Definition Of Stress Intensity Factors Research Articles

Unified definition of stress intensity factors at a sharp three-dimensional jointed corner

Unified definition of stress intensity factors at a sharp three-dimensional jointed corner

Thermal fracture of cracked cylinders associated with nonclassical heat conduction: The effect of material property

ABSTRACTThe thermoelastic problem of a transversely isotropic hollow cylinder containing a circumferential crack is investigated in the present article based on the non-Fourier heat conduction theory. The temperature and stress fields are obtained by solving the coupled partial differential equations in the Laplace domain, and corresponding thermal axial stress with minus sign is then applied to the crack surface to form a mode I crack problem. Three different kinds of crack are considered, and the singular integral equation method is adopted to solve the fracture problem. Finally, with the definition of stress intensity factor, the effect of material properties, coupling parameter, and crack geometry on the hyperbolic thermal fracture responses of a transversely isotropic hollow cylinder excited by a thermal loading is visualized.

Investigation of the stress intensity factors for interface corners

From the viewpoint of linear elastic fracture mechanics, the stress intensity factor is an important parameter denoting the magnitude of stress singularity. If the singular order is a single real value, no ambiguity or inconsistency occurs about the definitions of the stress intensity factors such as the singular order 0.5 for a crack in homogeneous materials. Since the singular order of general interface corners may be real or complex, distinct or repeated, the definitions proposed in the literature may not be consistent with each other. Due to the inconsistency of the definitions and units, a direct comparison of the magnitude of the stress intensity factors for different interface corners is meaningless. Thus, the fracture toughness or fracture criterion established for a certain interface corners (e.g. a crack specimen) cannot be applied directly to the other interface corners. In order to build a direct connection among all general interface corners (including cracks and interface cracks), some unified definitions of stress intensity factors were proposed in the literature. Based upon the analytical near tip solutions of singular stresses, a new unified definition valid for almost all possible interface corners is proposed in this paper. To calculate this newly defined stress intensity factor accurately and efficiently, the path-independent H-integral is used and a relation between the H-integral and the stress intensity factors is also derived. The comparison and discussion between the present definition and those proposed in the literature are then presented through some analytical relations and numerical examples.

Matrix form near tip solutions of interface corners

In this paper, the stresses near the tip of interface corners are expressed in matrix power function form. To make this matrix power function form valid for all possible cases of interface corners, all kinds of singularities including oscillatory and logarithmic singularity are discussed in this paper. The coefficient vector of this matrix power function form solution is then defined as a vector of stress intensity factors along the radial direction. Since the stress intensity factors are functions of radial direction, the maximum stress intensity factor of a certain radial direction may be useful for the fracture prediction of interface corners. This new definition of stress intensity factors is applicable for all possible singular orders—repeated or distinct, real or complex, and keeps the same unit for all possible interface corners. Therefore, it will be helpful for bridging the problems of cracks, corners, interface cracks and interface corners. Finally, the matrix form solutions are reduced to the scalar form solutions for two special cases. One is a special case of corner angles—cracks, and the other is a special case of anisotropic materials—isotropic materials. Through this reduction, new scalar form analytical solutions are obtained and specialized further to compare with the existing analytical solutions.

Interface corners in piezoelectric materials

Through proper arrangement, the constitutive law, strain-displacement relation and equilibrium equation of piezoelectric materials can be written in the same mathematical form as those of elastic materials and hence Stroh formalism can be extended for piezoelectric analysis. Based on this viewpoint, the authors’ previous works for fracture analysis of anisotropic elastic materials, e.g. the eigen-relation for determining singular orders, the near-tip solutions, and the unified definition of stress intensity factors for interface corners, can also be applied to piezoelectric materials. In this paper, the theoretical framework of our previous works is briefly introduced, and then an efficient and accurate computing method (H-integral) and its required auxiliary solutions are derived for extracting the stress/electric intensity factors of interface corners made up of piezoelectric materials. This theoretical framework and H-integral form a universal solution technique that is valid for the fracture analysis of cracks, corners, interface cracks, and interface corners. Besides, the special cases that suggest how we simulate elastic insulators/conductors from piezoelectric materials are discussed. Several numerical examples are dealt with to display the feasibility and applicability of the proposed approaches, and finally, a numerical example which exhibits how the electric load influences the fracture behavior is also studied.

Comments on the evaluation of the stress intensity factor for a general re-entrant corner in anisotropic bi-materials

This paper illustrates an efficient contour integral procedure to obtain stress intensity factors in combination of the asymptotic analysis with finite element analysis. Note that this set-up is very general: the material can be anisotropic elastic, and the specimen can be built as a bi-material system, notches of arbitrary opening angle can be analyzed ( γ = 0 → crack, γ = 180° → free edge). The purpose of this technical note is to comment on three issues in the notch mechanics: the interpretation of the eigenvalue equation, the definition of stress intensity factors, and the effect of the outer contour location on H-integral evaluations.

Method to calculate stress intensity factor of V-notch in bi-materials

Based on Zak's stress function, the eigen-equation of stress singularity of bi-materials with a V-notch was obtained. A new definition of stress intensity factor for a perpendicular inter-facial V-notch of bi-material was put forward. The effects of shear modulus and Poisson's ratio of the matrix material and attaching material on eigen-values were analyzed. A generalized expression for calculating K I of the perpendicular V-notch of bi-materials was obtained by means of stress extrapolation. Effects of notch depth, notch angle and Poisson's ratio of materials on the singular stress field near the tip of the V-notch were analyzed systematically with numerical simulations. As an example, a finite plate with double edge notches under uniaxial uniform tension was calculated by the method presented and the influence of the notch angle and Poisson's ratio on the stress singularity near the tip of notch was obtained.

Application of Finite-Part Integrals to Planar Interfacial Fracture Problems in Three-Dimensional Bimaterials

This paper deals with linear elastic fracture problems for a planar crack on an interface between two dissimilar elastic half-space solids bonded together. The finite-part integral concept is used to derive hypersingular integro-differential equations for the interfacial crack from the point-force solutions for a bimaterial space. Investigations on the singularities and the singular stress fields in the vicinity of the crack are made by the dominant-part analysis of the two-dimensional hypersingular integrals. Thereafter the stress intensity factor K-fields and the energy release rate G are exactly obtained by using the definitions of stress intensity factors and the principle of virtual work, respectively. The results show that, unlike the homogenous case, the asymptotic fields always consist of all three modes of fracture. Finally, some numerical examples of various aspects of elliptical cracks subjected to constant pressures are given.

破壊力学 実用的界面き裂応力拡大係数の新定義

破壊力学 実用的界面き裂応力拡大係数の新定義

Energy release rate for a dynamically growing crack at the interface of dissimilar isotropic materials

The strain energy release rate for a crack at the interface of dissimilar isotropic materials was derived from an existing crack tip field. In the derivation, the J-integral along a special near tip contour was used. A single expression of the strain energy release rate corresponding to different definitions of stress intensity factors was obtained. The validity of the general expression was discussed.

Stress Intensity Factors for Interface Crack between Dissimilar Orthotropic Materials. The Case Where Principal Axes Are Not Aligned with the Interface.

In this study, stress and displacement fields at the interface crack tip between dissimilar orthotropic materials are presented for the case where the principal axes of orthotropic materials are not aligned with the interface, based on the orthotropic elasticity theory. The correct form of the definition of stress intensity factors for the interface crack is clarified. This definition is consistent with that of orthotropic material and also of dissimilar isotropic materials. The extrapolation method to determine the stress intensity factors by numerical analysis is proposed based on this definition. Some interface cracks in a finite plate of dissimilar orthotropic materials are analyzed by BEM and the stress intensity factors are presented.

Interfacial dislocation and its applications to interface cracks in anisotropic bimaterials

Interfacial dislocations and cracks in anisotropic bimaterials are considered. The displacement and the stress fields due to an interfacial dislocation are obtained in a real and simple form. Explicit solutions to the traction along the interface and the crack opening displacement for a Griffith interface crack are derived. Possible definitions of stress intensity factors are given which reduce to the classical definition for a crack in a homogeneous medium. It is found that a planar interface between dissimilar anisotropic solids is completely characterized by no more than 9 independent parameters. Some invariant properties of the dislocation and crack solutions under coordinate transformation are also discussed.