## 1 Introduction  
Polymeric materials such as polymethyl-methacrylate (PMMA) and general-purpose polystyrene (GPPS) are widely used in industrial applications due to their good physical and mechanical properties. PMMA (or plexiglas(r)) is an artificial rigid amorphous polymer that can be combined with laser cutting, forming or bending processes. GPPS (also known as crystal polystyrene) is a thermoplastic multi-purpose polymer with brittle behavior and excellent X-ray resistance, low contraction and low production cost. Similar to other polymers, the mechanical properties of both PMMA and GPPS can be improved by adding a suitable percentage of short or long fibers [1; 2; 3]. Fibers and their orientations affect and control the damage mechanisms of polymers including fiber pull-out, growth of hackles, profuse crazing, energy absorbing, etc. [4; 5]. Due to design, lubrication and/or optimization requirements, notch-type defects such as round tip V-shaped (RV) notches may be present in polymeric components. These notches lead to stress concentrations at their vicinity and the load bearing capacity of the corresponding notched components decreases. Therefore, the fracture assessment of notched parts has always been of interest for structural engineers and researchers, particularly when dealing with brittle and quasi-brittle materials such as polymers, given that the fracture process of these materials is generally sudden and catastrophic. In this context, for example, [PERSON] et al. [6] investigated the mode I fracture behavior of rock samples weakened by RV and U-shaped notches via a modified form of the point stress criterion. [PERSON] et al. [7] inspected the failure of RV-notched parts manufactured from rubber-like materials, utilizing the averaged strain energy density (ASED) criterion. [PERSON] [8] assessed systematically the effectiveness of [PERSON]'s formulations to define stress fields at the notch tip vicinity of RV notches under pure mode I. [PERSON] et al. [9] probed the brittle fracture of RV-notches utilizing finite fracture mechanics criterion. [PERSON] and [PERSON] [10] carried out the assessment of mode I fracture in RV notches by means of the Point Stress (PS) and the MS criteria in polymeric materials. [PERSON] et al. [11] investigated the mixed mode I/II brittle fracture in U- and V-shaped notches applying the ASED criterion. A large number of studies associated with the fracture of cracked samples have demonstrated that the fracture behavior of brittle materials, such as polymers, ceramics, concretes and rocks, depends significantly on the size of the sample being analyzed. This has been mainly explained through a local damaged zone around the crack tip called the fracture process zone (FPZ). [PERSON] [12] suggested tools to determine the quantity of the size effect on the fracture toughness of brittle materials, such as the size effect law (SEL), for both cracked and non-cracked parts. [PERSON] et al. [13] modified [PERSON]'s SEL by adding an empirical constant. [PERSON] has published a number of articles analyzing the size effect since 1984, with applications in various quasi-brittle materials (e.g., [14; 15; 16; 17; 18; 19]). [PERSON] [20] suggested a criterion for the analysis of size effects based on the fractal theory. [PERSON] and coworkers [21; 22; 23; 24; 25] proposed and validated a new criterion to describe the size effect according to the length of the FPZ and a boundary effect model. [PERSON] [26] took into account the effect of the softening behavior of quasi-brittle materials in the FPZ by means of the [PERSON]'s model [27] and suggested a criterion to predict the size effect. [PERSON] et al. [28] proposed a criterion to consider the size effect on the basis of a combination of energy and strength criteria. [PERSON] and [PERSON] [29] analyzed the size effect on the fracture toughness of brittle materials, utilizing the modified MTS criterion (MMTS).