Stress-intensity factors for 3-D dynamic loading of a cracked half-space

A mixed mode crack problem in functionally graded materials is formulated to a system of Cauchy singular Fredholm integral equations, then the system is solved by the singular integral equation method (SIEM). This specific crack problem has already been solved by N. Konda and F. Erdogan (Konda & Erdogan 1994). However, many mathematical details have been left out. In this paper we provide a detailed derivation, both analytical and numerical, on the formulation as well as the solution to the system of singular Fredholm integral equations. The research results include crack displacement profiles and stress intensity factors for both mode I and mode II, and the outcomes are consistent with the paper by Konda & Erdogan (Konda & Erdogan 1994).

Fracture analysis of a cracked orthotropic strip bonded to a magneto-electro-elastic layer

The problem of a kinked crack is analysed for the most general case of elastic anisotropy. The kinked crack is modelled by means of continuous distributions of dislocations which are assumed to be singular both at the crack tips and at the kink vertex. The resulting system of singular integral equations is solved numerically using Chebyshev polynomials and the reciprocal theorem. The stress intensity factors for modes I, II and III and the generalised stress intensity factor at the vertex are obtained directly from the dislocation densities.

The processes of reflection of three-dimensional electromagnetic waves by locally irregular media interfaces are investigated. The boundary value problem for the system of Maxwell equations in an infinite half-space is reduced to the solution of two systems of singular integral equations. To construct a numerical algorithm for solving these systems of singular integral equations, the approximation and collocation method is used. Special attention is focused on calculation of the kernels of these equations. Solutions of systems of singular integral equations are used to calculated the far-field pattern for the scattered field in the far zone.

This paper investigates the theimoelectromechanical interaction among multi parallel cracks in a piezoelectric material under a uniform heat flow and a uniform mechanical load far away from the crack region The crack faces are supposed to be insulated thermally and electrically. By using the Fourier transform, the thermal and electromechanical problems are reduced to systems of singular integral equations, respectively. The singular integral equations are solved numerically by using the Gauss-Jacobi integration formula. Numerical calculations are carried out, and detailed results are presented to illustrate the influence of the thermoelectromechanical interaction on the stress and electric displacement intensity factors. The temperature-stress distributions are also presented. From numerical results, we can find that the normalized stress and electric displacement intensity factors are under the great influence of the crack spacing and the number of cracks. Especially, the influence of the thermoelectromechanical interaction on the fracture behavior is complicated when the crack spacing becomes small.

This paper investigates the thermoelectromechanical interaction among multi parallel axisymmetric cracks in a piezoelectric material under a uniform heat flow far away from the crack region. The crack faces are supposed to be insulated thermally and electrically. By using the Hankel transform, the thermal and electromechanical problems are reduced to systems of singular integral equations, respectively. The singular integral equations are solved numerically by using the Gauss-Jacobi integration formula. Numerical calculations are carried out, and detailed results are presented to illustrate the influence of the thermoelectromechanical interaction on the stress and electric displacement intensity factors. From numerical results, we can find that the normalized stress and electric displacement intensity factors are under the great influence of the crack spacing and the number of cracks. Especially, the influence of the thermoelectromechanical interaction on the fracture behavior is complicated when the crack spacing becomes small.

This paper presents an automatic fatigue crack propagation solution for particulate-reinforced composites. In this solution, the Eshelby’s equivalent inclusion method is used to solve the elastic fields of a two-dimensional plane containing multiple elliptical inclusions. Then the continuous distributed dislocations in an infinite plane are adopted to model the multiple cracks in the plane containing multiple elliptical inclusions. By combining the two methods, a system of singular integral equations can be formulated based on the stress condition of the cracks. The stress intensity factor of each crack can be obtained by solving the singular integral equations. The propagation of the cracks is studied based on the maximum circumferential stress criterion. Numerical examples are presented to show the complicated changes in the stress intensity factors and crack growth behaviors of the cracks affected by the inclusions.

An essential part of describing the damage state and predicting the damage growth in a multicracked plate is the accurate calculation of stress intensity factors (SIF). Here, a methodology and rigorous solution formulation for SIF of a multicracked plate, with fully interacting cracks, subjected to a far-field arbitrary stress state is presented. The fundamental perturbation problem is derived, and the steps needed to formulate the system of singular integral equations whose solution gives rise to the evaluation of the SIF are identified. This analytical derivation and numerical solution are obtained by using intelligent application of symbolic computations and automatic FORTRAN generation capabilities in form of symbolic/FORTRAN package, named SYMFRAC, that is capable of providing accurate SIF at each crack tip. The accuracy of the results has been validated for the two parallel interacting crack problem. Limits and sensitivity of the results for the problem of a horizontal notch interacting with ten microcracks have been analyzed.

An analytical solution to the fracture analysis of a functionally graded (FG) orthotropic substrate with FG piezoelectric coating weakened by a screw dislocation is carried out. The material properties are assumed to vary exponentially through the thickness of the layers. The problem is solved under various types of anti-plane shear and in-plane electric loadings. At first, by considering a single-screw dislocation at crack location, an analytical solution is developed. Next, by using the Fourier transform, the problem is reduced to a system of singular integral equations with Cauchy-type singularities. Then, by computing the dislocation densities, both the stress intensity factors and the stress fields at the crack tips under different electromechanical loadings are determined. In this investigation, various examples are solved to show the applicability of the proposed solution by studying the effects of the cracks configurations, material properties, and non-homogeneity parameter on the stress intensity factors.

The thermoelectromechanical fracture of a piezoelectric material strip with two parallel cracks of different lengths under electric and thermal loadings is considered. The crack faces are supposed to be insulated thermally and electrically. Fourier transform techniques are used to reduce the mixed boundary value problems to two systems of singular integral equations. The singular integral equations are solved by using the Gauss-Jacobi integration formula. Numerical calculations are carried out, and detailed results are presented to illustrate the influence of the parameters of the geometric parameters on the stress and electric displacement intensity factors.

This paper considers the crack problem for a semi‐infinite plate subjected to a thermal shock by using hyperbolic heat conduction equations and equations of motion. The Laplace transform and Fourier transform are used to reduce the problem to a system of singular integral equations which are solved numerically. Numerical results are presented illustrating the influence of non‐Fourier effect and inertia effect on the stress intensity factor and normalized crack opening displacements. The results show that the stress intensity factors have higher amplitude and an oscillating feature comparing to those obtained under the conventional Fourier thermal conduction condition and quasi‐static hypothesis. These results can help understand the crack behaviors of advanced materials under thermal impact loading.

may be reduced to a single linear integral equation whose kernel is defined on a?x ? a+n(b-a), a_s <a+n(b-a). Greggi? considered a system of the form (1) and by use of the transformation introduced by Fredholm showed the form of the resolvent matrix for the system; for the symmetric system where KKj(x; s) = Ksi(s; x) (i, j = 1, 2, , n) he also stated theorems analogous to those proved by Schmidtll for a single integral equation with symmetric kernel. System (1) also comes under the class of systems treated by Platrier.? Weatherburn** has treated the system (1) without using the transformation introduced by Fredholm, but by vector method throughout. He states all results for the case n = 3, but his method of procedure is equally applicable to the general case. In the present paper a special system of the form (1), to which is applied the term self-adjoint, is considered and the existence of a countable infinity of real characteristic numbers is established, together with expansion theorems in terms of the characteristic solutions of the system of integral equations. A definitely self-adjoint system of integral equations includes as a special case the symmetric system with closed matrix kernel. It also includes the system of integral equations to which a boundary value problem for a system of ordinary linear differential equations of the first order which

Axisymmetric dynamic contact problem for a viscoelastic half-space in the presence of adhesion under the stamp: PMM vol. 37, n≗4, 1973, pp. 731–738

A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analogy have direct applications in various areas of physics and biology. In particular, scalar and vector equations of this nature are encountered in the dynamic theory of p-adic strings, in the theory of radiative transfer, in the kinetic theory of gases, and in the mathematical theory of the spread of epidemic diseases. A constructive theorem of existence in the space of continuous and bounded vector functions is proved. The integral asymptotic of the constructed solution is studied. An effective iterative process for constructing an approximate solution to this system is proposed. In a certain class of bounded vector functions, the uniqueness of the solution is proved. In the class of bounded vector functions (with non-negative coordinates) with a zero limit at infinity, the absence of an identically zero solution is proved. Examples of the matrix kernel and nonlinearities are given to illustrate the importance of the obtained results. Some of the examples have applications in the above-mentioned branches of natural science.

In this article, we discuss the solvability of infinite systems of singular integral equations of two variables in the Banach sequence spaces C(I ? I, ?p) with I = [0, T], T &gt; 0 and 1 &lt; p &lt; ? with the help of Meir-Keeler condensing operators and Hausdorff measure of noncompactness. With an example, we illustrate our findings.