# Acoustic Emission Analysis of Fracture and Size Effect in Cementitious Mortars
## 1 Introduction  
The existing methods of analyzing and designing structures using strength-based criteria often lack the ability to explain structural phenomena, such as the size effect. Size effect is the phenomenon where the tensile strength and ductility of a material depend on the structure's geometrical size [1, 2, 3]. According to the strength failure criteria, the tensile strength and the ductility of a structure are size-independent. However, the existence of this effect in materials has been identified since the early 1900s by [PERSON] and [PERSON] [4] and it has been the subject of many studies [1, 2, 5, 6, 7, 8]. Structural engineers design new infrastructures using material strength determined from tests conducted on small- and medium-scale samples in a laboratory environment. Hence, utilizing these values without regard to the size effect can result in a possible erroneous estimation of the real-life structural performance [1, 6]. Recently, the application of advanced fracture monitoring techniques has provided new insights in this fundamental issue [9, 10, 11, 12, 13, 14, 15]. Acoustic emission (AE) [9, 10, 11, 12, 13, 14, 15], digital image correlation (DIC) [9, 10, 15], and X-ray imaging techniques [13] have been used to study the effect of specimen size on the energy release rate, the time of crack initiation, and the size of the fracture process zone (FPZ). In addition, for existing structures, researchers are developing AE-based crack monitoring methods [16]. [PERSON] [17] and [PERSON] et al. [18] correlated damage levels to specific values of AE parameters on concrete prisms and reinforced concrete beams, respectively. [PERSON] and [PERSON] [19] then used these reference values of AE parameters tomonitor the level of damage of a concrete bridge. However, since fracture behavior evolves with the size of the structure, the evolution of AE parameters with size requires further investigation. Hence, this paper seeks to understand if the geometrical size of a structure affects the AE-based fracture analysis. Size effect originates from two leading causes. The first one is the well-known Weibull statistical size effect, which stipulates that increasing the volume increases the probability of encountering micro-scale flaws that can initiate fracture. However, even for a purely deterministic (non-statistical) material, the second cause, being the mechanical size effect, would still exist [1; 2; 6]. This effect is due to the magnitude of the stored energy released at the crack tip. At the same nominal stress, larger structures release higher energy for a unit extension of a fracture. This means, for a larger structure, that the required fracture energy will be met at a lower nominal stress [8]. As the sample size increases, in addition to the decrease in the ultimate nominal stress, the failure also becomes more brittle [1]. Strength and ductility of a quasi-brittle material is related to the size of the fracture process zone (FPZ), which also varies with specimen size and geometry [12]. The FPZ is a region ahead of the main crack where micro-cracking accumulates. The size of this zone is wider than the material heterogeneity and is on the same order of magnitude as the sample size [7]. The FPZ is a region where tension softening occurs [1]. Hence, it is the region where fracture energy is released. Researchers have used direct observation [13], image-based techniques such as X-ray visualization [13], and digital image correlation [9] to measure the size of FPZ. AE-based techniques have been used by several researchers [9; 11; 12; 13; 14; 15]. The AE technique allows capturing the high-frequency elastic waves that are emitted upon micro-fracture [20; 21]. It can monitor the damage through the medium's three-dimensional space, and it can also track the damage in real time. In this paper, AE monitoring will be used to track the fracture progress, as well as to determine the FPZ. On a three-point bending test of notched beams, the size of FPZ was found to increase with sample size [12; 15].