$, the volume-average shear stress $\tau$, and the difference between the current pressure $P$ and the initial one $P_0$ constitute the output vector $\left\{Q,\tau ,P-P_0\right\}$. The ANN maps the input vector onto the output one, and training consists of variation of the coefficients of artificial neurons to obtain an optimal mapping on the training data set. The applied procedure of ANN training is described in the previous works [28,29,43]. We use an ANN containing 6 hidden layers with 20 artificial neurons with a “Leaky ReLU” transfer function in each hidden layer. The input layer is presented by three input values $\left\{C,P_0,\epsilon \right\}$, while the output layer containing 3 artificial neurons with “Sigmoid” transfer function forms the output values $\left\{Q,\tau ,P-P_0\right\}$.

Let us consider the preparation of the training data set. The stress-strain curves from MD are truncated until the moment of plasticity incipience; this procedure also gives us the threshold engineering strains ${\epsilon }_{\mathrm{n}0}$. Thereafter, the elastic parts of the stress-strain dependencies, $\tau \left(\epsilon \right)$ and $P\left(\epsilon \right)$, are approximated by the third-order polynomials, which let us to extrapolate the elastic response beyond the dislocation nucleation threshold. The polynomial approximation is efficient for a single MD trajectory, but it is inapplicable for the whole dataset. Then, the pairs of input-output vectors are recorded with the step of $0.01{\epsilon }_{\mathrm{n}0}$ in the range $\left[0,1.5{\epsilon }_{\mathrm{n}0}\right]$ using the approximating polynomials for stresses and Equation (1) for the nucleation strain distance function $Q$. The obtained training data set includes about 5000 pairs of input-output vectors.

After the training of the ANN, the threshold of plasticity incipience ${\epsilon }_{\mathrm{n}}$ can be restored for arbitrary initial pressure by means of the numerical solution of Equation (2). For consideration of other strain rates, the strain rate sensitivity parameters $\left\{{\mathrm{A}}_1,{\mathrm{A}}_2\right\}$ are identified using MD data for $\dot{\epsilon }={10}^8{\mathrm{s}}^{-1}$ and the Bayesian algorithm [29,32,33,34,44]. A number of trial pairs of these parameters are seeded randomly, and a probability of a pair $\mathsf{\Pi }\left({\mathrm{A}}_1,{\mathrm{A}}_2\right)$ is estimated from the comparison of the ANN with MD as follows:

$$\mathsf{\Pi }\left({\mathrm{A}}_1,{\mathrm{A}}_2\right)={\displaystyle \prod }_{k=1}^K\exp \left[-{\left(\frac{{\tau }_{\mathrm{n},\mathrm{ANN}}-{\tau }_{\mathrm{n},\mathrm{MD}}}{{\tau }_0}\right)}^2\right],$$

(4)

where ${\tau }_{\mathrm{n},\mathrm{ANN}}$ and ${\tau }_{\mathrm{n},\mathrm{MD}}$ are the critical stresses of plasticity initiation from the ANN combined with Equation (2) and from MD, respectively, ${\tau }_0=1\mathrm{GPa}$ is the scaling factor, and $K\approx 10$ is the number of comparison points. The best model parameters corresponds to the maximum of $\mathsf{\Pi }\left({\mathrm{A}}_1,{\mathrm{A}}_2\right)$.

3. Results

3.1. Stress-Strain Dependencies and Critical Stresses

After the application of shear strain, the shear stresses increase in the system, as can be seen in Figure 2 for different initial pressures. At the stage of linear (elastic) stress growth, their values coincide in both parts of the bisystem. When a critical shear stress, whose value depends on the initial pressure, is reached, plastic relaxation is activated in the bisystem, and the shear stresses rapidly decrease. After the decrease, there is a mismatch between the shear stresses in the aluminum and copper parts of the system. This mismatch is mostly of a stochastic nature, but to a certain extent, it is influenced by different structural transformations in aluminum and copper parts of bisystem.

The MD results for the dependences of the critical stresses in the Al-Cu bisystem on the initial pressure are collected in Figure 3a, whereas Figure 3b presents the same dependencies for pure metals. The pressure dependence of the critical shear stress in the bisystem demonstrates a nonmonotonic character with three clearly distinguishable areas of dependence (see Figure 3a). The initial increase in the critical stress with an increase in pressure from −3 to 10 GPa (10⁸ s⁻¹) or 15 GPa (10⁹ s⁻¹) is replaced by a decrease lasting to a pressure of 40 GPa, after which the stage of critical stress growth is again observed. The same dependence for copper is monotonic in the considered range of pressures, while aluminum demonstrates softening at pressures above 30 GPa.

3.2. Mechanisms of Plasticity in Al-Cu Bisystem

Let us consider typical structural transformations in the bisystem at the plasticity initiation for different initial pressures.

At an initial pressure of 0 GPa in the bisystem, the emission of dislocations occurs from the interface into the aluminum part, as shown in Figure 4a. Dislocation half-loops are formed at the interface between materials and begin to grow from the nodes of the dislocation network, which initially exists at the interface between materials. The formation of the first dislocation half-loops occurs at an engineering strain of ε = 0.089. The formed dislocations belong to the [110](111) slip system and are partial Shockley dislocations with Burgers vectors equivalent to the [112] direction. A stacking fault propagates behind the leading partial dislocation. Note that the trailing dislocations do not follow the leading ones. The formed dislocation half-loops propagate inside aluminum without penetrating into copper: when a half-loop approaches the opposite boundary, it is absorbed by the boundary. As a result, large planes of stacking faults are formed in aluminum, filling the entire space of the aluminum part of the bisystem. When the leading partial dislocations propagate, they intersect with each other, as a result of which dislocation loops begin to form in aluminum at these intersections. The secondary dislocation loops consist of leading and trailing partial dislocations with a stacking fault between them, as shown in Figure 4b at strain ε = 0.098. Activation of the emission of secondary dislocations from primary stacking faults leads to a rapid reduction in the number of stacking faults and the filling of aluminum with a dislocation network consisting of perfect dislocations, as seen in Figure 4c for strain ε = 0.108. The movement of dislocations lying simultaneously on different slip planes (including mutually rotated ones) leads to the formation of vacancies and vacancy clusters, as shown in Figure 4d at strain ε = 0.14. During the subsequent plastic deformation of the bisystem, the nature of the microstructure of the aluminum part of the bisystem remains unchanged, with a tendency to an increase in the number of vacancies with increasing deformation.

The copper part of the sample demonstrates elastic behavior up to the strain of ε = 0.266. Plastic deformation develops due to the emission of dislocations from the interface between materials. The dislocations emitted by the boundaries are Shockley partial dislocations in the [110](111) slip system and Burgers vectors oriented equivalently to the [112] direction (see Figure 5a). Expanding planes of stacking faults following partial dislocations rather quickly fill the copper part of the sample (at strain ε = 0.298). The intersection of stacking faults lying in different slip planes leads to the emission of secondary perfect dislocations in a system consisting of leading and trailing dislocations. However, unlike the aluminum part, the movement of secondary dislocations leads only to partial compression of primary stacking faults, leaving some of them unchanged. As a result, the copper part of the system remains filled with several parallel planes of stacking faults, as shown in Figure 5b for the engineering strain ε = 0.365. The nearest stacking fault planes are separated by one (111) atomic plane and form a twin layer (see Figure 5c). The formed system of twins remains stable for a sufficiently long period of time up to a strain of about ε = 0.432. On the stress dependence graph shown in Figure 1a, an increase in the effective shear stresses in copper is observed, which leads to the emission of new dislocations from the interface of the materials at the strain of ε = 0.436, as shown in Figure 5d. Further, the propagation of partial dislocations from the grain boundaries and the emission of secondary dislocations from the intersections of stacking faults are repeated.

In the undeformed state, the interface between the materials contains a network of dislocations formed due to the different lattice constants of aluminum and copper (see Figure 6a). The thickness of the boundary layer is about one interatomic distance in both metals. During the shear deformation, the dislocation network at the interface remains unchanged until the moment of the emission of dislocations propagating into aluminum. The nucleation of dislocations occurs at the junctions of dislocation segments that form a grid at the interface between materials, as shown in Figure 6a for the strain of ε = 0.089. The growth of a dislocation half-loop is accompanied by the formation of a region of disordered atoms in aluminum near the material interface. As a result, the friability of the interface in aluminum increases significantly and the thickness of the boundary layer in aluminum reaches 3–4 interatomic distances (about 0.7–0.9 nm) at strain ε = 0.1, as shown in Figure 6b. With the further development of plastic deformation, the emission of dislocations from the boundary into copper is activated; however, disordering of copper atoms near the boundary is not observed, which can be explained by a lower activation stress of plastic flow in aluminum. Therefore, at any moment of time, the thickness of the boundary layer is determined mainly by the thickness of the disordered region in aluminum and amounts to 3–4 interatomic distances.

The scenario of plastic flow development considered above is typical for pressures in the range from −3 GPa to 10 GPa. This range of pressures corresponds to an increasing pressure dependence of the critical shear stress in Figure 3.

Upon reaching the initial pressure of the value of 10 GPa, the nucleation of dislocations in the aluminum part occurs from the boundary between the materials at deformation ε = 0.087. The appearance of a dislocation is accompanied by a perturbation of the interface between the materials that leads to the generation and emission of dislocations into the copper part at a deformation of ε = 0.09, as shown in Figure 7a. The convergence of the moments of the formation of dislocations in aluminum and copper can be explained by the different pressure sensitivity of the critical stress of the dislocation nucleation in aluminum and copper as shown in [28,29]. In contrast to the cases of lower pressure, perfect dislocations are emitted in the aluminum part, which split into leading and trailing dislocations with a stacking fault between them. The development of plastic deformation leads to the formation of a dislocation network and the generation of vacancies in aluminum as shown in Figure 7b for the strain ε = 0.14. In the copper part, leading dislocations propagate, bounding stacking fault planes; vacancies are formed much less than in aluminum.

With an increase in the initial pressure up to 15 GPa, the nucleation of dislocations first occurs in copper from the interface between materials at the engineering strain ε = 0.085. Partial Shockley dislocations are emitted with stacking faults behind them without generating trailing partial dislocations. The generation of dislocations in aluminum occurs somewhat later than in the copper part of the system (ε = 0.088). The development of plastic deformation leads to the formation of a dislocation network in aluminum and the formation of vacancies (ε = 0.106). With the subsequent deformation, the nature of the resulting structure is preserved. In copper, after an initial increase in the number of dislocation half-loops, their decrease begins and the minimum is reached at strain ε = 0.12. Increasing shear stress generates new dislocations, the development of which leads to the formation of a system of twins at ε = 0.155, which fills the entire volume of the copper part of the bisystem. During the subsequent deformation, periodic fluctuations in the dislocation density occur in the copper part, associated with alternating absorption and emission of dislocations by the interfaces.

At the initial pressure of 20 GPa, the moment of generation of dislocations in copper (ε = 0.062) is also ahead of aluminum (ε = 0.068). Interestingly, at such a pressure, dislocations in copper become perfect split ones with the formation of partial leading and trailing dislocations. A dislocation network is formed in both materials.

With an increase in the initial pressure to 30 GPa, the formation of dislocations from the interface begins in the copper part at strain ε = 0.038, and after this, plastic flow is activated in aluminum as well, at ε = 0.042. Leading partial Shockley dislocations propagate in both copper and aluminum, bounding stacking fault planes (see Figure 8a). In this case, secondary dislocations are emitted in copper from the intersections of the stacking fault planes, which leads to the formation of a dislocation network. In aluminum, the formation of secondary dislocations is not observed; after the aluminum volume is filled with stacking faults, a system of twinning interlayers is formed in it, as shown in Figure 8b for ε = 0.07. Further development of plastic deformation in the bisystem leads to an increase in the number of stacking fault planes in aluminum. In copper, plastic deformation proceeds due to the slip of dislocations.

With an increase in the initial pressure to 40 GPa and above, a phase transition of aluminum from FCC state to BCC state occurs even at the stage of bringing the system to the target pressure before the onset of shear deformation, as shown in Figure 9a. Due to the decrease in specific volume per aluminum atom during this transformation, the aluminum part of the system tends to reduce the occupied volume, while the copper part of the system retains the FCC state with a large specific volume per atom. The conjugation of two such systems leads to the generation of defects in both materials before the onset of shear deformation. In aluminum, one can see the boundaries of subgrains with different lattice orientations, formed by the contact of subgrains grown up from different nuclei of the BCC phase. There are dislocations inside the subgrains. A small number of dislocations are generated in copper, bounding the stacking fault planes. When shear deformation is applied, plastic relaxation occurs in both materials simultaneously, with the onset of stress growth due to the presence of defects, the evolution of which ensures the removal of shear stresses (see Figure 2d). In aluminum, the initially present dislocations glide and those subgrains grow, which are most favorably oriented with respect to the applied shear in terms of the magnitude of the shear stresses arising in them for the chosen direction of deformation, as seen in Figure 9b for strain ε = 0.04. Over time, the entire aluminum part of the system is filled with one grain (ε = 0.12), the plastic flow in which is carried out by dislocation slip. Additional dislocations are formed in copper, which are emitted from the interface. At strain ε = 0.034, a system of twins is formed in copper. With further deformation, a dislocation network appears (ε = 0.216) in copper.

With a decrease in the strain rate to 10⁸ s⁻¹, all the characteristic features of the activation of plastic flow are preserved with one difference, which is that the activation of plastic flow in copper occurs earlier than in aluminum, at 10 GPa instead of 15 GPa. We also note a slight decrease in critical stresses in the system at initial pressures in the range from −3 to about 15 GPa and a significantly greater difference at pressures above 15 GPa.

3.3. Development of Plasticity in Pure Metals

In addition to the bisystem consisting of two parts, shear strain calculations are carried out for both pure metals. The activation of plastic flow in aluminum in the initial pressure range from –3 to 10 GPa occurs upon the formation of a partial Shockley dislocation belonging to the [110](111) slip system. The leading partial dislocations bound the stacking fault planes that grow together with the dislocation loops, as shown in Figure 10a at ε = 0.14. The development of deformation leads to the emission of secondary dislocations from the stacking fault planes, as seen in Figure 10b for ε = 0.16. With further plastic deformation, a dislocation network is formed and a large number of vacancies are generated, as shown in Figure 10c for strain ε = 0.3. At initial pressures above 5 GPa, dislocation activity develops in a limited volume of the substance, leaving a part of the substance unaffected by plastic deformation.

At an initial pressure of 15 GPa, dislocations are nucleated simultaneously on two slip planes, a conglomerate of atoms arises, forming a defect structure characteristic of partial dislocations and stacking faults on two slip planes in a limited part of the system volume. With an increase in the initial pressure to 30–40 GPa, the nucleation of dislocations on several planes occurs already distributed over a much larger volume of the substance (see Figure 10d). In the case of an initial pressure of 50 GPa in aluminum, a transition from the FCC phase to BCC occurs at the stage of initial pressure relaxation. Before plastic deformation begins, aluminum contains a certain number of dislocation loops. When a shear is applied, the dislocations begin to move which provides a significant reduction in the critical stresses in the material.

The development of plastic relaxation in copper begins with the nucleation of partial Shockley dislocations in the [110](111) system. At initial pressures from −3 to 30 GPa, growing loops of partial dislocations and stacking faults bounded by them initially fill the space of the material, as seen in Figure 11a for ε = 0.14, after which they are rather quickly replaced by a dislocation network due to the active emission of secondary dislocations in the material, as seen in Figure 11b for ε = 0.24. At initial pressures above 30 GPa, after the formation of primary loops of partial Shockley dislocations, secondary dislocations nucleate from the stacking faults, as shown in Figure 11c for strain ε = 0.17. The formation of a dislocation network occurs without the stages of filling the volume of the material with stacking faults, as seen in Figure 11d for ε = 0.21.

The dependences of the critical stress on pressure are shown in Figure 3b. For aluminum, the dependence has a nonmonotonic character with a transition from an increase to a decrease at a pressure of 30 GPa. For copper, however, the dependence demonstrates a monotonic growth for all considered pressures. Here, critical stresses show a weak sensitivity to a decrease in the strain rate in the entire considered pressure range.

3.4. ANN Training and Strain Rate Dependence

The ANN is trained until an average error of 0.1% and maximum error of 1%; the results are presented in Figure 12. One can see that the ANN perfectly reproduces the stress-strain curves and the dislocation nucleation thresholds as the roots of the equation $Q\left({\epsilon }_{\mathrm{n}0}\right)=0$. Data in Figure 12 are presented for all considered systems, including pure Cu, Al, and the bisystem, at different initial pressures. The wide range of shear stresses in Figure 12a,b is explained by the inclusion of data for pure copper (compare with Figure 3), as well as by the extrapolation beyond the elastic domain until $1.5{\epsilon }_{\mathrm{n}0}$ as described in Section 2.2. The weights and biases of neurons of the trained ANN are presented in a worksheet “AlCuInterface.ANNp” of the file “AlCuInterface.xls” (Supplementary Materials); the structure of this data file is described in previous papers [28,29,34].

The strain rate sensitivity parameters for all considered systems are identified by means of the Bayesian algorithm with the critical shear stresses from MD for $\dot{\epsilon }={10}^8{\mathrm{s}}^{-1}$ as the training data as described in Section 2.2. For both pure metals, the strain rate effect is uniform within the considered pressure range; therefore, we use the same value ${\mathrm{A}}_1={\mathrm{A}}_2$ for all pressures. The results are collected in

Table 1. Identified parameters of the strain rate sensitivity for different systems.

System	${\mathbf{A}}_1\left(\mathbf{eV}\right)$	${\mathbf{A}}_2\left(\mathbf{eV}\right)$
Al + Cu	8.2	3.6
Al	6.6	6.6
Cu	8.4	8.4

. As one can see in Figure 3, the Al-Cu bisystem clearly reveals different strain rate effects for moderate pressures (10 GPa and lower) and for high pressures (15 GPa and higher). In this case, the Bayesian algorithm is applied to identify two parameters. The obtained probability distribution is shown in Figure 13. The area of high probability forms a stripe along the ${\mathrm{A}}_1$ axis. It means that the parameter ${\mathrm{A}}_2$ for high pressures is well-defined, while the parameter ${\mathrm{A}}_1$ for moderate pressures can be selected in a wider range, because the results are less sensitive to it. The optimal values are collected in Table 1.

Figure 14 compares the results of the ANN and MD for the Al-Cu bisystem and for both considered strain rates. The coincidence for the reference strain rate of 10⁹ s⁻¹ completely relies on the quality of the trained ANN, while the strain rate effect is described by Equation (2) with the strain rate sensitivity parameters collected in Table 1. One can see that the correspondence between the ANN and MD is reasonable. ANN-based curves have excess kinks, but the quality of these curves can be improved using additional training data from MD.

Figure 15 presents an ANN-based prediction of the critical shear stress in the Al-Cu bisystem extrapolated to strain rates much lower than those considered in MD. This extrapolation is to the range of strain rates, which are typical for various dynamic applications, including high-velocity impact and related problems. One can see low shear strength at high pressures and considerably higher strength at moderate pressures.

3.5. Influence of Interface Orientation and Elevated Temperature

In addition to the main MD simulations for (100) interface presented above, we considered two other MD systems. In the first one with (110) interface, the lattice directions of both Al and Cu were oriented as follows: $\left[110\right]$ along the $x$-axis of the system, $\left[\overline{1}10\right]$ along the $y$-axis, and $\left[001\right]$ along the $z$-axis, while the interface was still perpendicular to the $x$-axis. In the second one with (110)+misorientation interface, the crystal lattices were additionally symmetrically inclined by an angle of 6.05° to form a symmetric tilt GB with the misorientation angle of 12.1°. For these two MD systems, we considered the initial pressures of −3, 0, 15 and 40 GPa, which formed a more sparse grid over pressures than MD simulations for the (100) interface. Therefore, we did not include these data in the training of the ANN; such training is prospective to take into account the orientation of the interface, but requires additional MD simulations. Figure 16 shows that the interface orientation critically influences the threshold of plasticity initiation and its dependence on pressure. While the pressure dependence for (110) is still nonmonotonic with a displaced maximum in comparison with the (100) interface, the addition of misorientation makes this dependence monotonic with quite different values of the critical stress of nucleation.

Figure 17 illustrates the case of the (110) interface at zero initial pressure. The activation of plastic flow begins in the aluminum part of the composite with the emission of Shockley partial dislocations from the interface at a strain of 0.08 (Figure 17a); dislocations are emitted on two slip planes, $\left(\overline{1}11\right)$ and $\left(1\overline{1}1\right)$. The activation of plasticity in copper occurs at a much higher strain of 0.25 (Figure 17b); the sliding of leading and trailing dislocations occurs on the $\left(111\right)$ plane. Further shear deformation of the system leads to the generation of secondary dislocations and vacancies in aluminum (see Figure 17d). In copper, the successive formation and disappearance of twinning layers between stacking faults occur; such a twinning layer stretching through the copper part of the system can be seen in Figure 17c. In Figure 17d, the stacking faults are absorbed by the interface, and the copper part of the system is found to be practically free of defect atoms.

The case of the (110) interface at a high initial pressure of 40 GPa is shown in Figure 18. At the high initial pressure, twinning occurs in the copper part of the composite even at the preliminary stage of bringing the system to a given pressure (Figure 18a). Shear deformation leads to an increase in the number of twinning layers (Figure 18b). In this case, stacking faults do not penetrate into the aluminum part of the system up to a strain of 0.07. At a strain of 0.1, both parts of the system are filled with stacking fault planes that form twinned interlayers (Figure 18c). The penetration of twins from one part of the system to another is clearly visible. The nuclei of the BCC phase in aluminum are also visible (the atoms are colored blue). An increase in strain to 0.2 is accompanied by a gradual filling of the aluminum part of the system with the BCC phase, and the formation of two subgrains is observed; the subgrain boundary in aluminum is shown in Figure 18d. Plastic deformation in the BCC phase of aluminum is realized due to the slip of dislocations. In the copper part of the system, plastic flow occurs during the formation of twinned interlayers and their absorption by the interface.

In the case of the (110)+misorientation interface shown in Figure 19, plasticity begins from the emission of Shockley partial dislocations in Al, as is the case for the previously discussed interfaces. Meanwhile, the misorientation of lattices significantly lowers the shear strain and shear stress of the dislocation emission, which can be attributed to the additional disordering of the interface atoms introduced by the misorientation. Another difference is that the dislocations are emitted on the slip plane (100) in Al (Figure 19a). The activation of plasticity in copper occurs at a much higher shear strain of 0.34 (Figure 19b), and the sliding of leading and trailing dislocations occurs on the (111) plane. Further shear deformation leads to the generation of secondary dislocations and vacancies in Al (see Figure 19c). In Cu, the successive formation (Figure 19b) and absorption (Figure 19d) of twinning layers bounded by stacking faults occur.

Figure 20 shows the case of the (110)+misorientation interface at a high initial pressure of 40 GPa. In this case, plastic relaxation is activated simultaneously in both metals immediately after the application of a shear strain of 0.001 (see Figure 20a). Planar defects grow in both parts. In copper, these interlayers represent typical stacking faults limited by dislocations. In aluminum, thicker layers of HCP atoms are formed with a thickness of 4 interatomic layers. At a strain of 0.015, a phase transition to the BCC phase is activated in the aluminum part (Figure 20b). In copper, plastic deformation develops due to the emission and absorption of twinning stacking faults by the interface. Deformation in the range 0.2–0.6 occurs due to the slip of dislocations in BCC aluminum and twinning interlayers in copper (see Figure 20c). At a strain of 0.6, HCP phase nuclei are formed in aluminum, which gradually increase in volume (Figure 20d). In copper, the nature of plastic deformation changes; instead of stacking faults on the (111) plane, HCP interlayers form on the (100) plane, as shown in Figure 20d.

The effect of an elevated temperature of 700 K was studied using the system with the (100) interface considered in the main MD simulations (see Figure 21). In contrast to room temperature, the elevated temperature leads to a violation of the interface structure to the moment of plasticity incipience (compare Figure 21a,b) and to emissions of split perfect dislocations instead of partial ones. The elevated temperature also leads to a significant decrease in the critical shear stress of plasticity initiation compared to 300 K: from 4.05 to 2.75 GPa. The dislocations are periodically absorbed by the interface (Figure 21c). The plasticity is governed by dislocations in the aluminum part and by twinning interlayers in the copper part (see Figure 21d).

4. Discussion

The interface between two metals in the Al-Cu composite forms a grid of perfect dislocations due to the constant lattice mismatch and due to lattice misorientation, if any. In most of the considered cases, plasticity of the composite starts with nucleation and emission of Shockley partial dislocations from this grid. The interface decreases the critical shear stress in comparison with both pure metals, because the homogeneous nucleation of dislocations triggers plasticity in pure metals. According to MD data for zero initial pressure, the shear strength of the laminar Al-Cu composite is about 4 GPa, which is about 20% lower than that of pure aluminum and 2.5-fold lower than that of pure copper (see Figure 3). Unsurprisingly, the plasticity starts in the aluminum part of the composite, and only with the following shear does it spread into the copper part. One can note in Figure 2 that the shear stresses in the copper part even decreases to the moment of plasticity incipience in this part in comparison with the critical stress that started plasticity in the aluminum part. It means that plasticity in the copper part is initiated by the shear stress level, which the copper part successfully withstands during the initial elastic part of deformation. The reason of this softening of the copper part during the plastic deformation of the aluminum part is the accumulation of additional defects at the interface during the dislocation activity in aluminum. As a result, the interface becomes more ‘defective’, which decreases the barrier of dislocation emission from the interface into the copper part of the composite.

Our previous studies [28,29] show that the pressure hardening coefficient $∆\tau /∆P_0$ of aluminum is about two times higher than that of copper. The higher pressure hardening of aluminum is also obvious in Figure 3b for initial pressures up to 20 GPa. This difference in pressure effect means plasticity first starts in the copper part at initial pressures of 15 GPa and higher.

An increase in pressure to about 40 GPa activates the FCC-to-BCC phase transformation in the aluminum part of the composite either during the preliminary relaxation of the system to this pressure for the (100) interface or during shear deformation for (110) interfaces with and without misorientation. This difference in behavior depending on the interface orientation indicates that the phase transition is provoked by the interface. The interface-induced HCP-to-BCC phase transition is reported in MD simulations [25] for Mg/Nb bimetallic composite. According to dynamic ramp compression experiments [45] combining nanosecond in situ X-ray diffraction and velocimetry measurements, the solid-solid phase transformations, FCC-HCP and HCP-BCC, in pure Al are in the ranges 216 ± 9 and 321 ± 12 GPa, respectively. Quasistatic diamond-anvil cell experiments [46] with a synchrotron-based X-ray diffraction also indicate the onset of the transition towards a BCC structure at pressures beyond 320 GPa. On the other hand, MD simulations [47] of ramp compression show that, in the case of nanocrystalline Al, the entire structure transforms to BCC at 76 GPa, while traces of BCC are observed at a pressure of 28 GPa. Thus, the grain boundaries and interfaces can substantially reduce the pressures required for the transformation to the BCC phase. In addition, MD simulations [34] for pure single crystal copper show a strong dependence of the pressure of the beginning of the BCC transition on the loading conditions, and one can expect similar dependence in the case of aluminum, while our loading conditions differ from that in [45,46,47]. Therefore, our results do not contradict to the literature data.

The plasticity development in both parts of the composite includes a complex interplay of partial dislocations leaving the stacking faults, split perfect dislocations, and twinning. As one can expect, the copper part is more easily susceptible to twinning due to its lower value of stacking fault energy. An interesting common feature of the plasticity evolution in both metals is the initial formation of a grid of stacking fault planes as the traces of primary leading Shockley partials are emitted from the interface. Intersections of stacking fault planes produce secondary dislocation, which are already split perfect dislocations. Activity of perfect dislocation results in the disappearance of the stacking fault planes, but produces vacancies. Thus, one can observe a change in the particular plasticity mechanism during the shear deformation of the composite.

We studied the (100) and (110) interfaces in the Al-Cu laminar composite and found the interface orientation influences the critical stress of plasticity initiation and the pattern of plasticity development. Depending on pressure, the critical stress of dislocation nucleation for the (110) interface can be either lower or higher than that for the (100) interface. Additional misorientation of Al and Cu lattices increases the density of GB dislocations at the interface, drastically decreasing the critical stress of plasticity initiation and making the pressure dependence of the critical stress monotonic. An increase in temperature from 300 K to 700 K violates the interface structure at shear strains close to the nucleation of lattice dislocations and leads to a two-fold decrease in the critical stress of nucleation.

During the shear deformation of the composite, lattice defects are periodically emitted from the interface and absorbed by the interface, which can be expected for a nanocomposite with a large density of interfaces. The defect absorption leads to temporary cleaning of the metal lattice of defects, which is especially pronounced for the copper part of the composite. On the one hand, this behavior substantiates the used initial system with perfect crystal lattices of both adjoined metals. On the other hand, the deformation modes with a defect-free copper part and a strain-accommodating aluminum part can be useful for technological applications related to deformable conducting materials.

The changeover of plasticity incipience from aluminum to copper and the following FCC-to-BCC phase transition in aluminum at high pressures make the pressure dependence of the critical shear stress of the composite nonmonotonic for both the (100) and (110) interfaces without misorientation. In addition, the strain rate sensitivity is much higher for initial pressures above 15 GPa. Strictly speaking, the initial system state for 40 GPa and higher pressures is already plastic due to the number of defects formed in the aluminum part during the phase transition; therefore, the plasticity incipience in this case is rather conditional and connected with the inertness of plasticity development at high strain rates. The revealed influence of the initial pressure on the nucleation of lattice dislocations at the Al-Cu interface is in line with the previous MD study [23] for a Cu-Ni bimetallic interface, where a strong dependence of the critical yield stress on the conditions of external loading was established.

In general, there is a complex dependence of the critical stress of plasticity initiation and further plastic behavior on the initial pressure, interface orientation, and the presence of misorientation between lattices. This diversity in properties is hard to take into account using a simple theoretical model, and the use of machine-learning-based approaches is beneficial in this field.

The ANN-based approach previously proposed and verified for pure metals [29,32,33,34] is fruitfully applied to the description of the plasticity initiation in the Al-Cu composite with the (100) interface in spite of a more complex behavior of the composite in comparison with pure metals. The only difference is in the introduction of two different values of strain rate sensitivity for moderate and high pressures. The achieved quality of the ANN-based description is reasonable, while it can be further improved by the utilizing of additional MD data for training. The use of the ANN together with the strain rate dependence of Equation (2) with the identified strain rate sensitivity parameters allows us to make an extrapolation of MD data to lower strain rates, which is of practical interest for various dynamic applications. This extrapolation predicts low dynamic shear strength (≤1 GPa) at pressures above 20 GPa for strain rates of the order of 10⁴ s⁻¹, which is typical for problems of high velocity impact. The present ANN for the (100) interface does not take into account data for other interfaces, because they require additional MD study to obtain a complete enough dataset for ANN training which can be completed in future work.

Further development of the present work can consist of the description of the plasticity evolution in the Al-Cu composite after its initiation by means of the machine-learning-based methods previously verified for pure metals [32,33,34]. Another possible issue to be further explored by means of MD simulations is the influence of intermetallic compounds on plasticity incipience and development in the composite.

5. Conclusions

We studied the shear deformation of a laminar Al-Cu composite perpendicular to the lamellae in comparison with pure single crystal Al and Cu at strain rates of 10⁹ s⁻¹ and 10⁸ s⁻¹ and different initial pressure in the range from −3 GPa to +50 GPa by means of molecular dynamics (MD) simulations. The interface between metals reduces the shear strength of the composite in comparison with both pure metals. At initial pressures below 10 GPa, the plasticity begins in the aluminum part of the composite, while at higher pressures, the plasticity of the copper part starts first. At pressures above 40 GPa, a phase transition in the aluminum part governs the plasticity development. All this leads to a nonmonotonic pressure dependence of the shear strength of the Al-Cu composite for the considered (100) and (110) interfaces without misorientation. Additional misorientation decreases the critical stress of the nucleation of the lattice dislocation and makes the pressure dependence of this stress monotonic. The observations in the MD deformation modes with a defect-free copper part and a strain-accommodating aluminum part can be useful for technological applications related to deformable conducting materials.

The results of MD for the plasticity initiation show complex dependencies, which are generalized by means of an artificial neural network (ANN) trained on MD data for 10⁹ s⁻¹, and a rate sensitivity parameter identified using MD data for 10⁸ s⁻¹. The ANN-based approach allows us to extrapolate MD data to much lower strain rates. The considered problem is of interest as an example of an application of the developed ANN-based approach to bimetallic systems, whereas previously it was tested only for pure metals; in addition, Al-Cu composites are of practical interest for technology.