Energy-based approach for fracture assessment of several rocks containing U-shaped notches through the application of the SED criterion

Abstract

This work presents an energetic continuum approach for the fracture assessment of rocks containing U-shaped notches and subjected to Mode I loading conditions. Three different methodologies are proposed in this article, all of them based on the premise that brittle failure will occur when the average strain energy density over a certain control area reaches a critical value that only depends on the material, as stated by the Strain Energy Density (SED) criterion.The first method proposed (A) deals with the application of the SED criterion through an expression with a series of already tabulated parameters, which are particularised for the analysed rocks by rational extrapolation. Therefore, this first method avoids the use of numerical analysis. By contrast, the second method (B) aims to obtain numerically the previously extrapolated parameters, and the third method (C) directly relates the strain energy density with the applied load, without the use of those parameters.The research is based on the results obtained from an exhaustive experimental programme comprising 300 fracture specimens tested in four-point bending conditions. These tests combine parallelepiped samples made of 6 different types of rocks (two marbles, two limestones, a sandstone and a granite) and containing 8 different notch radii (varying from 0.15 mm up to 15 mm).Thus, this work aims to show the potential, capacity and limitations of the SED criterion in rock fracture analyses, comparing with this purpose the experimentally obtained fracture loads and those predicted by the three proposed methodologies.

Critical Load Prediction in Notched E/Glass–Epoxy-Laminated Composites Using the Virtual Isotropic Material Concept Combined with the Average Strain Energy Density Criterion

“…With all these Equations ( 1)-( 7), it is straightforward to assess notched components according to the ASED fracture criterion. The results shown in the literature reveal the accuracy of this approach as long as the material being analysed presents a linear-elastic behaviour (e.g., [9,[13][14][15])…”

“…The different fracture theories that can be found in the literature dealing with the notch effect can be grouped into three different categories: (a) the global criterion [10][11][12], based on linear-elastic notch fracture mechanics, establishes that fracture occurs when the notch stress intensity factor reaches a critical value; (b) the local criteria, which bring together a series of approaches (e.g., the theory of critical distances (TDC) or the average strain energy density (ASED)) that have in common the analysis of the stress, strain, or energy fields at the defect tip. This paper focused, precisely, on the ASED criterion, which was validated in a wide range of materials [13][14][15]; (c) finally, the progressive damage models [16][17][18], which consider the material damage during the entire loading process, and the consequent changes in the stress distribution. The main issue found in the application of any of these failure models in laminated composites was to consider their orthotropic behaviour, the ply-by-ply analysis, and the first ply failure predictions, resulting in complex and time-consuming processes.…”

Fracture Load Predictions in Additively Manufactured ABS U-Notched Specimens Using Average Strain Energy Density Criteria

“…Thus, treating notches as if they were cracks tends to provide over-conservative analyses. In order to avoid this over-conservatism, different methodologies may be applied to take into consideration the notch effect (e.g., [ 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 ]): one example is the global criterion [ 19 , 20 , 21 ], which is based on linear-elastic notch fracture mechanics, and establishes that a fracture occurs when the notch stress intensity factor reaches a critical value. Other examples are the local criteria, based on the analysis of the stress, strain or energy fields at the defect tip, of which the Theory of Critical Distances (TDC) [ 22 ] or the Average Strain Energy Density (ASED) [ 23 ] can be highlighted.…”

Seismic Damage Prediction Method for Lining Structures Based on the SEDR Principle

“…With deep exploration of the SEDR principle, the range of its application was extended to all the orthotropic materials [22]. In the last decade, the SEDR principle has been widely applied in brittle materials (e.g., rock materials and concrete materials) to research the prediction methods of the crack position [23][24][25][26][27], crack expansion [28][29][30][31][32], and fatigue damage [33][34][35].…”