## 3 Results and Discussion
### Influence of Multiple Interactions on the Structure of Inclusion and Stress State of the MD System  
When the dislocation separates from the precipitate for the first time, the Orowan loop is closed around the precipitate. The Orowan loop is a region of disordered lattice, on the plane of which the atoms above and below differ in displacement along the \(x\)-axis by one perfect Burgers vector. Successive interactions of the dislocation with inclusion lead to the accumulation of lattice mismatch above and below the slip plane of the dislocation that causes the rise of shear stress acting on the inclusion. The first few interactions lead to elastic distortion of the layers of copper atoms in \(\theta^{\prime}\) phase structure (Figure 6, 1-4 interaction). However, an increase in shear stresses causes cutting of \(\theta^{\prime}\) phase after 5-6 interactions with the dislocation. Due to the difference between the slip systems of aluminum matrix and inclusion lattice, the inclusion structure is disordered (Figure 6, 6 th interaction). The resulting form of \(\theta^{\prime}\) phase in our simulations is very similar to the experimental image of the sheared \(\theta^{\prime}\) phase shown in [31]. Figure 4: Time dependences of the average stress in systems containing \(\theta^{\prime}\) precipitate for various temperatures. Diameter of \(\theta^{\prime}\) precipitate is 5 nm, thicknesses of systems, equal to the inter-precipitate distance, are 9.87 and 17.6 nm, shear velocity is 3 m/s. Figure 4 shows the time dependences of the shear stress averaged over the sample for two MD systems at various temperatures. In the dependences (Figure 4), each local maximum of stresses corresponds to the next interaction of the dislocation with the inclusion. For the system of 17.6 nm thickness, about 100 interactions are tracked, and for 9.87 nm--about 60. The system with thickness of 9.87 nm exhibits a significantly higher level of shear stresses due to the smaller distance between inclusions, which provides strong resistance for dislocation motion. At 300 K, the stresses at the first interactions reach 670 MPa in the case of such a small inter-precipitate distance. For a thicker system, the stresses are about 350 MPa. A diminution in the initial stresses acting in the region with increasing temperature is observed for both systems; this behavior was previously recorded in [34; 57; 58] for all hardening phases of copper in aluminum and is interpreted as a result of a diminution in the energy of interaction of dislocation with the inclusion surface upon heating. All curves in Figure 4 are characterized by a gradual diminution in the stresses acting in the system with time. However, local increases in stresses are possible that violate the general trend, such as, for example, an interval of 1-3 ns in Figure 4 (17.6 nm) for the temperature of 100 K. Note also the following feature of the plots observed for the system with thickness of 17.6 nm at 500 K after 8 ns and for the system with thickness of 9.87 nm at 100 K after 3 ns: After the indicated time, stabilization of stresses occurs at a certain level without further decrease in the maximum stresses. After reaching such a stationary regime, the amplitude of stress fluctuations in the system also significantly decreases. Figure 5: The first dislocation–precipitate interaction. Atoms with a centrosymmetry parameter more than 5 square angstroms are depicted. Aluminum atoms are colored in gray, copper atoms are red. Shockley partial dislocations are colored in green. Let us consider the processes occurring in the system at the atomic level to explain the obtained dependences of stresses on time. Figure 7 shows the stress and dislocation position graphs for the system with thickness of 17.6 nm at the temperature of 300 K together with the distribution of atoms in the system. It was shown in [34] that upon contact of dislocation with \(\theta^{\prime}\) precipitate on the flat surface of inclusion, the dislocation may exit from a slip plane into an adjacent one due to the climb process.