Dynamic Stress Intensity Factor and Scattering of SH Wave by Circle Canyon and Crack

The dynamic stress intensity factor (DSIF) and the scattering of SH wave by circle canyon and crack are studied with Green's function. In order to solve the problem, a suitable Green's function is constructed first, which is the solution of displacement fields for elastic half space with circle canyon under output plane harmonic line loading at horizontal surface. Then the integral equation for determining the unknown forces in the problem can be changed into the algebraic one and solved numerically so that crack DSIF can be determined. Last when the medium parameters are altered, the influence on the crack DSIF is discussed partially with the displacement between circle canyon and crack.

The dynamic stress intensity factor analysis of adhesively bonded material interface crack with damage under shear loading

This paper studies the dynamic stress intensity factor （DSIF） at the interface in an adhesive joint under shear loading. Material damage is considered. By introducing the dislocation density function and using the integral transform, the problem is reduced to algebraic equations and can be solved with the collocation dots method in the Laplace domain. Time response of DSIF is calculated with the inverse Laplace integral transform. The results show that the mode Ⅱ DSIF increases with the shear relaxation parameter, shear module and Poisson ratio, while decreases with the swell relaxation parameter. Damage shielding only occurs at the initial stage of crack propagation. The singular index of crack tip is -0.5 and independent on the material parameters, damage conditions of materials, and time. The oscillatory index is controlled by viscoelastic material parameters.

STUDY ON DYNAMIC STRESS INTENSITY FACTORS OF DISK WITH A RADIAL EDGE CRACK SUBJECTED TO EXTERNAL IMPULSIVE PRESSURE

A dynamic weight function method is presented for dynamic stress intensity factors of circular disk with a radial edge crack under external impulsive pressure. The dynamic stresses in a circular disk are solved under abrupt step external pressure using the eigenfunction method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary conditions. By making use of Fourier- Bessel series expansion, the history and distribution of dynamic stresses in the circular disk are derived. Furthermore, the equation for stress intensity factors under uniform pressure is used as the reference case, the weight function equation for the circular disk containing an edge crack is worked out, and the dynamic stress intensity factor equation for the circular disk containing a radial edge crack can be given. The results indicate that the stress intensity factors under sudden step external pressure vary periodically with time, and the ratio of the maximum value of dynamic stress intensity factors to the corresponding static value is about 2.0.

THE ANALYSIS OF DYNAMIC STRESS INTENSITY FACTOR FOR SEMI-CIRCULAR SURFACE CRACK USING TIME-DOMAIN BEM FORMULATION

The time-domain BEM was developed to analyze the dynamic stress intensity factor ( DSIF) of 3-D elastodynamic crack problems. To simulate the stress singularity along the front of a crack, eight-node isoparametric singular elements were used, and the DSIF for a semi-circular surface crack was firstly calculated based on displacement equation using the time-domain BEM formulation. The new scheme to determine the time step was brought forward. By the dynamic analysis program of time-domain BEM compiled by its, several numerical examples are presented, which demonstrate the unconditional stability and high accuracy of time-domain BEM applied to 3-D elastodynamic crack problems.

Analysis of dynamic stress intensity factors of thick-walled cylinder under internal impulsive pressure

Dynamic stress intensity factors are evaluated for thick-walled cylinder with a radial edge crack under internal impulsive pressure. Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary condi- tions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier-Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack sub- jected to internal impulsive pressure are given by dynamic weight function method. The finite element method is utilized to verify the results of numerical examples, showing the validity and feasibility of the proposed method.

Analysis of dynamic stress intensity factors of three-point bend specimen containing crack

A new formula is obtained to calculate dynamic stress intensity factors of the three-point bending specimen containing a single edge crack in this study. Firstly, the weight function for three-point bending specimen containing a single edge crack is derived from a general weight function form and two reference stress intensity factors, the coefficients of the weight function are given. Secondly, the history and distribution of dynamic stresses in uncracked three-point bending specimen are derived based on the vibration theory. Finally~ the dynamic stress intensity factors equations for three-pointing specimen with a single edge crack subjected to impact loadings are obtained by the weight function method. The obtained formula is verified by the comparison with the numerical results of the finite element method （FEM）. Good agreements have been achieved. The law of dynamic stress intensity factors of the three-point bending specimen under impact loadings varing with crack depths and loading rates is studied.

CONVOLUTION OF THE IMPACT THREE-DIMENSIONAL ELASTO-DYNAMICS AND DYNAMIC STRESS INTENSITY FACTOR FOR AN ELLIPTIC CRACK

This paper presents a formulation for three-dimensional elasto-dynamics with an elliptic crack based on the Laplace and Fourier transforms and the convolution theorem. The dynamic stress intensity factor for the crack is determined by solving a Fredholm integral equation of the first kind. The results of this paper are very close to those given by the two-dimensional dual integral equation method.

Effect of crack face contact on dynamic stress intensity factors for a hole-edge crack

In order to determine the dynamic stress intensity factors(DSIFs)for a single edge crack at the center hole of a finite plate under a compressive step loading parallel to the crack,the finite element method was employed to solve the cracked plate problem.The square-root stress singularity around the crack tip was simulated by quarter point singular elements collapsed by 8-node two-dimensional isoparametric elements.The DSIFs with and without considering crack face contact situations were evaluated by using the displacement correlation technique,and the influence of contact interaction between crack surfaces on DSIFs was investigated.The numerical results show that if the contact interaction between crack surfaces is ignored,the negative mode I DSIFs may be obtained and a physically impossible interpenetration or overlap of the crack surfaces will occur.Thus the crack face contact has a significant influence on the mode I DSIFs.

Effect of Blasting Stress Wave on Dynamic Crack Propagation

Stress waves affect the stress field at the crack tip and dominate the dynamic crack propagation.Therefore,evaluating the influence of blasting stress waves on the crack propagation behavior and the mechanical characteristics of crack propagation is of great significance for engineering blasting.In this study,ANSYS/LS-DYNA was used for blasting numerical simulation,in which the propagation characteristics of blasting stress waves and stress field distribution at the crack tip were closely observed.Moreover,ABAQUS was applied for simulating the crack propagation path and calculating dynamic stress intensity factors(DSIFs).The universal function was calculated by the fractalmethod.The results show that:the compressive wave causes the crack to close and the reflected tensile wave drives the crack to initiate and propagate,and failure mode is mainly tensile failure.The crack propagation velocity varies with time,which increases at first and then decreases,and the crack arrest occurs due to the attenuation of stress waves and dissipation of the blasting energy.In addition,crack arrest toughness is smaller than the crack initiation toughness,applied pressure waveforms(such as the peak pressure,duration,waveforms,wavelengths and loading rates)have a great influence on DSIFs.It is conducive to our deep understanding or the study of blasting stress waves dominated fracture,suggesting a broad reference for the further development of rock blasting in engineering practice.

DYNAMIC STRESS FIELD AROUND THE MODE Ⅲ CRACK TIP IN AN ORTHOTROPIC FUNCTIONALLY GRADED MATERIAL

The problem of a Griffith crack in an unbounded orthotropic functionally graded material subjected to antipole shear impact was studied. The shear moduli in two directions of the functionally graded material were assumed to vary proportionately as definite gradient. By using integral transforms and dual integral equations, the local dynamic stress field was obtained. The results of dynamic stress intensity factor show that increasing shear moduli's gradient of FGM or increasing the shear modulus in direction perpendicular to crack surface can restrain the magnitude of dynamic stress intensity factor.

THE THREE-DIMENSIONAL STRESS INTENSITY FACTOR UNDER MOVING LOADS ON THE CRACK FACES

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 combined mode point loads that move in a direction perpendicular to the crack edge is considered.The analytic expression for the combined mode stress intensity factors as a function of time for any point along the crack edge is obtained.The method of solution is based on the application of integral transform together with the Wiener-Hopf technique and the Cagniard-de Hoop method. Some features of the solution are discussed and graphical results for various point load speeds are presented.

Experimental study on dynamic fracture behavior of three-point bending beam with double deformity inclusions

The dynamic fracture behavior of the three-point bending beam with double deformity inclusions under impact loading is studied by using digital high-speed photography in combination with the transmission-type dynamic caustic method. The experimental results indicate that the fluctuation of crack propagation velocity v first increases and then decreases in the crack propagation process. During the process of crack propagating into the inclusion area, the fracture resistance effect of the circular inclusion is the most significant and the effects of triangular and square inclusions are less obvious. The stress intensity factor near the crack tip increases during the propagation process and reaches its maximum value when the crack tip is close to the inclusions. The crack tip’s dynamic stress intensity factor （ DSIF） decreases when the crack exceeds the middle area of the double inclusions. These results provide an experimental basis and scientific foundation to strengthen the evaluation and fracture analysis of the structure containing deformity inclusions.

Dynamic caustics experimental study on interaction between propagating crack and deformity inclusions in primary structure

The approach combining the dynamic caustics method with high-speed photography technology is used to study the interaction between propagating cracks and three kinds of deformity inclusions（ cylinder inclusion, quadruple inclusion and triangular inclusion） under lowvelocity impact loading. By recording the caustic spots of crack tips at different moments during the crack propagation, the variation regulations of dynamic stress intensity factors（ DSIF） and crack growth velocity with respect to time are obtained. The experimental results showthat the resistance effects to crack growth are varied with different shapes of inclusions in specimens, and the quadruple inclusion＇s effect is more apparent. The distortion degree of caustic spots is affected by the shapes of inclusions as well, and the situation is more serious for cylinder and quadruple inclusions. The overall values of DSIFs of triangular inclusion specimen are greater than the others, and the crack growth velocities, characteristic sizes and DSIFs showprocesses of fluctuations because of the disturbance of reflection waves in specimens. The results provide an experimental basis for the analysis of strength and impact-resistance ability in structures with deformity inclusions.

Caustics study of the effect of glass fibres on dynamic fracture of hardened cement paste

The reflected optical caustics method is applied to study dynamic fracture problems in hardened cement paste. First both the unreinforced cement paste and the glass fibres reinforced cement paste specimens were fabricated and the reflective coating on the surface of the specimen was prepared. Secondly the crack path and the shadow spot patterns during the crack propagation process for the two specimens were recorded by using a multi-spark high speed camera.Thirdly some dynamic parameters of two cement paste specimens including crack onset time the dynamic stress intensity factor and crack growth velocity were determined and analyzed comparatively.This indicates that the glass fibres can improve the fracture resistance and delay fracture time.These results will play an important role in evaluating the dynamic fracture properties of cement paste.

Dynamic caustics test of blast load impact on neighboring different cross-section roadways

Using digital laser dynamic caustics experimental system and conducting simulation experiment researched the influence rule of blasting excavation of a new roadway on neighboring existed different cross-section roadways. The experimental results show that the influence of blast load on adjacent roadway has a good relationship with the cross-section of roadway. The expansion distance of precrack existed in circular, arch-wall, rectangular roadway is respectively 1.76, 1.61 and 0 cm under blast load.At the same time, the direct-blast side of rectangular roadway has more obvious damage compared with circular and arch-wall roadway. It explains that plane reflects more stress wave than arc, so that it exerts more tensile failure in the direct-blast side, which leads to less stress wave diffracting to the precrack in the back-blast side. When the precrack extends, higher value dynamic stress intensity factor in circular roadway works longer than that of arch-wall roadway. Indirectly, it explains that plane's weakening function on stress wave is significantly stronger than arc. Stress wave brings about self-evident influence on the upper and bottom endpoints of the rectangular roadway, and it respectively extends 1.03, 2.06 cm along the line link direction of the center of the blasthole and the upper and bottom endpoints on the right wall.

Dynamic fracture behavior of rock under impact load using the caustics method

We studied the dynamic fracture mechanical behavior of rock under different impact rates. The fracture experiment was a three-point bending beam subjected to different impact loads monitored using the reflected caustics method. The mechanical parameters for fracture of the three-poim bending beam specimen under impact load are analyzed. The mechanism of crack propagation is discussed. Experimental results show that the dynamic stress intensity factor increases before crack initiation. When the dynamic stress intensity factor reaches its maximum value the crack starts to develop. After crack initiation the dynamic stress intensity factor decreases rapidly and oscillates. As the impact rate increases the cracks initiate earlier, the maximum value of crack growth velocity becomes smaller and the values of dynamic stress intensity factor also vary less during crack propagation. The results provide a theoretical basis for the study of rock dynamic fracture.

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.

Application of scaled boundary finite element method in static and dynamic fracture problems

The scaled boundary finite element method （SBFEM） is a recently developed numerical method combining advantages of both finite element methods （FEM） and boundary element methods （BEM） and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors （SIFs） directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.

Dynamic Crack Propagation Analysis Using Scaled Boundary Finite Element Method

The prediction of dynamic crack propagation in brittle materials is still an important issue in many engineering fields. The remeshing technique based on scaled boundary finite element method(SBFEM) is extended to predict the dynamic crack propagation in brittle materials. The structure is firstly divided into a number of superelements, only the boundaries of which need to be discretized with line elements. In the SBFEM formulation, the stiffness and mass matrices of the super-elements can be coupled seamlessly with standard finite elements, thus the advantages of versatility and flexibility of the FEM are well maintained. The transient response of the structure can be calculated directly in the time domain using a standard time-integration scheme. Then the dynamic stress intensity factor(DSIF) during crack propagation can be solved analytically due to the semi-analytical nature of SBFEM. Only the fine mesh discretization for the crack-tip super-element is needed to ensure the required accuracy for the determination of stress intensity factor(SIF). According to the predicted crack-tip position, a simple remeshing algorithm with the minimum mesh changes is suggested to simulate the dynamic crack propagation. Numerical examples indicate that the proposed method can be effectively used to deal with the dynamic crack propagation in a finite sized rectangular plate including a central crack. Comparison is made with the results available in the literature, which shows good agreement between each other.

Propagation and Coalescence of Blast-Induced Cracks in PMMA Material Containing an Empty Circular Hole Under Delayed Ignition Blasting Load by Using the Dynamic Caustic Method

In this paper,dynamic caustic method is applied to analyze the blast-induced crack propagation and distribution of the dynamic stress field around an empty circular hole in polymethyl methacrylate(PMMA)material under delayed ignition blasting loads.The following experimental results are obtained.(1)In directional-fracture-controlled blasting,the dynamic stress intensity factors(DSIFs)and the propagation paths of the blast-induced cracks are obviously influenced by the delayed ignition.(2) The circular hole situated between the two boreholes poses a strong guiding effect on the coelesence of the cracks,causing them to propagate towards each other when cracks are reaching the circular hole area.(3)Blast-induced cracks are not initiated preferentially because of the superimposed effect from the explosive stress waves on the cracking area.(4) By using the scanning electron microscopy(SEM)method,it is verified that the roughness of crack surfaces changes along the crack propagation paths.