Axial cracks in pressurised eroded autofrettaged thick cylinders

In this paper, the stress intensity factors associated with longitudinal axial cracks in pressurised autofrettaged thick cylinders are calculated using the Boundary Element (BE) method. The effect on the stress intensity factors of the presence of a semi-circular erosion on the bore is investigated. Two loading cases are considered; internal pressure and autofrettage residual stresses. The residual stresses are incorporated by using a crack face loading based on the principle of superposition. The effect of the erosions and cracks on the fatigue lifetimes is calculated using the Paris law.     

STRESS INTENSITY FACTOR EXPRESSIONS FOR REGULAR CRACK ARRAYS IN PRESSURISED CYLINDERS

Arrays of radial cracks are sometimes observed at the bore of pressurised cylinders. The stress intensity factors of closely spaced regular arrays of edge cracks depends primarily on the crack spacing and are approximately proportional to the square root of crack spacing for crack length to spacing ratios down to 0.16. A stress intensity factor expression for this range of spacing ratios and of engineering accuracy has been developed for a large regular array of radial cracks at the bore of a pressurised cylinde. For smaller spacing ratios the stress intensity factor depends on crack length than crack spacing and a complementary expression has been developed.     

Stress intensity factors for cracks emanating from a triangular or square hole in an infinite plate by boundary elements

This paper concerns stress intensity factors of cracks emanating from a triangular or square hole in an infinite plate subjected to internal pressure calculated by means of a boundary element method, which consists of constant displacement discontinuity element presented by Crouch and Starfied and crack tip displacement discontinuity elements proposed by the author. In the boundary element implementation the left or the right crack tip displacement discontinuity element is placed locally at corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Numerical examples are included to show that the method is very efficient and accurate for calculating stress intensity factors of plane elasticity crack problems. Specifically, the numerical results of stress intensity factors of cracks emanating from a triangular or square hole in an infinite plate subjected to internal pressure are given.     

Stress intensity factors for cracks in thin plates

This paper presents stress intensity factor solutions for several crack configurations in plates. The loadings considered include internal pressure, and also combined bending and tension. The dual boundary element method is used to model the plate and mixed mode stress intensity factors are evaluated by a crack surface displacement extrapolation technique and the J-integral technique. Several cases including centre crack, edge crack and cracks emanating from a hole in finite width plates are presented.     

Crack interaction in an infinite elastic strip

The problem considers an arbitrary number of colinear and unequal size Griffith cracks opened by a non-uniform internal pressure in an infinite elastic strip. The cracks are located halfway between and parallel to the surfaces of the 2-dimensional medium. By appropriate integral transformations the mixed boundary value problem is reduced to singular integral equations. The stress intensity factors, crack openings and crack energies are then determined for many different cases.     

Computation of shear mode weight functions for circular and elliptical cracks

Three-dimensional shear mode fundamental fields in finite bodies with mixed boundary conditions are analyzed by a special finite element method for circular and elliptical cracks. A procedure for determining the Fourier coefficients of the stress intensity factor for circular cracks is presented. A special series is proposed to represent the computed crack face weight functions for elliptical cracks.     

Stress intensity factors for cracks of arbitrary shape near an interfacial boundary

Modes I, II and III stress intensity factors for a crack of arbitrary planar shape near a bimaterial interface are calculated. The solution utilizes the body-force method and requires Green's functions for perfectly bonded elastic half-spaces. The formulation leads to a system of two-dimensional singular integral equations whose solutions represent the three modes of crack opening displacement. Numerical examples of a semicircular or semielliptical crack terminating at the interface and circular or elliptical cracks contained in one material are given for both internal pressure and farfield tension.     

Stress intensity factors for fatigue cracking of round bars

The stress intensity factor for a single edge crack of either straight or circular front in a round bar has been determined using both the degenerated quarter-point isoparametric finite element and experimental fatigue crack growth data, and compared with values found by earlier investigators.The results of this study confirm that the stress intensity factors for straight edged surface cracks are lower in round bars than in square bars and a comparison of finite element and experimental results indicates that the effective stress intensity factor at the centre of the fatigue crack front in a round bar is 17% greater than its theoretical value.A correction function is proposed to account for the effect on the stress intensity factor of the circular boundary of a round bar.     

Evaluation of dynamic crack instability criteria

Previously proposed dynamic crack instability criteria are reviewed. The conditions of crack length, pulse amplitude, and pulse duration predicted by each criterion for crack instability under stress wave loads are presented and compared. To discriminate among these criteria, a data base was generated by performing plate impact experiments on epoxy specimens embedded with thin circular disks that acted as internal penny-shaped cracks. The observed instability behavior of these cracks under 2-µs stress pulses of various amplitudes was best described by a criterion that requires the dynamic stress intensity to exceed the dynamic fracture toughness for a certain minimum time.     

Elastic analysis for a radial crack in a circular ring

The plane elastic problem corresponding to a radial crack emanating from the internal boundary of a circular ring is considered. Uniform external tension on the outer boundary is chosen as the applied load. The stress intensity factors at the crack tip are found by using the recently derived ‘modified mappingcollocation’ technique. Accurate data are found for varying crack depths over a representative range of wall ratios for fracture mechanics applications to pressurized hollow circular cylinders.     

裂纹面荷载作用下多裂纹应力强度因子计算

该文基于比例边界有限元法计算了裂纹面荷载作用下平面多裂纹应力强度因子.比例边界有限元法可以给出裂纹尖端位移场和应力场的解析表达式,该特点可以使应力强度因子根据定义直接计算,同时不需要对裂纹尖端进行特殊处理.联合子结构技术可以计算多裂纹问题的应力强度因子.数值算例表明该文方法是有效且高精确的,进而推广了比例边界有限元法的...     

Cracks emanating from a rhombus hole in infinite and finite plate subjected to internal pressure

This note deals with the stress intensity factors (SIFs) of cracks emanating from a rhombus hole in a rectangular plate subjected to internal pressure by means of the displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author. Moreover, an empirical formula of the SIFs of the crack problem is presented and examined. It is found that the empirical formula is very accurate for evaluating the SIFs of the crack problem.     

The effect of stringers and patches on the stress intensities around cracks in plates

In the present paper a method was developed to study a certain important class of mixed boundary value problems concerning the interaction between a reinforced isotropic and linearly elastic thin plate by rectilinear and curvilinear thin strip inclusions (stringers), and superimposed elastic thin sheets (patches) perfectly bonded to the plate along their peripheries, and the internal cracks existing in the plate. The method is based on the complex stress function and the singular integral equations theories. An exact expression for the complex stress function was given for the most general case. The method was applied with success to an example of a superimposed circular patch on an internal crack existing in a thin plate. The variation of the stress intensity factors at the tips of the internal crack in terms of its relative position with respect to the patch-centre, as well as, of the relative elastic properties of the patch and the plate, was determined numerically.     

Multiple-cracked fatigue crack growth by BEM

The dual boundary element method is applied for the two-dimensional linear elastic analysis of fatigue problem of multiple-cracked body. The traction integral equation is applied on ones of surfaces of cracks while the usual displacement integral equation simultaneously on the others. General multiple crack growth problem is solved in a single-region formulation. All crack surfaces are discretized with discontinuous quadratic boundary elements. J-integral technique is used to evaluate stress intensity factors. The real extension path of cracks is simulated by a linear incremental crack extension, based on the maximum principal stress criterion. For each increment analysis of the cracks, crack extension is conveniently modelled with new boundary elements. Remeshing is no longer necessary. Fatigue life analysis is carried out with Paris' formulae. Several numerical examples show high efficiency of present method.     

Boundary integral equation method to solve embedded planar crack problems under shear loading

The solution of three-dimensional planar cracks under shear loading are investigated by the boundary integral equation method. A system of two hypersingular integral equations of a three-dimensional elastic solid with an embedded planar crack are given. The solution of the boundary integral equations is succeeded taking into consideration an appropriate Gauss quadrature rule for finite part integrals which is suitable for the numerical treatment of any plane crack without a polygonal contour shape and permit the fast convergence for the results. The stress intensity factors at the crack front are calculated in the case of a circular and an elliptic crack and are compared with the analytical solution.     

A remeshing algorithm for three-dimensional crack growth and intersection with surfaces or cracks in non-coplanar planes

A recent procedure developed for crack growth in which three-dimensional stress intensity factors are calculated by boundary integral equations is used to compute fatigue crack growth as cracks grow in accordance with Paris’ law and also intersect each other or other surfaces. This paper concentrates on describing the remeshing algorithms needed as the cracks grow and when they intersect each other or other surfaces. The algorithms produced treat crack growth; prior to intersections, after intersection with a free surface, after intersection of a crack edge with a crack surface away from its edge, and after intersection of coplanar cracks.The method is applied here to the growth of an initially circular crack at the centre of a block under uniform tensile traction on the faces parallel to the crack. The crack grows to intersect either a free surface of the block or the centre of a square crack in an orthogonal plane.     

A general method for multiple crack problems in a finite plate

A novel method for the multiple crack problems in a finite plate is proposed in this paper. The basic stress functions of the solution consist of two parts. One is the Fredholm integral equation solution for the crack problem in an infinite plate, and the other is that of the weighted residual method for general plane problems. The combined stress functions are used in the analysis and the boundary conditions on the crack surfaces and the boundary are considered. After the coefficients of the functions have been determined, the stress intensity factors (SIF) at the crack tips can be calculated. Some numerical examples are given and it was observed that when the cracks are very short, the results compare very favorably with the existing results for an infinite plate. Furthermore, the influence of the boundary can be considered. This method can be used for arbitrary multiple crack problems in a finite plate.     

Boundary element analysis of thermal stress intensity factors for interface griffith and cusp cracks

The thermal stress intensity factors for interface cracks of Griffith and symmetric lip cusp types under vertical uniform heat flow in a finite body are calculated by the boundary element method. The boundary conditions on the crack surfaces are insulated or fixed to constant temperature. The relationship between the stress intensity factors and the displacements on the nodal point of a crack-tip element is derived. The numerical values of the thermal stress intensity factors for an interface Griffith crack in an infinite body are compared with the previous solutions. The thermal stress intensity factors for a symmetric lip cusp interface crack in a finite body are calculated with respect to various effective crack lengths, configuration parameters, material property ratios and the thermal boundary conditions on the crack surfaces. Under the same outer boundary conditions, there are no appreciable differences in the distribution of thermal stress intensity factors with respect to each material property. However, the effect of crack surface thermal boundary conditions on the thermal stress intensity factors is considerable.     

Thermoelectroelastic analysis of cracks in piezoelectric half-plane by BEM

The Green's function and the boundary element method for analysing fracture behaviour of cracks in piezoelectric half-plane are presented in this paper. By combining Stroh formalism and the concept of perturbation, a general thermoelectroelastic solution for half-plane solid subjected to point heat source and/or temperature discontinuity has been derived. Using the proposed solution and the potential variational principle, a boundary element model (BEM) for 2-D half-plane solid with multiple cracks has been developed and used to calculate the stress intensity factors of the multiple crack problem. The method is available for multiple crack problems in both finite and infinite solids. Numerical results for a two-crack system are presented and compared with those from finite element method (FEM).     

On the Elastic Compliance of a Circular Hole with Two Symmetric Radial Cracks Initiated at its Boundary

A circular hole with two symmetric rectilinear radial cracks initiated at its boundary is analyzed from the point of view of its elastic compliance (contribution to the overall elastic properties of a representative volume). Results are obtained using Rice’s connection between stress intensity factor and effect of a crack on the elastic properties of a material. We compare our result with that for a combine contribution of noninteracting circular pore and a rectilinear crack to show when this combination can be used for approximation of the elastic compliance contribution.