Combined Stress Intensity Factors Research Articles

A three-dimensional elastoplastic analysis of mixed-mode KI/KII around the crack front

Engineering problems that involve fatigue crack growth and fracture frequently can be studied by taking into account only mode-I features. However, many important problems that involve combined mode I and II loadings cannot be properly analyzed by a pure mode-I approach, which in particular may not be sufficient to estimate fracture toughness for practical purposes in such cases. Such mixed-mode problems involve crack orientation and/or load conditions that lead to combined local Stress Intensity Factors (SIFs) KI/KII around the crack front. Using multiaxial crack tip condition characterized by the crack inclination angle βin a mixed-mode KI/KII modified single edge tension SE(T) specimen, such mixed-mode effects on plastic zone shapes, volumes and plastic work UPL are taken into account to evaluate problems that involve fatigue and fracture.

X-ray CT characterization and fracture simulation of ASR damage of glass particles in alkaline solution and mortar

The alkali-silica reaction (ASR) damage in reactive aggregates affects the long-term durability of the concrete infrastructure. The generated ASR gel can expand by imbibing water from the pore solution and the resulting expansion pressure causes the aggregate fracture. This study aims to simulate the development of ASR damage in glass particles of two types of samples (glass in alkali solution and glass mortars). The dynamic micro X-ray CT technique was conducted to monitor the crack propagation in glass aggregates at different reaction stages (up to 64h). The Boundary Element Method (BEM) and Displacement Discontinuity Method (DDM) were used to efficiently simulate the crack propagation within irregular glass particles under gel expansion pressures. The aggregate boundaries were built with the BEM elements and the initial cracks were meshed with the DDM elements. The estimated expansion pressure was applied to the initial crack surfaces. The discontinuous displacements and stresses were calculated along the crack path and crack tip. The mixed-mode Stress Intensity Factors (SIFs) were calculated based on plane stress conditions. The maximum circumferential stress criteria were used to simulate the propagation of cracks along a specific angle. The simulation results include the simulated crack path and the combined SIFs changing with the increments. With the estimate expansion pressure, the glass particle damages were simulated within conditions of alkali solution and confined mortar samples. The predicted crack propagation path was compared with the X-ray CT imaging data. The comparison results demonstrate the DDM has the ability to predicting the ASR damage propagation inside aggregates.

Analysis of a three-dimensional arbitrarily shaped interface crack in a one-dimensional hexagonal thermo-electro-elastic quasicrystal bi-material. Part 1: Theoretical solution

The extended displacement discontinuity boundary integral-differential equation method is adapted to analyze a three-dimensional interface crack of arbitrary shape in a one-dimensional, hexagonal thermo-electro-elastic quasicrystals bi-material. The extended displacement discontinuities include phonon and phason displacement discontinuities, electric potential discontinuity, as well as temperature discontinuity across the interface crack; while the extended stresses represent phonon and phason stresses, electric displacement and heat flux, respectively. An analysis method is proposed based on the analogy between the governing equations for one-dimensional hexagonal electro-thermo-elastic quasicrystals and three-dimensional transversely isotropic magnetoelectrothermoelastic media. By using the analogy method, the fundamental solutions for unit-point extended displacement discontinuities on the interface are obtained. Using the superposition principal, the extended displacement discontinuity boundary integral-differential equations are established. The singular indices and the singular behaviors of the near crack border fields are studied, and the combined extended stress intensity factors (SIFs) are derived in terms of the EDDs.

Analysis of an interface crack of arbitrary shape in a three-dimensional transversely isotropic magnetoelectrothermoelastic bimaterial—part 1: Theoretical solution

ABSTRACTThe extended displacement discontinuity boundary integral–differential equation method is developed for the analysis of an interface crack of arbitrary shape in a three-dimensional (3D), transversely isotropic magnetoelectrothermoelastic bimaterial. The extended displacement discontinuities (EDDs) include conventional displacement discontinuities, electric potential discontinuity, magnetic potential discontinuity as well as temperature discontinuity across the interface crack faces, correspondingly, while the extended stresses represent conventional mechanical stresses, electric displacement, magnetic induction, heat flux, etc. By virtue of the potential functions and Hankel transformation technique, the fundamental solutions for unit-point EDDs on the interface in a 3D transversely isotropic magnetoelectrothermoelastic bimaterial are derived, then the extended displacements and stresses are all obtained in terms of EDDs. An analysis method is proposed based on the analogy with the solution in an isotropic thermoelastic bimaterial. The singular indices and the singular behaviors of the near crack-tip fields are studied. The combined extended stress intensity factors for three new fracture modes are derived in terms of the EDDs and are compared with those in magnetoelectroelastic bimaterials.

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.

Excitation Action Triggered by Perilous Rock Avalanche to the Stability of Perilous Rock

The mechanism failure of massive perilous rock should consider the interaction among perilous rock masses. Study on the stability of adjacent perilous rock from the excitation wave, which is produced by the perilous rock mass at the collapse instantaneousness, has important significance. Focusing on the falling-type perilous rock, physical model of perilous rock with excitation wave is considered and the stress characteristics for the excitation wave of perilous rock avalanche on dominant fissure with normal incidence is analyzed. Based on the fracture mechanics, a method to calculate the combined stress intensity factors of dominant fissure under falling excitation action of perilous rock is established. As the instance results showed, two cites of nature and rainfall, the stability coefficient are both reduce, specially in the horizontal, stability coefficient reduced by about 10% respectively, while in vertical about 2%. The results provided some scientific progresses disasters prevention and mitigation of perilous rock.

A Study of the Combined Effects of Erosions, Cracks and Partial Autofrettage on the Stress Intensity Factors of a Thick Walled Pressurized Cylinder

For the investigation of cracked problems in thick-walled pressurized cylindrical vessels, the displacement-based finite element method has become one of the main computational tools to extract stress intensity results for their fatigue life predictions. The process of autofrettage, practically from the partial autofrettage level of 30% to full autofrettage level of 100%, is known to introduce favorable compressive residual hoop stresses at the cylinder bore in order to increase its service life. In order to extract the fatigue life, stress intensity factors (SIFs) need to be obtained a priori. The necessity for determining SIFs and their practical importance are well understood. However, it is usually not a trivial task to obtain the SIFs required since the SIFs largely depend on not only the external loading scenarios, but also the geometrical configurations of the cylinder. Our recent work has shown that the Bauschinger effect (BE) may come into play and affect the effective SIFs significantly for an eroded fully autofrettaged thick-walled cylinder. In this study, we further investigate the SIFs for the Bauschinger effect dependent autofrettage (BEDA) and the Bauschinger effect independent autofrettage (BEIA) at various autofrettage levels. The crack is considered to emanate from the erosion's deepest point in a multiply eroded cylinder. The commercial finite element package, ANSYS v12, was employed to perform the necessary analysis. A two-dimensional model, analogous to the authors' previous studies, has been adopted for this investigation. The residual stress field of autofrettage process, based on von Mises yield criterion, is simulated by thermal loading. The combined SIFs are evaluated for a variety of relative crack lengths with cracks emanating from the tip of erosions with various geometrical configurations and span angles. The effective SIFs for relatively short cracks are found to be increased by the presence of the erosion and further increased due to the BE at the same autofrettage level, which may result in a significant decrease in the vessel's fatigue life. Deep cracks are found to be almost unaffected by the erosion, but may be considerably affected by BE as well as by the level of partial autofrettage.

Stress Intensity Factors for Partially Autofrettaged Pressurized Thick-Walled Cylinders Containing Closely and Densely Packed Cracks

Due to acute temperature gradients and repetitive high-pressure impulses, extremely dense internal surface cracks can be practically developed in highly pressurized thick-walled vessels, typically in gun barrels. In the authors’ previous studies, networks of typical radial and longitudinal-coplanar, semi-elliptical, internal surface cracks have been investigated assuming both ideal and realistic full autofrettage residual stress fields (ε=100%). The aim of the present work is to extend the analysis twofold: to include various levels of partially autofrettaged cylinders and to consider configurations of closely and densely packed radial crack arrays. To accurately assess the stress intensity factors (SIFs), significant computational efforts and strategies are necessary, especially for networks with closely and densely packed cracks. This study focuses on the determination of the distributions along the crack fronts of KIP, the stress intensity factor due to internal pressure KIA, the negative stress intensity factor resulting from the residual stress field due to ideal or realistic autofrettage, and KIN, the combined SIF KIN=KIP−|KIA|. The analysis is performed for over 1000 configurations of closely and densely packed semicircular and semi-elliptical networked cracks affected by pressure and partial-to-full autofrettage levels of ε=30–100%, which is of practical benefit in autofrettaged thick-walled pressure vessels. The 3-D analysis is performed via the finite element method and the submodeling technique employing singular elements along the crack front and the various symmetries of the problem. The network cracks will include up to 128 equally spaced cracks in the radial direction: with relative longitudinal crack spacing, 2c/d, from 0.1 to 0.99; autofrettage level of 30–100%; crack depth to wall thickness ratios, a/t, from 0.01 to 0.4; and, cracks with various ellipticities of crack depth to semicrack length, a/c, from 0.2 to 2. The results clearly indicate that the combined SIFs are considerably influenced by the three dimensionality of the problem and the Bauschinger effect (BE). The Bauschinger effect is found to have a dramatic effect on the prevailing combined stress intensity factors, resulting in a considerable reduction of the fatigue life of the pressure vessel. While the fatigue life can be finite for ideal autofrettage, it is normally finite for realistic autofrettage for the same crack network. Furthermore, it has been found that there are differences in the character of the SIFs between closely packed and densely packed crack networks, namely, more dramatic drop-offs in KIA and KIN at the crack-inner bore interface for densely packed cracks further influenced by crack depth.

The Combined Stress Intensity Factors of Multiple Longitudinally Coplanar Cracks in Autofrettaged Pressurized Tubes Influenced by the Bauschinger Effect

The influence of the Bauschinger effect (BE) on the three dimensional, Mode I, combined stress intensity factor (SIF) distributions for arrays of longitudinal coplanar, surface cracks emanating from the bore of a fully or partially autofrettaged thick-walled cylinder is investigated. The combined SIFs, KIN, that depend on pressure effects and the “realistic”—Bauschinger effect dependent Autofrettage (BEDA), or, that depend on pressure effects and the “ideal”—Bauschinger effect independent autofrettage (BEIA), are obtained and compared for crack depth to wall thickness, a∕t=0.01–0.25; crack ellipticity, a∕c=0.5–1.5; crack spacing ratio, 2c∕d=0.25–0.75; and autofrettage level, e=30%, 60%, and 100%. The 3D analysis is performed via the finite element method and the submodeling technique, employing singular elements along the crack front. Both autofrettage residual stress fields, BEDA and BEIA, are simulated using an equivalent temperature field. The combined SIF, KIN, is found to vary along the crack front with the maximum determined by the crack ellipticity, crack depth, and crack spacing ratio. For a partially autofrettaged cylinder, the influence of the BE on the combined SIF, KIN, is substantially reduced as the level of overstrain becomes smaller. For some cases, when comparing like crack distributions, the KIN values obtained from the BEDA model are found to be as much as 100% higher than the KIN values that are computed using the BEIA model. A pressurized thick-walled cylinder with BEDA can be most critical when small cracks are farther apart. As crack depth increases, or when the spacing between cracks is smaller, the SIFs increase. Though the differences in the BEDA SIF, KIA, between e=100% and 60% are small (7–15%, in most cases), the increased level of autofrettage produces a 23–30% decrease in the combined SIF values, KIN. In certain cases, the BEIA model implies an infinite fatigue life, whereas the BEDA model for the same parameters implies a finite life. Therefore, it is important to perform a full 3D analysis to determine the real life cycle of the pressurized cylinder for materials that exhibit the BE.

Error estimation of stress intensity factors for mixed‐mode cracks

AbstractThis paper presents an a posteriori error estimator for mixed‐mode stress intensity factors in plane linear elasticity. A surface integral over an arbitrary crown is used for the separate calculation of the combined mode's stress intensity factors. The error in the quantity of interest is based on goal‐oriented error measures and estimated through an error in the constitutive relation. Copyright © 2006 John Wiley & Sons, Ltd.

3-D Stress Intensity Factors for Internal Cracks in an Overstrained Cylindrical Pressure Vessel—Part II: The Combined Effect of Pressure and Autofrettage

K IA and KIP stress intensity factors (SIF) for three-dimensional semi-elliptical, surface, radial cracks prevailing in a pressurized or autofrettaged thick-walled cylinder were evaluated and discussed in Part I of this paper and in Perl et al. 1996, “Three-Dimensional Interaction Effects in an Internally Multicracked Pressurized Thick-Walled Cylinder—Part I: Radial Surface Cracks,” AMSE J. Pressure Vessel Technol. 118, pp. 357–363), respectively. These SIFs were calculated for a wide range of configurations: for cracks pertaining to large arrays of up to 180 cracks, with ellipticities of a/c=0.2, 0.5, 1, 1.5, depth ratios of a/t=0.05−0.6, and for various levels of autofrettage. In Part II of this paper, the effect of the combined SIF KIN=KIP+KIA is considered, which enables the prediction of fracture endurance, crack growth rate, and the total fatigue life for a modern gun barrel. The results reconfirm the impact autofrettage has on delaying crack initiation and propagation. This favorable effect is found to be governed by ψ=σ0/p—the ratio of the vessel’s material yield stress to its internal pressure. The higher ψ is, the more effective autofrettage becomes. While KIA and KIP reach their maximum absolute values, usually, for an array of n=2 cracks, the largest combined SIF-KIN occurs for arrays of 2–16 cracks. Finally, the similarity in the behavior of KIA and KIP along the crack front is studied as well as its relation to the respective stress fields.

Experimental analysis of an arbitrarily inclined semiinfinite crack terminated at the bimaterial interface

In this paper, the digital photoelastic technique was employed to investigate the effect of different material combinations and different crack inclination angles on the stress-intensity factors (SIFs). To produce a true bimaterial plate, the two component materials were naturally adhered together by a special casting procedure. The experimental results show that dimensionless combined SIF increases with increasingG1/G2 (or crack inclination angles) for different crack inclination angles (orG1/G2's).

Elastodynamic stress-intensity factors for a semi-infinite crack under 3-D combined mode loading

The dynamic stress intensity factor histories for a half plane crack in an otherwise unbounded elastic body are analyzed. The crack is subjected to a traction distribution consisting of two pairs of suddenly-applied shear point loads, at a distance L away from the crack tip. The exact expression for the combined mode stress intensity factors as the function of time and position along the crack edge is obtained. The method of solution is based on the direct application of integral transforms together with the Wiener-Hopf technique and the Cagniard-de Hoop method, which were previously believed to be inappropriate. Some features of solutions are discussed and the results are displayed in several figures.

A half plane crack under three-dimensional combined mode impact loading

The dynamic stress intensity factor history for a half plane crack in an otherwise unbounded elastic body, with the crack faces subjected to a traction distribution consisting Of two pairs of suddenly-applied shear line loads is consid- ered. The analytic expression for the combined mode stress intensity factors as a function of time is obtained. The method of solution is based on the application of integral transforms and the Wiener-Hopf technique. Some features of the solutions are discussed and graphical numerical results are presented.

Stress intensity factors for curvilinear cracks loaded by bending and torsional moments

The geometry of a thin flat plate containing a curvilinear crack of finite size is investigated. The plate is loaded by uniform bending and torsional moments at infinite distance from the crack contour, while distributed normal bending moments and torques exist at the upper and lower crack surfaces. The bending stress intensity factors for the curvilinear crack are calculated on the basis of classical plate theory. The displacements and internal moments are represented by two complex analytic functions. Extra conditions are imposed to ensure the univalence of the displacements, which is not evident because the plate comprises a multiply connected domain due to the presence of the crack. A linearization with respect to the crack-curvature function has been performed and the bending stress intensity factors are calculated as the first-order solutions for slightly curved cracks. The results are illustrated with a few examples, such as uniform loading configurations and the geometry of a crack along a circular arc. The loading of thin flat plates by a combination of tensile forces and bending moments is also investigated. In analogy with the variation of the stress components over the cross section of the plate, two combined stress intensity factors are introduced having the same dependence on the perpendicular coordinate and being related to the symmetric and anti-symmetric stress intensity factors of the separate plane-stress and bending problems. The resulting energy release rate is shown to be in full agreement with known results in the literature.

A contour integral computation of mixed-mode stress intensity factors

A path independent contour integral formula for the distinct calculation of combined mode stress intensity factors in linear plane elasticity problems is presented. The method is based on a Somigliana type singular integral representation and is easily appended to existing finite element computer codes. Numerical results to three problems with known perturbation solutions are given and demonstrate the accuracy and stability of the method.