P-and SV-wave dispersion and attenuation in saturated microcracked porous rock with aligned penny-shaped fractures

P-and SV-wave dispersion and attenuation have been extensively investigated in saturated poroelastic media with aligned fractures.However,there are few existing models that incorporate the multiple wave attenuation mechanisms from the microscopic scale to the macroscopic scale.Hence,in this work,we developed a unified model to incorporate the wave attenuation mechanisms at different scales,which includes the microscopic squirt flow between the microcracks and pores,the mesoscopic wave-induced fluid flow between fractures and background(FB-WIFF),and the macroscopic Biot's global flow and elastic scattering(ES)from the fractures.Using Tang's modified Biot's theory and the mixed-boundary conditions,we derived the exact frequency-dependent solutions of the scattering problem for a single penny-shaped fracture with oblique incident P-and SV-waves.We then developed theoretical models for a set of aligned fractures and randomly oriented fractures using the Foldy approximation.The results indicated that microcrack squirt flow considerably influences the dispersion and attenuation of P-and SV-wave velocities.The coupling effects of microcrack squirt flow with the FB-WIFF and ES of fractures cause much higher velocity dispersion and attenuation for P waves than for SV waves.Randomly oriented fractures substantially reduce the attenuation caused by the FB-WIFF and ES,particularly for the ES attenuation of SV waves.Through a comparison with existing models in the limiting cases and previous experimental measurements,we validated our model.

Characteristic stress variation and microcrack evolution of granite subjected to uniaxial compression using acoustic emission methods

The size of mineral grain has a significant impact on the initiation and propagation of microcracks within rocks.In this study,fine-,medium-,and coarse-grained granites were used to investigate microcrack evolution and characteristic stress under uniaxial compression using the acoustic emission(AE),digital image correlation(DIC),and nuclear magnetic resonance(NMR)measurements.The experimental results show that the characteristic stress of each granite decreased considerably with increasing grain sizes.The inflection points of the b-value occurred earlier with an increase in grain sizes,indicating that the larger grains promote the generation and propagation of microcracks.The distribution characteristics of the average frequency(AF)and the ratio of rise time to amplitude(RA)indicate that the proportion of shear microcracks increases with increasing grain size.The NMR results indicate that the porosity and the proportion of large pores increased with increasing grain size,which may intensify the microcrack evolution.Moreover,analysis of the DIC and AE event rates suggests that the high-displacement regions could serve as a criterion for the degree of microcrack propagation.The study found that granites with larger grains had a higher proportion of high-displacement regions,which can lead to larger-scale cracking or even spalling.These findings are not only beneficial to understand the pattern of microcrack evolution with different grain sizes,but also provide guidance for rock monitoring and instability assessment.

Phase-field-crystal simulation of nano-single crystal microcrack propagation under different orientation angles

The propagation mechanism of microcracks in nanocrystalline single crystal systems under uniaxial dynamic and static tension is investigated using the phase-field-crystal method.Both dynamic and static stretching results show that different orientation angles can induce the crack propagation mode,microscopic morphology,the free energy,crack area change,and causing fracture failure.Crack propagation mode depends on the dislocation activity near the crack tip.Brittle propagation of the crack occurs due to dislocation always at crack tip.Dislocation is emitted at the front end of the crack tip and plastic deformation occurs,which belongs to ductile propagation.The orientation angles of 9°and 14°are brittleductile mixed propagation,while the orientation angles of 19°and 30°are brittle propagation and no dislocation is formed under dynamic tension.The vacancy and vacancy connectivity phenomenon would appear when the orientation angle is14°under static tension,and the crack would be ductile propagation.While the orientation angle is 19°and 30°,the crack propagates in a certain direction,which is a kind of brittle propagation.This work has some practical significance in preventing material fracture failure and improving material performance.

Microcrack fracturing of coal specimens under quasi-static combined compression-shear loading

Coal pillars are usually loaded under combined compression-shear stresses at underground coal mines.Their long-term stability is critical to the utilization of underground structures,such as underground reservoirs at coal mines.In this study,a modified rock property testing system was used to explore the mechanical properties of coal specimens under quasi-static combined compression-shear loading conditions.The acoustic emission technique was applied to investigating the microcrack fracturing of coal specimens at various inclination angles.The experimental results show that specimen inclination has remarkable effects on the microcrack initiation,microcrack damage and ultimate failure of the coal specimen.The failure mode of the coal specimen tends to transit from axial splitting to shear failure with increasing specimen inclination,and its peak strength is closely associated with the microcrack damage threshold.In practice,it is recommended to consider coal strength under combined compression-shear loading when using empirical pillar strength formulae so that the effect of pillar inclination can be included.

Two species of microcracks

We identify two interrelated but independent species of microcracks with different origins and different distributions. One species is the classic high-stress microcracks identified in laboratory stress-cells associated with acoustic emissions as microcracks open with increasing stress. The other species is the low-stress distributions of closely-spaced stress-aligned fluid-saturated microcracks that observations of shear-wave splitting(SWS) demonstrate pervade almost all in situ rocks in the upper crust, the lower crust, and the uppermost 400 km of the mantle. On some occasions these two sets of microcracks may be interrelated and similar(hence ‘species') but they typically have fundamentally-different properties, different distributions, and different implications. The importance for hydrocarbon exploration and recovery is that SWS in hydrocarbon reservoirs monitors crack alignments and preferred directions of fluid-flow. The importance for earthquake seismology is that SWS above small earthquakes monitors the effects of increasing stress on the pervasive low-stress microcrack distributions so that stress-accumulation before, possibly distant, earthquakes can be recognised and impending earthquakes stress-forecast.

FINITE ELEMENT ANALYSIS ON EVOLUTION PROCESS FOR DAMAGE MICROCRACK HEALING

Based on the thermal kinetic and mass conservation, a series of controlling equations for the finite element are derived and related programs are developed to simulate the damage microcrack healing process controlled by surface diffusion. Two kinds of typical models for microcrack splitting are proposed, i.e., the grain boundary energy existing on the crack surface and residual stresses applying on the crack surface. And the conditions of microcrack splitting in the two models are given as a function of the microcrack aspect ratio. The microcrack with traction-free surfaces will directly evolve into a spheroid.

Acoustic emission characterization of microcracking in laboratory-scale hydraulic fracturing tests

Understanding microcracking near coalesced fracture generation is critically important for hydrocarbon and geothermal reservoir characterization as well as damage evaluation in civil engineering structures. Dense and sometimes random microcracking near coalesced fracture formation alters the mechanical properties of the nearby virgin material. Individual microcrack characterization is also significant in quantifying the material changes near the fracture faces （i.e. damage）. Acoustic emission （AE） monitoring and analysis provide unique information regarding the microcracking process temporally, and infor- mation concerning the source characterization of individual microcracks can be extracted. In this context, laboratory hydraulic fracture tests were carried out while monitoring the AEs from several piezoelectric transducers. In-depth post-processing of the AE event data was performed for the purpose of under- standing the individual source mechanisms. Several source characterization techniques including moment tensor inversion, event parametric analysis, and volumetric deformation analysis were adopted. Post-test fracture characterization through coring, slicing and micro-computed tomographic imaging was performed to determine the coalesced fracture location and structure. Distinct differences in fracture characteristics were found spatially in relation to the openhole injection interval. Individual microcrack AE analysis showed substantial energy reduction emanating spatially from the injection interval. It was quantitatively observed that the recorded AE signals provided sufficient information to generalize the damage radiating spatially away from the injection wellbore.

CHARACTERISTICS OF FATIGUE SURFACE MICROCRACK GROWTH IN VICINAL INCLUSION FOR POWDER METALLURGY ALLOYS

Inclusion flaw is one of the worst flaws of powder metallurgy.The inclusion flaw plays an important role in the failure of high temperature turbine materials in aircraft components and automotive parts,especially fatigue failure.In this paper,an experimental investigation of fatigue microcrack propagation in the vicinal inclusion were carried out by the servo-hydraulic fatigue test system with scanning electron microscope(SEM).It has been found from the SEM images that the fatigue surface microcrack occurs in the matrix and inclusion.According to the SEM images,the characteristics of fatigue crack initiation and growth in vicinal inclusion for powder metallurgy alloys are analyzed in detail.The effect of the geometrical shape and material type of surface inclusions on the cracking is also discussed with the finite element method(FEM).

Effect of Interconnect Linewidth on Evolution of Intragranular Microcracks Due to Electromigration Analyzed by Finite Element Method

The effect of interconnect linewidth on the evolution of intragranular microcracks due to surface diffusion induced by electromigration is analyzed by finite element method.The numerical results indicate that there exists critical values of the linewidth hc,the electric fieldχc and the aspect ratioβc.When h>hc,χ<χc orβ<βc,the microcrack will evolve into a stable shape as it migrates along the interconnect line.When h≤hc,χ≥χc orβ≥βc,the microcrack will split into two smaller microcracks.The critical electric field,the critical aspect ratio and the splitting time have a stronger dependence on the linewidth when h≤6.In addition,the decrease of the linewidth,the increase of the electric field or the aspect ratio is beneficial to accelerate microcrack splitting,which may delay the open failure of the interconnect line.

A UNIFIED ENERGY APPROACH TO A CLASS OF MICROMECHANICS MODELS FOR MICROCRACKED SOLIDS

Micromechanics models have been developed For the determination of the elastic moduli of microcracked solids based on different approaches and interpretations, including the dilute or non-interacting solution, the Mori-Tanaka method, the self-consistent method, and the generalized self-consistent method. It is shown in the present study that all these micromechanics models can be unified within an energy-equivalence framework, and that they differ only in the way in which the microcrack opening and sliding displacements are evaluated. Relevance to the differential methods and the verification of these models are discussed.

Numerical Simulation on Intergranular Microcracks in Interconnect Lines Due to Surface Diffusion Induced by Stress-,Electro-and Thermo-migration

Based on the weak formulation for combined surface diffusion and evaporation-condensation,a governing equation of the finite element is derived for simulating the evolution of intergranular microcracks in copper interconnects induced simultaneously by stressmigration,electromigration and thermomigration.Unlike previously published works,the effect of thermomigration is considered.The results show that thermomigration can contribute to the microcrack splitting and accelerate the drifting process along the direction of the electric field.The evolution of the intergranular microcracks depends on the mechanical stress field,the temperature gradient field,the electric field,the initial aspect ratio and the linewidth.And there exists a critical electric fieldχ_c,a critical stress field■,a critical aspect ratioβ_c and a critical linewidth■.When■or■,the intergranular microcrack will split into two or three small intergranular microcracks.Otherwise,the microcrack will evolve into a stable shape as it migrates along the interconnect line.The critical stress field,the critical electric field and the critical aspect ratio decrease with a decrease in the linewidth,and the critical linewidth increases with an increase in the electric field and the aspect ratio.The increase of the stress field,the electric field or the aspect ratio and the decrease of the linewidth are not only beneficial for the intergranular microcrack to split but also accelerate the microcrack splitting process.

The experimental investigation of microcracks nucleation in typical tectonics

he evolution and nucleation of microcracks in typical tectonics are investigated in the experiment of fracture of marble specimen. The change of state during nucleation of microcracks is observed. The controlling effect of tectonics on evolution of microcracks is analyzed by using thc damage mechanics theory. These characteristics can be analogized to kilometer meters as the first effect of earthquake precursors. These studies may be helpful to interpret-the foreshock or general foreshock in the moderate or short stage before strong earthquakes. The other physical precursors are second or third effect. The local density of microcracks increasing abruptly may be helpful to interpret the phenomenon that part precursor records appear catastrophic jump. The part out of nucleation where some microcracks heal and the density change reversibly may be helpful to interpret the phenomenon that some precursors records appear reverse change. The area difference of microcracks accumulation and evolution in different part of typital tectonics is studied. This difference may be helpful to interpret the characteristics (including the area) of earthquake preparation of diffcrent tectonics, and further to interpret the difference of the precursors beween plate edge and intraplate. These differences may be introduced by the scholars with different points of view as to discuss about the existence of precursors before earthquakes. However, when the precursor records are studied, one must notice the geology background in different areas.

Phonon spectrum and related thermodynamic properties of microcrack in bcc-Fe

The phonon spectrum and the related thermodynamic properties of microcracks in bcc-Fe are studied with the recursion method by using the Finnis-Sinclair （F-S） N-body potential. The initial configuration of the microcracks is established from an anisotropic linear elastic solution and relaxed to an equilibrium by molecular dynamics method. It is shown that the local vibrational density of states of the atoms near a crack tip is considerably different from the bulk phonon spectrum, which is closely associated with the local stress field around the crack tip; meanwhile, the local vibrational energies of atoms near the crack tip are higher than those of atoms in a perfect crystal. These results imply that the crack tip zone is in a complex stress state and closely related to the structure evolution of cracks. It is also found that the phonon excitation is a kind of local effect induced by microcracks. In addition, the microcrack system has a higher vibrational entropy, which reflects the character of phonon spectrum related to the stress field induced by cracks.

MOLECULAR DYNAMICS SIMULATION OF THE ROLE OF DISLOCATIONS IN MICROCRACK HEALING

The molecular dynamics method is used to simulate microcrack healing during heating or/and under compressive stress.A centre microcrack in Cu crystal would be sealed under compressive stress or by heating.The role of com- pressive stress and heating in crack healing was additive.During microcrack healing, dislocation generation and motion occurred.When there were pre-existing disloca- tions around the microcrack,the critical temperature or compressive stress necessary for microcrack healing would decrease,and,the higher the number of dislocations, the lower the critical temperature or compressive stress.The critical temperature necessary for microcrack healing depended upon the orientation of the crack plane. For example,the critical temperature for the crack along the(001)plane was the lowest,i.e.770K.

Experimental studies on the evolution process of microcrack patterns in concrete samples con-taining hard inclusions

Under biaxial pressure, the microcrack patterns of concrete samples with hard inclusion are as followings: Microcracks generate around the sample at the early pressured period, and gap is formed in the middle part with the increase of σ 1; microcrack gap is becoming smaller gradually with σ 1 increase again; microcracks become active within the original gap, but they in an original active area become small. Approaching the main fracture, microcracks form as a belt and jump back and forth in the belt. The spatial fractal D s of microcracks changes from small to big, but turns decrease when approaching the main fracture. All of the features were seldom mentioned in the past experiment, however, which have some similarities with the long seismicity patterns before strong earthquakes. In this paper, Lancang Gengma earthquake was taken as an example to analyse.〖KH*2D]

Crack deflection occurs by constrained microcracking in nacre

For decades, nacre has inspired researchers because of its sophisticated hierarchical structure and remarkable mechanical properties, especially its extreme fracture toughness compared with that of its predominant constituent,CaCO3, in the form of aragonite. Crack deflection has been extensively reported and regarded as the principal toughening mechanism for nacre. In this paper, our attention is focused on crack evolution in nacre under a quasi-static state. We use the notched three-point bending test of dehydrated nacre in situ in a scanning electron microscope(SEM) to monitor the evolution of damage mechanisms ahead of the crack tip. The observations show that the crack deflection actually occurs by constrained microcracking. On the basis of our findings, a crack propagation model is proposed, which will contribute to uncovering the underlying mechanisms of nacre’s fracture toughness and its damage evolution. These investigations would be of great value to the design and synthesis of novel biomimetic materials.

DETERMINATION OF MICROCRACK BOUNDARY RESULTING FROM ROCK BLASTING WITH SEISMIC TRAVELTIME TOMOGRAPHY

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EVOLUTION OF THE MICROCRACKS IN WHISKER TOUGHENING CERAMIC MATRIX COMPOSITES

The modified equivalent inclusion theory by the authors and the internal variable theory are employed to investigate the evolution of the microcracks in whisker toughening ceramics and the influence of the microcracks on the mechanical properties of the material. The effect of residual thermostrain, whisker content and aspect ratio is considered. The modulus, initial nonlinear load, strength and nonlinear constitutive relation are calculated and some important conclusions are given.

Microcrack localization using a collinear Lamb wave frequency-mixing technique in a thin plate

A novel Lamb wave frequency-mixing technique is proposed for locating microcracks in a thin plate,which does not require the resonance condition of Lamb wave mixing and can accurately locate the microcracks through only one-time sensing.Based on the bilinear stress-strain constitutive model,a two-dimensional finite element(FE)model is built to investigate the frequency-mixing response induced by the interaction between two primary Lamb waves and a microcrack.When two primary Lamb waves of A0 and S0 modes with different frequencies excited on the same side of the plate simultaneously impinge on the examined microcrack,under the modulation of the contact acoustic nonlinearity,the microcrack itself can be deemed as the secondary sound source and it will radiate the Lamb waves of new combined frequencies.Based on the time of flight of the generated A0 mode at difference frequency,an indicator named normalized amplitude index(NAI)is defined to directly locate the multi-microcracks in the given plate.It is found that the number and location of the microcracks can be intuitively visualized by using the NAI based frequency-mixing technique.It is also demonstrated that the proposed frequency mixing technique is a promising approach for the microcrack localization.

MICROMECHANICAL MODELLING OF STRAIN SOFTENING IN MICROCRACK-WEAKENED QUASI-BRITTLE MATERIALS

By using the concept of domain of microcrack growth(DMG),the micromechanisms of damage in quasi-brittle materials subjected to triaxial either tensile or compressive loading are investigated and the complete strew-strain relation including four stages is obtained from micromechanical analysis.The regime of pre-peak nonlinear hardening corresponds to the distributed damage,i.e.the stable propagation of microcracks.After the attainment of the ultimate strength of load-bearing capacity, some microcracks experience the second unstable growth and the distributed damage is transmitted to the localization of damage.These analyses improve our understanding of the hardening and softening behaviors of quasi-brittle materials.