Dynamic Stress Intensity Factor Research Articles

Interaction of one-periodic disk-shaped cracks under an incident elastic harmonic wave

We study a symmetric problem of harmonic wave propagation in an elastic space with a one-periodic array of interacting disk-shaped cracks. Using the Green function obtained by the Fourier transform, we reduce the problem to a boundary integral equation (BIE) for the function characterizing the displacement discontinuity on one of the cracks and numerically determine the desired function by solving the BIE. We present graphs of the dynamic stress intensity factors near a circular crack versus the wave number for various distances between the defects.

Dynamic fracture analysis of crack–defect interaction for mode I running crack using digital dynamic caustics method

The crack–defect interaction mechanism was studied both experimentally and numerically. Experimental results found that the presence of empty hole before crack results in both the velocity and stress intensity factor of crack decrease. More energy accumulated at crack–hole tip before second initiation. Dynamic stress intensity factor is qualitatively in accord with Crack velocity, but it oscillates strongly with hole size increasing. Numerical study shows that the stress concentration would be reduced significantly when the modulus radio between the inclusion and the matrix is more than 0.5. Results may shed lights on the interaction behavior between running crack and inclusion.

Dynamic stress-intensity factors of an in-plane shear crack in saturated porous medium

Based on the classical Biot theory of propagation of elastic waves in fluid-saturated porous media, two classes of plane problem are considered. One is the transient problem of a finite crack subjected to a suddenly applied in-plane shear, and another one is dealing with diffraction of transverse SV-wave by the same crack. The formulation utilizes the Laplace and integral transforms to reduce the mixed boundary-value problems to Fredholm integral equations of the second kind. The equations are then solved numerically for time and frequency dependent dynamic stress-intensity factors (mode II), and the influence of pore fluid on the dynamic stress-intensity factor is investigated. Pore fluid is found to have impact on the magnitude of the stress-intensity factor the extent of which depends on the two fluid parameter values, namely ratio of fluid mass with respect to the whole bulk mass and viscosity-to-permeability ratio. Comparisons of the solutions obtained from the present study with the corresponding known solutions of dry elastic medium are also provided to verify the validity of the present solution scheme.

Non-Fourier effect and inertia effect analysis of a strip with an induced crack under thermal shock loading

In this paper, the transient temperature fields and the dynamic stress intensity factors of a thermo-elastic strip containing an inner crack parallel to the heated surface under thermal shock are studied. The Biot number of the crack gap, hyperbolic heat conduction theory and equation of motion are considered to investigate the behavior of the temperature fields around the crack and the stress intensity factors. Fourier transform and Laplace transform are used to reduce this mixed boundary value problem. Numerical methods are used to solved the singular integrate equations. Finally, the numerical results are presented illustrating the influence of Biot number, non-Fourier effect and inertia effect on temperature field and stress intensity factors. It is found that the Biot number strongly affect the uniformity of the temperature field and the magnitude of the stress intensity factors. The stress intensity factors have higher amplitude and an oscillating feature comparing to those obtained under conventional Fourier thermal conduction condition and quasi-static hypothesis, which can help to better understand the crack behaviors of advanced materials under thermal impact loading.

Brittle crack propagation/arrest behavior in steel plate – Part I: Model formulation

A formulation to simulate brittle crack propagation/arrest behavior in steel plates is proposed based on the local fracture criterion. The crack behavior is simulated within a short time by repeated calculations solving the simultaneous governing equations at the crack front: (a) fracture condition, (b) strain hardening, (c) yield point and (d) dynamic stress intensity factor, without any arbitrary parameters and any complicated procedures. The crack is predicted to be arrested when the above simultaneous equations do not give any solutions or when the uncracked side-ligaments cover all the thickness of the plate at the crack front.

Dynamic Stress Intensity Factors for an Interfacial Crack near a Non-Circular Cavity in Piezoelectric Bi-Materials

Abstract A theoretical analysis is followed to calculate the dynamic stress intensity factors (DSIFs) due to existence of an interfacial crack near the right edge of a non-circular cavity, in transversely isotropic piezoelectric bi-materials. The model is subjected to dynamic incident anti-plane shearing (SH-wave). Green’s functions are constructed Based on complex variable and conformal mapping methods. DSIFs at the crack inner and outer tips are obtained by conjunction and cracks-deviation techniques. The boundary value problems are solved by applying the orthogonal function expansion technique. Based on FORTRAN language program, some numerical calculations with an elliptic cavity are provided for different elliptic axial length ratios, different wave numbers and different piezoelectric parameters. For calibration, a comparison is accomplished between the present model and similar model with a crack emerging from a circular cavity edge. Calculating results showed the influences on DSIFs and how affected the efficiency of piezoelectric devices and materials.

Numerical simulation of dynamic brittle fracture of pipeline steel subjected to DWTT using XFEM-based cohesive segment technique

In the past several numerical studies have addressed the ductile mode of fracture propagation. However, the brittle mode of pipeline failure has not received as much attention yet. The main objective of this study is to predict brittle fracture behaviour of API X70 pipeline steel by means of a numerical approach. To this end, the eXtended Finite Element Method (XFEM)-based cohesive segment technique is used to model Drop Weight Tear Test (DWTT) of X70 pipeline steel at -100°C. In this model the dynamic stress intensity factor and crack velocity are calculated at the crack tip at each step of crack propagation.

Investigation of dynamic mode I matrix crack-fiber bundle interaction in composites using caustics

In this work, the dynamic mode I matrix crack-fiber bundle interaction was studied using caustics. First, the strain fields at the dynamic mode I matrix crack tip ahead of the fiber bundles were deduced using transformation toughening theory. Subsequently, the caustic equation at mode I dynamic matrix crack tip ahead of the fiber bundles was established to investigate the influences of the fiber bundle and the crack propagating velocity on the initial curves and caustic curves at the dynamic matrix crack tip. Finally, a series of dynamic caustic spots surrounding the propagating crack tip were recorded using optical caustic experiment, and dynamic stress intensity factor were extracted from the shadow spots.

Dynamic stress intensity factor analysis of the interaction between multiple impact-loaded cracks in infinite domains

In this work, the dynamic interaction between multiple cracks whose surfaces are symmetrically impact-loaded in infinite domains is investigated. Toward this end, the symmetric-Galerkin boundary element method (SGBEM) for 2-D elastodynamics in the Laplace-space frequency (LaplaceSGBEM) was employed to compute the dynamic stress intensity factors (DSIFs) for the cracks during their interaction under dynamic loading conditions. Three examples of multi-crack dynamic interaction were considered. The Laplace-SGBEM results show that the DSIFs will reach their maximum value after the cracks are loaded. It is followed by a damped-like oscillation of the DSIFs about their corresponding static value. In addition, as the cracks approach each other, the dynamic stress field in the vicinity of their crack tips interacts which results in an increase or decrease of the maximum DSIFs.

Dynamic Stress Intensity Factor for Interfacial Cracks of Mode III Emanating from Circular Cavities in Piezoelectric Bimaterials

This paper investigates dynamic stress intensity factors in piezoelectric bimaterials with interfacial cracks emanating from the circular cavities under steady SH-waves. The interfacial cracks are assumed to be permeable. The Green functions for the experiment were constructed through complex variable and wave function expansion methods. Based on the crack-division and conjunction techniques, a series of Fredholm integral equations of the first kind were established to calculate the stress intensity of the crack tips. Direct numerical integration was used to solve the equations. Some numerical results were plotted to indicate the influence of the defect geometry, material constants and SH-wave frequencies on dynamic stress intensity factors.

Investigation on Dynamic Propagation Characteristics of In-Plane Cracks in PVB Laminated Glass Plates

Polyvinyl butyral (PVB) laminated glass has been widely used as an important component of mechanical and construction materials. Cracks on PVB laminated glass are rich in impact information, which contribute to its impact resistance design. In this paper, a three-dimensional (3D) numerical simulation model describing PVB laminated glass under impact loading is firstly established and validated qualitatively and quantitatively compared with the corresponding experimental results recorded by the high-speed photography system. In the meantime, the extended finite element method (XFEM) is introduced to analyze the crack propagation mechanism of laminated glass based on dynamic stress intensity factors (DSIFs) and propagations of stress waves. Parametric studies are then carried out to investigate the influence of five critical parameters, that is, plate dimension, crack length, impact energy, glass properties, and PVB properties, on crack propagation characteristics of laminated glass. Results show that the interaction between crack tip and stress waves as well as the propagations of stress waves corresponds to the fluctuations of DSIFs at crack tip. Both the structure and material variables are proven to play a very important role in glass cracking DSIFs and thus govern the crack propagation behavior. Results may provide fundamental explanation to the basic crack propagation mechanism on radial cracks in PVB laminated glass under impact loading conditions, thus to instruct its impact design improvement.

Experimental Research of Crack Propagation in Polymethyl Methacrylate Material Containing Flaws Under Explosive Stress Waves

Abstract The crack propagation behavior of the material polymethyl methacrylate with flaws under the effects of explosive stress waves were studied using a digital laser dynamic caustics method. Four different kinds of experimental conditions were set: open joints, closed joints, confined pressure around the specimen, and double boreholes. A digital high-speed camera was utilized to record a series of dynamic caustics spots at the tip of the propagation wing cracks. The cracks' paths and the dynamic stress intensity factor (DSIF) at the tip of the two wing cracks are evaluated. Crack patterns, variation of DSIF, and the mechanisms of the wing cracking process are analyzed and discussed. The results provided an effective experimental basis for evaluating and designing directional controlled blasting for excavating rock faces and tunnels.

Analysis of dynamic stress intensity factor of finite piezoelectric composite plate under a dynamic load

Piezoelectric materials are widely utilized in electronic device applications such as sensors. This paper investigates the dynamic response of a central crack in a finite piezoelectric layered composite plate under impact load. This novel project studies the crack effect on the finite geometries of a piezoelectric layered composite plate. A finite element method for transient dynamic crack analysis in two-dimensional, homogeneous, anisotropic and linear elastic composites was used for this investigation. Initially, the simulation method was verified and calibrated using a simple case study of a piezoelectric material (BaTiO3) with a pre-crack. The results were in good agreement with previous studies in this field. Later, the verified model was used to simulate the piezoelectric layered composite plate. The results showed that the maximum dynamic stress intensity factor depends on the thickness and material properties of the piezoelectric layer and these are crucial parameters in the design and evaluation of a piezoelectric.

Peridynamicsを用いた混合モード動的応力拡大係数評価に関する研究

Peridynamicsを用いた混合モード動的応力拡大係数評価に関する研究

Dynamic Stress Intensity Factors of Three Collinear Cracks in an Orthotropic Plate Subjected to Time-Harmonic Disturbance

AbstractAbstract-The dynamic stresses around three collinear cracks in an infinite orthotropic plate are solved. In this configuration, two equal cracks are situated symmetrically on either side of a central crack, and time-harmonic elastic waves impinge perpendicularly to the cracks. The problem is solved by superimposing two types of solutions. One solution is that for a crack in an infinite orthotropic plate, and the other is for two collinear cracks. The unknown coefficients in the superimposed solution are determined by applying the boundary conditions at the surfaces of the three cracks using the Schmidt method. The dynamic stress intensity factors are calculated numerically for an orthotropic plate that corresponds to the elastic properties of a boron-epoxy composite.

Numerical Simulation of Brittle Crack Propagation and Arrest in Steels Considering Shear-Lip Formation

A model for simulating brittle crack propagation and arrest in steel plates is presented. The model considers the influence of shear lips formed on a fracture surface acting as a crack closure force and the influence of the loss of the plane-strain condition at a propagating crack tip with an increasing dynamic stress intensity factor. The shear lips are assumed not to fracture during the test, so they will yield and provide a crack closure force. The crack closure effect depends on not only the stress intensity factor but also the crack velocity. The model was applied to temperature-gradient crack-arrest tests and ultrawide duplex crack-arrest tests. The model successfully explained anomalous crack-arrest toughness under excessively high applied stress in the temperature-gradient tests and crack arrest at a stress intensity factor far above the cleavage crack-arrest toughness in the ultrawide duplex tests.

Dynamic stress intensity factor of 2A12T4 Al compact tension specimen with loading point displacement and spring mass model

Loading point displacement and spring mass model were introduced into the calculation of the dynamic stress intensity factor for a fatigue pre-cracked 2A12T4 aluminium alloy compact tension specimen. A simple formula of dynamic stress intensity factor for a fatigue pre-cracked compact tension specimen is derived using the vibration analysis method. By determining equivalent mass and equivalent stiffness of 2A12T4 aluminium alloy compact tension specimen, the dynamic stress intensity factor expression has been given. Three examples of simple dynamic loading were calculated, the results were in good agreement with their finite element model values.

Elastodynamic analysis of mode III multiple cracks in a functionally graded orthotropic half-plane

This paper presents a set of dynamic analyses of multiple parallel or perpendicular cracks to the boundary in a functionally graded orthotropic half-plane subjected to anti-plane shear stresses. The material properties are assumed to vary based on an exponential law. Integral transformations (Laplace and Fourier) and Green’s function method are applied to elastodynamic equations. The displacement discontinuous distribution method is used to model the crack problems which are solved by using a set of appropriate boundary conditions. As a result, a set of stress equations with both hypersingular and logarithm singular terms is obtained. Using Chebyshev series expansion and collocation points in Laplace domain, the solution of hypersingular integral equation for multiple cracks is achieved. Finally, different algorithms of numerical Laplace inversion are presented and the dynamic stress intensity factors (DSIFs) are obtained. The presented results are compared with the available published data and a very good agreement is observed. Moreover, it is also demonstrated that the present theoretical study is capable of modeling multiple cracks with different arrangements and variety of FG Orthotropic material properties. Furthermore, influence of FGM constant and shear modulus ratio on the dynamic overshoot of stress intensity is investigated.

Transient dynamic stress intensity factors around three stacked parallel cracks in an infinite medium during passage of an impact normal stress

Transient dynamic stresses around three stacked parallel cracks in an infinite elastic plate are estimated for an incident impact stress wave impinging normal to the cracks. Using Fourier and Laplace transform techniques, the boundary conditions are reduced to six simultaneous integral equations in the Laplace domain. The differences in the displacements inside the cracks are expanded in a series of functions that have zero value outside the cracks. The Schmidt method is used to solve the unknown coefficients in the series such that the conditions inside the cracks are satisfied. The stress intensity factors are defined in the Laplace domain, and these are inverted using the numerical method. The stress intensity factors are calculated numerically for some crack configurations.

Dynamic stress intensity factors of two 3D rectangular permeable cracks in a transversely isotropic piezoelectric material under a time‐harmonic elastic P‐wave

SummaryThe dynamic behavior of two 3D rectangular permeable cracks in a transversely isotropic piezoelectric material is investigated under an incident harmonic stress wave by using the generalized Almansi's theorem and the Schmidt method. The problem is formulated through double Fourier transform into three pairs of dual integral equations with the displacement jumps across the crack surfaces as the unknown variables. To solve the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. Finally, the relations among the dynamic stress field and the dynamic electric displacement filed near the crack edges are obtained, and the effects of the shape of the rectangular crack, the characteristics of the harmonic wave, and the distance between two rectangular cracks on the stress and the electric intensity factors in a piezoelectric composite material are analyzed. Copyright © 2015 John Wiley & Sons, Ltd.