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This paper applies and validates the Notch Master Curve in two ferritic steels with medium (steel S460M) and high (steel S690Q) strength. The Notch Master Curve is an engineering tool that allows the fracture resistance of notched ferritic steels operating within their corresponding ductile-to-brittle transition zone to be estimated. It combines the Master Curve and the Theory of Critical Distances in order to take into account the temperature and the notch effect respectively, assuming that both effects are independent. The results, derived from 168 fracture tests on notched specimens, demonstrate the capability of the Notch Master Curve for the prediction of the fracture resistance of medium and high strength ferritic steels operating within their ductile-to-brittle transition zone and containing notches.

This paper presents a model for the prediction of the apparent fracture toughness of ferriticpearlitic steels in notched conditions and operating at temperatures corresponding to their ductile-to-brittle transition zone. The model, here named the Notch-Master Curve, is based on the combination of the Master Curve of the material in cracked conditions and the notch corrections provided by the Theory of Critical Distances. In order to validate the model, the fracture resistance results obtained in 168 tests performed on CT specimens (84 for each material) are presented. These tests were carried out, for each material, in specimens with six different notch radii, from 0 mm up to 2.0 mm, and at three different temperatures within their corresponding ductile-to-brittle transition zone. It has been observed that the model provides good predictions of the fracture resistance in notched conditions for the two materials analysed.

Please cite this article as: Cicero, S., García, T., Castro, J., Madrazo, V., Andrés, D., Analysis of notch effect on the fracture behaviour of granite and limestone: An ABSTRACT This paper presents the analysis of the notch effect on granite and limestone fracture specimens.The research is based on the results obtained in an experimental programme composed of 84 fracture specimens, combining the two materials and 7 different notch radii varying from 0.15 mm up to 10 mm. The notch effect is analysed through the evolution of the apparent fracture toughness and the application of the Theory of the Critical Distances.The results reveal a significant notch effect in the limestone, whereas the notch effect in the granite is negligible for the range of notch radii analysed. Both observations are justified by the corresponding critical distance of the material. ACCEPTED MANUSCRIPT3 reduction in the resistant section). Additionally, the terms "sharp" and "blunt" are not absolute, but rather they depend on the material: there are materials that present a clear notch effect (e.g., increase in load-bearing capacity and apparent fracture toughness) for very small notch radii (e.g, Madrazo et al., 2012), and there are others that require a certain notch radius to develop a notch effect (e.g., Cicero et al., 2012). This particular nature of notches has led to a great deal of research work over the last few decades, aiming to provide specific tools for the assessment of notched components, beyond the simple and generally overconservative application of ordinary fracture mechanics. However, the analysis of these phenomena in rocks has been scarce, as detailed in the following section.Moreover, size effects are an important issue in rock fracture mechanics, given that the material behaviour (e.g., fracture toughness, tensile strength) and the notch sensitivity may change with the size of the component being analysed (

When the structural integrity of notched components is analysed, it is generally assumed that notches behave as cracks, something which generally provides overconservative results. The proposal of this paper consists, on the one hand, in the application of the Theory of Critical Distances for the estimation of the notch fracture toughness and, therefore, for the conversion of the notched situation into an equivalent cracked situation in which the material develops a higher fracture resistance. On the other hand, once the notch fracture toughness has been defined, the assessment is performed using the Failure Assessment Diagram methodology, and assuming that the notch effect on the limit load is negligible. The methodology has been applied to 336 CT notched fracture specimens made of two different structural steels, covering temperatures from the corresponding lower shelf up to the upper shelf, providing satisfactory results and a noticeable reduction in the overconservatism derived from the analyses in which the notch effect is not considered. INTRODUTION: NOTCH EFFECT, THE THEORY OF CRITICAL DISTANCES AND FAILURE ASSESSMENT DIAGRAMSThere are many situations where the defects responsible for structural failure are not sharp. Actually, notched components develop a fracture resistance that is greater than that developed by cracked components (e.g., [1][2][3][4][5][6][7]) and this, generally, is directly related to the load-bearing capacity of the component. Hence, the development of an adequate methodology for the assessment of the notch effect would reduce the conservatism in many practical situations.There are two main failure criteria in notch theory: the global fracture criterion and local fracture criteria [2,3]. The global criterion establishes that failure occurs when the notch stress intensity factor reaches a critical value, K ρ c :This approach is totally analogous to that used in cracks, but its application is very limited because of the lack of analytical solutions for K ρ (as there are for K I ) or/and standardized procedures for the experimental definition of K ρ c .Local criteria are based on the stress field on the notch tip. Among them, the Point Method (PM), the Line Method (LM) and the Finite Fracture Mechanics stand out [8], all of them being different versions of the Theory of Critical Distances (TCD) and, then, using a characteristic material length parameter (the critical distance, L) when performing fracture assessments [8]:K c is the material fracture toughness and σ 0 is a characteristic material strength parameter (the inherent strength) that must be calibrated. Only in those materials with linear-elastic behaviour at both the macro and the micro scales (e.g., ceramics), does σ 0 coincide with the ultimate tensile strength (σ u ) [8].The notch analysis following these methodologies is relatively simple. For example, the PM [9] establishes that fracture occurs when the stress reaches the inherent strength (σ 0 ) at a distance from the defect tip equal to L/2:For its part, the LM [...

The fracture resistance of materials is generally higher in notched conditions that in cracked conditions. In other words, when the notch radius increases there is also an increase in the apparent fracture toughness, which is that exhibited in notched conditions. This paper presents an analysis of the notch effect on two ferritic-pearlitic steels operating within their corresponding lower shelf, and develops an experimental The research is completed with the analysis of the evolution of fracture micromechanisms when the notch radius increases, revealing a direct relation between this evolution and the apparent fracture toughness observations.