## 1 Introduction  
Thermoplastic composites reinforced with short fibers have high specific strength [1]. The use of such lightweight and durable materials makes it possible to manufacture a wide range of highly loaded products, including aerospace structures [2, 3]. The mechanical behavior of short fibers is determined by the influence of their ends; therefore, a significant reduction in the length of a voxel leads to a decrease in its efficiency [4]. The critical length of a fiber is defined as the minimum length at which it can be destroyed, that is, the fiber holding the load up to its strength limit without separating from the binder [5]. The critical fiber length depends on the mechanical characteristics of the matrix and fibers and varies depending on the type of composite. For example, the critical length of carbon fiber in an epoxy binder was 0.2 mm (about 35 diameters) and that in the polycarbonate binder was 0.7 mm (about 105 diameters) [6]. The typical length of fibers used to fabricate polymer composites can be up to 3 mm in length if a thermoplastic-based matrix is used. Using microtomography technology, fiber reconstruction was performed [7],and it was found that the fiber is mainly distributed along the injection molding direction [8], and the twin screw process changed the shape and length of the fiber. The fibers together with the binder pass at least twice through the screws in which the fibers are broken, first during the compound mixing process and then during manufacturing of the part in the injection molding machine. Recycling further breaks down short fibers. Thus, in a material, fibers can have various lengths depending on the fiber type, matrix, and molding method [6]. A homogenization approach was used to model a short fiber-reinforced composite material. The models for the mechanical performance of homogeneous materials are based on the Eshelby approach [9], the Mori-Tanaka method [10], and Advani-Tucker averaging [11]. Material samples were tested to calibrate the elastic and strength properties of the materials in the main directions [12]. The studies in [7; 13; 14; 15] have shown that volume fraction, aspect ratio, and fiber orientation significantly affect the tensile strength of reinforced composite materials. Numerical methods can be used to predict the elastic properties of materials, including those depending on the aspect ratio of the fibers [16]. A comparative study on the various elastoplastic micromechanics models of a composite [17] shows that the anisotropic Eshelby tensor approach delivers much stiffer results. The ratio of the fiber length involved in mechanical work to its full length determines the effective fiber length [18]. A more detailed analysis of the effective length of the short-reinforced composites was presented in [19]. Knowledge of both the total fiber length, which was observed experimentally, and the fiber length involved in mechanical work, which can be derived from models of the mechanical characteristics of the composite material, is necessary to determine the effective fiber length. An experimental evaluation of the microstructure of composites requires fiber pattern recognition in electron microscope images [15] or in spatial images obtained from microtomography [20]. The study of short, reinforced composites using microtomography (\(\mu\)CT) is presented in [21; 22; 23; 24]. The advantage of microtomography is the possibility of the simultaneous estimation of all parameters of the material microstructure--fiber size, position, and orientation--as well as the possibility of using simple image segmentation methods, including threshold segmentation, due to the presence of gaps between the fibers in space. On the other hand, microtomography of polymers reinforced with short carbon fibers with small diameters and low density differences with the matrix requires the use of high-sensitivity equipment. High-resolution microtomography is used for small sample sizes, which also imposed testing limitations.