Stress Intensity Factor Distribution Research Articles

Extended layerwise method for laminated composite plates with multiple delaminations and transverse cracks

In this paper, the extended layerwise method (XLWM), which was developed for laminated composite beams with multiple delaminations and transverse cracks (Li et al. in Int J Numer Methods Eng 101:407---434, 2015), is extended to laminated composite plates. The strong and weak discontinuous functions along the thickness direction are adopted to simulate multiple delaminations and interlaminar interfaces, respectively, whilst transverse cracks are modeled by the extended finite element method (XFEM). The interaction integral method and maximum circumferential tensile criterion are used to calculate the stress intensity factor (SIF) and crack growth angle, respectively. The XLWM for laminated composite plates can accurately predicts the displacement and stress fields near the crack tips and delamination fronts. The thickness distribution of SIF and thus the crack growth angles in different layers can be obtained. These information cannot be predicted by using other existing shell elements enriched by XFEM. Several numerical examples are studied to demonstrate the capabilities of the XLWM in static response analyses, SIF calculations and crack growth predictions.

A plastic stress intensity factor approach to turbine disk structural integrity assessment

This study based on a new fracture mechanics parameter is concerned with assessing the integrity of cracked steam turbine disk which operate under startup-shutdown cyclic loading conditions. Damage accumulation and growth in service have occurred on the inner surface of slot fillet of key. In order to determine elastic-plastic fracture mechanics parameters full-size stress-strain state analysis of turbine disk was performed for a quote-elliptical part-through cracks under considering loading conditions. As a result distributions of elastic and plastic stress intensity factors along crack front in slot fillet of key of turbine disk depending on surface crack form are defined. An engineering approach to the prediction of carrying capacity of cracked turbine disk which is sensitive to the loading history at maintenance is proposed. The predictions of the rate of crack growth and residual lifetime of steam turbine disk are compared for elastic and elastic-plastic solutions. It is shown that the previously proposed elastic crack growth models provide overestimate the lifetime with respect to the present one. An advantage to use the plastic stress intensity factor to characterize the fracture resistance as the self-dependent unified parameter for a variety of turbine disk configurations rather than the magnitude of the elastic stress intensity factors alone is discussed.

Stress intensity factor of semi-elliptical surface crack in a thermo-mechanically loaded cylinder with hoop wrapped FGM layer

This article focused on three dimensional fracture analyses of a pressurized cylinder with hoop wrapped functionally graded material layer, which contains a longitudinal semielliptical internal surface crack and subjected to temperature gradient. The effect of non-uniform coefficient of thermal expansion and the hoop wrapped layer thickness on the distribution of the stress intensity factor along the crack front for different crack profiles is also studied. The results, which are normalized for the advantage of non-dimensional analysis show that the hoop wrapped functionally graded material cylinder, can significantly influence on the amount and distribution of stress intensity factors along the crack front.

3-D Stress Intensity Factors due to Full Autofrettage for Inner Radial or Coplanar Crack Arrays and Ring Cracks in a Spherical Pressure Vessel

Three dimensional, Mode I, Stress Intensity Factor (SIF) distributions for radial or coplanar crack arrays as well as ring cracks emanating from the inner surface of an autofrettaged spherical pressure vessel are evaluated. The 3-D analysis is performed via the finite element (FE) method employing singular elements along the crack front. A novel realistic autofrettage residual stress field incorporating the Bauschinger effect is applied to the vessel. The residual stress field is simulated in the FE analysis using an equivalent temperature field. Numerous radial and coplanar crack array configurations are analyzed as well as ring cracks of various depths. SIFs distributions are evaluated for arrays of radial or coplanar cracks consisting of cracks of depth to wall thickness ratios of a/t=0.1-0.6, and ellipticities of a/c=0.2-1.0 prevailing in a fully autofrettaged spherical vessels, ε=100%, of different geometries R0/Ri=1.1, 1.2, and 1.7. SIFs are evaluated for radial arrays containing n=1-20 cracks, and for arrays of coplanar cracks of δ=0-0.95 densities. Furthermore, SIFs for inner ring cracks of various crack depth to wall thickness ratios of a/t=0.025-0.6 are also evaluated. In total, about three hundred different crack configurations are analyzed. A detailed study of the influence of the above parameters on the prevailing SIF is conducted. The results clearly demonstrate the favorable effect of autofrettage which may considerably reduce the prevailing effective stress intensity factor, thus delaying crack initiation and slowing down crack growth rate, and hence, substantially prolonging the total fatigue life of the vessel. Furthermore, the results emphasize the importance of properly accounting for the Bauschinger effect including re-yielding, as well as the significance of the three dimensional analysis herein performed. Furthermore, it is shown that in some cases the commonly accepted approach that the SIF for a ring crack of any given depth is the upper bound to the maximum SIF occurring in an array of coplanar cracks of the same depth is not universal.

Numerical simulation of fatigue crack growth in friction stir welded T joint made of Al 2024 T351 alloy

The Extended Finite Element Method (xFEM) has been applied to simulate fatigue crack growth in an AA2024-T351 T welded joint, 5 mm thick, made by friction stir welding. The ABAQUS and Morfeo software has been used. Tensile fatigue loading (mean stress 10 MPa, stress ratio R=0) is applied to Tjoints with a configuration suitable for reinforced panels where both skin and the web (reinforcement or stiffener) is made of a high strength AA2024-T351. Crack is introduced in one edge of the skin base material. The properties of materials in the areas of joints and geometry measures of Tjoint are adopted from available experiments. Following numerical results are obtained: crack front coordinates (x, y, z) and stress intensity factors (KI, KII, KIII and Kef) distribution along the crack tip, as well as the fatigue life estimation for every crack propagation step. The main objective of this research is to better understand fatigue behaviour of friction stir welded T joint of AA2024-T351.

The Bauschinger Effect's Influence on the Stress Intensity Factors of a Semi-Elliptical Crack Emanating From an Erosion at the Bore of a Fully Autofrettaged Pressurized Cylinder

The benefits of autofrettage for thick-walled cylindrical vessels as a means of improving the vessel's durability and sustainability have been addressed in the published literature. However, the presence of the Bauschinger effect (BE) complicates the overall effect of autofrettage, especially when complex three-dimensional crack geometries emanating from erosions at the cylinder bore are considered. In this paper, the BE's impact on the stress intensity factors (SIFs) on such cracks is investigated. The effect of various erosion geometrical configurations on the mode I SIF distribution along the front of a semi-elliptical crack, emanating from the deepest line of the erosion surface (DLES) at the bore of an autofrettaged, pressurized thick-walled cylinder of outer-to-inner radius ratio, Ro/Ri = 2, is investigated. Both autofrettage with BE (BEDA) and Hill's ideal autofrettage residual stress field (BEIA) are considered and simulated by an equivalent thermal load. The SIFs are determined for the semi-elliptical cracks of various crack depths to wall thickness ratio, a/t = 0.05–0.25, and ellipticities, a/c, ranging from 0.5 to 1.5, emanating from the DLES via Ansys software and the nodal displacement method. Three groups of erosion geometries are considered: (a) arc erosions of constant relative depth, d/t, equal to 5% and with relative radii of curvature, r′/t, between 5% and 30%; (b) semi-elliptic erosions of constant relative depth, d/t, of 5% with erosion ellipticity, d/h, varying from 0.3 to 2.0; and (c) semicircular erosions of relative depth, d/t, between 1% and 10% of the wall thickness. KIP, the SIF due to pressurization, is highly dependent on the stress concentration ahead of the DLES which directly relates to the erosion geometry. It is found that the absolute value of KIA, the SIF due to autofrettage, is just slightly reduced by the presence of the erosion. Its change solely depends on, and is directly proportional to, the erosion depth. Thus, the combined SIFs of deep cracks are found to be significantly enhanced by the presence of autofrettage and might result in a shortening of the vessel's fatigue life by up to an order of magnitude. Counteracting this, the combined SIFs are found to be significantly higher for BEDA cases than for BEIA cases. Therefore, the vessel's fatigue life can be profoundly influenced by the presence of the BE.

Influence of crack offset distance on the interaction of multiple cracks on the same side in a rectangular plate

In the present work finite element method has been employed to study the interaction of multiple cracks in a finite rectangular plate of unit thickness with cracks on the same side under uniaxial loading conditions. The variation of the stress intensity factor and stress distribution around the crack tip with crack offset distance has been studied. Due to the presence of a neighbouring crack, two types of interactions viz. intensification and shielding effect have been observed. The interaction between the cracks is seen to be dependent on the crack offset distance. It is seen that the presence of a neighbouring crack results in the appearance of mode II stress intensity factor which was otherwise absent for a single edge crack. It can be said that the proximity of cracks is non-desirable for structural integrity. The von-Mises stress for different crack orientations has been computed. Linear elastic analysis of state of stress around the crack tip has also been done.

Effect of vertex singularities on stress intensities near plate free surfaces

AbstractThe stress intensity factor (SIF) distribution along the front of a through‐the‐thickness crack is significantly influenced by the presence of the 3D corner (vertex) singularities. All past 3D finite element studies indicated that for mode I, SIF rapidly decreases near the free surface and for mode II, it sharply increases. From the previous numerical simulations, it is unclear what the limiting values of SIF near the surface are and whether these values are infinite or bounded at the vertex point. In this paper, we conduct a careful finite element study and propose a theoretical equation, which describes the SIF behaviour near the vertex. We demonstrate that the asymptotic behaviour of SIF near the surface is governed by the difference in the strength of the corner and edge singularities. Furthermore, we validate our numerical approach and calculations by utilising the invariant properties of J‐integral.

Analysis of Cracked and Notched Round Bars Under Rotary Bending

Abstract The fatigue growth of surface flaws in both smooth and notched round bars subjected to rotary bending was numerically simulated by means of a two-parameter theoretical model proposed by the first author. The stress intensity factor distribution along the crack front was needed in order to apply the model. Therefore, finite element analyses and the superposition principle were used to determine such a distribution for a wide range of crack configurations and any position of the flaw with respect to the bending moment axis. The results related to rotary bending are compared to those related to pulsating cyclic bending, and a qualitative comparison is made with some data reported in the literature.

Characteristics of crack front stress fields in three-dimensional single edge cracked plate specimens under general loading conditions

In the present article, extensive three-dimensional finite element analyses are conducted for elastic single edge cracked plate (SECP) specimens, which is one of the most widely used specimen for fracture toughness testing. A wide range of geometrical parameters variations are considered including in-plane crack depth to plate width ratio (a/W) and out-of-plane plate thickness to width ratio (t/W). Furthermore, for each three-dimensional specimen, four different crack loading conditions are considered including uniform, linear, parabolic and cubic stress distributions applied on the crack surface. Complete solutions of stress intensity factor, in-plane T-stress (T11) and out-of-plane T-stress (T33) stresses along the edge-crack front are obtained. Characterizations of crack front stress fields using stress intensity factor and T11 and T33 parameters are carried out. By using superposition method, the present solutions enable the calculations of the stress intensity factors, and T-stresses for wide range of a/W,t/W and under generally loading conditions. Application of this method for the determination of these fracture mechanics parameters for other arbitrary loading conditions, are carried out. The combination of the effects of crack depths (a/W), plate thickness (t/W), and loading conditions on the crack front distributions of stress intensity factor, T11 and T33 stress are thus discussed. Solutions obtained will be very useful for analyzing fracture toughness test data for single edge cracked plate specimens with different crack depths (a/W), thickness ratios (t/W), and under general loading conditions.

G0301201 微小三次元表面き裂の応力拡大係数の分布の定式化

G0301201 微小三次元表面き裂の応力拡大係数の分布の定式化

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.

3-D stress intensity factors due to autofrettage for an inner radial lunular or crescentic crack in a spherical pressure vessel

Three dimensional Mode I Stress Intensity Factor (SIF) distributions along the front of an inner radial lunular or crescentic crack emanating from the bore of an autofrettaged spherical pressure vessel are evaluated. The 3-D analysis is performed using the finite element (FE) method employing singular elements along the crack front. A novel realistic autofrettage residual stress field incorporating the Bauschinger effect is applied to the vessel. The residual stress field is simulated in the FE analysis using an equivalent temperature field. SIFs for three vessel geometries (R0/Ri=1.1, 1.2, and 1.7), a wide range of crack depth to wall thickness ratios (a/t=0.01–0.8), various ellipticities (a/c=0.2–1.5), and three levels of autofrettage (ε=50%, 75%, and 100%) are evaluated. In total, about two hundred and seventy different crack configurations are analyzed. A detailed study of the influence of the above parameters on the prevailing SIF is conducted. The results clearly indicate the possible favorable effect of autofrettage in considerably reducing the prevailing effective stress intensity factor i.e., delaying crack initiation, slowing crack growth rate, and thus, substantially prolonging the total fatigue life of the vessel. Furthermore, the results emphasize the importance of properly accounting for the Bauschinger effect including re-yielding, as well as the significance of the three dimensional analysis herein performed.

The elastic and plastic constraint parameters for three-dimensional problems

Fracture toughness and the in-plane and out-of-plane constraint effects are studied through experiments and computations for high-strength carbon steel 34ХН3МА. The subjects for the studies are single-edge-notched bend specimens under three-point bending and compact specimens under tension. Both types of specimens are of non-standard configuration because the specimen thickness-to-width ratio was varied in the range of 0.1–1.0, and the relative crack length was changed in the range of 0.24–0.64. Characterization of the constraint effects was performed using the non-singular T-stresses, the local triaxiality parameter h, and the TZ and TZZ, factors of the stress-state in a 3D cracked body. For the particular geometries of the specimens considered, the numerical constant of the plastic stress field In and the plastic stress intensity factor distributions along the crack front are obtained as a function of the dimensionless crack length and the specimen thickness. It is further demonstrated that the plastic stress intensity factor accounting for the in-plane and out-of-plane constraint effects can be used to characterize the fracture resistance characteristics as a unified single parameter for a variety of specimen geometries.

The complex variable fast multipole boundary element method for the analysis of strongly inhomogeneous media

The paper aims to develop the efficient method tailored for accurate, robust and stable calculations of 2D local fields in strongly inhomogeneous materials with arbitrary interaction conditions on multiple contacts of structural blocks. The method is also to be of immediate use for solving homogenisation problems. To reach the goal we employ: (i) special forms of the complex variable singular and hypersingular integral equations with the densities representing those physical quantities, which enter the contact conditions; (ii) circular-arc boundary elements (in addition to straight elements) for smooth approximation of smooth parts of the external boundaries and contacts; (iii) higher order approximations of densities, which account for arbitrary power asymptotics of physical fields near singular points (crack tips, corner points, common apexes of structural blocks); (iv) analytical recurrent evaluation of all influence coefficients; (v) analytical recurrent evaluation of all moments; (vi) the complex variable fast multipole method (CV FMM), for solving the resulting system of the complex variable boundary element method (CV BEM), with large number (up to million) of unknowns. As a result, we obtain free of numerical integration, higher-order CV fast multipole boundary element method (CV FM-BEM) for a medium with multiple structural elements and multiple singular points. In the due course, we suggest the simplified starting quadrature formulae for singular boundary elements, the adjustment of the procedure for building the hierarchical tree and the proper choice of the key parameters of the developed CV FM-BEM: the number of elements in a leaf; the number of moments in the truncated Taylor expansions; the reasonable tolerance, when iteratively solving the system by the FMM. Numerical examples illustrate the abilities of the method developed, as regard to local fields in strongly inhomogeneous structures with multiple singular points. The study of local fields shows application of the method to finding extreme distributions of stress intensity factors in a medium with many cracks, which may intersect. The homogenisation problem is solved, as well.

Numerical Modelling of Crack Propagation in Friction Stir Welded Joint Made of Aluminium Alloy

In this work, fatigue crack propagation in thin-walled aluminium alloy structure with two friction stir welded (FSW) joints has been numerically modelled. Crack propagation in unstiffened part of the structure between two FSW joints is analyzed. Numerical method, so-called eXtended Finite Element Method (XFEM) has been used, including software Abaqus, as well as Morfeo, for modelling and results display. Tensile fatigue loading is applied, with stress ratio R=0. The analyzed model is made from aluminium alloy 2024-T351. Material properties in joints zones and geometry measures of FSW joint are adopted from available experiments.Following results are obtained by numerical analysis:•stress-displacement state in the structure, where special attention is dedicated to the crack tip zone,•coordinates of the crack front (x, y, z) for every propagation step,•distributions of stress intensity factors - KI, KII, KIII and Keq along the crack front for each propagation step,•structural life in form of change of applied number of load cycles, N, for each step of propagation.Besides numerical results, Abaqus provides visualization of crack propagation in the structure. On the basis of obtained data, analysis of crack growth stability is done.

Crack Front Shapes and Stress Intensity Factors in Plates under a Pure Bending Loading that Induces Partial Closure of the Crack Faces

This paper investigates, both experimentally and numerically, stress intensity factors and evolving geometry of through edge cracks in plates loaded under pure transverse bending; the loading induces partial closure of the crack faces. After performing experiments on steel specimens, it was found that a kink in the crack front forms as the crack grows, changing the initial straight front into an L-shape. To understand the distribution of stress intensity factors along such crack fronts, the observed crack shapes were reproduced in a three-dimensional fracture code (FRANC3D) coupled with a finite element analysis program (ABAQUS). With this coupled system, linear elastic stress analyses were performed considering the nonlinear effects caused by the crack face contact in the compressed region. The proposed methodology computes stress intensity factors along the crack front based on observed crack front shapes obtained from the experimental tests. A method is proposed to treat numerical noise around the crack front kink and at crack front end. In addition, normalized empirical expressions for stress intensity factors are proposed.

A 50‐year retrospective review of three‐dimensional effects at cracks and sharp notches

ABSTRACTThis review is a brief survey of three‐dimensional effects at cracks and sharp notches. The overall aim is to review developments over the past 50 years leading up to the current state of the art. The review is restricted to linear elastic, homogeneous, isotropic materials, with any yielding confined to a small region at a crack or notch tip. It is also restricted to static loading and to constant amplitude fatigue loading. An enormous amount of theoretical and experimental information relevant to three‐dimensional effects has been published in the past five decades, so the review is, of necessity, highly selective. Theoretical topics covered are linear elastic fracture mechanics, including Volterra distorsioni, stress intensity factors, corner point singularities, crack front line tension, displacement analysis of cracks and notches, and through thickness distributions of stresses and stress intensity factors. Crack path topics covered are fatigue crack path constraints, determination of fatigue crack paths, oscillating crack fronts in thin sheets and the transition to slant crack propagation in thin sheets. Plane strain fracture toughness testing, including standards, is covered. Overall, it can be concluded that the existence of three‐dimensional effects at cracks and sharp notches has been known for many years, but understanding has been limited, and for some situations still is. Understanding improved when the existence of corner point singularities and their implications became known. Increasingly powerful computers made it possible to investigate three‐dimensional effects numerically in detail. Despite increased understanding, three‐dimensional effects are sometimes ignored in situations where they may be important.

Influence of p-method finite element parameters on predictions of crack front geometry

The effect of various p-method finite element model parameters on the prediction of planar crack front geometry in three dimensional structures is evaluated. An automatic crack growth method was developed using the commercial software StressCheck coupled with Microsoft Excel. The geometry of the evolving crack front was predicted using iterations of three dimensional finite element models to determine the stress intensity values at discrete points along the crack front and incrementing the crack length locally using the Paris growth law. Modeling parameters such as the global mesh size, p-level, crack tip mesh size, and the extraction radius used for determining the stress intensity factors were all considered. The effect of these parameters on the predicted shape of a growing elliptical crack front was evaluated through a series of simulations of a corner crack emanating from a centered hole in a plate. A single model of a through crack with a straight crack front was also used to compare the effects of the model parameters on a different geometric configuration. This study has shown that the corner crack geometry and the growth series are more sensitive to the number of elements along the crack front and the extraction radius than the through thickness crack. In addition, convergence of the predicted crack front geometry does not guarantee convergence of the distribution of stress intensity factors along the crack front. It was also determined that for the models considered, using a smaller overall mesh size is a more effective way of decreasing discretization error than increasing the p-level.

Weight function method to determine stress intensity factor for semi-elliptical crack with high aspect ratio in cylindrical vessels

Failure of cylindrical vessels can be caused by stress singularity at pitting corrosion induced cracks. Literature suggests that most of research focuses on stress intensity factors for surface cracks with low aspect ratios, i.e., a/c⩽1.0. Situation may well arise where the aspect ratio of cracks is larger than one. This paper attempts to propose a weight function method to determine stress intensity factors for high aspect ratio semi-elliptical cracks in cylindrical vessels. The weight functions are derived based on three dimensional finite element analysis. The proposed weight function method is verified both numerically and analytically. It is found that the higher the aspect ratio of cracks the larger the stress intensity factors at the surface point, and that the aspect ratio of cracks tends to change the distribution of stress intensity factor along the cracks which can alter the failure mode of cylindrical vessels. The paper concludes that the proposed weight function method can serve as a useful tool for the accurate and efficient prediction of stress intensity factors for longitudinal surface cracks with various aspect ratios in cylindrical vessels subjected to arbitrary loads.