STRESS INTENSITY FACTORS FOR SURFACE CRACKS AT A HOLE BY A THREE-DIMENSIONAL WEIGHT FUNCTION METHOD WITH STRESSES FROM THE FINITE ELEMENT METHOD

Stress intensity factors for semielliptical surface cracks emanating from a circular hole are reported in this paper. The three-dimensional weight function method with three-dimensional finite element solutions for the uncracked stress distribution is used for the analysis. Two different loading conditions, i.e. remote tension and wedge loading, are considered for a wide range of geometrical parameters. Both single and double surface cracks are studied and compared with other solutions available in the literature. Typical crack opening displacements are also provided.     

Approximate weight function method for elliptical arc through cracks in mechanical joints

Mechanical joints such as bolted, riveted or pinned joints are widely used to join the constituent parts of structural components. Reliable stress intensity factor analysis of arbitrary cracks in mechanical joints is required for the safety evaluation or fracture mechanics design. It has been reported that cracks in mechanical joints usually nucleate as the corner crack and grow as the elliptical arc through crack. The weight function method is a useful technique to calculate the stress intensity factor using the appropriate weight function for a cracked body and the stress field of an uncracked body. In this paper, the weight function method for the two surface points of elliptical arc through cracks in mechanical joints is developed to analyze the mixed-mode stress intensity factors. Unknown coefficients included in the weight function are determined using the reference stress intensity factors obtained from finite element analysis.     

Parametric equations for T-butt weld toe stress intensity factors

This paper describes the generation of parametric equations for weld toe stress intensity factors. The methodology employed used a two-dimensional finite element analysis to evaluate the ‘crack opening’ stress distribution in the uncracked plane of T-butt geometries. This was then used as input into a dedicated weight function solution for the determination of stress intensity factors. The final parametric equations describe the stress intensity factor distributions for tension and bending as a function of plate thickness, weld attachment width, weld angle, weld root radius, crack length and crack shape. The equations are compared and validated against a wide spectrum of published values and appear by comparison accurate and wide ranging. The validation exercise uncovered situations where present design guidance is unconservative.     

Uncracked body analysis for accurate estimates of mode I stress intensity factor for cracks normal to an interface

A bonded crack model method is presented for estimation of the stress intensity factor (SIF) for a 3D half-penny shaped crack originating at a bonded interface subjected to remote constant tensile and proportional bending loadings. Closed-form approximations are obtained for the SIF as a function of modulus ratio of bonded dissimilar materials. A combination of bonded crack model method and macro-level stress calculations in a structure without a crack (uncracked body analysis) significantly simplifies accurate estimation of SIF. The method was validated using 3D finite element computations. Since the proposed method requires no repetitive stress calculation as crack size changes, it is useful in life predictions.     

Elastic stress distributions in finite size plates with edge notches

In fatigue crack growth analysis it is essential to know the stress distributions in the neighbourhood of stress raisers. If such distributions ahead of the uncracked notch are known, stress intensity factors may be obtained via the weight function or other methods. The procedure described in the present paper reconsiders the principal elastic stress expressions already reported by the authors for infinite plates with semi-infinite symmetric V-shaped notches and adapts them to some practical cases, in which the mutual influence of the notches as well as that of the plate finite size play an important role in stress distributions. The aim is therefore to give an approximate close-form solution for the longitudinal stress, valid for the entire ligament length, namely from notch tip to notch tip. Theoretical and numerical stress values are compared on this line, examining plates with semicircular, V and U-shaped notches subjected to remote uniaxial tension. This revised version was published online in August 2006 with corrections to the Cover Date.     

Fracture and fatigue analysis of an agitator shaft with a circumferential notch

This paper is concerned with the fracture analysis of an agitator shaft of a large vessel and predicting its high cycle fatigue life. The agitator shaft has a circumferential notch around it and is subjected to remote bending and torque created by the mixing operation. The problem is comprised (i) the analyses of the bending force and torque acting on the agitator by using the analytical method, (ii) calculation of stress intensity factors under mode I and III loading conditions by using finite element method and, (iii) fatigue analysis of the agitator shaft failed in service.An agitator model is set up and data obtained from the agitator are processed to make more realistic approximations for bending forces, since they form a base for stress analysis, in which mode I stress intensity factors are evaluated. Mode I stress intensity factors obtained by finite element analysis are compared with the results provided by using the body force method.     

Analysis of thermal stress intensity factors for cracked cylinders using weight function method

In this paper a general weight function was derived to evaluate the thermal stress intensity factors of a circumferential crack in cylinders. The weight function derived is valid for a wide range of thin- to thick-walled cylinders and relative crack depth. Closed-form stress intensity factor based on the weight function method was derived as a function of the Biot number and relative depth and various inner-to-outer radius ratios of cylinders. The accuracy of the analysis has been examined using the finite element method results and were compared to existing solutions for uniform loading in the literature for special geometries, indicating an excellent agreement.     

Stress intensity factors for corner cracks in single‐edge notch bend specimen by a three‐dimensional weight function method

A three‐dimensional (3D) weight function method is employed to calculate stress intensity factors of quarter‐elliptical corner cracks at a semi‐circular notch in the newly developed single‐edge notch bend specimen. Corner cracks covering a wide range of geometrical parameters under pin‐loading and remote tension conditions are analysed. Stress intensity factors from the 3D weight function analysis agree well with ABAQUS‐Franc3D finite element results. An engineering similitude approach previously developed for the half‐elliptical surface crack in single‐edge notch bend specimen is also applied to the present corner crack configuration. The results compare well with those from the present weight function analysis.     

STRESS INTENSITY FACTORS AND WEIGHT FUNCTIONS FOR SEMI-ELLIPTICAL SURFACE CRACKS IN FINITE-THICKNESS PLATES UNDER TWO-DIMENSIONAL STRESS DISTRIBUTION

Abstract— A Fourier series approach is proposed to calculate stress intensity factors using weight functions for semi-elliptical surface cracks in flat plates subjected to two-dimensional stress distributions. The weight functions were derived from reference stress intensity factors obtained by three-dimensional finite element analyses. The close form weight functions derived are suitable for the calculation of stress intensity factors for semi-elliptical surface cracks in flat plates under two-dimensional stress distributions with the crack aspect ratio in the range of 0.1 ≤ a/c ≤ 1 and relative depth in the range of 0 ≤ a/t ≤ 0.8. Solutions were verified using several two-dimensional non-linear stress distributions; the maximum difference being 6%.     

Effect of residual stress around cold worked holes on fracture under superimposed mechanical load

Cold working is one method used to enhance the fatigue life of holes in aerospace structures. The method introduces a compressive stress field in the material around the hole and this reduces the tendency for fatigue cracks to initiate and grow under superimposed cyclic mechanical load. To include the benefit of cold working in design the stress intensity factors must be evaluated for cracks growing from the hole edge. Two-dimensional (2D) finite element analyses have been carried out to quantify the residual stresses surrounding the cold worked hole. These residual stresses have been used in a finite element calculation of the effective stress intensity factor for cracks emanating from the hole edge normal to the loading direction. The results of the 2D analysis have been compared with those derived using a weight function method. The weight function results have been shown always to underestimate the stress intensity factor. A three-dimensional (3D) FEA has been carried out using the same technique for stress intensity factor evaluation to investigate the effect of through thickness variation of residual stress. Stress intensity factors calculated with the 3D analysis are generally higher than those calculated using the 2D analysis.     

A wide range weight function for a single edge cracked geometry with clamped ends

A single edge cracked geometry with clamped ends is well suited for fracture toughness and fatigue crack growth testing of composites and thin materials. Stress intensity factors may be determined by the weight function method. A weight function for the single edge cracked geometry with clamped ends is developed and verified in this paper. It is based on analytical forms for the reference stress intensity factor and crack mouth opening displacement. The analytical forms are shown to be valid, by comparison with finite element results, over a wide range of crack depths and plate aspect ratios. Use of the analytical form enables the weight function to be calculated for any plate aspect ratio without the need for preliminary finite element analysis. Stress intensity factors and crack mouth opening displacements, predicted using this weight function, correlated well with finite element results for non-uniform crack surface stress distributions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Evaluation of K-factors and weight functions for 2-d mixed-mode multiple cracks by the boundary element alternating method

The concept of the Schwartz-Neumann alternating method, in conjunction with the boundary element method to solve for the stresses in an uncracked body and an analytical solution for an embedded 2-D crack subjected to arbitrary crack face loading in an infinite domain, is used to detennine the mixed-mode K-factors and weight functions for cracks in finite bodies. Situations of edge-cracks, as well as multiple cracks, all under mixed mode loading, are considered. The boundary element method is better suited for these problems since, pointwise evaluation of stresses at the location of the crack in the uncracked body is more accurate and simple once the tractions and displacements on the boundary are determined. It is expected that the above method would yield highly accurate results in the least expensive way, even compared to the finite element alternating method.     

Stress intensity factors and T-stresses for offset double edge-cracked plates under mixed-mode loadings

A particular weight function method is used in this study to determine the stress intensity factors (SIFs) and T-stresses for offset double edge-cracked plates (ODECPs). By using reference loading conditions prescribed on the crack flanks for finite element analyses, the coefficients of weight functions are derived and compiled in the form of tables. With the weight functions, the SIFs and T-stresses for several loading cases are calculated. The results compare well with those obtained using the displacement method. Applying the derived weight functions, the SIFs and T-stresses for ODECPs under several loading conditions are determined. The results can be used as references for related applications.     

Stress intensity factors for long axial surface cracks at the outer wall of a pipe loaded by stress gradients

By means of the finite element method crack opening displacements were calculated for long axial surface cracks at the outer wall of a pipe. The wall thickness to inner radius ratio of the pipe was 1 to 10. Following a procedure introduced be Mattheck et al. weight functions were evaluated by means of the finite element results. Using these weight functions it is possible to calculate stress intensity factors for arbitrary radially varying stress distributions. In this paper stress intensity factors were evaluated for a constant hoop stress loading as well as for stress distributions with a linear and a quadratic dependence on the radius.     

Calculation of stress intensity factors for functionally graded materials by using the weight functions derived by the virtual crack extension technique

The weight function method provides a powerful approach for calculating the stress intensity factors for a homogeneous cracked body subjected to mechanical loadings. In this paper, the basic equations of weight function method for mode I and mixed mode crack problems in a two-dimensional functionally graded crack system are derived based on the Betti’s reciprocal theorem. The weight functions derived by the virtual crack extension technique are further used to calculate the stress intensity factors of functionally graded materials (FGMs). The practicability and accuracy of this proposed method has been confirmed by the comparison with theoretical or numerical solutions available in the literatures. On account that the repeated extractions of the distributions of normal stress and shear stress in the uncracked component along the prospective crack line under different loadings can be avoided using the method presented in this paper, this method can be potentially used for optimal design for FGMs under multiple-load cases.     

Stress intensity factors for internal circular cracks in fibers under tensile loading

Stress intensity factors for inner circular cracks placed eccentrically in a fiber with round cross section were computed and are presented in this paper in both analytical and graphical form. The crack plane was perpendicular to the fiber axis and remote tensile loading was assumed. The stress intensity factors were numerically computed using the finite element method. Mesh objectivity and some other aspects of computational precision are considered. The asymptotic behaviour when the crack size and the ligament depth vanish were considered in order to formulate accurate interpolation expressions.     

Stress intensity factor analysis of elliptical corner cracks in mechanical joints by weight function method

Mixed-mode stress intensity factors at the surface and deepest points of quarter elliptical corner cracks in mechanical joints such as bolted or riveted joints are analyzed by weight function method. The weight function method is an efficient technique to calculate the stress intensity factors using uncracked stress field. The extended form of the weight function method for 2D mixed-mode problems to 3D mixed-mode is presented and the accuracy due to the number of terms included in the weight function is examined. The effects of the amount of clearance between the hole and the bolt or rivet on the stress intensity factors are investigated, and the critical angle causing the mode I stress intensity factor to be maximized is determined by analyzing the variation of the stress intensity factors along incline angle of crack.     

Calculation of Stress Intensity Factors for axial semi-elliptical surface cracks in a pipe with cladding loaded thermally

By means of the weight functions method stress intensity factors were calculated for axial semi-elliptical surface cracks in a pipe with cladding. The component is loaded by a thermoshock. Starting from a stress-free state the inner surface of the cladding is suddenly cooled down. The time-dependent temperature and hoop stress distributions of the uncracked component were calculated for the loading case considered. Numerical values of the stress intensity factors at the deepest point and at the surface points of the crack were evaluated at different time steps for a wide range of crack depths and crack lengths.     

STRESS INTENSITY FACTORS FOR A FUNCTIONALLY GRADED MATERIAL CYLINDER WITH AN EXTERNAL CIRCUMFERENTIAL CRACK

This paper presents mode I stress intensity factors for external circumferentially cracked hollow cylinders, which are assumed to be made of functionally graded materials and subjected to remote uniform tension. The conventional finite element method is improved by introducing isoparametric transformation for simulating the gradient variations of material properties in the finite elements. This improved finite element method is verified to be effective and efficient. Various types of functionally graded materials and different gradient compositions for each type are investigated. The results show that the material property distribution has a quite considerable influence on the stress intensity factors.     

Numerical study on fatigue crack growth in railway wheels under the influence of residual stresses

Accurate prediction of fatigue crack growth on railway wheels and the influence of residual stresses by finite element method (FEM) modeling can affect the maintenance planning. Therefore, investigation of rolling contact fatigue and its effect on rolling members life seem necessary. The objective of this paper is to provide a prediction of rolling contact fatigue crack growth in the rail wheel under the influence of stress field from mechanical loads and heat treatment process of a railway wheel. A 3D nonlinear stress analysis model has been applied to estimate stress fields of the railway mono-block wheel in heat treatment process. Finite element analysis model is presented applying the elastic–plastic finite element analysis for the rail wheel under variable thermal loads. The stress history is then used to calculate stress intensity factors (SIFs) and fatigue life of railway wheel. The effect of several parameters, vertical loads, initial crack length and friction coefficient between the wheel and rail, on the fatigue life in railway wheels is investigated using the suggested 3-D finite element model. Three-dimensional finite element analysis results obtained show good agreement with those achieved in field measurements.