Crack Orientation Distribution Research Articles

Migration of Mechanical Perturbations Estimated by Seismic Coda Wave Interferometry During the 2018 Pre‐Eruptive Period at Kīlauea Volcano, Hawaii

AbstractWe use seismic ambient noise correlation and coda wave interferometry to estimate velocity variations at high temporal resolution, during the pre‐eruptive period and the onset of the 2018 eruption of Kīlauea volcano. A progressive velocity increase is observed from March to the end of April. It is followed by rapid decrease starting a few days before the onset of the East Rift Zone (ERZ) eruption and then by sharp velocity drop when the eruption started. The change of trend from velocity increase to decrease is progressively delayed by a few days from the summit caldera toward the ERZ. The location of the velocity perturbations shows a migration of the sources of velocity changes from the summit caldera toward the ERZ before the eruption. Using a model of pressure source, we show that the simultaneous caldera inflation and velocity increase probably result from an anisotropic distribution of fault and crack orientations. The velocity decrease could be due to damaging processes above the shallow reservoir and to plastic deformations around the caldera. We introduce a forward model of rock damage associated with the volcano‐tectonic seismicity to calculate the velocity decrease. The good agreement between the calculated and the observed velocity variations shows that a large part of the velocity decrease results from damage of the medium. The delayed onsets of velocity decrease and the source migration of velocity perturbations are probably related to progressive fault openings in the Southern and Eastern parts of the caldera and to magma transfer toward the ERZ.

DEM study on the macro- and micromechanical behaviours of breakable granular materials under cyclic loading

The effect of cyclic loading on the macro- and micromechanical behaviours of breakable granular materials was investigated via DEM. Breakable particle models composed of Voronoi cells with realistic shapes were constructed. A series of confined cyclic loading tests were performed at different loading amplitudes. The macroscopic deformation behaviours were investigated in terms of the cumulative plastic strain and dynamic resilience modulus. Then, particle breakage characteristics, including the extent of particle breakage, crack orientation distribution, breakage pattern and correlation between the particle breakage and energy input, were explored. Furthermore, micromechanical results, including the coordination number, sliding contact and contact orientation anisotropy, were examined. It is found that both particle breakage and cumulative plastic strain increase rapidly in the early stage of loading. In the stable state, both showed an S-shaped increase with increasing loading amplitude. This study highlights that particle breakage is one of the main sources of permanent deformation.

Nondestructive Photoelastic and Machine Learning Characterization of Surface Cracks and Prediction of Weibull Parameters for Photovoltaic Silicon Wafers

Abstract A nondestructive photoelastic method is presented for characterizing surface microcracks in monocrystalline silicon wafers, calculating the strength of the wafers, and predicting Weibull parameters under various loading conditions. Defects are first classified through thickness infrared photoelastic images using a support vector machine-learning algorithm. Characteristic wafer strength is shown to vary with the angle of applied uniaxial tensile load, showing greater strength when loaded perpendicular to the wire speed direction than when loaded along the wire speed direction. Observed variations in characteristic strength and Weibull shape modulus with applied tensile loading direction stem from the distribution of crack orientations and the bulk stress field acting on the microcracks. Using this method, it is possible to improve manufacturing processes for silicon wafers by rapidly, accurately, and nondestructively characterizing large batches in an automated way.

The use of the empirical crack orientation tensor to characterize the damage anisotropy

In practice, a dominant failure mode of brittle materials, such as fiber-reinforced thermosets is the initiation and propagation of cracks under cyclic loading. In general, the damage in composites with irregular microstructure do not occur in regular patterns. There are several state-of-the-art continuum mechanical models which take the anisotropic damage for predicting the material behavior into account. Since damage generally occurs in an anisotropic way, methods that experimentally characterize the damage anisotropy are needed.Micro-Computed Tomography systems (μCT) acquire volumetric images in a non-destructive way. By combining μCT scanning and mechanical in-situ testing, detailed microstructure data of specimens under load are generated. Based on image processing methods, the damage propagation from crack initiation to fracture is analyzed. In practice, cyclic load is a common load case for many components. Consequently, fatigue and cycle load tests are essential for a comprehensive material characterization.In this contribution interrupted in-situ μCT tests with cyclic tensile load are performed on Sheet Molding Compounds (SMC), a discontinuous glass fiber-reinforced thermset composite. Image processing methods are introduced for the experimental determination of the anisotropic damage characteristic based on volumetric images. The methods enable analyzing the spatial crack orientation distribution. In order to quantify the damage anisotropy, empirical formulations of the crack density distribution and second-order crack orientation tensor are applied. The presented work in this contribution extends the results of preliminary experimental damage investigations. In addition to previous studies, the damage anisotropy is quantified and analyzed.

Influence of amygdale on crack evolution and failure behavior of basalt

Amygdaloidal basalt is one of the two major types of surrounding rocks that are widely exposed in the super large-scale underground powerhouse caverns of Baihetan Hydropower Station, China. Excavation of the caverns induced a series of mechanical responses, including cracking and fracture relaxation. This study comprehensively explored the deformation and failure characteristics and the fracture evolution process of the amygdaloidal basalt using conventional MTS triaxial laboratory testing equipment and continuous–discontinuous modeling (FDEM) with the aim of clarifying its failure mechanism. The research results indicate that: (1) amygdales significantly changed the deformation and failure characteristics of basalt. Whereas the post-peak mechanical behavior of cryptocrystalline basalt was brittle, that of amygdaloidal basalt was brittle under low confining stresses and ductile under high confining stresses. Meanwhile, whereas the failure mode of cryptocrystalline basalt was fragmentation failure, that of amygdaloidal basalt was splitting failure at low confining stresses and shear failure at high confining stresses. (2) An FDEM model considering the heterogeneity of the rock mesostructure was established based on the statistical laws of the amygdales in real samples, and this confirmed the stress–strain curve characteristics, failure modes, and characteristic strengths measured in laboratory tests. (3) A complicated inhomogeneous stress field formed readily around amygdales and had a significant effect on the fracture path. (4) With an increase in confining stresses, the degree of tensile stress concentration at the upper and lower tips of amygdales decreased and the lateral displacement became restricted. Consequently, the total number of micro-cracks and the ratio of tensile cracks to shear cracks decreased, the crack initiation mode changed from tensional cracking to shear cracking at the tips of the amygdale, and the distribution of crack orientations transitioned from an approximately vertical direction to preferential concentration along fracture planes. The research results form a solid foundation for the accurate understanding of the mechanical response and fracture mechanism of the rock surrounding underground powerhouse caverns at Baihetan hydropower station, and also provide a reference for the prediction of the mechanical properties of rock with flaws and the stability control of engineering rockmasses.

On the anisotropy of cracked solids

We consider the effective elastic properties of cracked solids, and verify the hypothesis that the effect of crack interactions on the overall anisotropy – its type and orientation – is negligible (even though the effect on the overall elastic constants may be strong), provided crack centers are located randomly. This hypothesis is confirmed by computational studies on large number of 2-D crack arrays of high crack density (up to 0.8) that are realizations of several orientation distributions. Therefore, the anisotropy can be accurately determined analytically in the non-interaction approximation (NIA). Since the effective elastic properties possess the orthotropic symmetry in the NIA (for any orientation distribution of cracks, including cases when, geometrically, the crack orientation pattern does not have this symmetry), the orthotropy of cracked solids is not affected by interactions.

The influence of crack-orientation distribution on the mechanical properties of pre-cracked brittle media

Cracks in kerogen-rich shales and other brittle rock-like materials have a tremendous impact on their elastic properties and strength. In this paper, we investigate the effective mechanical properties of shale plates with pre-existing cracks. We employ the extended finite element method (XFEM) to investigate a pre-cracked medium with an elastic, isotropic and brittle shale matrix. We show how the mechanical properties of the orthotropic shale plates are dependent on the crack density and the standard deviation of crack angles. Both the Young's modulus and the Poisson's ratio of the cracked media exhibit a linear dependence on the standard deviation of crack angles, in contrast to the nonlinear dependence of the strength on the angle deviation. Finally, we propose mechanical models to capture the relationship between the mechanical properties and the distribution characteristics of pre-existing cracks in shales. These phenomenological models could be applied to estimate the fracking behavior of shales in engineering practice.

Overall thermal conductivity of a fiber reinforced composite with partially debonded inhomogeneities

A homogenization problem for conductivity of a composite containing infinite fibers of circular cross-section with interface arc cracks is solved with the account of the orientation distribution of cracks. Solution for a single inhomogeneity with debonded zone is based on the known result on heat flux intensity factor and utilizes the connection between this quantity and resistivity contribution tensor. Maxwell's scheme is used for the homogenization procedure. The results are compared with exact numerical solution for the case when all the fibers are debonded and all the interfacial cracks have the same length and orientation. The application of the proposed approach is illustrated on the example of the recovery of information on damage accumulated in the process of hydrothermal aging.

Effective properties of linear viscoelastic microcracked materials: Application of Maxwell homogenization scheme

The present paper focuses on the effect of microcracks on the overall properties of viscoelastic materials. For this goal we extend Maxwell homogenization scheme to the case of viscoelasticity and derive explicit formulas for components of the anisotropic creep operator in dependence on scatter parameter characterizing orientation distribution of cracks. Microcracks can have any orientation distribution with randomly oriented and strictly parallel being the limiting cases. Viscoelastic behavior is described using fraction-exponential operators. The results are illustrated on example of microckracked polymethylmethacrylate (PMMA).

Generalized Kelvin model for micro-cracked viscoelastic materials

The aim of this paper is to model the viscoelastic properties of micro-cracked materials based on the homogenization micro–macro approach. The isotropic case with random orientation distribution of micro-crack in Burgers nonageing linear viscoelastic solid was previously modeled. This study develops an alternative generalized Kelvin viscoelastic model (GKM) for fractured viscoelastic materials. The use of the same GKM of the non-cracked materials to model the viscoelastic properties of the micro-cracked materials is an approximation. This is a new technique to avoid the complexity of the inverse Laplace–Carson (LC) transform. This approximation is carried out in short and long term behavior in the LC space and is validated in transient situation with exact solution obtained from the inverse LC transform for simple loading condition. This paper focuses on the isotropic case with random orientation distribution of open cracks.

A Technical Note: Orientation of Cracks and Hydrology in a Shrink-Swell Soil

Crack orientations are an important soil physical property that affects water flow, particularly in vertic soils. However, the spatial and temporal variability of crack orientations across different land uses and gilgai features is not well-documented and addressed in hydrology models. Thus; there is a need to quantify crack orientations for different land uses and to incorporate their spatial and temporal dynamics into hydrological models. Our objectives were to document the spatial variability of cracks orientations across two land uses and to demonstrate the potential importance of crack orientation related to the hydrology of Vertisols. The exploratory field measurements of the spatial distribution of crack orientations across two Vertisol catenae of two land uses and gilgai features are presented. The field survey showed the complexity of crack geometry in a field, the potential impact of crack orientation on Vertisol hydrology and the challenges associated with measurement of crack orientations.

Scalar, vectorial, and tensorial damage parameters from the mesoscopic background

In the mesoscopic theory a distribution of different crack sizes and crack orientations is introduced. A scalar damage parameter, a second order damage tensor and a vectorial damage parameter are defined in terms of this distribution function. As an example of a constitutive quantity the free energy density is given as a function of the damage tensor. This equation is reduced in the uniaxial case to a function of the damage vector and in case of a special geometry to a function of the scalar damage parameter.

Dynamics of the Size and Orientation Distribution of Microcracks and Evolution of Macroscopic Damage Parameters

We are dealing with damage of brittle materials caused by growth of microcracks. In our model the cracks are penny-shaped. They can only enlarge but not heal. For a single crack a Rice–Griffith growth law is assumed: There is crack growth only if tension is applied normally to the crack surface, exceeding a critical value. Our aim is to investigate the effect of crack growth on macroscopic constitutive quantities. A possible approach taking into account such an internal structure within continuum mechanics is the mesoscopic theory. A distribution of crack lengths and crack orientations within the continuum element is introduced. Macroscopic quantities are calculated as averages with the distribution function. A macroscopic measure of the progressing damage, i.e., a damage parameter, is the average crack length. For this scalar damage parameter we derive an evolution equation. Due to the unilateral growth law for the single crack, it turns out that the form of this differential equation depends explicitly on the initial crack length distribution. In order to treat biaxial loading, it is necessary to introduce a tensorial damage parameter. We define a second-order tensor damage parameter in terms of the crack length and orientation distribution function.

Elastic wave velocities and permeability of cracked rocks

Cracks play a major role in most rocks submitted to crustal conditions. Mechanically, cracks make the rock much more compliant. They also make it much easier for fluid to flow through any rock body. Relying on Fracture Mechanics and Statistical Physics, we introduce a few key concepts, which allow to understand and quantify how cracks do modify both the elastic and transport properties of rocks. The main different schemes, which can be used to derive the elastic effective moduli of a rock, are presented. It is shown from experimental results that an excellent approximation is the so-called non-interactive scheme. The main consequences of the existence of cracks on the elastic waves is the development of elastic anisotropy (due to the anisotropic distribution of crack orientations) and the dispersion effect (due to microscopic local fluid flow). At a larger scale, macroscopic fluid flow takes place through the crack network above the percolation threshold. Two macroscopic fluid flow regimes can be distinguished: the percolative regime close to the percolation threshold and the connected regime well above it. Experimental data on very different rock types show both of these behaviors.

Effect of loading condition and stress state on damage evolution of silicon particles in an Al-Si-Mg-Base cast alloy

Damage evolution of Si particles in a Sr modified cast A356(T6) Al alloy is quantitatively characterized as a function of strain under tension, compression, and torsion. The fraction of damaged Si particles, their size distributions, and orientation distribution of particle cracks are measured by image analysis and stereological techniques. Silicon particle cracking and debonding are the predominant damage modes. Particle debonding is observed only under externally applied tensile loads, whereas particle cracking is observed under all loading conditions. The relative contributions of Si particle debonding and fracture to the total damage strongly depend on stress state and temperature. For all loading conditions and stress states studied, the average size of damaged Si particles is considerably larger than the bulk average size. The rate of damage accumulation is different for different loading conditions. At a given strain level, Si particle damage is lowest under compression and highest under torsion. The anisotropy of the damage is highly dependent on the deformation path and stress state. Under uniaxial tension, the cracks in the broken Si particles are mostly perpendicular to the loading direction, whereas in the compression test specimens they are parallel to the loading direction. The Si particle cracks in the torsion and notch-tension test specimens do not exhibit preferred orientations. The quantitative microstructural data are used to test damage evolution models.

The mechanics of cracks and a statistical strength theory for rocks

Features of the crack structure of intact rock are systematically investigated by using advanced video microscope, electronic microscope and graphic analysis technology. The fractal effects of the discontinuous structure on the macro-mechanical behavior are discussed. Damage evolution in rocks is described by means of statistical mathematics. Based on the fractal distribution of cracks and on the theory of the weakest link, a general statistical formula of rock strength under a complex stress state has been developed, of which the influence of orientation distribution of cracks and irregularity of crack growth on rock strength has been taken into account. The new expression for rock strength reflects the collective effects of the scale of crack distribution, crack orientation distribution and the irregularity of crack surfaces on rock strength. It relates the macro-strength of rocks to its intrinsic structural properties. It is shown that the Weibull strength formula is a special case of the statistical strength expression when the orientational distribution of cracks is neglected.

P wave anisotropy, stress, and crack distribution at Coso geothermal field, California

A new inversion method for P wave anisotropy [Wu and Lees, 1999a] has been applied to high‐precision, microseismic traveltime data collected at Coso geothermal region, California. Direction‐dependent P wave velocity and thus its perturbation, are represented by a symmetric positive definite matrix A instead of a scalar. The resulting anisotropy distribution is used to estimate variations in crack density, stress distribution and permeability within the producing geothermal field. A circular dome‐like structure is observed at the southwestern part of the geothermal region southwest of Sugarloaf Mountain. Using a linear stress‐bulk modulus relationship, deviatoric stress is estimated to be 3–6 MPa at geothermal production depths (1–2 km), assuming all the anisotropy is related to stress. The stress field is compressional NNE‐SSW and dilational WNW‐ESE, coinciding with a previous, independent study using earthquake focal mechanisms. Following a theory on flat, elliptic cracks, residual crack density estimated from P anisotropy is ∼0.0078 assuming crack aspect ratios ≫ 1:60 and is ∼0.041 when crack aspect ratios are close to 1:60. Residual crack orientation distribution is related to velocity anisotropy. On the basis of anisotropic part of crack density distribution function, the anisotropic part of permeability distribution may be calculated by a statistical approach via simple parallel fluid flow along cracks.

A study of the crack network in thermally and mechanically cracked granite samples using confocal scanning laser microscopy

Confocal Scanning Laser Microscopy (CSLM) was used to characterise 3D crack networks in La Peyratte granite samples in which cracking was artificially induced either by heating samples at selected temperatures in order to induce thermal cracking, or by performing mechanical tests in order to develop stress-induced cracking at room temperature. Our goal was to recognise typical crack patterns associated with the different cracking mechanisms. We have taken advantage of the ability of CSLM to image thin slices within the rock sample in two different ways: first there are no overprojection problems for stereological studies, and second, one can obtain series of images at different depths from which the 3-D crack network can be reconstructed. Stereological analysis and 3D reconstructions revealed that thermally cracked and mechanically cracked samples differ in anisotropy of crack orientation distribution, with mechanically cracked samples characterised by strongly anisotropic crack networks.

Thermal shock behaviour of various first-wall materials under simulation load tests by laser beam irradiation

For materials selection of plasma-facing components in nuclear fusion devices it is necessary to determine threshold values of materials damage under short-time high heat fluxes in laboratory experiments. Plasma disruption loads were simulated with different nonmetallic candidate materials using Nd-YAG high power solid state lasers. The impinging energy density was varied between 0.2 and 20 MJ/m 2 with pulse lengths t p ranging from 0.1 to 10 ms. Special experiments were carried out in situ in a scanning electron microscope coupled with a pulsed Nd-YAG laser and various analytical equipments. Thermal shock crack formation and propagation response, erosion behaviour and distribution of elements after successive thermal shock loading can be studied in situ with high lateral resolution inside a SEM. The dependence of damage initiation and propagation on the laser beam parameters such as pulse energy and number, spot size and pulse length was studied for fine grain graphites, nitride and carbide ceramics, CFC compound and coated materials. The threshold values for these structural damages were quantified using a heat flux parameter φ abs√ t p. Detected damage parameters are 3D-erosion profiles, length and orientation distribution of cracks, redeposition rate, etc. Threshold values received by electron beam loads and by numerical calculations under comparable conditions are in approximate agreement with the laser load experimental results. It can be concluded that laser beam simulation represents a simple method for thermal shock testing.

A self-consistent mechanics method for solids containing inclusions and a general distribution of cracks

The damage in a composite material due to a distribution of cracks manifests itself as a reduction of moduli and/or change in elastic constants. This paper presents the effective elastic moduli of a solid containing inclusions and a general distribution of tunnel cracks. Both in-plane and out-of-plane elastic constants are determined. In addition to crack density and inclusion volume fraction, the effective elastic constants are found to depend on a function ϱ(θ), which characterizes the crack orientation distribution, while the anisotropy of a cracked composite is solely induced by the crack orientation distribution. It is established that the effect of inclusions and microcracks on effective moduli is decoupled, i.e., one can obtain the moduli of a solid containing microcracks and inclusions by the corresponding moduli of the solids with microcracks only and with inclusions only. For a solid containing a crack distribution with mirror symmetry, the effective elastic constants can be greatly simplified and can be expressed in terms of two scalar quantities rather than a general function ϱ(θ). This conclusion is particularly useful in the analysis of the micromechanical model. The effect of the asymmetry of ϱ(θ) on the effective elastic constants is also investigated.