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.

ANALYSIS OF NONLINEAR DYNAMIC RESPONSE FOR VISCOELASTIC COMPOSITE PLATE WITH TRANSVERSE MATRIX CRACKS

Based on the Schapery three-dimensional viscoelastic constitutive relationship with growing damage, a damage model with transverse matrix cracks for the unidirectional ?bre rein- forced viscoelastic composite plates is developed. By using Karman theory, the nonlinear dynamic governing equations of the viscoelastic composite plates under transverse periodic loading are es- tablished. By applying the ?nite di?erence method in spatial domain and the Newton-Newmark method in time domain, and using the iterative procedure, the integral-partial di?erential gov- erning equations are solved. Some examples are given and the results are compared with available data.

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.

Dynamic Fracture Analysis of Functionally Gradient Materials with Two Cracks By Peridynamic Modeling

In the research,the dynamic fracture failure problem of functionally graded materials(FGMs)containing two pre-cracks was analyzed using a bond-based Peridynamic(PD)method numerical model.The two convergence of decreasing the area of PD horizon(δ-convergence)and uniform mesh refinement(m-convergence)were studied.The effects of both crack position and distance between two cracks on crack propagation pattern in FGMs plate under tensile loads are studied.Furthermore,the effects of different gradient patterns on the dynamic propagation of cracks in FGMs are also investigated.The simulate results suggest that the cracks positions and the distance between them can significantly influence the dynamic propagation of crack in FGMs.Gradient mode also has a certain effect on crack propagation,but the effect of specific gradient variation patterns on dynamic propagation of crack is finite.

Effect of Concrete Cracks on Dynamic Characteristics of Powerhouse for Giant-Scale Hydrostation

With the increase of capacity and size of the hydro-generator unit, the spiral case becomes a more super-giant hydraulic structure with very high HD value, where H and D denote water head and maximum intake diameter of spiral case, respectively. Due to the induced lower stiffness by the more giant size and adverse operation conditions, dynamic performances of the powerhouse and the supporting structure for the giant units have become more important and attracted much attention. If the manner of steel spiral case embedded directly in concrete is adopted, on some locations of the concrete surrounding the spiral case, distributed and concentrated cracks will emerge due to high tensile stress. Although the concrete is reinforced well to control the maximum crack width, definitely these cracks will reduce the local and entire stiffness of the powerhouse. Under dynamic loads such as hydraulic forces including water pressure pulsation in flow passage acting on the structure, effect of the cracks on the dynamic characteristics of the local members and entire structure needs to be evaluated. However, research on this subject is few in hydroelectric engineering. In this paper, Three-Gorge Project was taken as an example to evaluate effect of such cracks on natural frequencies and the vibration responses of the powerhouse under hydraulic and earthquake forces in detail. Results show that cracks only reduce the local structural stiffness greatly but have little effect on the entire powerhouse especially the superstructure; vibrations of powerhouse with cracks in concrete surrounding the spiral case are still under the design limits. Results in this paper have been verified by practice of Three-Gorge Project.

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.

Dynamic experimental study on rock meso-cracks growth by digital image processing technique

A new meso-mechanical testing scheme based on SEM was developed to carry out the experiment of microfracturing process of rocks. The microfracturing process of the pre-crack marble sample on surrounding rock in the immerged Long-big tunnel in Jinping Cascade II Hydropower Station under uniaxial compression was recorded by using the testing scheme. According to the stereology theory, the propagation and coalescent of cracks at meso-scale were quantitatively investigated with digital technology. Therefore, the basic geometric information of rock microcracks such as area, angle, length, width, perimeter, was obtained from binary images after segmentation. The failure mechanism of specimen under uniaxial compression with the quantitative information was studied from macro and microscopic point of view. The results show that the image of microfracturing process of the specimen can be observed and recorded digitally. During the damage of the specimen, the distribution of microcracks in the specimen is still subjected to exponential distribution with some microcracks concentrated in certain regions. Finally, the change law of the fractal dimension of the local element in marble sample under different external load conditions is obtained by means of the statistical calculation of the fractal dimension.

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.

Reflective cracking viscoelastic response of asphalt concrete under dynamic vehicle loading

In order to investigate the mechanical response of reflective cracking in asphalt concrete pavement under dynamic vehicle loading, a finite element model is established in ABAQUS. The viscoelastic behavior is described by a prony series which is calculated through nonlinear fitting to the creep test data obtained in the laboratory. Based on the viscoelastic theory, the time-temperature equivalence principle, fracture mechanics and the dynamic finite element method, both the Jintegral and the mix-mode stress intensity factor are utilized as fracture evaluation parameters, and a half-sine dynamic loading is used to simulate the vehicle loading. Finally, the mechanical response of the pavement reflective cracking is analyzed under different vehicle speeds, different environmental conditions and various damping factors. The results indicate that increasing either the vehicle speed or the structure damping factor decreases the maximum values of fracture parameters, while the structure temperature has little effect on the fracture parameters. Due to the fact that the vehicle speed can be enhanced by improving the road traffic conditions, and the pavement damping factor can become greater by modifying the components of materials, the development of reflective cracking can be delayed and the asphalt pavement service life can be effectively extended through both of these ways.

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.

Representation Theory of Three-Dimensional Elliptical Crack Under Dynamic Loading

The relation between the normal displacement on the surface of a dynamical elliptical crack and the normal stress over the crack surface was studied. The three dimensional elastodynamic equations and Fourier Laplace transforms are used. Based on the influence function and the inversion of integral transforms, one can find that if the distribution of normal displacement on the surface of a dynamic elliptical crack is a polynomial of degree n in x 1 and x 2 , then the normal pressure acting over the ellipse is also a polynomial P n(x 1,x 2) of the same degree in x 1 and x 2 .

Dynamic Characteristics of Multi-degrees of Freedom System Rotor-bearing System with Coupling Faults of Rub-impact and Crack

Extensive studies on rotor systems with single or coupled multiple faults have been carried out. However these studies are limited to single-span rotor systems. A finite element model for a complex rotor-bearing system with coupled faults is presented. The dynamic responses of the rotor-bearing system are obtained by using the rotor dynamics theory and the modern nonlinear dynamics theory in connection with the continuation-shooting algorithm（commonly used for obtaining a periodic solution for a nonlinear system） for a range of rub-impact clearances and crack depths. The stability and Hopf instability of the periodic motion of the rotor-bearing system with coupled faults are analyzed by using the procedure described. The results indicate that the finite element method is an effective way for determining the dynamic responses of such complex rotor-bearing systems. Further for a rotor system with rub-impact and crack faults, the influences of the clearances are significantly different for different rub-impact stiffness. On the contrary, the influence of crack depths is rather small. The instability speeds of the rotor-bearing system increase due to the presence of the crack fault. The results obtained using the new finite element model, presented for computation and analysis of dynamic responses of the rotor-bearing systems with coupled faults, are in accordance with measurements in experiment. The formulations given can be used for diagnosis of faults, vibration control, and safe and stable operations of real rotor-bearing systems.

DYNAMIC BEHAVIOR OF A CRACKED FLEXIBLE ROTOR SUPPORTED ON JOURNAL BEARINGS

The dynamic behavior of a cracked flexible rotor supported on three kinds ofjournal bearings is presented. Numerical experiments show that nonsynchronous responseswill happen due to the rotor crack, and the amplitudes of the nonsynchronous componentsbecome larger with the increase of crack. On the other hand, the fluid forces of journalbearings can suppress the nonsynchronous response. The (1/2) × or (3/2) × harmoniccomponent rarely appears for small crack near the rotating speed ratio Ω = 2Ωc or Ω =(2/3)Ωc. In the case of supercritical rotating speed, the additional 0× harmonic component is increased as the crack increases. The bearing parameters affect greatly the occur-rence of the nonsynchronous responses by means of exerting innuence on the critical spedand the stabi1ity of the system.

ZONAL DISINTEGRATION MECHANISM OF DEEP CRACK-WEAKENED ROCK MASSES UNDER DYNAMIC UNLOADING

Size and quantity of fractured zone and non-fractured zone are controlled by cracks contained in deep rock masses. Zonal disintegration mechanism is strongly dependent on the interaction among cracks. The strong interaction among cracks is investigated using stress superposition principle and the Chebyshev polynomials expansion of the pseudo-traction. It is found from numerical results that crack nucleation, growth and coalescence lead to failure of deep crack- weakened rock masses. The stress redistribution around the surrounding rock mass induced by unloading excavation is studied. The effect of the excavation time on nucleation, growth, interaction and coalescence of cracks was analyzed. Moreover, the influence of the excavation time on the size and quantity of fractured zone and non-fractured zone was given. When the excavation time is short, zonal disintegration phenomenon may occur in deep rock masses. It is shown from numerical results that the size and quantity of fractured zone increase with decreasing excavation time, and the size and quantity of fractured zone increase with the increasing value of in-situ geostress.

Dynamic tensile behaviour and crack propagation of coal under coupled static-dynamic loading

The fracture behaviour and crack propagation features of coal under coupled static-dynamic loading conditions are important when evaluating the dynamic failure of coal.In this study,coupled static-dynamic loading tests are conducted on Brazilian disc(BD)coal specimens using a modified split Hopkinson pressure bar(SHPB).The effects of the static axial pre-stress and loading rate on the dynamic tensile strength and crack propagation characteristics of BD coal specimens are studied.The average dynamic indirect tensile strength of coal specimens increases first and then decreases with the static axial pre-stress increasing.When no static axial pre-stress is applied,or the static axial pre-stress is 30%of the static tensile strength,the dynamic indirect tensile strength of coal specimens shows an increase trend as the loading rate increases.When the static axial pre-stress is 60%of the static tensile strength,the dynamic indirect tensile strength shows a fluctuant trend as the loading rate increases.According to the crack propagation process of coal specimens recorded by high-speed camera,the impact velocity influences the mode of crack propagation,while the static axial pre-stress influences the direction of crack propagation.The failure of coal specimens is a coupled tensile-shear failure under high impact velocity.When there is no static axial pre-stress,tensile cracks occur in the vertical loading direction.When the static axial pre-stress is applied,the number of cracks perpendicular to the loading direction decreases,and more cracks occur in the parallel loading direction.

MOLECULAR DYNAMICS SIMULATION OF CRACK-TIP PROCESSES IN COPPER

The crack tip processes in copper under mode II loading have been simulated by a molecular dynamics method. The nucleation, emission, dislocation free zone (DFZ) and pile-up of the dislocations are analyzed by using a suitable atom lattice configuration and Finnis & Sinclair potential. The simulated results show that the dislocation emitted always exhibits a dissociated fashion. The stress intensity factor for dislocation nucleation, DFZ and dissociated width of partial dislocations are strongly dependent on the loading rate. The stress distributions are in agreement with the elasticity solution before the dislocation emission, but are not in agreement after the emission. The dislocation can move at subsonic wave speed (less than the shear wave speed) or at transonic speed (greater than the shear wave speed but less than the longitudinal wave speed), but at the longitudinal wave speed the atom lattice breaks down.

Dislocation formation and twinning from the crack tip in Ni_3Al:molecular dynamics simulations

The mechanism of low-temperature deformation in a fracture process of Ll2 Ni3Al is studied by molecular dynamic simulations. Owing to the unstable stacking energy, the [011] superdislocation is dissociated into partial dislocations separated by a stacking fault. The simulation results show that when the crack speed is larger than a critical speed, the Shockley partial dislocations will break forth from both the crack tip and the vicinity of the crack tip; subsequently the super intrinsic stacking faults are formed in adjacent {111} planes, meanwhile the super extrinsic stacking faults and twinning also occur. Our simulation results suggest that at low temperatures the ductile fracture in Ll2 Ni3Al is accompanied by twinning, which is produced by super-intrinsic stacking faults formed in adjacent {111} planes.

Influence of interface crack on dynamic characteristics of CRTSⅢslab ballastless track on bridge

The damage of the self-compacting concrete in CRTSⅢslab ballastless track on bridge will lead to a partial void of the track slab,which will affect the comfort and safety of the train and the durability of the track slab and bridge structure.In order to study the impact of the interface crack on the dynamic response of CRTSⅢballastless track system on bridge,based on the principle of multi-body dynamics theory and ANSYS+SIMPACK co-simulation,the spatial model of vehicle-track-bridge integration considering the longitudinal stiffness of supports,the track structure and interlayer contact characteristics were established.The dynamic characteristics of the system under different conditions of the width,length and position of the interface crack were analysed,and the limited values of the length and width of the cracks at the track slab edge were proposed.The results show that when the self-compacting concrete does not completely void along the transverse direction of the track slab,the crack has little effect on the dynamic characteristics of the vehicle-track-bridge system.However,when the self-compacting concrete is completely hollowed out along the transverse direction of the track slab,the dynamic amplitudes of the system increase.When the crack length is 1.6 m,the wheel load reduction rate reaches 0.769,which exceeds the limit value and threatens the safety of train operation.The vertical acceleration of the track slab increases by 250.1%,which affects the service life of the track system under the train speed of 200 km/h.

Dynamic Characteristics of Rotor System with a Slant Crack Based on Fractional Damping

The traditional modeling method of rotor system with a slant crack considers only integer-order calculus.However,the model of rotor system based on integer-order calculus can merely describe local characteristics,not historical dependent process.The occur of fractional order calculus just makes up for the deficiency in integer-order calculus.Therefore,a new dynamic model with a slant crack based on fractional damping is proposed.Here,the stiffness of rotor system with a slant crack is solved by zero stress intensity factor method.The proposed model is simulated by Runge-Kutta method and continued fraction Euler method.The influence of the fractional order,rotating speed,and crack depth on the dynamic characteristics of rotor system is discussed.The simulation results show that the amplitude of torsional excitation frequency increases significantly with the increase of the fractional order.With the increase of the rotating speed,the amplitude of first harmonic component becomes gradually larger,the amplitude of the second harmonic becomes smaller,while the amplitude of the other frequency components is almost invariant.The shaft orbit changes gradually from an internal 8-type shape to an ellipse-type shape without overlapping.With the increase of the slant crack depth,the amplitude of the transverse response frequency in the rotor system with a slant crack increases,and the amplitude in the second harmonic component also increases significantly.In addition,the torsional excitation frequency and other coupling frequency components also occur.The proposed model is further verified by the experiment.The valuable conclusion can provide an important guideline for the fault diagnosis of rotor system with a slant crack.

Review Paper: Challenges and Limitations in Studying the Shrink-Swell and Crack Dynamics of Vertisol Soils

The need to study the shrink-swell and crack properties of vertic soils has long been recognized given their dynamics in time and space, which modifies the physical properties that impact water and air movement in the soil, flow of water into the subsoil and ground water, and generally alter the hydrology of vertic soils. Measurement of crack properties has been made by numerous researchers with the purpose to understand and quantify the spatial and temporal dynamics of shrinking and swelling and the associated formation of cracks. These crack properties, which are important in modifying hydrology of soils are: width, length, depth and orientation of soil’s cracks. To better understand the hydrology of vertic soils and incorporate crack properties into hydrologic simulation models, several techniques have been developed to measure crack properties. However, little attention is given to evaluate both the advantages and the limitations associated with these techniques. Thus, the purpose of this review is to highlight challenges and limitations that have been used or might be used to measure cracking in vertic soils.