3-D stress intensity factors for arrays of inner radial lunular or crescentic cracks in a typical spherical pressure vessel

Many spherical pressure vessels are manufactured by methods such as the integrated hydro-bulge forming (IHBF) method, where the sphere is composed of a series of double curved petals welded along their meridional lines. Such vessels are susceptible to multiple radial cracking along the welds. For fatigue life assessment and fracture endurance of such vessels one needs to evaluate the stress intensity factors (SIFs) distribution along the fronts of these cracks. However, to date, only two 3-D solutions for the SIF for one inner semi-elliptical crack in thin or thick spheres are available, as well as 2-D SIFs for one through-the-thickness crack in thin spherical shells. In the present paper, mode I SIF distributions for a wide range of lunular and crescentic cracks are evaluated. The 3-D analysis is performed, via the FE method employing singular elements along the crack front, for a typical spherical pressure vessel with outer to inner radius ratios of η = R_o/R_i = 1.1. SIFs are evaluated for arrays containing n = 1-20 cracks; for a wide range of crack depth to wall thickness ratio, a/t, from 0.025 to 0.95; and for various ellipticities of the crack, i.e., the ratio of crack depth to semi crack length, a/c, from 0.2 to 1.5. The obtained results clearly indicate that the SIFs are considerably affected by the three-dimensionality of the problem, and the following parameters: the number of cracks in the array-n, the relative crack depth a/t, and the crack ellipticity a/c.     

Weight functions and stress intensity factors for quarter-elliptical corner cracks in fastener holes

Approximate weight functions for a quarter‐elliptical crack in a fastener hole were derived from a general weight function form and two reference stress intensity factors. Closed‐form expressions were obtained for the coefficients of the weight functions. The derived weight functions were validated against numerical data by comparison of stress intensity factors calculated for several nonlinear stress fields. Good agreements were achieved. These derived weight functions are valid for the geometric range of 0.5 ≤a/c≤ 1.5 and 0 ≤a/t≤ 0.8 and R/t= 0.5; and are given in forms suitable for computer numerical integration. The weight functions appear to be particularly suitable for fatigue crack growth prediction of corner cracks in fastener holes and fracture analysis of such cracks in complex stress fields.     

On estimating stress intensity factors and modulus of cohesion for fractal cracks

Existing solutions for the singular stress field in the vicinity of a fractal crack tip have been adapted for a somewhat modified problem. Since the integration along the fractal curve is prohibitive and does not lend itself to the presently available mathematical treatments, a simplified one has replaced the original problem. The latter involves a smooth crack embedded in a singular stress field, for which the order of singularity is adjusted to match exactly the one obtained from the analyses pertaining to the fractal crack. Of course, this is only an approximation, and we may only hope that it leads toward correct results, at least in a cursory sense. The advantage of such an approach becomes obvious when one inspects the final closed-form solutions for (a) the stress intensity factor in mode I fractal fracture, and (b) cohesion modulus, which results from the cohesive zone model and serves as a measure of the material resistance to crack propagation. As expected for the fractal geometry employed here, our results are strongly dependent on the fractal dimension D (or roughness exponent H).     

FE analysis of stresses and stress intensity factors of interfacial cracks in a CTS specimen

A plane stress finite element analysis was implemented to understand the stress fields for a crack lying at an aluminium/epoxy interface of a compact tension and shear specimen. The interaction integral method was used to separate the mixed-mode stress intensity factors at the interfacial crack-tip under different loading modes, which can have important implications for characterisation of interfacial crack growth.     

Extraction of stress intensity factors for 3D small fatigue cracks using digital volume correlation and X-ray tomography

This paper describes a methodology used to compute stress intensity factor values along the curved front of a fatigue crack inside a nodular cast iron. An artificial defect is introduced at the surface of a small sample. The initiation and growth of a fatigue crack from this defect during constant amplitude cycling is monitored in situ by laboratory X-ray tomography. The method for processing the 3D images in order to compute SIF values is described in detail. The results obtained show variations of the stress intensity factor values along the crack front.     

Analysis of stress intensity factors for three-dimensional interface crack problems in electronic packages using the virtual crack closure technique

In this study the fracture mechanics parameters, including the strain energy release rate, the stress intensity factors and phase angles, along the curvilinear front of a three-dimensional bimaterial interface crack in electronic packages are considered by using finite element method with the virtual crack closure technique (VCCT). In the numerical procedure normalized complex stress intensity factors and the corresponding phase angles (Rice, J Appl Mech 55:98–103, 1988) are calculated from the crack closure integrals for an opening interface crack tip. Alternative procedures are also described for the cases of crack under inner pressure and crack faces under large-scale contact. Validation for the procedure is performed by comparing numerical results to analytical solutions for the problems of interface crack subjected to either remote tension or mixed loading. The numerical approach is then applied to study interface crack problems in electronic packages. Solutions for semi-circular surface crack and quarter-circular corner crack on the interface of epoxy molding compound and silicon die under uniform temperature excursion are presented. In addition, embedded corner delaminations on the interface of silicon die and underfill in flip-chip package under thermomechanical load are investigated. Based on the distribution of the fracture mechanics parameters along the interface crack front, qualitative predictions on the propensity of interface crack propagation under thermomechanical loads are given.     

Boundary element method for <Emphasis Type="Italic">J</Emphasis>-integral and stress intensity factor computations in three-dimensional interface cracks

A general numerical tool for the analysis of three–dimensional bimaterial interface cracks is presented in this paper. The proposed tool is based on a multidomain formulation of the Boundary Element Method (BEM), with the crack located at the interface of the domain. Mixed mode stress intensity factors are computed along the three-dimensional crack fronts using the Energy Domain Integral (EDI) methodology and decoupled via the Interaction Integral. The capability of the procedure is demonstrated by solving a number of examples. The last of these examples consists in a thick centre cracked panel for which the behaviour of the J-integral and the mixed-mode stress intensity factors along the crack front is studied as a function of the material mismatch.     

Dynamic stress intensity factors of two 3D rectangular permeable cracks in a transversely isotropic piezoelectric material under a time‐harmonic elastic P‐wave

The dynamic behavior of two 3D rectangular permeable cracks in a transversely isotropic piezoelectric material is investigated under an incident harmonic stress wave by using the generalized Almansi's theorem and the Schmidt method. The problem is formulated through double Fourier transform into three pairs of dual integral equations with the displacement jumps across the crack surfaces as the unknown variables. To solve the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. Finally, the relations among the dynamic stress field and the dynamic electric displacement filed near the crack edges are obtained, and the effects of the shape of the rectangular crack, the characteristics of the harmonic wave, and the distance between two rectangular cracks on the stress and the electric intensity factors in a piezoelectric composite material are analyzed. Copyright © 2015 John Wiley & Sons, Ltd.     

A general weight function approach to compute mode-II stress intensity factors and crack paths for slightly curved or kinked cracks in finite bodies

A simple procedure is proposed that allows computing the stress intensity factors for slightly curved and kinked cracks in finite bodies. Basis of the method is the computation of the stress field around a straight crack under externally applied tractions. Then, this auxiliary crack is replaced by the crack of interest. The stress intensity factors are computed from the stresses caused by the auxiliary crack using the weight function technique. In a practical application of the method, mode-II stress intensity factors are computed for the edge-cracked half-space. From the usual crack path condition, K_II = 0, the paths of propagating cracks under biaxial loading and the critical biaxiality ratio for global directional instability are computed. The results are in very good agreement with finite element computations.     

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.     

Determination of stress intensity factors for semielliptical surface cracks in the WWER-1000 reactor pressure vessel from the results of solving thermoelasticity boundary value problems based on the mixed mesh-projection scheme of the finite element method

Results of numerical analysis of stress intensity factors K_I for semielliptical surface cracks in the WWER-1000 reactor pressure vessel by emergency cooling simulation with known engineering procedures, the equivalent spatial integration and direct methods are presented. Engineering procedures employ the results of numerical solution of axially symmetric boundary value problems of thermoelasticity based on the mixed mesh-projection scheme of the finite element method implemented in the RELAX software. The three-dimensional K_I computations were performed with the SPACE software. __________ Translated from Problemy Prochnosti, No. 2, pp. 45–51, March–April, 2007.