## 4 Discussion
ProTaper Next X2 has an off-centered rectangular cross-section. Despite this difference in cross-section, both Protaper Next X2 and One curve instruments showed similar stress peak values (155.50 and 151.02 MPa, respectively). Interestingly, Hyflex CM showed markedly lower stress peak values (35.73 and 44.30 MPa) in both types of dentine (18 and 42 GPa, respectively) and demonstrated a low stress distribution along the curved dentine canal. Hyflex CM alloys are characterized by a quadrangular cross section with four blades and four flutes. They are obtained through an thermomechanical process in which the NiTi alloy shows \"controlled memory\" properties rather than \"superelastic properties\" [23]. Their diameter and conicity (#25 0.4) are associated with a reduced volume and higher flexibility in bending. Therefore, an elastic instrument--such as Hyflex CM--may rotate (and work) for a greater time inside the root canal with a reduced risk of fracture. From a clinical point of view, it is important to prevent any unexpected instrument separation/fracture inside the root canal. NiTi instruments may rotate inside the root dentine canal for approximately 30 s [38], but a complex canal anatomy may require more time. It has been documented that 40-120 s may represent a sufficient time to fracture [23; 25]. The operator should be able to evaluate the portion of the canal in which the stress is higher in order to prevent any risk of instrument fracture. Endodontic instruments produce--during their rotational movement--a great amount of debris mainly composed of predentine and dentine, a smear layer, and collagen-pulpal debris which must be removed from the root canal lumen [40; 41]. Their effect on friction must be evaluated in future studies. Many studies have reported rapid surface deterioration of NiTi instruments, as detected by scanning electron microscopy (SEM), environmental scanning electron microscopy (ESEM) coupled with energy-dispersive X-ray analysis (EDX) and by metallurgical analysis [22; 23]. The presence of small alloy defects and small cracks induce a fast fracture formation, easily detectable via SEM fractographic inspection [22; 23]. The elastic modulus of the dentine canal affects the stress and strain distributions of rotary instruments. The different mineralization of different types of dentine (sound and highly mineralized root dentine) represents a critical factor and greatly contributes to the fracture risk for instruments in the area (radius of root canal) where stress is concentrated [22; 23; 24]. In particular, the higher the elastic modulus, the more rigid the dentine and the higher the strain and stress concentrations for the instrument. Interestingly, as shown by the von Mises stress distribution, the higher concentration of the stress was located at the initial part of the curvature of the root canal (and of the instrument), approximately 7 mm from the apex/tip of the instrument. The frictional contact, assumed as being 0.2 between all instruments and root canal models, is a simplification that does not occur clinically. This value was considered in the present simulation to standardize the processing step and allow for comparison between the results. Further in vitro tests must be carried out to calculate the optimal coefficient that should be used for each instrument and dentin tissue. The FEA demonstrated that the stress induced by rotating instruments in the dentine canal created a stress propagation into a large area of deep dentine and was easily detectable at 3-4 mm from the canal wall. This means that all apical root dentin thicknesses are stressed by instrument movement (rotation). The stress propagation was evident along the entire radius of the root curvature, from the coronal to the apex direction as a sort of \"stress tunnel\". It does not represent a peak, but a well-defined area with different stress gradients. Similar to other mineralized human tissues, the root dentin presents a quasi-brittle characteristic and anisotropy of the mechanical properties under shear stress.