Eccentric Crack Research Articles

Analytical Solution for a 1D Hexagonal Quasicrystal Strip with Two Collinear Mode-III Cracks Perpendicular to the Strip Boundaries

We considered the problem of determining the singular elastic fields in a one-dimensional (1D) hexagonal quasicrystal strip containing two collinear cracks perpendicular to the strip boundaries under antiplane shear loading. The Fourier series method was used to reduce the boundary value problem to triple series equations, then to singular integral equations with Cauchy kernel. The analytical solutions are in a closed form for the stress field, and the stress intensity factors and the energy release rates of the phonon and phason fields near the crack tip are expressed using the first and third complete elliptic integrals. The effects of the geometrical parameters of the crack configuration on the dimensionless stress intensity factors are presented graphically. The studied crack model can be used to solve the problems of a periodic array of two collinear cracks of equal length in a 1D hexagonal quasicrystal strip and an eccentric crack in a 1D hexagonal quasicrystal strip. The propagation of cracks produced during their manufacturing process may result in the premature failure of quasicrystalline materials. Therefore, it is very important to study the crack problem of quasicrystalline materials with defects as mentioned above. It can provide a theoretical basis for the application of quasicrystalline materials containing the above defects.

Notch Effects on the Stress Intensity Factor and on the Fatigue Crack Path for Eccentric Circular Internal Cracks in Elliptically Notched Round Bars under Tensile Loading.

In this paper, stress intensity factor (SIF) solutions are numerically obtained for notched bars subjected to tensile loading containing an eccentric circular inner crack located in the cross-section corresponding to the notch root. The finite element method and the J-integral have been used to obtain the SIF and to analyze the effect on it of three elliptical notch geometries (of equal radial depth). The results show how the SIF is greater in the notched bars than in the smooth bar and within the former when the axial semi-axis of the notch rises, its effect being greater as the diameter and eccentricity of the inner crack increase. In addition, the fatigue growth of an eccentric crack induces an increase in such eccentricity, greater as the notch axial semi-axis increases. The cause of these phenomena can be attributed to the constraint loss caused by the notch, which also facilitates bending of the specimen due to the asymmetry generated by the crack eccentricity.

Eccentric penny-shaped crack in a long circular cylinder

The three-dimensional analysis of the stress distribution in a long circular cylinder that contains an eccentric penny-shaped crack is discussed in this paper. The surface of the crack is subjected to a known pressure and is perpendicular to the axis of the cylinder. We solve the equations of the classical theory of elasticity in terms of an unknown function. This function is then shown to be the solution of an integro-differential equation. We also discuss the case when the crack is concentric, and show that the final solution agrees with the known result.

Influence of a static torque on plasticity and asperity-induced closure effects during fatigue crack growth in bainitic steel cylinders loaded in push-pull

Mode I fatigue crack growth with a superimposed static torque was investigated in bainitic steel. The torque had little effect on crack growth kinetics and path. However, the non-singular stress parallel to the crack front, and bending stresses due to eccentric crack growth triggered crack twisting, even in mode I. A progressive increase in crack sliding displacement was due to a rise in elastic torsional compliance, but also to plastic ratchetting at the crack tip, and to a progressive shearing of crack face asperities, which reduced the enhancement of roughness-induced closure by the torque, however shown to enhance plasticity-induced closure.

Investigation on mixed-mode II-III fracture of the sandstone by using eccentric cracked disk

Most of the fractures in deep rock mass are in compression condition. The deep rock failure is complex and different modes of failure play important roles. In this study, the central cracked circular disk specimen was improved by deviating from the distance between the crack on the circular surface and the center of the circle, and a new mixed-mode II-III fracture specimen called the eccentric crack disk (ECD) specimen was proposed. The ECD specimen was a simple structure and easy to machining with low cost. In addition, it could be tested in conventional loading machines without extra fixtures. The finite element was used to calculate mode I, mode II and mode III stress intensity factors for different loading angles and crack deviation distances. The critical loading angles of mixed-mode II-III fracture under different crack deviation distances were obtained. And the mixed-mode II-III fracture experiments were carried out with sandstone. The experimental results clearly revealed that the crack initiation started from the middle of the crack. The experimental data also conformed to the effective stress intensity factor criterion of mixed-mode II-III mode fracture from the literature.

Stochastic Study on Discontinuous Slow Crack Growth Kinetics from an Arbitrarily Located Defect of Polyethylene Based on the Crack Layer Theory

The major failure aspect of high-density polyethylene pipes under the service condition is the discontinuous slow crack growth (DSCG) from the initial defects inside the pipe wall. In this study, the DSCG kinetics for an internal eccentric crack is theoretically simulated by developing a crack-layer growth model for an eccentric crack. The present model precisely mimics the experimental DSCG kinetics for the eccentric crack, and it also estimates the final failure time accurately. Furthermore, to investigate the reliability of the DSCG-dominated failure concerning the uncertainties related to the initial crack, a stochastic study on the lifetime distribution due to the probabilistic distribution of the initial crack size is performed. Additionally, lifetime distribution fitting using the Birnbaum–Saunders (B-S) distribution function and the maximum likelihood estimation method is conducted for various initial crack locations, sizes, and applied stresses. The B-S function accurately describes the simulated lifetime distribution, and the equations for estimating the scale and shape parameters of the B-S function with regard to the initial crack distributions at various crack locations and remote stress levels are presented.

Propagation conditions of an eccentric crack in a semi-circular disk loaded in I+II mixed mode

Multi-parameter fracture mechanics concept is applied to investigate crack propagation conditions during a three-point bending (3PB) test performed on an asymmetrical semi-circular disk under I+II mixedmode loading. The asymmetry is represented by an eccentricity of the angled crack as well as by different distances of both supports during the 3PB test from the middle of the specimen. The Williams series expansion is used for the crack-tip stress field approximation and fracture response of the crack is assessed by means of the combination of the numerical and analytical solution. Comparison between the individual configurations is carried out and discussion on the importance of the higher-order terms considered in the Williams expansion for various cases of asymmetry is presented.

Deflection of an eccentric crack under mixed-mode conditions in an SCB specimen

Deflection of an eccentric crack under mixed-mode conditions in an SCB specimen

Transient fracture of a piezoelectric-piezomagnetic sandwich structure: anti-plane case

In this article, we investigate the transient fracture behavior of piezoelectric (PE)–piezomagnetic (PM) sandwich structures under combined anti-plane shear mechanical and in-plane electrical impacts. A PM layer with an eccentric crack is sandwiched between two dissimilar PE layers. The Laplace and Fourier transforms are employed to reduce the mixed boundary valued problem to a standard Cauchy singular integral equation of the first kind in the Laplace transform domain. Then the Cauchy singular integral equation is solved by the Gauss–Chebyshev collocation method. By utilizing the numerical Laplace inversion, the dynamic stress intensity factors (DSIFs) are obtained in the time domain. Numerical results are presented to show the effects of the material combinations, crack location, structure geometries and electromechanical coupled loads on DSIFs. The findings of the present paper may be useful for the design and fracture prediction of layered PE–PM structures.

Eccentric annular crack under general nonuniform internal pressure

AbstractFor a better approximation of ring-shaped and toroidal cracks, a new eccentric annular crack model is proposed and an analytical approach for determination of the corresponding stress intensity factors is given. The crack is subjected to arbitrary mode I loading. A rigorous solution is provided by mapping the eccentric annular crack to a concentric annular crack. The analysis leads to two decoupled Fredholm integral equations of the second kind. For the sake of verification, the problem of a conventional annular crack is examined. Furthermore, for various crack configurations of an eccentric annular crack under uniform tension, the stress intensity factors pertaining to the inner and outer crack edges are delineated in dimensionless plots.

Antiplane Response of Cylindrical Inclusion with Eccentric Crack to Incident SH Waves

The analytical solution to a cylindrical inclusion with an eccentric crack impacted incident SH waves was studied by using the methods of Green function and conjunction. Firstly, Green function was constructed, which was an essentical solution of displacement field for an elastic half space containing a half cylindrical inclusion while bearing out-of-plane harmonic line source force at any point of its horizontal boundary. Secondly, the whole space was divided into two parts via conjunction technology, a series of unknown forces were loaded at the linking sections to satisfy continuity conditions.Thirdly, the Fredholm integral equations of the first kind were set up through the continuity conditions and the Green function. Finally, a example for dynamic stress intensity factor for mode III at the crack tip was given. Numerical results show that the dynamic stress intensity factors is influenced by wave numbers and media parameters.

Stress intensity factors for an inclined and/or eccentric crack in a finite orthotropic lamina

Stress intensity factors (SIF) are determined for an inclined and / or eccentric crack in a finite orthotropic lamina using the boundary collocation method. The stress functions are defined such that they satisfy governing equations in the domain, the boundary condition on the crack surface and also the singularity at the crack tip. The unknown coefficients in the stress functions are determined such that the boundary condition on the edges of lamina is satisfied. The analysis is also being carried out for isotropic material using finite element analysis software ANSYS for comparison of results. Also, comparison of results with existing solutions is found in good agreement.

Stress Intensity Factor of Different Position Plates with Eccentric Crack

Aim for calculating stress intensity factor (short for SIF) of different position plates with eccentric crack, and the change tendency between different positions and SIF, the crack model is built by finite element software, and the SIF change tendency line with different width plates is got. It is seen from the von Mises stress cloud chart of ANSYS that the deformation of plate is effected by crack; as the center of crack is gradually close to the edge of plate, SIF is increasing. When the distance between the center and edge of crack is decreasing down to 3/8, SIF is increasing fiercely, that means, the plate at this time has already reached the edge of fracture. If continue loading the stretch, the crack will be apparent on the plate. And the curvature equation is got by index decay adapting.

Stress concentration factor expression for tension strip with eccentric elliptical hole

Two explicit expressions of the stress concentration factor for a tension finite-width strip with a central elliptical hole and an eccentric elliptical hole, respectively, are formulated by using a semi-analytical and semi-empirical method. Accuracy of the results obtained from these expressions is better, and application scope is wider, than the results of Durelli’s photo-elastic experiment and Isida’s formula. When eccentricity of the elliptical hole is within a certain range, the error is less than 8%. Based on the relation between the stress concentration factor and the stress intensity factor, a stress intensity factor expression for tension strips with a center or an eccentric crack is derived with the obtained stress concentration factor expressions. Compared with the existing formulae and the finite element analysis, this stress intensity factor expression also has sufficient accuracy.

Elastoplasticity of crack loaded by two pairs of isolated shear forces in finite width plate

The failure behavior of an elastic-perfectly plastic body with a crack loaded by two pairs of concentrated shear forces is discussed. The analytical solutions of an eccentric crack in a finite plate loaded by two pairs of point shear forces are obtained. It includes the unit normal vector of the elastic–plastic boundary near the crack line, the elastic–plastic stress fields near crack line and the law of the plastic zone along the crack line with external loads. The solutions of this paper are sufficiently precise near the crack line in elastic-perfectly plastic materials. Subsequently, the present results are compared with solutions based on the minimum strain energy density theory and elastic–plastic solutions under small scale yielding condition. On the basis of the minimum strain energy density (SED) theory, the minimum values of SED in the vicinity of the crack tip are determined, the initial growth orientation of crack are determined. It is found that the normalized load under large scale yielding condition is higher than those under small scale yielding condition when the length of the plastic zone is the same.

Elastic–plastic near field solution of an eccentric crack under shear in a finite width plate

The near crack line analysis method is used to investigate an eccentric crack loaded by shear forces in a finite width plate, and the analytical solution is obtained in this paper. The solution includes: the unit normal vector of the elastic–plastic boundary near the crack line, the elastic–plastic stress fields near crack line, variations of the length of the plastic zone along the crack line with an external loads, and the bearing capacity of a finite plate with a centric crack loaded by shear stress in the far field. The results obtained in this paper are sufficiently precise near the crack line because the assumptions of small scale yielding theory have not been made and no other assumptions have been taken. Subsequently, the present results are compared with the traditional line elastic fracture mechanical solutions and elastoplastic near field solutions under small scale yielding condition. On the basis of the minimum strain energy density (SED) theory, the minimum values of SED in the vicinity of the crack tip are determined, the initial growth orientation of crack are determined. It is found that the normalized load under large scale yielding condition is higher than those under small scale yielding condition when the length of the plastic zone is the same.

Elastoplastic solution for an eccentric crack loaded by two pairs of point tensile forces

The strain energy density theory and the near crack line analysis method are applied to investigate an eccentric crack loaded by two pairs of tensile point forces in a finite plate. The minimum values of SED in the vicinity of the crack tip are determined, the initial growth orientation of crack are determined. Obtained is the elastic–plastic solution near the crack line of an eccentric crack loaded by two pairs of point tensile forces under large scale yielding condition. More specifically, the near field solution contains the unit normal vector of the elastic–plastic boundary and the elastic–plastic stress field. The length of the plastic zone along the crack line is found to vary with the external load and the bearing capacity of a finite plate with an eccentric crack loaded by two pairs of tensile point forces. Compared with small scale yielding condition, the normalized load obtained is higher than those under small scale yielding condition when the length of the plastic zone is the same.

Dynamic propagation of a finite eccentric crack in a functionally graded piezoelectric ceramic strip

The dynamic propagation of an eccentric Griffith crack in a functionally graded piezoelectric ceramic strip under anti-plane shear is analyzed using the integral transform method. A constant velocity Yoffe-type moving crack is considered. Fourier transform is used to reduce the problem to a pair of dual integral equations, which is then expressed in a Fredholm integral equation of the second kind. We assume that the properties of the functionally graded piezoelectric material vary continuously along the thickness. The impermeable crack boundary condition is adopted. Numerical values on the dynamic stress intensity factors are presented for the functionally graded piezoelectric material to show the dependence of the gradient of material properties, crack moving velocity, and eccentricity. The dynamic stress intensity factors of a moving crack in functionally graded piezoelectric material increases when the crack moving velocity, eccentricity of crack location, material property gradient, and crack length increase.

Closed-form solution for an eccentric anti-plane shear crack normal to the edges of a magnetoelectroelastic strip

The problem of an anti-plane shear crack embedded in a magnetoelectroelastic strip is investigated. The crack is assumed to be normal to the strip edges. By using the finite Fourier transform, the associated mixed boundary-value problem is reduced to triple series equations, then to singular integral equations. Solving the resulting equations analytically, the field intensity factors and energy release rates at the crack tips can be determined in explicit form. The influences of applied electric and magnetic loadings on the normalized energy release rate and mechanical strain energy release rate are presented graphically. Obtained results reveal that applied electric and magnetic loadings affect crack growth, depending on their directions and adopted fracture criteria. The derived solution is applicable to other cases including two collinear cracks distributed symmetrically in a magnetoelectroelastic strip, and a periodic array of collinear cracks in a magnetoelectroelastic plane.

Mode III eccentric crack in a functionally graded piezoelectric strip

This paper studies the internal crack problem located within one functionally graded piezoelectric strip. One crack is normal to the edge of the strip and the material properties vary along the direction of crack length. Three different boundary conditions and both impermeable and permeable cases are discussed. The problem can be reduced to a system of singular integral equations and solved by using the Gauss–Chebyshev formulas. The results show that the edge boundary conditions and the nonhomogeneous parameter significantly control the magnitudes of stress and electric displacement intensity factors.