Stress intensity factors for several groups of equal and parallel cracks in finite plates

Several groups of equal and parallel 2D cracks in finite width plates subjected to remote tensile loading have been studied. Formulae for calculating the stress intensity factors of these crack configurations have been proposed from the finite element analysis, and the difference between the formulae and the finite element results is smaller than 3%. On this basis, the influence of crack interactions on stress intensity factors (SIF) is discussed, and it can be seen that interaction between multiple cracks could produce either strong enhancement or shielding effects on the SIF depending on the crack positions and lengths.     

A discussion about a class of stress intensity factors and its verification

In this paper, new formulae of a class of stress intensity factors for an infinite plane with two collinear semi-infinite cracks are presented. The formulae differ from those gathered in several handbooks used all over the world. Some experiments and finite element calculations have been developed to verify the new formulae and the results have shown its reliability. Finally, the new formulae and the old are listed to show the differences between them.     

Fully automated mixed mode crack propagation analyses based on tetrahedral finite element and VCCM (virtual crack closure-integral method)

The authors have been developing a crack propagation analysis system that can deal with arbitrary shaped cracks in three-dimensional solids. The system is consisting of mesh generation software, a large-scale finite element analysis program and a fracture mechanics module. To evaluate the stress intensity factors, virtual crack closure-integral method (VCCM) for the quadratic tetrahedral finite element is adopted and is included in the fracture mechanics module. The rate and direction of crack propagation are predicted by using appropriate formulae based on the stress intensity factors. In this paper, the crack propagation system is briefly described and some numerical results are presented.     

Weight functions for composite repairs to stiffened panels

This paper presents a weight function technique for calculating the stress intensity factors for composite repairs to cracks emanating from an internal notch, corrosion blend out, or a free edge under arbitrary loading in rib stiffened panels. The predictions are compared with both finite element and experimental values. This methodology represents a significant extension to existing assessment and design formulae that are currently limited to the case of uniform loading and flat unstiffened panels.     

Stress intensity factors and weight functions for deep semi-elliptical surface cracks in finite-thickness plates

ABSTRACT Three-dimensional finite element analyses have been conducted to calculate the stress intensity factors for deep semi-elliptical cracks in flat plates. The stress intensity factors are presented for the deepest and surface points on semi-elliptic cracks with a/t -values of 0.9 and 0.95 and aspect ratios ( a/c ) from 0.05 to 2. Uniform, linear, parabolic or cubic stress distributions were applied to the crack face. The results for uniform and linear stress distributions were combined with corresponding results for surface cracks with a/t = 0.6 and 0.8 to derive weight functions over the range 0.05 ≤  a/c  ≤ 2.0 and 0.6 ≤  a/t  ≤ 0.95. The weight functions were then verified against finite element data for parabolic or cubic stress distributions. Excellent agreements are achieved for both the deepest and surface points. The present results complement stress intensity factors and weight functions for surface cracks in finite thickness plate developed previously.     

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.     

Numerical and experimental evaluation of SIF for threaded connectors

This paper presents a methodology for fatigue crack growth analysis in tubular threaded connectors. A solution for stress intensity factor for semi-elliptical surface cracks emanating from a thread root in a screw connector is also discussed in the paper. The solution is based on a mixed approach incorporating weight function and finite element methods. The weight functions used are the universal functions for cracks in mode I and these are linked with a thread through-thickness stress distribution obtained from finite element analysis to produce a stress intensity factor for a crack at the critical tooth of a thread. The resulting crack growth data are then validated experimentally.     

Growth prediction of two interacting surface cracks of dissimilar sizes

When multiple cracks approach one another, the stress intensity factor changes due to the interaction of the stress field. This causes variation in the crack growth rate and shape of cracks. In particular, when cracks are parallel to the loading direction, their shape becomes non-planar due to the mixed mode stress intensity factor. In this study, the growth of interacting surface cracks was simulated by using the S-version finite element method, in which a local detailed finite element mesh (local model) is superposed on a coarse finite element model (global model) representing the global structure. First, simulations were performed for fatigue crack growth experiments and the method validity was shown. Second, simulations were conducted for various relative sizes and spacings of twin cracks. It was shown that the offset distance and the relative size were both important parameters to determine the interaction between two surface cracks; the smaller crack stopped growing when the difference in size was large. It was possible to judge whether the effect of interaction should be considered based on the correlation between the relative spacing and relative size.     

Stress intensity factors for large arrays of radial cracks in thick-walled steel cylinders

Mode I stress intensity factors for large arrays of up to 512 radial cracks emanating from the inner surface of a pressurized thick-walled cylinder are evaluated. Furthermore, for cylinders that underwent autofrettage, the negative stress intensity factors due to the compressive residual stresses are also calculated. Both stress intensity factors are evaluated, for numerous crack arrays (2–512), for a wide range of crack lengths and for a fully autofrettaged cylinder, via the finite element (FE) method. The present results accentuate the considerable influence of the number of cracks in the array, as well as that of the autofrettage on the actual stress intensity factor prevailing at the tip of these cracks.     

Stress intensity factors in spot welds

This paper looks at stress intensity factors of cracks in resistance spot welded joints. Stress intensity factors have been used in the past to predict fatigue crack propagation life of resistance spot welds. However, the stress intensity factors from all previous work was based on assumed initial notch cracks at the nugget, parallel to the sheets. Physical evidence shows, however, that fatigue cracks in spot welds propagate through the thickness of the sheets rather than through the nugget. In this work, stress intensity factors of assumed notch cracks and through thickness cracks in tensile shear (TS) and modified coach peel (MCP) specimens were determined by the finite element method. The finite element results from the assumed notch cracks were compared with the results in the literature and were found to be in agreement with the results from Zhang’s equations [Int. J. Fract. 88 (1997) 167]. The stress intensity factors of assumed notch cracks were found to be different from those of through thickness cracks. To date, no analytic equations for stress intensity factors of through thickness cracks in spot welds have been published. In the current work, simple equations are proposed to estimate the K_I and K_II values of through thickness cracks in TS and MCP specimens.     

Stress intensity factors in spot welds

This paper looks at stress intensity factors of cracks in resistance spot welded joints. Stress intensity factors have been used in the past to predict fatigue crack propagation life of resistance spot welds. However, the stress intensity factors from all previous work was based on assumed initial notch cracks at the nugget, parallel to the sheets. Physical evidence shows, however, that fatigue cracks in spot welds propagate through the thickness of the sheets rather than through the nugget. In this work, stress intensity factors of assumed notch cracks and through thickness cracks in tensile shear (TS) and modified coach peel (MCP) specimens were determined by the finite element method. The finite element results from the assumed notch cracks were compared with the results in the literature and were found to be in agreement with the results from Zhang’s equations [Int. J. Fract. 88 (1997) 167]. The stress intensity factors of assumed notch cracks were found to be different from those of through thickness cracks. To date, no analytic equations for stress intensity factors of through thickness cracks in spot welds have been published. In the current work, simple equations are proposed to estimate the K_I and K_II values of through thickness cracks in TS and MCP specimens.     

The solution of a torsion problem by finite Mellin transform techniques

Summary In this paper the author makes use of a recent development in the theory of finite Mellin transforms to find formulae for the stress intensity factors and crack formation energy of a radial system of edge cracks in a circular elastic cylinder under torsion.     

轮轨摩擦接触下钢轨多裂纹相互作用研究

利用热机耦合有限元法,建立了轮轨摩擦接触时钢轨表面多裂纹的热弹性平面应变有限元模型。数值模型中,考虑轮轨摩擦温升对轮轨材料参数的影响,通过移动载荷和热源来模拟运动车轮对钢轨的作用。分析了轮轨滑动接触时多裂纹相互作用和表面裂纹数量对钢轨疲劳裂纹扩展特性的影响。计算结果表明：与单个裂纹相比,多裂纹有降低钢轨疲劳裂纹扩展的作用;钢轨裂纹尖端应力强度因子K1和应力强度因子范围?K2均随裂纹数的增多而减小;钢轨表面裂纹数为5条时可以反映更多裂纹时的裂纹扩展特性。     

Stress intensity factor solutions for estimation of fatigue lives of laser welds in lap-shear specimens

Fatigue behavior of laser welds in lap-shear specimens of high strength low alloy (HSLA) steel is investigated based on experimental observations and two fatigue life estimation models. Fatigue experiments of laser welded lap-shear specimens are first reviewed. Analytical stress intensity factor solutions for laser welded lap-shear specimens based on the beam bending theory are derived and compared with the analytical solutions for two semi-infinite solids with connection. Finite element analyses of laser welded lap-shear specimens with different weld widths were also conducted to obtain the stress intensity factor solutions. Approximate closed-form stress intensity factor solutions based on the results of the finite element analyses in combination with the analytical solutions based on the beam bending theory and Westergaard stress function for a full range of the normalized weld widths are developed for future engineering applications. Next, finite element analyses for laser welded lap-shear specimens with three weld widths were conducted to obtain the local stress intensity factor solutions for kinked cracks as functions of the kink length. The computational results indicate that the kinked cracks are under dominant mode I loading conditions and the normalized local stress intensity factor solutions can be used in combination with the global stress intensity factor solutions to estimate fatigue lives of laser welds with the weld width as small as the sheet thickness. The global stress intensity factor solutions and the local stress intensity factor solutions for vanishing and finite kinked cracks are then adopted in a fatigue crack growth model to estimate the fatigue lives of the laser welds. Also, a structural stress model based on the beam bending theory is adopted to estimate the fatigue lives of the welds. The fatigue life estimations based on the kinked fatigue crack growth model agree well with the experimental results whereas the fatigue life estimations based on the structural stress model agree with the experimental results under larger load ranges but are higher than the experimental results under smaller load ranges.     

Some asymptotic behavior and formulae of stress intensity factors for collinear and parallel cracks under various loadings

In this paper, the relations between stress intensity factors and N are given in a more refined manner with theoretical proofs than previously. They apply to cracks, holes and inclusions of arbitrary shapes. Based on these relations, reliable formulae of the stress intensity factors are proposed for collinear and parallel cracks under various loadings.     

Stress intensity factor solutions for cracks in finite-width three layer laminates with and without residual stress effects

Approximate stress intensity factor solutions for cracks in finite-width three layer laminates, with the crack located in the middle layer, were derived on the basis of force-balance between the applied stress and the modified Westergaard form of normal stress distribution ahead of the crack tip. This yielded a simple and closed form equation for the stress intensity factor that included the effects of the ratio of the moduli of the layers and the relative layer thicknesses. A comparison of the stress intensity factor values from this equation and with finite element data indicated that the difference between these two data sets was small for most of the crack lengths and the modulus ratio of the layers. The maximum difference occurred at crack lengths approaching the interface and at high moduli ratios, but was less than 10%, in general. The equations were also modified to incorporate the effects of residual stresses that arise during cooling after laminate processing, on the stress intensity factor. A comparison of the analytical data with the finite element data obtained by imposing thermal and mechanical boundary loads on the laminate specimens indicated a good agreement. The present closed form approximate solutions may be useful in fracture analyses of finite-width laminates containing cracks.     

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 and Failure Analysis of Brittle Matrix Composites. Part II: Failure Analysis

A linear elastic fracture mechanics analysis of a cylindrical element of matrix with a single fiber and two matrix annular cracks perpendicular to the fiber direction under longitudinal tensile load was undertaken. The order of singularity and the angular dependence of the stress field in the neighborhood of the crack periphery were determined by using the stress function approach proposed by Zak and Williams. The stress intensity factor was evaluated by combining the results of the local stress solution with a finite element analysis. The case of fiber debonding originating from the periphery of the annular cracks was also studied. For that problem both opening-mode and sliding-mode stress intensity factors and the strain energy release rate were determined. These results help to understand the various failure mechanisms including matrix cracking, debonding along interfaces and kinking of interface cracks into fibers in brittle matrix composites. This revised version was published online in July 2006 with corrections to the Cover Date.     

A novel singular finite element on mixed-mode bimaterial interfacial cracks with arbitrary crack surface tractions

This paper investigates interfacial cracks with arbitrary crack surface tractions. A novel singular finite element which is constructed with the analytical solution around interfacial cracks is presented. Interfacial crack problems can be analyzed numerically using the singular finite element, and Mode I and/or Mode II stress intensity factors can be obtained directly. Unlike other enriched elements for cracks, neither extra unknowns nor transition elements are required. Numerical examples are given to illustrate the validity of present method.     

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.