Local stress fields in solids estimated by acoustical emission method

Based on the Zhurkov’s kinetic concept of solids’ fracture a local internal stress estimation method is introduced. Stress field is computed from the time series of acoustic emission intervals between successive signals. For the case of two structurally different materials the time evolution of these stresses is examined. It is shown that temporal changes of these stresses’ accumulation law may serve as a precursor of incoming macroscopic fracture.

Study on Fracture Distribution and Local Brittleness Characteristics Based on Stepwise Regression Method

The brittleness of rock is an important parameter that influences and controls the evolution mechanism of the fracture and formation of a fracture net. The existing methods of brittle characterization are describing the brittleness of rock mass as a whole. They lack reliability descriptions to guide the fracture strike and improve the volume of the reservoir. It is considered that the macroscopic brittle fracture of a rock is the process of continuous initiation and propagation of local fractures in the rock mass under the action of external loads. The macroscopic fracture is the appearance caused by a local rupture to a certain extent, and the local rupture is the root cause of macroscopic fracture. The study of the local brittleness of a rock can reveal the intrinsic nature of its fracture behavior and can reflect the evolution mechanism of fracture more directly and accurately. In this paper, coring sampling in field outcrop is first carried out, and the break evolution law of core is described by a CT scanner. The mineral compositions in the core are determined by a mineral analysis diffractometer. The regulation of the rock local brittleness with different mineral contents is analyzed. And a new method for local brittle region division and characterization of rock has been developed. This method gives the connotation relation of the rock brittle fracture as a whole induced by a local brittle fracture. And it provides a new approach to study the law of a rock fracture.

Mechanism Dictates Mechanics: A Molecular Substituent Effect in the Macroscopic Fracture of a Covalent Polymer Network

<div><p>Here, we report covalent polymer gels in which the macroscopic fracture “reaction” is controlled by mechanophores embedded within mechanically active network strands. We synthesized poly(ethylene glycol) (PEG) gels through the end-linking of azide-terminated tetra-arm PEG (M_n= 5 kDa) with bis-alkyne linkers. Networks were formed under identical conditions, except that the bis-alkyne was varied to include either a <i>cis</i>-diaryl (<b>1</b>) or <i>cis</i>-dialkyl (<b>2</b>) linked cyclobutane mechanophore that acts as a mechanochemical “weak link” through a force-coupled cycloreversion. A control network featuring a bis-alkyne without cyclobutane (<b>3</b>) was also synthesized. The networks show the same linear elasticity (G' = 23~24 kPa, 0.1 – 100 Hz) and equilibrium mass swelling ratios (Q = 10~11 in tetrahydrofuran), but they exhibit tearing energies that span a factor of 8 (3.4 J∙m^-2, 10.5 J∙m^-2, and 27.1 J∙m^-2 for networks with <b>1</b>, <b>2</b>, and <b>3</b>, respectively). The difference in fracture energy is well aligned with the force-coupled scission kinetics of the mechanophores observed in single-molecule force spectroscopy experiments, implicating local resonance stabilization of a diradical transition state in the cycloreversion of <b>1 </b>as a key determinant of the relative ease with which its network is torn. The connection between macroscopic fracture and small molecule reaction mechanism suggests opportunities for molecular understanding and optimization of polymer network behavior. </p></div>

Mechanism Dictates Mechanics: A Molecular Substituent Effect in the Macroscopic Fracture of a Covalent Polymer Network

<div><p>Here, we report covalent polymer gels in which the macroscopic fracture “reaction” is controlled by mechanophores embedded within mechanically active network strands. We synthesized poly(ethylene glycol) (PEG) gels through the end-linking of azide-terminated tetra-arm PEG (M_n= 5 kDa) with bis-alkyne linkers. Networks were formed under identical conditions, except that the bis-alkyne was varied to include either a <i>cis</i>-diaryl (<b>1</b>) or <i>cis</i>-dialkyl (<b>2</b>) linked cyclobutane mechanophore that acts as a mechanochemical “weak link” through a force-coupled cycloreversion. A control network featuring a bis-alkyne without cyclobutane (<b>3</b>) was also synthesized. The networks show the same linear elasticity (G' = 23~24 kPa, 0.1 – 100 Hz) and equilibrium mass swelling ratios (Q = 10~11 in tetrahydrofuran), but they exhibit tearing energies that span a factor of 8 (3.4 J∙m^-2, 10.5 J∙m^-2, and 27.1 J∙m^-2 for networks with <b>1</b>, <b>2</b>, and <b>3</b>, respectively). The difference in fracture energy is well aligned with the force-coupled scission kinetics of the mechanophores observed in single-molecule force spectroscopy experiments, implicating local resonance stabilization of a diradical transition state in the cycloreversion of <b>1 </b>as a key determinant of the relative ease with which its network is torn. The connection between macroscopic fracture and small molecule reaction mechanism suggests opportunities for molecular understanding and optimization of polymer network behavior. </p></div>

Influence of Three-Dimensional Stress Field Variation on Fracture Evolution Characteristics of a Roof

Excavation disturbance on the dynamic variation of the three-dimensional stress field is the main cause for the dynamic disasters of the surrounding rock mass of the roof. The stress condition in the surrounding rock mass of the roof during entry excavation and its impact on entry stability are systemically studied in this study. It is found that the surrounding rock mass of the roof is mainly influenced by the combined effect of the stress unloading and stress transference induced by entry excavation. A servo-controlled true triaxial material testing system is used to conduct the true triaxial loading and unloading experiments of rocks under different stress paths. The influence of different stress paths, especially the variation of the principal stress direction, on the mechanical characteristics and fracture characteristics of rocks is investigated. The results indicate that the variation of the principal stress direction has a significant impact on the macroscopic fracture characteristics of the rock. The main macroscopic fracture plane of the rock highly depends on the intermediate principal stress. The fracture evolution of the roof rock mass during entry excavation is analyzed. The results show that the change of the three-dimensional stress field induces the formation of complex fracture networks in the surrounding rock mass of the roof. The roof is likely to dislocate horizontally and collapse. The corners of the entry are seriously damaged. Based on the above findings, a support scheme is proposed to maintain the stability of a gob-side entry. The field experience suggests that the support scheme can achieve good results.

Applications of Micro-Indentation Technology to Estimate Fracture Toughness of Shale

The fracture toughness of shale is a basic parameter that can provide effective theoretical support for wellbore stability and hydraulic fracturing of a shale reservoir. Due to the composition and microstructure, there are many problems in evaluating the mechanical properties of shale in a macroscopic test. In this paper, the composition and pore distribution of shale were studied by X-ray diffraction and nuclear magnetic resonance. Scanning electron microscopy was used to characterize the pore structure. The setting of experimental parameters and the selection of the indenter were discussed. Micro-indentation technique was proposed and applied to fracture toughness analysis of shale. The results show that Berkovich indenter is more suitable for shale indentation test than Vickers indenter. Fracture toughness of shale indentation is obviously affected by surface roughness and indentation position. Fracture toughness of shale decreases slightly with the increase of the indentation load. The energy analysis result presents that the effect of cracking on the ratio of total/unloading work is minimal when there is no significant stripping on the shale surface. Compared with the experimental method, energy methods can obtain all the analysis parameters from a single indentation test. The results of comparative analysis with macroscopic experiments display that micro-indentation test can effectively predict the macroscopic fracture toughness of shale.

Statistical Volume Elements for the Characterization of Angle-Dependent Fracture Strengths in Anisotropic Microcracked Materials

Statistical volume elements (SVEs) are used to homogenize fracture strength of rock, based on the microcrack statistics of a real-world Yuen-Long marble sample. The small size of SVEs enables maintaining inhomogeneities in fracture properties with lower computational cost compared to methods that explicitly model microcracks at macroscale. Maintaining inhomogeneity is important to capture realistic fracture patterns in rock as a quasi-brittle material. Uniaxial tensile, uniaxial compressive, and shear strengths are derived for arbitrary angle for loading and orientation of a single crack by using the linear elastic fracture mechanics (LEFM) method and incorporating frictional effects. Mesoscopic fracture strength fields are generated for different strengths and angle of loading by traversing the spatial domain with circular SVEs. Increasing the SVE size smoothens the spatial inhomogeneity and angular anisotropy of homogenized strengths. Spatial and angular covariance functions of the random fields are obtained to demonstrate how fracture strength varies in space and by changing the angle of loading. Two isotropic and anisotropic rock domains are studied and shown to have very different single- and two-point statistics. Macroscopic fracture simulations by an asynchronous spacetime discontinuous Galerkin (aSDG) method demonstrate that most macroscopic cracks for the anisotropic domain are aligned with the weakest strength planes.

Microscale characterisation of damage evolution in curling stones used in international competition

&lt;p&gt;The rocks used to produce curling stones for international competition are only sourced from two localities in the world: Ailsa Craig, Scotland and Trefor, Wales. Curling stones consist of two components: (1) the running band (the ring-shaped bottom surface of the stone which rests on the ice) and (2) the striking band (the convex band on the profile of stones which collides with those of other stones). With a focus on the striking bands, we aim to document the damage evolution of curling stones using synchrotron microtomography (3D characterisation of pristine samples and 4D damage evolution), optical and scanning electron microscopy (quantitative characterisation of pristine samples and microfracture characterisation of damaged striking bands), and petrophysical testing (fracture characteristics and comparative data). These data will be complemented by an on-ice experiment that will determine the mechanics (e.g., stress distribution, contact area, and velocity) of curling stone impacts. Out of four curling stone varieties (from Ailsa Craig and Trefor), we observe the striking bands of three varieties to show macroscopic, incipient to mature, curvilinear fractures. The curvature of these fractures is consistent and does not vary significantly between individual stones and between curling stone varieties. However, the degree of macroscopic fracture development differs between aged striking bands of curling stone types: Blue Trefor (macroscopic fractures not observed), Red Trefor (weakly incipient), Ailsa Craig Common Green (incipient to juvenile), and Ailsa Craig Blue Hone (juvenile to mature). Unfortunately, it is not possible to determine the degree of usage (age) of the selected samples and thus it is not possible to normalize these apparent differences in damage. Given that the striking band limits the lifetime of curling stones, understanding the damage evolution of curling stones can contribute valuable information to the maintenance of curling stones. The rock physics of curling stone impacts is linked to dynamic spalling and more broadly to rock failure, as these processes are ultimately related to the initiation and propagation of fractures.&lt;/p&gt;

Influence of the Test Configuration and Temperature on the Mechanical Behaviour of WC-Co

In this work, the effect of the test configuration and temperature on the mechanical behaviour of cemented carbides (WC-Co) with different carbide grain sizes (dWC) and cobalt volume fractions (VCo), implying different binder mean free paths (λCo), was studied. The mechanical strength was measured at 600 °C with bar-shaped specimens subjected to uniaxial four-point bending (4PB) tests and with disc specimens subjected to biaxial ball-on-three-balls (B3B) tests. The results were analysed within the frame of the Weibull theory and compared with strength measurements performed at room temperature under the same loading conditions. A mechanical degradation greater than 30% was observed when the samples were tested at 600 °C due to oxidation phenomena, but higher Weibull moduli were obtained as a result of narrower defect size distributions. A fractographic analysis was conducted with broken specimens from each test configuration. The number of fragments (Nf) and the macroscopic fracture surface were related to the flexural strength and fracture toughness of WC-Co. For a given number of fragments, higher mechanical strength values were always obtained for WC-Co grades with higher KIc. The observed differences were discussed based on a linear elastic fracture mechanics (LEFM) model, taking into account the effect of the temperature and microstructure of the cemented carbides on the mechanical strength.