Energy Requirement for Rock Breakage in Laboratory Experiments and Engineering Operations: A Review

Based on the review of a wide range of literature, this paper finds that: (1) the average specific surface energy of various single crystals is only 0.8 J/m2. (2) The average specific fracture energy of the rocks with a pre-crack under static cleavage tests is 4.6 J/m2. (3) The average specific fracture energy of the rocks with a pre-cut notch but with no pre-crack under static tensile fracture (mode I) tests is 4.6 J/m2. (4) The average specific fracture energies of regular rock specimens with neither pre-made crack nor pre-cut notch are 26.6, 13.9 and 25.7 J/m2 under uniaxial compression, tension and shear tests, respectively. (5) The average specific fracture energy of irregular single quartz particles under uniaxial compression is 13.8 J/m2. (6) The average specific fracture energy of particle beds under drop weight tests is 74.0 J/m2. (7) The average specific fracture energy of multi-particles in milling tests is 72.5 J/m2. (8) The average specific energy of rocks in percussive drilling is 399 J/m3, that in full-scale cutting is 131 J/m3, and that in rotary drilling is 157 J/m3. (9) The average energy efficiency of milling is only 1.10%. (10) The accurate measurements of specific fracture energy in blasting are too few to draw reliable conclusions. In the last part of the paper, the effects of inter-granular displacement, loading rate, confining pressure, surface area measurement, premade crack, attrition and thermal energy on the specific fracture energy of rock are discussed.

Identification of AAAS Composites Mechanical Fracture Parameters

The paper deals with selected alkali-activated aluminosilicate (AAAS) composites based on ceramic precursors in terms of characterization by mechanical fracture parameters. Two composites made of brick dust as a precursor and an alkaline activator with a silicate modulus Ms = 1.0 were investigated. The composites differed in the fineness of grinding of the precursor – in the first set it was 0 to 1 mm, in the second set 0 to 0.3 mm. The filler was crushed brick. The test specimens had nominal dimensions of 40 × 40 × 160 mm and were provided with notches in the middle of the span up to 1/3 of the depth of the specimens after 28 days of hardening. Five to six specimens from each composite set were tested. The specimens were subjected to three-point bending tests, in which force vs. displacement (deflection in the middle of the span) diagrams (F–d diagrams) and force vs. crack mouth opening displacement (F–CMOD) diagrams were recorded. After correction of these diagrams, the values of static modulus of elasticity, effective fracture toughness, effective toughness and specific fracture energy were determined using the Effective Crack Model and the Work-of-Fracture method. After the fracture experiments, the values of informative compressive strength were determined on one of the fractured parts. At the same time, the values of static modulus of elasticity, tensile strength and specific fracture energy were identified using artificial neural networks and F–d diagrams measured and simulated in the ATENA FEM software. All evaluations included the determination of basic statistics of parameters.

Dynamic crack propagation in weak snowpack layers: Insights from high-resolution, high-speed photography

To assess snow avalanche release probability, information on failure initiation and crack propagation in weak snowpack layers underlying cohesive slab layers are required. With the introduction of the Propagation Saw Test (PST) in the mid-2000s, various studies used particle tracking analysis of high-speed video recordings of PST experiments to gain insight into crack propagation processes, including slab bending, weak layer collapse, crack propagation speed and the frictional behavior after weak layer fracture. However, the resolution of the videos and the methodology used did not allow insight into dynamic processes such as the evolution of crack speed within a PST or the touchdown distance, which is the length from the crack tip to the trailing point where the slab sits on the crushed weak layer at rest again. Therefore, to study the dynamics of crack propagation we recorded PST experiments using a powerful portable high-speed camera with a horizontal resolution of 1280 pixels at rates up to 20,000 frames per second. By applying a high-density speckling pattern on the entire PST column, we then used digital image correlation (DIC) to derive high-resolution displacement and strain fields in the slab, weak layer, and substrate. The high frame rates allowed time derivatives to obtain velocity and acceleration fields. On the one hand, we demonstrate the versatile capabilities and accuracy of the DIC method by showing three PST experiments resulting in slab fracture, crack arrest and full propagation. On the other hand, we present a methodology to determine relevant characteristics of crack propagation: the crack speed and touchdown distance within a PST, and the specific fracture energy of the weak layer. To estimate the effective elastic modulus of the slab and weak layer as well as the weak layer specific fracture energy we used a recently proposed mechanical model. A comparison to already established methods showed good agreement. Furthermore, our methodology also provides insight into the three different propagation results found with the PST and reveals intricate dynamics that are otherwise not accessible.

Определение трещиностойкости образцов с шевронным надрезом с использованием трехточечного изгиба

A method is proposed for the experimental determination of the specific fracture energy of a material under loading by a 3-point bending of a rectangular specimen with a chevron notch. It is shown that at the initial stages of crack propagation in the chevron notch zone, a linear dependence of the specimen compliance on the crack length is observed. This makes it possible to calculate the specific fracture energy of the material without using the phenomenological equations used under standard test conditions. The calculations were carried out for technical titanium VT1-0.

Wedge-Splitting Test on Carbon-Containing Refractories at High Temperatures

The mode I fracture behavior of ordinary refractory materials is usually tested with the wedge-splitting test. At elevated temperatures, the optical displacement measurement is difficult because of the convection in the furnace and possible reactions of refractory components with the ambient atmosphere. The present paper introduces a newly developed testing device, which is able to perform such experiments up to 1500 °C. For the testing of carbon-containing refractories a gas purging, for example, with argon, is possible. Laser speckle extensometers are applied for the displacement measurement. A carbon-containing magnesia refractory (MgO–C) was selected for a case study. Based on the results obtained from tests, fracture mechanical parameters such as the specific fracture energy and the nominal notch tensile strength were calculated. An inverse simulation procedure applying the finite element method yields tensile strength, the total specific fracture energy, and the strain-softening behavior. Additionally, the creep behavior was also considered for the evaluation.

Probabilistic Fracture Energy Assessment of Natural Fibre Reinforced Concrete by Two Parameter Weibull Distribution

Fracture energy is the post-crack energy absorption ability of the material that represents the energy absorbed by the structure at the time of failure. Its analysis has gained importance and hence requires a powerfulmethod for its development. A two parameter Weibull distribution proves to be an efficient tool in analysing the scattered experimental test results. In this paper, the specific fracture energy of plain concrete and concrete reinforced with natural fibres of hemp, wheat straw and elephant grass are statistically analysed by two parameter Weibull distribution by using graphical method. For determining Weibull parameters, 21 equations have been used and the best equation is taken for the reliability analysis. A Weibull reliability curve is plotted, which shows the specific fracture energy at each reliability level. This curve enables an engineer to choose the fracture energy of a particular mix based on its reliability requirement and safety limit. Therefore, reliability curves are a pioneer in statistical analysis as they eliminate the time-consuming and costly experimental process. This method can be applied in areas with similar uncertainties.

Estimating the effective elastic modulus and specific fracture energy of snowpack layers from field experiments

ABSTRACTMeasurements of the mechanical properties of snow are essential for improving our understanding and the prediction of snow failure and hence avalanche release. We performed fracture mechanical experiments in which a crack was initiated by a saw in a weak snow layer underlying cohesive snow slab layers. Using particle tracking velocimetry (PTV), the displacement field of the slab was determined and used to derive the mechanical energy of the system as a function of crack length. By fitting the estimates of mechanical energy to an analytical expression, we determined the slab effective elastic modulus and weak layer specific fracture energy for 80 different snowpack combinations, including persistent and nonpersistent weak snow layers. The effective elastic modulus of the slab ranged from 0.08 to 34 MPa and increased with mean slab density following a power-law relationship. The weak layer specific fracture energy ranged from 0.08 to 2.7 J m−2 and increased with overburden. While the values obtained for the effective elastic modulus of the slab agree with previously published low-frequency laboratory measurements over the entire density range, the values of the weak layer specific fracture energy are in some cases unrealistically high as they exceeded those of ice. We attribute this discrepancy to the fact that our linear elastic approach does not account for energy dissipation due to non-linear parts of the deformation in the slab and/or weak layer, which would undoubtedly decrease the amount of strain energy available for crack propagation.