Multiple Interfacial Cracks Research Articles

Scattering of SH waves in a bi-material half space with a circular hole and periodic type III interfacial cracks

The dynamic anti-plane response of a bi-material half space including a circular hole and periodic interfacial cracks is investigated. An analytical model is established for periodic type III cracks that adopt the idea of “conjunction” modeling. The definite integral equations suitable for modeling the existence of multiple interfacial cracks are derived that satisfy the continuity conditions at the interface. Numerical calculations are carried out to find the dynamic stress concentration factor (DSCF), whose results indicate that the number of interfacial cracks has a significant effect on the dynamic stress concentration around the hole edge, especially for low-frequency incident SH waves.

Dynamic mode III stress intensity factors of multiple axisymmetric interfacial cracks in an FGM coated orthotropic layer

In the present study, mode III dynamic stress intensity factors (DSIFs) for the multiple axisymmetric interfacial cracks in an orthotropic layer with FGM orthotropic coating under transient torsional loading are formulated. It is assumed that the mass density and the shear modulus of the FGM orthotropic coating vary exponentially and power-law form along the thickness of the layer. At first, the solution for Somigliana-type dynamic rotational ring dislocation in the layer and its coating is obtained by using the Laplace and Hankel transforms. Then, the dislocation solution is used to derive a set of singular integral equations for a system of coaxial axisymmetric interfacial cracks, including penny-shaped and annular cracks. The integral equations are of Cauchy singular type, which are solved by Erdogan’s collocation method for dislocation density on the surface of interfacial crack and the results are used to determine DSIFs for axisymmetric interfacial cracks. Finally, several examples are provided to study the effects of the non-homogeneity constant, orthotropy parameter and thickness of FGM coating as well as the interaction of multiple interfacial cracks on the DSIFs.

Transient analysis of multiple interface cracks between two dissimilar functionally graded magneto-electro-elastic layers

In this paper, we examine the transient response of two bonded dissimilar functionally graded magneto-electro-elastic (MEE) layers with multiple interfacial cracks under magneto-electro-mechanical impacts. Material properties of the MEE layers are assumed to vary exponentially in the thickness direction of the layers. However, the rate of material properties gradation are different. First, the analytical solution is developed by considering a dynamic magneto-electro-elastic dislocation with time-dependent Burgers vector be situated at the interface of bonded layers by means of the Fourier and Laplace transform. The solutions are used to derive singular integral equations for the MEE layers containing interfacial cracks. Then, the integral equations are solved numerically for the density of dislocations on a crack surface. The dislocation densities are employed to determine the field intensity factors and the dynamic energy release rate. The effects of crack spacing and FGM exponent as well as crack interaction are studied.

Multiple interfacial cracks in dissimilar piezoelectric layers under time harmonic loadings

AbstractIn this study, the dislocation‐based model is developed to study the interaction between time‐harmonic elastic waves and multiple interface cracks in 2 bonded dissimilar piezoelectric layers. In this model, cracks are represented by a distribution of so‐called electro‐elastic dislocations whose density is to be determined by satisfying the boundary conditions. Using the Fourier transform, this formulation leads to 2 singular integral equations, which can be solved numerically for the densities of electro‐elastic dislocations on a crack surface. The formulation is used to determine dynamic field intensity factors for multiple interface cracks without limitation of number of cracks. The dynamic field intensity factors are then calculated for both permeable and impermeable crack, and finally, numerical results are presented to illustrate the variation of these quantities with the electromechanical coupling, crack spacing, and the frequency of loading.

Transient response of dissimilar piezoelectric layers with multiple interacting interface cracks

In this study, we examine the dynamic behavior of two bonded dissimilar piezoelectric layers containing multiple interfacial cracks subjected to electro-mechanical impact loading. The problem was formulated through Fourier transformation into singular integral equations in which the unknown variables are the jumps of displacement and electric potential across the crack surface in the Laplace transform domain. The resulting integral equations together with the corresponding single-valued conditions are solved numerically for the densities of electro-elastic dislocations on a crack surface. The dynamic field intensity factors and dynamic energy release rate (DERR) history are obtained for both permeable and impermeable crack. The stress field is also obtained for the interface crack under impact loads. The results show that the field intensity factors at the crack tips and dynamic energy release rate depend on the interfacial crack geometry, electromechanical coupling and the electric boundary conditions on the crack surface.

Multiple interfacial cracks in a bi-layered multiferroic composite under magnetostriction or electrostriction

The purpose of the present paper is to investigate the problem of interfacial fracture in a multiferroic composite under magnetostriction or electrostriction. Methods of distributed interfacial dislocations, Green’s function and Cauchy singular integral equations are employed to solve the problem of multiple cracks on the interface. Numerical results of the fracture parameter are discussed, and the magnetostrictive or electrostrictive interfacial fracture is explained via the physical phenomena of “active/passive deformation”, “magneto/electro-mechanical coupling” and “piezomagnetic/piezoelectric stiffening”.

Fracture Analysis of Bounded Magnetoelectroelastic Layers with Interfacial Cracks under Magnetoelectromechanical Loads: Plane Problem

Fracture behaviors of multiple interfacial cracks between dissimilar magnetoelectroelastic layers subjected to in-plane magnetoelectromechanical loads are investigated by using integral transform method and singular integral equation technique. The number of the interfacial cracks is arbitrary, and the crack surfaces are assumed to be magnetoelectrically impermeable. The field intensity factors including stress, electric displacement and magnetic induction intensity factors as well as the energy release rates (ERRs) are derived. The effects of loading combinations, crack configurations and material property parameters on the fracture behaviors are evaluated according to energy release rate criterion. Numerical results show that both negative electrical and magnetic loads inhibit crack extension, and that the material constants have different and important effects on the ERRs. The results presented here should have potential applications to the design of multilayered magnetoelectroelastic structures.

Analysis of multiple interfacial cracks in an orthotropic bi-material subjected to anti-plane shear loading

The present work concerns with the elasto-static problem of double interfacial cracks located between two dissimilar orthotropic plates. The dimensions of the bi-material composite, are assumed to be finite. The crack faces are subjected to anti-plane shear traction. Finite Fourier transforms are applied to reduce the problem to a triple series equations, and then to a system of singular integral equations with Cauchy type singularity. That are solved numerically using Gauss–Chebyshev integration formulae. The stress intensity factors, are determined in a closed form expressions. The obtained results agreed with the previous analytical ones. Further, a parametric study is introduced to investigate the effects of the geometric and elastic characteristics of the composite on the values of the stress intensity factors.

Analysis of multiple interfacial cracks in three-dimensional bimaterials using hypersingular integro-differential equation method

By using the concept of finite-part integral, a set of hypersingular integro-differential equations for multiple interfacial cracks in a three-dimensional infinite bimaterial subjected to arbitrary loads is derived. In the numerical analysis, unknown displacement discontinuities are approximated with the products of the fundamental density functions and power series. The fundamental functions are chosen to express a two-dimensional interface crack rigorously. As illustrative examples, the stress intensity factors for two rectangular interface cracks are calculated for various spacing, crack shape and elastic constants. It is shown that the stress intensity factors decrease with the crack spacing.

An efficient approach for the numerical inversion of Laplace transform and its application in dynamic fracture analysis of a piezoelectric laminate

A numerical method is developed for the inversion of Laplace transform, and its accuracy is shown through examples. As an application of the method, the transient analysis of a piezoelectric laminate with multiple interfacial cracks is performed. Both the permeable and impermeable boundary conditions are discussed. The solution procedures are based on the use of integral transforms, singular integral equations and Chebyshev polynomial expansions. Numerical results are provided to show the effect of crack geometry, applied electric fields, electric boundary conditions along the crack faces and the wave fronts of incident waves or the reflecting waves from surface boundaries on the resulting dynamic stress intensity factor and electric displacement intensity factor.

Fatigue voids and their significance

ABSTRACT Fractures from tests on 2014‐T6511 and 2024‐T3 test coupons under specially designed programmed loading reveal voids with distinct fatigue markings. These ‘fatigue voids’ appear to form as a consequence of the separation of noncoherent secondary particulates from the matrix in early fatigue. The process of their formation is through the initiation, growth and coalescence of multiple interfacial cracks around the particulate. Such voids become visible on the fatigue fracture surface if and when the crack front advances through them. In vacuum, each fatigue void is the potential initiator of an embedded penny‐shaped crack. The one closest to the specimen surface is likely to become the dominant crack, indicating that fatigue voids appear to be the likely origins of the dominant crack in vacuum. In air, the dominant crack forms at the notch surface and grows much faster, giving less opportunity for multiple internal cracks to spawn off from the innumerable internal fatigue‐voids. Thus in air, fatigue voids do not appear to affect the fatigue process at low and intermediate growth rates. At high crack growth rates involving considerable crack tip shear, slip planes with particulate concentration offer the path of least resistance. This explains the increasing density of fatigue voids with growth rate. Very high growth rates signal the onset of a quasi‐static crack growth component that manifests itself through growing clusters of microvoid coalescence associated with static fracture. Fatigue voids are likely to form in other Al‐alloys with secondary noncoherent particulates. They have nothing in common with microvoids associated with ductile fracture.