Application of the Theory of Critical Distances for the Fracture Assessment of a Notched Limestone Subjected to Different Temperatures and Mixed Mode with Predominant Mode I Loading Conditions

Abstract

This work aims to assess the fracture of U-notched limestone samples subjected to mixed mode I+II loading conditions with a predominant mode I influence, both at room temperature and at 250ºC. This analysis is based on the use of the Theory of the Critical Distances, and more specifically on the use of the Line Method, considering both an analytical and a numerical approach for the definition of the stress fields. An experimental campaign of almost 400 three-point bending tests has been performed as a basis for the fracture assessment of the limestone, using Single Edge Notched Bend (SENB) specimens with notch radii varying from 0.15 mm up to 15 mm, different temperature conditions and variable loading positions. The Theory of Critical Distances has successfully been applied to study the experimental results. The analytical and numerical stress fields for pure mode I fracture assessments provide similar accurate results both at 23ºC and 250ºC. Similarly, the mixed mode (I+II) fracture assessments allow the critical distance (𝐿𝐿) to be characterised for different mode mixities (𝑀𝑀 𝑒𝑒 ), using the stress field around the notch tip obtained from the numerical models. Comparing the values of the critical distance against the mode mixity in isolation, a slight decrease of 𝐿𝐿 is observed as it approaches pure mode I conditions (𝑀𝑀 𝑒𝑒 = 1). However, if the results are analysed separately for each notch radius, 𝐿𝐿 seems to be relatively constant with 𝑀𝑀 𝑒𝑒 . In parallel, a certain influence of the notch radius on the critical distance is appreciated, which shows an increment both at 23ºC and 250ºC.

A new methodology inspired from the Theory of Critical Distances for determination of inherent tensile strength and fracture toughness of rock materials

“…Therefore, the accurate determination of their failure properties is key to assess the structural resistance of rock masses, an important issue in many rock engineering practices such as tunnelling, rock cutting processes, hydraulic fracturing and rock slope stability. 7 In the following, the term structural properties is used when the geometrical features of the specimens or bodies do play a significant role on top of the intrinsic properties that depend only on the microstructural features of the rock materials as well as the surrounding environment. 8 A suitable solution for defining the tensile strength of rocks consists in considering the characteristic stress level at which the material fails within the process zone of a stress concentrator or a running crack.…”