Stress intensity factors for three‐dimensional weld toe cracks using weld toe magnification factors

In welded components, particularly those with complex geometrical shapes, evaluating stress intensity factors is a difficult task. To effectively calculate the stress intensity factors, a weld toe magnification factor is introduced that can be derived from data obtained in a parametric study performed by finite element method (FEM). Although solutions for the weld toe magnification factor have been presented, these are applicable only to non‐load‐carrying cruciform or T‐butt joints, due possibly to the requirement of very complicated calculations. In the majority of cases for various welded joints, the currently used weld toe magnification factors do not adequately describe the behaviour of weld toe cracks. In this study, the weld toe magnification factor solutions for the three types of welded joints such as cruciform, cover plate and longitudinal stiffener joints were provided through a parametric study using three‐dimensional finite elements. The solutions were formed with exponents and fractions that have polynomial functions in terms of a/c and a/t – that is, crack depths normalised by corresponding half crack lengths and specimen thickness. The proposed weld toe magnification factors were applied to evaluate the fatigue crack propagation life considering the propagation mechanisms of multiple‐surface cracks for all welded joints. It showed good agreement within a deviation factor of two between the experimental and calculated results for the fatigue crack propagation life.     

New weld toe magnification factors for semi-elliptical cracks in double-sided T-butt joints and cruciform X-joints

British Standard BS7910:2005 has a single set of equations for estimating the weld toe magnification factor (M_k) of different types of welded joints containing a surface crack. The equations are based on the finite element (FE) results of single sided T-butt joint. In this study, extensive FE analyses are carried out to determine the M_k of double-sided T-butt joint and cruciform X-joint. Both the joints are subjected to axial and bending loading, and M_k at crack ends and deepest points of the surface crack are determined. It is found that M_k results for cruciform X-joint differ with those of double-sided T-butt joint with percentage difference in values being as high as 136% and 76% for axial and bending loading cases, respectively. Finally, a new set of M_k equations for cracked double-sided T-butt joint and X-joint are proposed based on multiple regression analyses.     

Mode mixity for tubular K-joints with weld toe cracks

This paper examines the mode-mixity of stress-intensity factors for surface cracks located near weld toes of the crown point at the toe of the tension brace in circular hollow section K-joints under different chord/brace end constraints. The remote loading applies a uniform stress at the end of the brace along its axis. The 3-D finite element models employ mesh-tieing between a topologically continuous, global mesh and a separate, local crack-front mesh. The linear-elastic analyses compute the mixed-mode stress-intensity factors along the crack front using an interaction-integral approach. The analyses for three different crack locations along the brace-chord intersection demonstrate that the critical location for the surface flaw lies at the crown point of the brace toe. The numerical investigation of six different boundary conditions indicate that the unbalanced loading conditions cause significant bending stresses in the chord and generate a considerably larger mode I stress-intensity factor than found for the balanced loading case. The mixed-mode stress-intensity factors indicate that the crack front experiences predominantly mode I loading, with K_III → 0 near the deepest point on the front (? = π/2). The non-dimensional, mode I crack driving force, described by , reaches a maximum value at the deepest point of the crack for the crack aspect ratio a/c = 0.25 considered here. The mode-mixity angle, ψ = tan⁻¹(K_II/K_I), at ? = π/2 is compared for a range of practical K-joint configurations. The present study demonstrates that the mode-mixity angle ψ becomes significantly larger in the balanced loading conditions than in the unbalanced loading condition. Values of the non-dimensional stress-intensity factors ( and ), however, decrease for the balanced loading condition. Variations in the brace-to-chord diameter ratio (β) and chord radius to wall thickness ratio (γ) generate significant changes in the mode mixity. Thin-walled joints (γ = 20) generally experience a larger crack driving force with a higher mode-mixity angle.     

Weight functions for the determination of stress intensity factor and T‐stress for semi‐elliptical cracks in finite thickness plate

This paper presents the application of weight function method for the calculation of stress intensity factors (K) and T‐stress for surface semi‐elliptical crack in finite thickness plates subjected to arbitrary two‐dimensional stress fields. New general mathematical forms of point load weight functions for K and T have been formulated by taking advantage of the knowledge of a few specific weight functions for two‐dimensional planar cracks available in the literature and certain properties of weight function in general. The existence of the generalised forms of the weight functions simplifies the determination of specific weight functions for specific crack configurations. The determination of a specific weight function is reduced to the determination of the parameters of the generalised weight function expression. These unknown parameters can be determined from reference stress intensity factor and T‐stress solutions. This method is used to derive the weight functions for both K and T for semi‐elliptical surface cracks in finite thickness plates, covering a wide range of crack aspect ratio (a/c) and relative depth (a/t) at any point along the crack front. The derived weight functions are then validated against stress intensity factor and T‐stress solutions for several linear and nonlinear two‐dimensional stress distributions. These derived weight functions are particularly useful for the development of two‐parameter fracture and fatigue models for surface cracks subjected to fluctuating nonlinear stress fields, such as these resulting from surface treatment (shot peening), stress concentration or welding (residual stress).     

A parametric study on fatigue strength of spot‐weld joints

Fastening elements usually lead to high stress concentrations; fatigue failure thus becomes the most critical failure mode for a fastening element itself or the region around it under fluctuating stresses. A designer should seek the ways of increasing fatigue strength of a joint to ensure the safety of the whole structure. Resistance spot welding is the most preferred method to join metal sheets. The design variables for spot‐weld joints affecting their strengths are basically sheet thickness, spot‐weld nugget diameter, number of spot welds and the joint type as exemplified in tensile shear (TS), modified tensile shear (MTS), coach peel (CP) and modified coach peel (MCP) specimens. In this study, the effects of these parameters on the fatigue life of spot‐weld joints have been investigated. For this purpose, one of the most reliable fatigue assessment models, Coffin–Manson approach, was used. In order to accurately determine the stress and strain states, a nonlinear finite element analysis was carried out taking into account plastic deformations, residual stresses developed after unloading and contacting surfaces. The results provide designers with some guidelines to foresee the impact of design changes on fatigue strength of spot‐weld joints.     

Crack aspect development curves and fatigue life prediction for surface cracks at weld toes in the presence of residual stress

An engineering procedure is proposed for estimating the crack growth behaviour and fatigue lives of semi-elliptical surface cracks at weld toes, based on a database of stress intensity factors. Some examples of crack aspect development curves (CADC) are given for some typical cracked welded joints subjected to service loading and residual stress conditions. The significance for predicting fatigue life according to the natural crack growth path, namely along the CADC, is emphasized through examples.     

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.     

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.     

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 and crack opening displacements for slanted axial through-wall cracks in pressurized pipes

This paper proposes elastic stress intensity factors and crack opening displacements (CODs) for a slanted axial through-wall cracked cylinder under an internal pressure based on detailed three-dimensional (3D) elastic finite element (FE) analyses. The FE model and analysis procedure were validated against existing solutions for both elastic stress intensity factor and COD of an idealized axial through-wall cracked cylinder. To cover a practical range, four different values of the ratio of the mean radius of cylinder to the thickness ( R _m/ t ) were selected. Furthermore, four different values of the normalized crack length and five different values of the ratio of the crack length at the inner surface to the crack length at the outer surface representing the slant angle were selected. Based on the elastic FE results, the stress intensity factors along the crack front and CODs through the thickness at the centre of the crack were provided. These values were also tabulated for three selected points, that is, the inner and outer surfaces and at the mid-thickness. The present results can be used to evaluate the crack growth rate and leak rate of a slanted axial through-wall crack due to stress corrosion cracking and fatigue. Moreover, the present results can be used to perform a detailed leak-before-break analysis considering more realistic crack shape development.     

Through‐wall welding residual stress profiles for dissimilar metal nozzle butt welds in pressurized water reactors

This paper provides approximate expressions for through‐wall welding residual stresses in dissimilar metal nozzle butt welds of pressurized water reactors. An idealized shape of nozzle is proposed, based on which systematic elastic–plastic thermo‐mechanical finite element analyses are conducted by varying the thickness and radius of the nozzle and the length of the safe‐end. Based on the results, a through‐wall welding residual stress profile for dissimilar metal nozzle butt welds is proposed by modifying the existing welding residual stress profile for austenitic pipe butt welds in the R6 procedure.     

Stress intensity factors of a central interface crack in a bonded finite plate and periodic interface cracks under arbitrary material combinations

Although a lot of interface crack problems were previously treated, few solutions are available under arbitrary material combinations. This paper deals with a central interface crack in a bonded finite plate and periodic interface cracks. Then, the effects of material combination and relative crack length on the stress intensity factors are discussed. A useful method to calculate the stress intensity factor of interface crack is presented with focusing on the stress at the crack tip calculated by the finite element method.     

Stress intensity factors for circumferential through‐wall cracks in thin‐walled cylindrical shells subjected to tension and torsion

In order to assess the structural integrity of tubular members or pipes containing circumferential through‐wall cracks, their stress intensity factor solutions are required. While stress intensity factors for tension and bending are available, few solutions exist for the case of torsion, even though these components may also be subjected to torque. In this paper, the finite element method is used to compute the stress intensity factors for this geometry under tension and torsion. Shell elements are employed to compute the results for thin shells by the means of the displacement extrapolation technique. The computed results indicate that the available analytical solution for torsional loading, which is based on shallow shell theory, is nonconservative for long cracks in thin shells. Shallow shell theory is in general not applicable to long cracks, and the present work is therefore able to provide solutions for a wider range of crack lengths than what is currently available.     

Material‐dependent crack‐tip enrichment functions in XFEM for modeling interfacial cracks in bimaterials

A novel set of enrichment functions within the framework of the extended finite element method is proposed for linear elastic fracture analysis of interface cracks in bimaterials. The motivation for the new enrichment set stems from the revelation that the accuracy and conditioning of the widely accepted 12‐fold bimaterial enrichment functions significantly deteriorates with the increase in material mismatch. To this end, we propose an 8‐fold material‐dependent enrichment set, derived from the analytical asymptotic displacement field, that well captures the near‐tip oscillating singular fields of interface cracks, including the transition to weak discontinuities of bimaterials. The performance of the proposed material‐dependent enrichment functions is studied on 2 benchmark examples. Comparisons are made with the 12‐fold bimaterial enrichment as well as the classical 4‐fold homogeneous branch functions, which have also been used for bimaterials. The numerical studies clearly demonstrate the superiority of the new enrichment functions, which yield the most accurate results but with less number of degrees of freedom and significantly improved conditioning than the 12‐fold functions.     

Driving forces for localized corrosion‐to‐fatigue crack transition in Al–Zn–Mg–Cu

Research on fatigue crack formation from a corroded 7075‐T651 surface provides insight into the governing mechanical driving forces at microstructure‐scale lengths that are intermediate between safe life and damage tolerant feature sizes. Crack surface marker‐bands accurately quantify cycles (N_i) to form a 10–20 μm fatigue crack emanating from both an isolated pit perimeter and EXCO corroded surface. The N_i decreases with increasing‐applied stress. Fatigue crack formation involves a complex interaction of elastic stress concentration due to three‐dimensional pit macro‐topography coupled with local micro‐topographic plastic strain concentration, further enhanced by microstructure (particularly sub‐surface constituents). These driving force interactions lead to high variability in cycles to form a fatigue crack, but from an engineering perspective, a broadly corroded surface should contain an extreme group of features that are likely to drive the portion of life to form a crack to near 0. At low‐applied stresses, crack formation can constitute a significant portion of life, which is predicted by coupling macro‐pit and micro‐feature elastic–plastic stress/strain concentrations from finite element analysis with empirical low‐cycle fatigue life models. The presented experimental results provide a foundation to validate next‐generation crack formation models and prognosis methods.     

Out‐of‐plane singular stress fields in V‐notched plates and welded lap joints induced by in‐plane shear load conditions

When a crack or sharp notch is subjected to antisymmetric plane loading the Poisson's effect leads to the generation of a coupled out‐of‐plane singular mode. The latter was known to exist for problems with cracks for a long period of time; meanwhile this mode was largely ignored in theoretical studies of V‐shaped notches subjected to in‐plane loading as well as in practical fracture problems associated with such geometries. Only recently a characteristic equation describing the strength of the singularity of this mode was derived within the first order plate theory. Preliminary numerical investigations confirmed that a highly localized out‐of‐plane singular state linked to the transverse shear stress components does exist in the close vicinity of the notch tip with the singular behaviour as theoretically predicted. However, until now it is unclear how significant this mode is and whether it has to be taken into consideration in the stress analysis of engineering structures. This paper is aimed to discuss important features of this recently identified singular mode, out‐of‐plane singular mode, conduct a comprehensive three‐dimensional numerical study of a typical problem of a welded lap joint to investigate the contribution of this mode into the overall stress state in the close vicinity of the notch tip and discuss the implementation of these new results to the failure and integrity assessment of plate structures with sharp notches.     

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

Stress intensity factors for half‐elliptical surface cracks at a semi‐circular notch in a recently developed single‐edge notch bend specimen are determined for a wide range of geometrical parameters using a three‐dimensional weight function method. Two load cases of pin loading and uniform remote tension are considered. The results are in good agreement with abaqus/franc3d finite element analysis. It is found that the Ziegler–Newman engineering similitude approach (programmed into the Fatigue Crack Growth Structural Analysis life‐prediction code) produces good results for a wide range in a/c ratios. Expressions by multi‐variable curve fitting to the weight function results are presented for easy engineering applications.     

Assessing the accuracy of fatigue life in surface‐cracked straight pipes

The demonstration of leak before brake (LBB) based on fracture mechanics requires information on the initial size of a defect, initiation of crack growth from the inherent defect and subsequent crack growth rates. In the present paper the prediction methodologies have been tested for three different full scale pipes geometry experimentally tested data. The prediction accuracy of two SIF solutions available in the literature has also been judged. The effect of fatigue crack closure and corrections needed in the numerical prediction methodology using FEM have also been included. The results showed that the FEM could fairly predict the fatigue crack initiation and crack growth life of full‐scale piping components having a constant depth crack profile.     

Direct evaluation of stress intensity factors for curved cracks using Irwin's integral and XFEM with high‐order enrichment functions

This paper presents a comprehensive study on the use of Irwin's crack closure integral for direct evaluation of mixed‐mode stress intensity factors (SIFs) in curved crack problems, within the extended finite element method. The approach employs high‐order enrichment functions derived from the standard Williams asymptotic solution, and SIFs are computed in closed form without any special post‐processing requirements. Linear triangular elements are used to discretize the domain, and the crack curvature within an element is represented explicitly. An improved quadrature scheme using high‐order isoparametric mapping together with a generalized Duffy transformation is proposed to integrate singular fields in tip elements with curved cracks. Furthermore, because the Williams asymptotic solution is derived for straight cracks, an appropriate definition of the angle in the enrichment functions is presented and discussed. This contribution is an important extension of our previous work on straight cracks and illustrates the applicability of the SIF extraction method to curved cracks. The performance of the method is studied on several circular and parabolic arc crack benchmark examples. With two layers of elements enriched in the vicinity of the crack tip, striking accuracy, even on relatively coarse meshes, is obtained, and the method converges to the reference SIFs for the circular arc crack problem with mesh refinement. Furthermore, while the popular interaction integral (a variant of the J‐integral method) requires special auxiliary fields for curved cracks and also needs cracks to be sufficiently apart from each other in multicracks systems, the proposed approach shows none of those limitations. Copyright © 2017 John Wiley & Sons, Ltd.     

XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi‐materials

The extended finite element method (XFEM) is improved to directly evaluate mixed mode stress intensity factors (SIFs) without extra post‐processing, for homogeneous materials as well as for bimaterials. This is achieved by enriching the finite element (FE) approximation of the nodes surrounding the crack tip with not only the first term but also the higher order terms of the crack tip asymptotic field using a partition of unity method (PUM). The crack faces behind the tip(s) are modelled independently of the mesh by displacement jump functions. The additional coefficients corresponding to the enrichments at the nodes of the elements surrounding the crack tip are forced to be equal by a penalty function method, thus ensuring that the displacement approximations reduce to the actual asymptotic fields adjacent to the crack tip. The numerical results so obtained are in excellent agreement with analytical and numerical results available in the literature. Copyright © 2004 John Wiley & Sons, Ltd.