Analysis Of Interaction Between InterfaceCracks And Internal Cracks Using SingularIntegral Equations Of The Body Force Method (original) (raw)
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Stress Intensity Factors of an Interface Crack under Polynomial Distribution of Stress
Journal of Solid Mechanics and Materials Engineering, 2010
In this paper, stress intensity factors for a two-dimensional interface crack under polynomial distribution of stress are considered. The problem is formulated as a system of hypersingular integral equations on the idea of the body force method. In this analysis, unknown body force densities are approximated by the products of the fundamental densities and power series; here the fundamental densities are chosen to express singular stress fields due to an interface crack under constant distribution of stress exactly. The stress intensity factors of a 2D interfacial crack under polynomial distribution of stress are expressed as formulas for the reader's convenience with the varying polynomial exponent n. The exact expressions of crack opening displacements are also indicated.
STRESS SINGULARITY ANALYSIS IN INTERFACE CRACK PROBLEMS FOR COMPOSITE STRUCTURES
We investigate three-dimensional interface crack problems (ICP) for metallic-piezoelectric composite bodies with regard to thermal effects. We give a mathematical formulation of the physical problem when the metallic and piezoelectric bodies are bonded along some proper parts of their boundaries where interface cracks occur. By potential methods the ICP is reduced to an equivalent strongly elliptic system of pseudodifferential equations on manifolds with boundary. We study the solvability of this system in different function spaces and prove uniqueness and existence theorems for the original ICP. We analyse the regularity properties of the corresponding thermo-mechanical and electric fields near the crack edges and near the curves where the different boundary conditions collide. In particular, we characterize the stress singularity exponents and show that they can be explicitly calculated with the help of the principal homogeneous symbol matrices of the corresponding pseudodifferential operators. We expose some numerical calculations which demonstrate that the stress singularity exponents depend on the material parameters essentially.
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UDC 539.3 We develop a method for the solution of two-dimensional dynamic problems of the theory of elasticity for infinite bodies with smooth curvilinear cracks combining a modified method of finite differences in time with the method of singular integrodifferential equations in the space variables. Integral representations of the wave potentials are constructed and used to reduce the first boundary-value problem to the solution of systems of integrodifferential equations by the method of mechanical quadratures. The time dependences of the computed dynamic stress intensity factors at the tips of a rectilinear crack are analyzed for various impact and pulsed loads acting upon the crack lips.
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Acta Mechanica Solida Sinica, 2012
In this paper interfacial edge crack problems are considered by the application of the finite element method. The stress intensity factors are accurately determined from the ratio of crack-tip-stress value between the target given unknown and reference problems. The reference problem is chosen to produce the singular stress fields proportional to the ones of the given unknown problem. Here the original proportional method is improved through utilizing very refined meshes and post-processing technique of linear extrapolation. The results for a double-edge interface crack in a bonded strip are newly obtained and compared with the ones of a single-edge interface crack for various material combinations. It is found that the stress intensity factors should be compared in the three different zones of relative crack lengths. Differently from the case of a cracked homogenous strip, the results for the double edge interface cracks are found to possibly be bigger than those for a single edge interface crack under the same relative crack length.
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In the present article the problem for composite (piece-wise homogeneous) body weakened by crack when the crack intersect an interface or penetrate it at rectangular angle is studied. The problem is reduced to the singular integral equation (when crack spreads to the interface) and system of singular integral equations (when crack intersects the interface) with respect to the unknown characteristic function of disclosing of cracks containing an immovable singularity. First time behavior of solutions in the neighborhood of the crack endpoints is studied by a method of discrete singularity in the both uniform, and non-uniformly cases of the knots arrangement. A general scheme of the approximate solution of the task by collocation method is presented. Some results of numerical investigations are presented. Key-Words: Crack, composite body, singular integral equations, collocation method
Engineering Analysis With Boundary Elements, 2003
This paper attempts to answer the commonly raised question: what are the parameters controlling the solution accuracy and stability when the hyper-singular traction boundary-integral equations (BIEs) are used for the dynamic (time-harmonic) linear elastic fracture analysis of a finite cracked structure.The usage of the traction BIEs together with the parabolic discretization mesh leads to hyper-singularity, when the crack lies on the boundary, even after application of a regularization procedure. In this paper two new ways, average method and shifted point method to overcome this difficulty, are proposed and compared. It is shown by numerical experiments on the examples of a cracked rectangular plate and of a cracked infinite plane that the accuracy and the convergence of the method solution depends mainly on the smoothness requirements of the solution at all collocation points.
Numerical Solution for Crack Phenomenon in Dissimilar Materials under Various Mechanical Loadings
Symmetry
A new mathematical model is developed for the analytical study of two cracks in the upper plane of dissimilar materials under various mechanical loadings, i.e., shear, normal, tearing and mixed stresses with different geometry conditions. This problem is developed into a new mathematical model of hypersingular integral equations (HSIEs) by using the modified complex potentials (MCPs) function and the continuity conditions of the resultant force and displacement with the crack opening displacement (COD) function as the unknown. The newly obtained mathematical model of HSIEs are solved numerically by utilizing the appropriate quadrature formulas. Numerical computations and graphical demonstrations are carried out to observe the profound effect of the elastic constants ratio, mode of stresses and geometry conditions on the dimensionless stress intensity factors (SIFs) at the crack tips.
International Journal of Engineering Science, 1975
Closed form expression\ are obtained for the \tres\es at a crack tip when a crack is approaching a welded boundary (or a free surface) and when it has just passed through the interface. The solutions which are obtained in terms of a small pxameter. the distance from or through the interface. are given in explicit form for the mode 3 situation and for \ome mode I and 2 ca\es. The importance of the change of stress singularity when the crack meet\ the interface i\ demon\tr;ttrd. On the stress intensity factory x~ociated with cracks 491
International Journal of Solids and Structures, 2011
A boundary element formulation is developed to determine the complex stress intensity factors associated with cracks on the interface between dissimilar materials. This represents an extension of the methodology developed previously by the authors for determination of free-edge generalized stress intensity factors on bi-material interfaces, which employs displacements and weighted tractions as primary variables. However, in the present work, the characteristic oscillating stress singularity is addressed through the introduction of complex weighting functions for both displacements and tractions, along with corresponding non-standard numerical quadrature formulas. As a result, this boundary-only approach provides extremely accurate meshindependent solutions for a range of two-dimensional interface crack problems. A number of computational examples are considered to assess the performance of the method in comparison with analytical solutions and previous work on the subject. As a final application, the method is applied to study the scaling behavior of epoxy-metal butt joints.