## 1 Introduction  
Aluminum alloys are widely used as construction materials. They are especially widespread in those fields where a low weight together with sufficiently high strength is required, such as aviation and space engineering. During deformation of aluminum alloys, the development of bands of plastic flow localization is possible, the deformation in which can exceed many times the deformation in the surrounding material, reaching 90% of the total deformation [1, 2, 3, 4]. There are two classical points of view on the development of plastic localization: (1) plastic localization occurs as the result of thermal softening [1], and (2) the cause of plastic localization is the heterogeneity of the properties of the material subjected to deformation [5, 6, 7, 8, 9]. A more detailed analysis assumes taking into account the contributions of both thermal and microstructural factors to the initiation of plastic flow localization [10, 11, 12, 13, 14]. The development of localization bands is a multi-stage hierarchical process that occurs at several levels. Interaction of dislocations with precipitates and evolution of the later ones is relevant at a micro scale. Multiple cutting of the strengthening particles is the cause of catastrophic strain localization [15], since it activates the flow of dislocations in the slip plane passing through the cut precipitates. The presence of easily cut precipitates in alloy usually manifests itself in a decrease in the strain hardening rate [16]. One of the possible reasons for this may be a decrease in the efficiency of accumulation of the Orowan loops around the inclusion after the cutting [15]. The authors of work [17] observed the softening of AA2139 alloy samples under cycle loading; this softening was explained as a consequence of the repeated cutting of \(\Omega\) phases. Besides precipitate cutting, accumulation of microvoids is observed in the shear bands that can further initiate the fracture of the deformed sample [18]. Aging of alloys, which leads to the precipitation of cut-resistant particles of hardening phases, can make deformation more uniform and increase the fatigue resistance of the samples [15; 19]. In an Al-Cu system, the hardening phases precipitate during aging in the following sequence: supersaturated solution, Guinier-Preston (GP) zones, \(\theta^{\prime}\), \(\theta^{\prime}\) and \(\theta\) phases [20; 21; 22; 23; 24]. \(\theta^{\prime}\) phase inclusions were traditionally considered as non-cuttable particles; therefore, they are considered as the most preferable for strengthening in an aging process of Al-Cu alloys. However, in the last decade there has been more and more evidence in favor of the fact that cutting and even dissolution of \(\theta^{\prime}\) phase can occur with the accumulation of plastic deformation [18; 25; 26; 27; 28; 29; 30; 31; 32]. The transmission electron microscopy and X-ray tomography images showing cut \(\theta^{\prime}\) phase was presented in [31; 32]. Cutting of \(\theta^{\prime}\) phase was also observed in molecular dynamics (MD) studies using realistic models of interatomic interaction [33; 34; 35]. Depending on the aging conditions, the size of released \(\theta^{\prime}\) precipitates can vary significantly, starting from a few nanometers in diameter and reaching hundreds of nanometers [36; 37; 32; 33]. In the experimental work [32], it was shown that the cutting of \(\theta^{\prime}\) phase has a threshold character: cutting of particles only with a size less than 60 nm was observed. It is known that fine particles of \(\theta^{\prime}\) phase contribute to an increase in the shear strength of copper-containing alloys [36; 37; 38] more efficiently in comparison with larger ones. On the other hand, the stability of large \(\theta^{\prime}\) phase during prolonged plastic deformation can increase the fatigue resistance of alloy [32].