Elastic stress intensity factors and crack opening displacements for circumferential through-walled cracked elbows

This paper provides tabulated solutions of elastic stress intensity factors and crack opening displacements for circumferential through-wall cracked elbows under internal pressure and under in-plane bending, based on extensive three-dimensional elastic finite element analyses covering a wide range of crack lengths and elbow/pipe geometries. The effect of crack length and elbow/pipe geometry on the results is discussed, with particular emphasis on the crack closure behaviour under in-plane bending.     

Minimization of stress concentration factors in fatigue crack repairs

A numerical study is reported of a repair by flaw removal on a conventional welded joint. The repair profile is optimized with respect to the flaw and joint dimensions in order to minimize the resulting stress concentration factor (SCF). Two dimensional (edge repair) and three dimensional (surface repair) finite element analyses were made for the determination of SCF values and a graphical representation of results is presented. A relation between edge repair and surface repair is obtained and short and long repairs are defined. The weld geometry and repair orientation effects on SCF values are discussed. Finally, implications on using short and long repairs on fatigue initiation and inspection are presented.     

Evaluating stress intensity factors of a surface crack in lubricated rolling contacts

The three-dimensional finite element method and the least-squares method were used to find the stress intensity factors (SIFs) of a surface crack in a lubricated roller. A steel roller on a rigid plane was modeled, in which a semi-elliptical surface crack is inclined at an angle ψ to the vertical axis. A distance c is set between the crack base and the roller edge. The results indicate that the mode-I SIF reaches the maximum value when the angle θ is equal to 0° (on the roller surface), and the mode-II SIF reaches the absolute maximum value when the angle θ is near or equal to 90° (inside the roller), where θ is the angle of the semi-ellipse from 0° to 180°. The influence of mode-III SIFs in this model is minor since they are much smaller than the mode-I and mode-II SIFs. The SIFs increase greatly when the crack location approaches the uncrowned edge. At this time, a crowned profile can be used to significantly reduce the SIFs near the roller edge. This revised version was published online in July 2006 with corrections to the Cover Date.     

Calculation of stress intensity factors by the force method

The force method is a simple and accurate technique for calculating stress intensity factors (SIFs) from finite element (FE) models, but it has been scarcely used. This paper shows three important advantages of the force method, which make it particularly attractive for designers and researchers. First, it can be employed without special singular quadratic finite elements at the crack tip. Actually, linear reduced integration elements may be used. Second, the force method can be applied to highly anisotropic materials without requiring knowledge of complicated elasticity relations for the stress field around the crack tip. Third, it can handle mixed-mode fracture problems.     

Dislocation-based semi-analytical method for calculating stress intensity factors of cracks: Two-dimensional cases

Determination of the stress intensity factors of cracks is a fundamental issue for assessing the performance safety and predicting the service lifetime of engineering structures. In the present paper, a dislocation-based semi-analytical method is presented by integrating the continuous dislocation model with the finite element method together. Using the superposition principle, a two-dimensional crack problem in a finite elastic body is reduced to the solution of a set of coupled singular integral equations and the calculation of the stress fields of a body which has the same shape as the original one but has no crack. It can easily solve crack problems of structures with arbitrary shape, and the calculated stress intensity factors show almost no dependence upon the finite element mesh. Some representative examples are given to illustrate the efficacy and accuracy of this novel numerical method. Only two-dimensional cases are addressed here, but this method can be extended to three-dimensional problems.     

Numerical methods for determination of stress intensity factors of singular stress field

The asymptotic solution of the singular stress field near a singular point is generally comprised of one or more singular terms in the form of Kr^λ-1f_ij(θ). Based on the asymptotic solution of the singular stress field and the common numerical solution (stresses or displacements) obtained by an ordinary tool such as the finite element method or boundary element method, a simple and effective numerical method is developed to calculate stress intensity factors for one and two singularities. Three examples show that the stress intensity factors evaluated using the method proposed in this paper are very accurate.     

Evaluating mixed-mode stress intensity factors from full-field displacement fields obtained by optical methods

A method for evaluating mode I, mode II and mixed-mode stress intensity factors from in-plane displacement fields using the method of nonlinear least-squares is proposed in this paper. Along with stress intensity factors, crack tip location and rigid body displacement components are determined simultaneously from both displacement components obtained using full-field optical methods or numerical methods. The effectiveness is validated by applying the proposed method to mixed-mode displacement fields obtained through digital image correlation, displacement fields obtained by analysis using elasto-plastic finite element method, and displacement fields around a fatigue crack obtained by electronic speckle pattern interferometry. Results show that the proposed method can extract stress intensity factors from the displacement fields both accurately and easily. Furthermore, they can be determined even if the material at a crack tip exhibits small-scale yielding. It is expected that the proposed method is applicable to various fracture problems during experimental and numerical evaluation of structural components.     

A new method of crack-tip opening displacement determined based on maximum crack opening displacement

In this paper a new method is presented to determine the crack-tip opening displacement (CTOD) for the center cracked plate with uniaxial uniform tension load. The maximum crack opening displacement (MCOD) is adopted to estimate CTOD. Based on the series of calculation results by elastic–plastic finite element simulation, an explicit function expression for the CTOD versus MCOD is determined, which enables to consider the influence effects of crack geometries, plate sizes, applied loads, plane state and material properties. Hence, the presented method of CTOD determined by MCOD is suitable to any center crack finite plate of any material under uniaxial tension.     

Computation of the stress intensity factors for repaired cracks with bonded composite patch in mode I and mixed mode

In this study, the finite element method is used to analyse the behaviour of repaired cracks with bonded composite patches in mode I and mixed mode by computing the stress intensity factors at the crack tip. The effects of the patch size and the adhesive properties on the stress intensity factors variation were highlighted. The plot of the stress intensity factors according to the crack length in mode I, shows that the stress intensity factor exhibits an asymptotic behaviour as the crack length increases. In mixed mode, the obtained results show that the Mode I stress intensity factor is more affected by the presence of the patch than that of mode II.     

Weight function,stress intensity factor and crack opening displacement solutions to periodic collinear edge hole cracks

Periodic collinear edge hole cracks and arbitrary small cracks emanating from collinear holes, which are two typical multiple site damages occurred in the aircraft structures, are studied by using the weigh function method. An explicit closed form weight function for periodic edge hole cracks in an infinite sheet is obtained and further used to calculate the stress intensity factor and crack opening displacement for various loading cases. Compared to finite element method, the present weight function is accurate and highly efficient. The interactions of the holes and cracks on the stress intensity factor and crack opening displacement are quantitatively determined by using the present weight function. An approximate weight function method is also proposed for arbitrary small cracks emanating from multiple collinear holes. This method is very useful for calculating the stress intensity factor for arbitrary small cracks.     

Stress intensity factors for an inclined edge crack in a semiplane

Mode I and II Stress Intensity Factors under uniform general biaxial loadings were derived for an inclined edge crack in a semiplane. By interpolating Finite Element results in the angular range [0°÷80°], analytical expressions were obtained for both K_I and K_II with an accuracy better than 1%. Influence coefficients were defined in the crack reference frame thus highlighting the coupling effects between Modes I and II due to the loss of symmetry when the crack is not normal to the surface.     

Crack tip opening displacement of a Dugdale crack in a three-phase cylindrical model composite material

The analytical investigation of the plastic zone size of a crack in three-phase cylindrical model composite material was carried out. The physical problem is simulated as a crack near a circular inclusion (a single fiber) in the composite matrix, while the three-phase cylindrical composite model is used to represent the composite matrix. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. With the Dugdale model of small scale yielding, a thin strip of yielded plastic zone is introduced at each crack tip. Using the solution for a three-phase model with a single dislocation in the matrix phase as the Green’s function, the physical problem is formulated into a set of singular integral equations. By employing Erdogan and Gupta’s method, as well as iterative numerical procedures, the singular integral equations are solved numerically for the plastic zone sizes and crack tip opening displacements.     

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.     

The fracture toughness of Ni/Al2O3 laminates by digital image correlation I: Experimental crack opening displacement and R-curves

The crack opening displacement of laminates made of alumina/nickel was measured using digital image correlation (DIC). The crack opening displacements were validated with a finite-element model that uses the characteristic bridging-stress bridging-displacement relationship obtained experimentally by testing a constrained nickel sandwich in tension. The method is a simple, accurate way of measuring the crack opening displacement (COD) in ceramic/metal laminates.     

Stress intensity factor for center-cracked plate with crack surface interference

This paper presents a simple and physically acceptable analysis of stress intensity factor (SIF) for the center-cracked infinite and finite-width plates. The analysis includes the effect of crack surface interference (i.e., the upper and lower crack surfaces are not allowed to overlap) that influences both the SIF at the tension-side crack tip and the crack opening displacement (COD) profile. For an infinite plate, exact solutions are obtained by superimposing the classical (overlapping) solutions. For a finite-width plate, where the SIF solutions cannot be found in closed form, the solutions are carried out numerically. The overlapping SIF solutions from the weight function method are used. An example is given for the case of a finite-width plate under bending. It was found that the overlapping solutions underestimate the stress intensity factor at the tension-side crack tip up to 15%. The analysis results are also compared with the finite element solutions for verification purpose.     

Stress intensity factors for functionally graded solid cylinders

This paper presents the mode I stress intensity factors for functionally graded solid cylinders with an embedded penny-shaped crack or an external circumferential crack. The solid cylinders are assumed under remote uniform tension. The multiple isoparametric finite element method is used. 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. The influence for embedded cracks is quite different from that for external cracks.     

Stress intensity factors evaluation for through-transverse crack in slab track system under vehicle dynamic load

The stress intensity factors (SIFs) for through-transverse crack in the China Railway Track System (CRTS II) slab track system under vehicle dynamic load are evaluated in this paper. A coupled dynamic model of a half-vehicle and the slab track is presented in which the half-vehicle is treated as a 18-degree-of-freedom multi-body system. The slab track is modeled as two continuous Bernoulli–Euler beams supported by a series of elastic rectangle plates on a viscoelastic foundation. The model is applied to calculate the vertical and lateral dynamic wheel–rail forces. A three-dimensional finite element model of the slab track system is then established in which the through-transverse crack at the bottom of concrete base is created by using extended finite element method (XFEM). The wheel–rail forces obtained by the vehicle-track dynamics calculation are utilized as the inputs to finite element model, and then the values of dynamic SIFs at the crack-tip are extracted from the XFEM solution by domain based interaction integral approach. The influences of subgrade modulus, crack length, crack angle, friction coefficient between cracked surfaces, and friction coefficient between faces of concrete base and subgrade on dynamic SIFs are investigated in detail. The analysis indicates that the subgrade modulus, crack length and crack angle have great effects on dynamic SIFs at the crack-tip, while both of the friction coefficients have negligible influences on variations of dynamic SIFs. Also the statistical characteristics of varying SIFs due to random wheel–rail forces are studied and results reveal that the distributions of dynamic SIFs follow an approximately Gaussian distribution with different mean values and standard deviations. The numerical results obtained are very useful in the maintenance of the slab track system.     

Calculation of stress intensity factors based on mode I crack opening integral parameters

We present stress intensity factor assessment using nodal displacements of the crack surfaces determined by the finite element method for cracked bodies. The equation is solved by expanding the crack opening displacement in the Chebyshev function, where crack front asymptotic behavior corresponds to the regulations of the linear elastic fracture mechanics. Results of the stress intensity factor calculations are obtained for test problems with analytical solution. Crack opening displacements are defined with the help of the 3D SPACE software package designed to model mixed variational formulation of the finite element method for displacements and strains of the thermoelastic boundary value problems. Translated from Problemy Prochnosti, No. 6, pp. 122–127, November–December, 2008.     

Optimum strain gage location for evaluating stress intensity factors in single and double ended cracked configurations

A general methodology has been proposed for calculation of optimum radial strain gage locations for measurement of the stress intensity factors using strain gage technique. The upper bound (r_max) of strain gage locations for complex single ended and double ended cracked configurations has been determined using the proposed method. Further, dependency of the r_max on the crack length to width ratio and on the state of stress is investigated. Numerical results obtained from the present investigation are observed to be in accordance with the theoretical predictions. Using the proposed approach the correctness of strain gage locations used by the earlier researchers is also verified.     

The effect of material combinations and relative crack size to the stress intensity factors at the crack tip of a bi-material bonded strip

Several types of singular stress fields may appear at the corner where an interface between two bonded materials intersects a traction-free edge depending on the material combinations. Since the failure of the multi-layer systems often originates at the free-edge corner, the analysis of the edge interface crack is the most fundamental to simulate crack extension. In this study, the stress intensity factors for an edge interfacial crack in a bi-material bonded strip subjected to longitudinal tensile stress are evaluated for various combinations of materials using the finite element method. Then, the stress intensity factors are calculated systematically with varying the relative crack sizes from shallow to very deep cracks. Finally, the variations of stress intensity factors of a bi-material bonded strip are discussed with varying the relative crack size and material combinations. This investigation may contribute to a better understanding of the initiation and propagation of the interfacial cracks.