Damage and failure characteristics of rock similar materials with pre-existing cracks

In order to further study the damage and failure mechanism for rock similar materials,this study investigated the mechanical properties and failure characteristics,law of damage space development,and damage evolution characteristics for rock similar materials with pre-existing cracks of varying length under uniaxial compression load.The equipment used in this study is the self-developed YYW-Ⅱ strain controlled unconfined compression apparatus and the PCIE-8 acoustic emission monitoring system.Results show that,as the length of pre-existing crack increases:(1) the peak and residual strength reduces,and the peak axial strain and the strain during the initial compression phase increases;(2) the major failure mode is changed from shear failure to tensile failure along a vertical plane that passes the middle of the pre-existing crack;(3) The damage increases during the stable and accelerated development stage,and the effect of the pre-existing cracks is more during the accelerated development stage than the stable development stage.

A method to model the effect of pre-existing cracks on P-wave velocity in rocks

Crack closure is one of the reasons inducing changes of P-wave velocity of rocks under compression.In this context,a method is proposed to investigate the relationships among P-wave velocity,pre-existing cracks,and confining pressure based on the discrete element method(DEM).Pre-existing open cracks inside the rocks are generated by the initial gap of the flat-joint model.The validity of the method is evaluated by comparing the P-wave velocity tested on a sandstone specimen with numerical result.As the crack size is determined by the diameter of particles,the effects of three factors,i.e.number,aspect ratio,and orientation of cracks on the P-wave velocity are discussed.The results show that P-wave velocity is controlled by the(i.e.number) of open micro-cracks,while the closure pressure is determined by the aspect ratio of crack.The reason accounting for the anisotropy of P-wave velocity is the difference in crack number in measurement paths.Both of the number and aspect ratio of cracks can affect the responses of P-wave velocity to the applied confining pressure.Under confining pressure,the number of open cracks inside rocks will dominate the lowest P-wave velocity,and the P-wave velocity of the rock containing narrower cracks is more sensitive to the confining pressure.In this sense,crack density is difficult to be back-calculated merely by P-wave velocity.The proposed method offers a means to analyze the effect of pre-existing cracks on P-wave velocity.

Effects of pre-existing cracks and infillings on strength of natural rocks--Cases of sandstone, argillite and basalt

This study aims to examine the influence of pre-existing discontinuities on the strengths of four natural rocks of different origins.A series of unconfined compression tests was performed on specimens of two types of sandstones,argillite and basalt that contain open and filled cracks.It was found that the presence of cracks tends to decrease the overall strength for all studied rocks;however,the magnitude of strength reduction is related to the property of rock.The larger strength decrease was observed for the relatively harder argillite and basalt,compared to the softer sandstone.It was also found that the infill material could increase the strength of rock specimens,while the obtained strength depended on the characteristics of the fill material.

Anti-Plane Elasticity Problem and Mode Ⅲ Crack Problem of Cubic Quasicrystal

The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. The results show that the stress intensity factor is independent of material constants, and the strain energy release rate is dependent on all material constants. These provide important information for studying the deformation and fracture of the new solid material.

Finite Element Analysis on Plane Stress Crack Growth in a Power-Law Hardening Material

Aim To determine numerically the field characteristics in the vied at the tip of a place crack growing steadily in a power-law hardening material. Meteods. Methods on the Euler mode and small-scale yield assumption, the numerical results were given by nonlinear finite element analysis. Results The numerical results of the shape of the active plastic sone, the angular distribution of stresseses and Clack tip opening displacement (CTOD) in the vicinity at the hp of the steadily groWing CraCk are determined. Conclusion The comparison between the numerical results given by the present wort and those given by analytic asymptotic analysis shows that the present work reached a very high accuracy.

GENERAL FORM OF MATCHING EQUATION OF ELASTIC-PLASTIC FIELD NEAR CRACK LINE FOR MODE I CRACK UNDER PLANE STRESS CONDITION

Crack line field analysis method has become an independent method for crack elastic-plastic analysis, which greatly simplifies the complexity of crack elastic-plastic problems and overcomes the corresponding mathematical difficulty. With this method, the precise elastic-plastic solutions near crack lines for variety of crack problems can be obtained. But up to now all solutions obtained by this method were for different concrete problems, no general steps and no general form of matching equations near crack line are given out. With crack line analysis method, this paper proposes the general steps of elastic plastic analysis near crack line for mode I crack in elastic-perfectly plastic solids under plane stress condition, and in turn given out the solving process and result for a specific problem.

Exact solution of plane isolated crack normal to a bimaterial interface of infinite extent

This paper presents an exact solution for the transverse interface crack in the plane strain case. The crack is perpendicular to the interface and in one material. The exact complex stress functions are first obtained with some unknown constants. The satisfactions of all boundary conditions are then checked, the condition at infinity is considered and the unknown constants are determined. Further study may focus on the case with different shear moduli and the influence of the large deformation.

THE EVALUATION OF STRESS INTENSITY FACTORS OF PLANE CRACK FOR ORTHOTROPIC PLATE WITH EQUAL PARAMETER BY F2LFEM

In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor （SIF）.

CRACK INITIATION AND STEADY PROPAGATION OF ELASTIC-PLASTIC MATERIALS IN PLANE STRESS CONDITION

The crack tip stress-strain fields of the elastic-plastic cracked specimens have been analyzed using finite element calculations.The crack initiation and steady propagation behaviours have also been investigated by means of slip line pattern etching technique and mechanical tests. The results show that there are HRR near field and distant field in the crack tip region,and the later depends on the specimen configuration.The crack initiation behaviour is controlled by a single parameter J.In contrast,the steady crack propagation is affected by the distant strain field and can not be described by single parameter only.

Interaction of a circular cavity and a beeline crack in right-angle plane impacted by SH-wave

The problem of scattering of SH-wave by a circular cavity and an arbitrary beeline crack in right-angle plane was investigated using the methods of Green's function,complex variables and muti-polar coordinates.Firstly,we constructed a suitable Green's function,which is an essential solution to the displacement field for the elastic right-angle plane possessing a circular cavity while bearing out-of-plane harmonic line source load at arbitrary point.Secondly,based on the method of crack-division,integration for solution was established,then expressions of displacement and stress were obtained while crack and circular cavities were both in existence.Finally,the dynamic stress concentration factor around the circular cavity and the dynamic stress intensity factor at crack tip were discussed to the cases of different parameters in numerical examples.Calculation results show that the crack produces adverse engineering influence on both of the dynamic stress concentration factor and the dynamic stress intensity factor.

THE SCATTERING OF GENERAL SH PLANE WAVE BY INTERFACE CRACK BETWEEN TWO DISSIMILAR VISCOELASTIC BODIES

The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored.

EXACT SOLUTIONS OF NEAR CRACK LINE FIELDS FOR MODE I CRACK UNDER PLANE STRESS CONDITION IN AN ELASTIC－PERFECTLY PLASTIC SOLID

The near crack line analysis method has been used in the present paper,The classical small scale yielding conditions have been completely abandoned in the analyses and one inappropriate matching condition used to be used at the elasticplastic boundary has been corrected.The reasonable solution of the plastic stresses near the crack line region has been established.By matching the plastic stresses with the exact elastic stresses at the elastic-plastic boundary,the plastic stresses the length of the plastic zone and the unit normal vector of the elastic-plastic boundary near the crock line region have been obtained for a mode I crack under uniaxial tension,as well as a mode I crack under biaxial tension,which shows that for both conditions the plastic stress componentsσy, and σsy.he length of the plastic zone and the unit normal vector of the elastic-plastic boundary are quite the same while the plastic stress σs is different.

ELASTIC-PLASTIC CRACK GROWTH ON PLANE STRAIN BIMATERIAL INTERFACE

Finite element computations are carried out to simulate plane strain crack growth on a bimaterial interface under the assumption of small scale yielding.The modified Guron constitutive equation and the element vanish technique introduced by Tvergaard et al.are used to model the final formation of an open crack.It is found from the calculation that the critical fracture toughness for crack growth is much low- er in bimaterials than that in homogeneous material.The critical fracture toughness is strongly dependent on material properties of the bimaterial pair and the mixed mode of remote loads.The interface crack grows in the more compliant(lower hardening)material or in the weaker(lower yield strength)material.In Mode-Ⅰ loading,the crack grows zigzag along the interface.

A HALF PLANE CRACK UNDER THREE-DIMENSIONAL COMBINED MODE IMPACT LOADING

The dynamic stress intensity factor history for a half plane crack in an otherwise unbounded elastic body, with the crack faces subjected to a traction distribution consisting of two pairs of suddenly-applied shear line loads is consid- ered. The analytic expression for the combined mode stress intensity factors as a function of time is obtained. The method of solution is based on the application of integral transforms and the Wiener-Hopf technique. Some features of the solutions are discussed and graphical numerical results are presented.

THE FUNDAMENTAL SOLUTIONS FOR THE PLANE PROBLEM IN PIEZOELECTRIC MEDIA WITH AN ELLIPTIC HOLE OR A CRACK

Based on the complex potential method, the Greed’s functions of the plane problem in transversely isotropic piezoelectric media with an elliptic hole are obtained in terms of exact electric boundary conditions at the rim of the hole. When foe elliptic hole degenerates into a crack, the fundamental solutions for the field intensity factors arc given. The general solutions for concentrated and distributed loads applied on the surface of the hole or crack are produced through the superposition of fundamental solutions With the aid of these solutions , some erroneous results provided previously in other works are pointed out More important is that these solutions can be used as the fundamental solutions of boundary element method to solve more practical problems in piezoelectric media.

Theoretical Analysis and Experimental Verification of Crack Initiation Characteristics of Compression-Shear Plane Crack with Hydraulic Pressure

In this paper, the crack initiation characteristics of compression-shear plane crack with hydraulic pressure were studied by using theoretical analysis and experimental verification methods. The formula derivation process of stress intensity factor of crack tip and open-type crack initiation angle and initiation strength was expounded in detail. Cement mortar specimens prefabricated with open-type crack were made for biaxial compression test. The results show that the mode I stress intensity factor is inversely proportional to the dip angle of pre-exciting crack, water pressure and crack width. The fracture toughness is most easily achieved when the dip angle of pre-exciting crack is 60°. The mode II stress intensity factor is symmetrically distributed with the dip angle and independent of the water pressure and crack width. For open-type crack, the crack initiation angle decreases with the increase of the dip angle of pre-exciting crack, water pressure and crack width;the crack initiation strength is inversely proportional to the water pressure and proportional to the lateral pressure. The research results can provide ideas for the study of crack initiation under the coupling of ground stress and osmotic pressure in tunnel engineering.

ON CRACK PROBLEMS IN AN INFINITE PLANE CONSISTING OF THREE DIFFERENT MEDIA

The mathematical problem of an infinite elastic plane consisting of three different media with an arbitrary number of cracks is considered. It is reduced to singular integral equations along the interfaces and the cracks by a constructive method. Those along the interfaces are further reduced to Fredholm ones.

THREE-DIMENSIONAL INTERACTIONS OF A HALF-PLANE CRACK IN A TRANSVERSELY ISOTROPIC PIEZOELECTRIC SPACE WITH RESULTANT SOURCES

Exact solutions in elementary functions are derived for the stress and electric displacement intensity factors of a half-plane crack in a transversely isotropic piezoelectric space interacting with various resultant sources, including force dipole, electric dipole, moment, force dilatation and rotation. Such force and charge sources may model defects like vacancies, foreign particles and dislocations. The locations and orientations of the stress and charge sources with respect to the crack are arbitrary.

EXACT SOLUTION TO THE PROBLEM OF A HALF-PLANE CRACK IN A TRANSVERSELY ISOTROPIC PIEZOELECTRIC BODY SUBJECTED TO ANTISYMMETRIC TANGENTIAL POINT FORCES

An exact and complete solution of the problem of a half-planecrack in an infinite transversely isotropic piezoelectric body ispresented. The upper and lower crack faces are assumed to be loadedantisym- metrically by a couple of tangential point forces inopposite directions. The solution is derived through a lim- itingprocedure from that of a penny-shaped crack. The expressions for theelectroelastic field are given in terms of elementary functions.Finally, the numerical results of the second and third mode stressintensity factors k_2 and k_3 of piezoelectric materials and elasticmaterials are compared in figures.

Dynamic anti-plane analysis for two symmetrically interfacial cracks near circular cavity in piezoelectric bi-materials

The present paper is exposed theoretically to the influence on the dynamic stress intensity factor （DSIF） in the piezoelectric bi-materials model with two symmet- rically permeable interracial cracks near the edges of a circular cavity, subjected to the dynamic incident anti-plane shearing wave （SH-wave）. An available theoretical method to dynamic analysis in the related research field is provided. The formulations are based on Green＇s function method. The DSIFs at the inner and outer tips of the left crack are obtained by solving the boundary value problems with the conjunction and crack- simulation technique. The numerical results are obtained by the FORTRAN language program and plotted to show the influence of the variations of the physical parameters, the structural geometry, and the wave frequencies of incident wave on the dimensionless DSIFs. Comparisons with previous work and between the inner and outer tips are con- cluded.