Experimental study on 3D internal penny-shaped crack propagation in brittle materials under uniaxial compression

Fractures are widely present in geomaterials of civil engineering and deep underground engineering.Given that geomaterials are usually brittle,the fractures can significantly affect the evaluation of underground engineering construction safety and the early warning of rock failure.However,the crack initiation and propagation in brittle materials under composite loading remain unknown so far.In this study,a three-dimensional internal laser-engraved cracking technique was applied to produce internal cracks without causing damage to the surfaces.The uniaxial compression tests were performed on a brittle material with internal cracks to investigate the propagation of these internal cracks at different dip angles under compression and shear.The test results show that the wing crack propagation mainly occurs in the specimen with an inclined internal crack,which is a mixed-ModeⅠ–Ⅱ–Ⅲfracture;in contrast,ModeⅠfracture is present in the specimen with a vertical internal crack.The fractography characteristics of ModeⅢfracture display a lance-like pattern.The fracture mechanism in the brittle material under compression is that the internal wing cracks propagate to the ends of the whole sample and cause the final failure.The initial deflection angle of the wing crack is determined by the participation ratio of stress intensity factors KII to KI at the tip of the internal crack.

A PENNY-SHAPED CRACK IN A TRANSVERSELY ISOTROPIC PIEZOELECTRIC SOLID:MODES Ⅱ AND Ⅲ PROBLEMS

An exact analysis of the modes Ⅱ and Ⅲ problems of a penny- shaped crack in a transversely isotropic piezoelectric medium is performed in this paper.The potential theory method is employed based on the general solution of three-dimensional piezoelasticity and the four harmonics involved are represented by one complex potential.Previous results in potential theory are then utilized to obtain the exact solution that is expressed in terms of elementary functions.Comparison is made between the current results with those published and good agreement is obtained.

A PENNY-SHAPED CRACK IN A MAGNETOELECTROELASTIC LAYER UNDER RADIAL SHEAR IMPACT LOADING

This paper analyzes the dynamic magnetoelectroelastic behavior induced by a pennyshaped crack in a magnetoelectroelastic layer. The crack surfaces are subjected to only radial shear impact loading. The Laplace and Hankel transform techniques are employed to reduce the problem to solving a Fredholm integral equation. The dynamic stress intensity factor is obtained and numerically calculated for different layer heights. And the corresponding static solution is given by simple analysis. It is seen that the dynamic stress intensity factor for cracks in a magnetoelectroelastic layer has the same expression as that in a purely elastic material. And the influences of layer height on both the dynamic and static stress intensity factors are insignificant as h/a 〉 2.

PENNY-SHAPED CRACK IN TRANSVERSELY ISOTROPIC PIEZOELECTRIC MATERIALS

Using a method of potential functions introduced successively to integrate the field equations of three-dimensional problems for transversely isotropic piezoelectric materials, we obtain the so-called general solution in which the dis- placement components and electric potential functions are represented by a singular function satisfying some special partial differential equations of 6th order. In order to analyse the mechanical-electric coupling behaviour of penny-shaped crack for above materials, another form of the general solution is obtained under cylindrical coordi- nate system by introducing three quasi-harmonic functions into the general equations obtained above. It is shown that both the two forms of the general solutions are complete. Furthermore, the mechanical-electric coupling behaviour of penny-shaped crack in transversely isotropic piezoelectric media is analysed under axisymmetric tensile loading case, and the crack-tip stress field and electric displacement field are obtained. The results show that the stress and the electric displacement components near the crack tip have (r^(-1/2)) singularity.

Interactions of penny-shaped cracks in three-dimensional solids

The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is devel- oped in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks.

Wave-induced flow of pore fluid in a cracked porous solid containing penny-shaped inclusions

An aim of current study is to analyze the contribution of reflected longitudinal waves to wave-induced fluid flow(WIFF) in the cracked porous solid.Initially,we investigate the time harmonic plane waves in cracked porous solid by employing the mathematical model proposed by Zhang et al.(2019).The solution is obtained in form of the Christoffel equations.The solution of the Christoffel equations indicates that there exist four(three dilatational and one shear) waves.These waves are attenuated in nature due to their complex and frequency-dependent velocities.The reflection coefficients are calculated at the sealed pore stress-free surface of cracked porous solid for the incidence of P1 and SV waves.It is found that three longitudinal waves contribute to WIFF and the contribution of these waves to the induced fluid in the cracked porous solid is analyzed using the reflection coefficients of these longitudinal waves.We analytically show that the fluid flow induced by these longitudinal waves is linked directly to their respective reflection coefficients.Finally,a specific numerical example is considered to discuss and to depict the impact of various parameters on the characteristics of propagation like phase velocity/attenuation,reflection coefficients and WIFF of longitudinal waves.

TORSIONAL IMPACT RESPONSE OF A PENNY-SHAPED CRACK IN A FUNCTIONAL GRADED STRIP

The torsional impact response of a penny-shaped crack in a nonhomogeneous strip is considered. The shear modulus is assumed to be functionally graded such that the mathematics is tractable. Laplace and Hankel transforms were used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function. Explicit expressions of both the dynamic stress intensity factor and the energy density factor were derived.And it is shown that, as crack driving force, they are equivalent for the present crack problem. Investigated are the effects of material nonhomogeneity and (strip's) highness on the dynamic fracture behavior. Numerical results reveal that the peak of the dynamic stress intensity factor can be suppressed by increasing the nonhomogeneity parameter of the shear modulus, and that the dynamic behavior varies little with the adjusting of the strip's highness.

Penny-shaped interfacial crack between dissimilar magnetoelectroelastic layers

A penny-shaped interfacial crack between dissimilar magnetoelectroelastic layers subjected to magnetoelectromechanical loads is investigated,where the magnetoelectrically impermeable crack surface condition is adopted. By using Hankel transform technique,the mixed boundary value problem is firstly reduced to a system of singular integral equations,which are further reduced to a system of algebraic equations. The field intensity factors and energy release rate are finally derived. Numerical results elucidate the eects of crack configuration,electric and/or magnetic loads,and material parameters of the magnetoelectroelastic layers on crack propagation and growth. This work should be useful for the design of magnetoelectroelastic composite structures.

THE EFFECTS OF THREE-DIMENSIONAL PENNY-SHAPED CRACKS ON ZONAL DISINTEGRATION OF THE SURROUNDING ROCK MASSES AROUND A DEEP CIRCULAR TUNNEL

In this study, it was assumed that three-dimensional penny-shaped cracks existed in deep rock masses. A new non-Euclidean model was established, in which the effects of penny- shaped cracks and axial in-situ stress on zonal disintegration of deep rock masses were taken into account. Based on the non-Euclidean model, the stress intensity factors at tips of the penny- shaped cracks were determined. The strain energy density factor was applied to investigate the occurrence of fractured zones. It was observed from the numerical results that the magnitude and location of fractured zones were sensitive to micro- and macro-mechanical parameters, as well as the value of in-situ stress. The numerical results were in good agreement with the experimental data.

CRACK TIP PLASTICITY OF A THERMALLY LOADED PENNY-SHAPED CRACK IN AN INFINITE SPACE OF 1D QC

The present work is concerned with a penny-shaped Dugdale crack embedded in an infinite space of one-dimensional （1D） hexagonal quasicrystals and subjected to two identical axisymmetric temperature loadings on the upper and lower crack surfaces. Applying Dugdale hypothesis to thermo-elastic results, the extent of the plastic zone at the crack tip is determined. The normal stress outside the plastic zone and crack surface displacement are derived in terms of special functions. For a uniform loading case, the corresponding results are presented by simpli- fying the preceding results. Numerical calculations are carried out to show the influence of some parameters.

Fracture of two three-dimensional parallel internal cracks in brittle solid under ultrasonic fracturing

Similar to hydraulic fracturing(HF), the coalescence and fracture of cracks are induced within a rock under the action of an ultrasonic field, known as ultrasonic fracturing(UF). Investigating UF is important in both hard rock drilling and oil and gas recovery. A three-dimensional internal laser-engraved crack(3D-ILC) method was introduced to prefabricate two parallel internal cracks within the samples without any damage to the surface. The samples were subjected to UF. The mechanism of UF was elucidated by analyzing the characteristics of fracture surfaces. The crack propagation path under different ultrasonic parameters was obtained by numerical simulation based on the Paris fatigue model and compared to the experimental results of UF. The results show that the 3D-ILC method is a powerful tool for UF research.Under the action of an ultrasonic field, the fracture surface shows the characteristics of beach marks and contains powder locally, indicating that the UF mechanism includes high-cycle fatigue fracture, shear and friction, and temperature load. The two internal cracks become close under UF. The numerical result obtained by the Paris fatigue model also shows the attraction of the two cracks, consistent with the test results. The 3D-ILC method provides a new tool for the experimental study of UF. Compared to the conventional numerical methods based on the analysis of stress-strain and plastic zone, numerical simulation can be a good alternative method to obtain the crack path under UF.

SELF-SIMILAR SOLUTIONS OF FRACTURE DYNAMICS PROBLEMS ON AXIALLY SYMMETRY

By the theory of complex functions, a penny-shaped crack on axially symmetric propagating problems for composite materials, was studied. The general representations of the analytical solutions with arbitrary index of self-similarity, were presented for fracture elastodynamics problems on axially symmetry by the ways of self-similarity under the ladder-shaped loads. The problems dealt with can be transformed into Riemann-Hilbert problems and their closed analytical solutions are obtained rather simple by this method. After those analytical solutions are utilized by using the method of rotational superposition theorem in conjunction with that of Smirnov-Sobolev, the solutions of arbitrary complicated problems can be obtained.