## 1 Introduction
There are other research papers in association with the size effect on the fracture toughness of cracked samples, such as those studied by [PERSON] et al. [30; 31], [PERSON] and [PERSON] [32], [PERSON] et al. [33], [PERSON] et al. [34], [PERSON] et al. [35], [PERSON] and [PERSON] [36], [PERSON] and [PERSON] [37], [PERSON] et al. [38], [PERSON] et al. [39] and [PERSON] et al. [40], among others, demonstrating the great interest in this phenomenon among the research community. Contrary to the cracked specimens, there is very limited research in the literature investigating the effect of specimen size on notch fracture resistance (NFR). For example, the size effect on the mixed mode fracture resistance of polymeric U and key-hole notched specimens has been assessed by [PERSON] et al. [41] using the PS method. Additionally, [PERSON] et al. [42] used the PS criterion to appraise the size effect on NFR of graphite specimens with various notch types. [PERSON] and [PERSON] [43] conducted some fracture tests on rectangular samples with RV notches of various sizes and then utilized the cohesive zone model (CZM) for assessing the onset of fracture in (RV-notched) specimens. Combining the energy release rate approach with an elastic-plastic model, [PERSON] et al. [44] investigated the size and geometry effects on U-notched compact-tension (CT) steel samples. [PERSON] et al. [45] predicted the onset of crack growth in RV notches and voids (cavities) considering the influence of the specimen size by using the finite fracture mechanics (FFM) theory. Furthermore, the effect of notch size has been assessed in some studies such as those published by [PERSON] et al. [46] and [PERSON] et al. [47; 48]. According to the literature, it can be found that there is no previous analysis estimating the size effect on mode I fracture resistance of RV-notched samples made of PMMA and GPPS. Therefore, this paper aims to analyze the effect of the specimen size on the fracture resistance of polymeric RV-notched samples. Since there are no previous experimental data for polymeric RV-notched specimens with different sizes, 120 RV-notched Brazilian disk (RVNBD) and RV-notched semi-circular bending (RVSCB) samples with different notch radii were prepared and tested. It is shown that the values of the NFT obtained from fracture tests on RVNBD and RVSCB specimens are size-dependent. In order to explain the size dependency of the NFT, a variant of the mean stress criterion, namely MS-Schmidt, used frequently for fracture analyses of notched samples is applied. Additionally, for the first time, the modified mean stress criterion (MMS) is introduced, which considers higher order terms of the stress field when calculating the FPZ length around the defect tip. In both the MS-Schmidt and the MMS criteria, the length of the FPZ is considered to be dependent on the size of the specimen being analyzed. The size-dependent values of the FPZ length are also defined for cracked Brazilian disk (CBD) and cracked semi-circular bending (SCB) specimens with various radii employing a semi-empirical relation. It is finally observed how the suggested criteria successfully predict the mode I NFR of PMMA and GPPS materials considering size and geometry effects.