Calculation Of Stress Intensity Factors Research Articles

Model for Calculating Stress Intensity Factors for an Inclined Crack at the Leading Edge of a Gas Turbine Engine Blade Under the Influence of Centrifugal Forces

The study is devoted to the issue of the destruction of a body with an inclined crack during rotation. A mathematical model for calculating stress intensity factors in a rectangular plate with an inclined crack under the influence of centrifugal tensile forces during rotation around an axis lying in the plane of the plate is constructed in the article. Based on the equations of the theory of elasticity and the principles of brittle fracture mechanics, relationships were obtained that relate the stress intensity factors of type I and II, the rotation speed and geometry of the plate, as well as the parameters of the crack: length, angle of inclination to the axis of rotation, distance from the axis of rotation to the crack. The complexity of the study is because the plate in question with an inclined crack is under the action of mass forces. Therefore, the values of the effective stresses are not the same along the crack edge. Accordingly, stress intensity factors will depend on the location of the crack relative to the axis of rotation. The influence of the crack location and plate rotation speed on the change in stress intensity factor values is analyzed based on the results obtained. As the distance from the axis of rotation to the crack increases, the values of the stress intensity factors decrease. As the plate rotation frequency increases, the stress intensity coefficients increase according to a parabolic law. The results of the study can be used to assess the limit state of the rotating blades of a gas turbine engine in the presence of an inclined crack. The mathematical model can find practical application for assessing the critical speed regime of blade rotation in the presence of cracks of various lengths and angles of inclination to the rotation axis.

Analytical computation of stress intensity factor for multi-physics problems

This work presents a methodology for the analytical calculation of the stress intensity factor when the stress distribution on the crack surfaces is non-homogeneous. At first, a polynomial function is used to express the non-homogenous stress distribution. Subsequently, the principle of superposition of effects is applied, and the stress intensity factor is computed by multiplying each polynomial term by its respective geometric factor. Finite element fracture model is used to compute the geometric factor of the single polynomial grade. To explain the method, a spherical body is considered, with central and superficial cracks. Each geometric factor depends on a normalized geometrical parameter (the ratio between the crack length and sphere radius). The proposed methodology is applied to determine the stress intensity factor in the case of a crack driving force caused by diffusive fields, such as the concentration gradient in particles of electrodes active material in lithium-ion batteries. The methodology allows to speed up the fracture computation, then it is used to give electrode design guidelines to limit the fracture likeliness and mechanical degradation in lithium-ion batteries, as well as it is the basis for the development of algorithms assessing the capacity loss and the remaining useful life of lithium-ion batteries in real-time.

Determining Stress Intensity Factors at Varied Inclination Angles through Innovative Discontinuous Digital Image Correlation

An innovative method is proposed for determining stress intensity factors at crack tips with different inclination angles, based on the Adaptive Digital Image Correlation (AD-DIC) method. This method involves fitting a set of nonlinear equations with unknown parameters using displacement field data. The initial values for crack tip coordinates and inclination angles, computed through the AD-DIC method, are employed in this process to obtain stress intensity factors at the crack tips. The results demonstrate that this approach accurately captures the crack tip positions and calculates stress intensity factors for cracks at various inclination angles. This addresses the challenge of computing stress intensity factors during the crack propagation stage, where cracks may deviate, making conventional calculations impractical.

Experimental and numerical analysis of the behavior of rehabilitated aluminum structures using chopped strand mat GFRP composite patches

PurposeThis paper comprehensively addresses the influence of chopped strand mat glass fiber-reinforced polymer (GFRP) patch configurations such as geometry, dimensions, position and the number of layers of patches, whether a single or double patch is used and how well debonding the area under the patch improves the strength of the cracked aluminum plates with different crack lengths.Design/methodology/approachSingle-edge cracked aluminum specimens of 150 mm in length and 50 mm in width were tested using the tensile test. The cracked aluminum specimens were then repaired using GFRP patches with various configurations. A three-dimensional (3D) finite element method (FEM) was adopted to simulate the repaired cracked aluminum plates using composite patches to obtain the stress intensity factor (SIF). The numerical modeling and validation of ABAQUS software and the contour integral method for SIF calculations provide a valuable tool for further investigation and design optimization.FindingsThe width of the GFRP patches affected the efficiency of the rehabilitated cracked aluminum plate. Increasing patch width WP from 5 mm to 15 mm increases the peak load by 9.7 and 17.5%, respectively, if compared with the specimen without the patch. The efficiency of the GFRP patch in reducing the SIF increased as the number of layers increased, i.e. the maximum load was enhanced by 5%.Originality/valueThis study assessed repairing metallic structures using the chopped strand mat GFRP. Furthermore, it demonstrated the superiority of rectangular patches over semicircular ones, along with the benefit of using double patches for out-of-plane bending prevention and it emphasizes the detrimental effect of defects in the bonding area between the patch and the cracked component. This underlines the importance of proper surface preparation and bonding techniques for successful repair.Graphical abstract

Fracture mechanics approach to TRISO fuel particle failure analysis

Weibull stress-based methods for failure probability assessment have been developed and analyzed to assess the integrity of tristructural isotropic (TRISO) fuel particles during fuel life cycles and accident operating conditions. While simple, these methods entail a number of drawbacks when stress concentrates near crack tips, including finite element mesh size dependency when the Weibull stress is averaged over the finite element domain. Fracture mechanics approaches involving the use of interaction integrals eliminate this lack of mesh convergence and produce consistent fracture predictions. In this work, we use an interaction integral approach to computing stress intensity factors for a crack in the inner pyrolytic carbon layer perpendicular to the silicon carbide layer, which is simplified representation of a failure mode in TRISO particles. The interface between these two TRISO layers has been shown to become porous, which we simulate by considering a transition of mechanical properties over such porous length, i.e. the layers are modeled as a functionally graded material. Aspects such as porosity and thermal and irradiation eigenstrains are considered in computing the stress intensity factor from a fracture mechanics approach and compared with the known Weibull stress failure approach. The methodology introduced in this paper enables a more general fracture probability assessment in TRISO particles and eliminates the need to identify best suited parameters when using local or averaged stress-based failure criterion. Finally, the numerical sensitivity studies show how parameters such as the porous transition zone length, the material stiffness, and creep affect the probability of TRISO fuel particle failure.

Geomechanical analysis of lost circulation control in tight formations

Unconventional oil and gas reservoirs, especially that in tight formations, contribute great parts to the global energy. During drilling in tight formations, lost circulation was one of the major problems, which can cause large amount of non operation time and millions of losses. In order to migrate the problem, lost circulation materials (LCMs) were used to prevent reopening of the fracture by isolating the fracture tip while the calculation of stress intensity factor (SIF) and fracture width is the key to LCMs design. In this paper, a dual porosity medium flow model suitable for tight formation is established to calculate the pressure distribution in fracture, and the fracture width and fracture reopening pressure (FROP) is then calculated by using the semi-analytical fracture mechanics model. Sensitivity analysis of critical parameters, for example, fracture length, wellbore radius, LCMs permeability, viscosity, wellbore pressure, and two rock-mechanics-related properties are implemented. The fracture width is larger in the formation with large horizontal principal stress anisotropy, low Young’s modulus and Poisson’s ratio. The increase in fracture length, wellbore radius and wellbore pressure also contributes to fracture opening. Meanwhile, we compared the situation before and after fracture plugging and the results emphasize that the fracture reopening is less likely to occur under the conditions of high viscosity and low permeability LCMs. The method proposed in this study can be used to calculate fracture width and FROP, which has potential significant application for lost circulation control in tight formation.

Analytical Solution of Ice–Rock-Model Stress Field and Stress Intensity Factors in Inhomogeneous Media

The stress distribution and fracture parameter calibration of ice–rock models are important aspects of studying rock properties at high altitudes and latitudes. However, progress in ice–rock modeling has been slow and singular, and it is limited due to the discrete nature of rocks and the applicability of fracture mechanics. In this study, a circular inhomogeneous ice–rock model is proposed for the first time, and a method is provided for calculating the stress field of the model under biaxial loading. A method for calculating the single-crack stress intensity factor of the model subjected to biaxial compressive loading is also provided. The novelty of this work is that the inhomogeneous ice–rock model is treated as a superposition of two models, namely, a circular pore plate and circular ice, according to the superposition principle. The key is that the stress field distribution law of the ice–rock model is obtained based on the basis of the displacement continuity of the ice–rock interface. The analytical and approximate solutions of the stress intensity factor of a single crack were also obtained by considering the normal phase effect of the crack surface and combining the stress distribution law of the ice–rock model. Comparison with the CAE method was made to verify the correctness of the stress field and stress intensity factor calculation methods. The evolution laws of lateral pressure coefficients, the elastic modulus ratio of ice and rock on the stress field, and the stress intensity factor were analyzed. The effects of lateral pressure coefficients, elastic modulus ratios, and crack distributions on the failure modes were investigated using the extended finite element method (XFEM). This study can provide a theoretical basis for the evaluation of mechanical properties and prediction of the failure modes of frozen rock bodies.

Analysis and calculation of stress intensity factors for type I cracks on the edge of elliptical holes under internal pressure

Analysis and calculation of stress intensity factors for type I cracks on the edge of elliptical holes under internal pressure

Effect of external magnetic field on electric current-induced fracture of notched thin metallic conductors: Part 2- High magnetic fields

In the companion report (Telpande et al., n.d.), we discussed the impact of a weak external magnetic field (up to 0.4 T) on the electric current-induced fracture of pre-notched thin metallic conductors, revealing a linear decrease in critical current density, jc, necessary for crack propagation. This study extends the investigation to explore the effects of stronger external magnetic fields (0.6–1 T) on the fracture of pre-notched, current-carrying metallic foils. The experimental analysis reveals a substantial, albeit linear, drop (up to 40 %) in jc under stronger magnetic fields. Interestingly, calculations of the dynamic stress intensity factor, KIE,t, which assesses the interplay between applied current density and external magnetic field, indicate crack growth under a strong magnetic field even when KIE,t is below the plane stress critical stress intensity factor, KIC. A remarkable phenomenon emerges: the application of electric current pulses combined with strong external magnetic fields induces observable surface undulations near the notch tip. A comprehensive 3D finite element model, integrating linear and nonlinear buckling analyses under multiphysics stimuli, attributes these undulations to localized buckling near the notch tip. This buckling-induced stress redistribution near the crack tip contributes to an overall reduction in fracture toughness due to mode mixity, leading to the fracture of the Al foil below KIC. This investigation, along with the companion report (Telpande et al., n.d.), significantly advances our understanding of the effects of magnetic fields on the fracture of current-carrying conductors.

Investigating the Influence of Holes as Crack Arrestors in Simulating Crack Growth Behavior Using Finite Element Method

The primary focus of this paper is to investigate the application of ANSYS Workbench 19.2 software’s advanced feature, known as Separating Morphing and Adaptive Remeshing Technology (SMART), in simulating the growth of cracks within structures that incorporate holes. Holes are strategically utilized as crack arrestors in engineering structures to prevent catastrophic failures. This technique redistributes stress concentrations and alters crack propagation paths, enhancing structural integrity and preventing crack propagation. This paper explores the concept of using holes as crack arrestors, highlighting their significance in increasing structural resilience and mitigating the risks associated with crack propagation. The crack growth path is estimated by applying the maximum circumferential stress criterion, while the calculation of the associated stress intensity factors is performed by applying the interaction integral technique. To analyze the impact of holes on the crack growth path and evaluate their effectiveness as crack arrestors, additional specimens with identical external dimensions but without any internal holes were tested. This comparison was conducted to provide a basis for assessing the role of holes in altering crack propagation behavior and their potential as effective crack arrestors. The results of this study demonstrated that the presence of a hole had a significant influence on the crack growth behavior. The crack was observed to be attracted towards the hole, leading to a deviation in its trajectory either towards the hole or deflecting around it. Conversely, in the absence of a hole, the crack propagated without any alteration in its path. To validate these findings, the computed crack growth paths and associated stress intensity factors were compared with experimental and numerical data available in the open literature. The remarkable consistency between the computational study results for crack growth path, stress intensity factors, and von Mises stress distribution, and the corresponding experimental and numerical data, is a testament to the accuracy and reliability of the computational simulations.

Fracture analysis of Brazilian circular hole disk under mixed mode loading

The paper presents an investigation into a Brazilian disk specimen featuring a concentric circular hole, accompanied by two internal edge radial cracks. By introducing rotations of the cracks relative to the vertical axis, a combination of fracture modes I and II is induced. Employing the finite element method, we compute stress intensity factors related to fracture modes I and II, alongside T-stresses, while varying geometric parameters such as inner and outer diameters, crack length-to-ring width ratio, and crack inclination angle. Experimental analyses of ebonite's fracture toughness in the mixed mode are conducted, subjecting samples to static loading until complete failure. Each test provides the angle at which crack initiation occurs and the corresponding critical load. Three distinct fracture criteria - the generalized maximum tangential stress criterion (GMTS), extended maximum tangential strain criterion (EMTSN), and generalized strain energy density (GSED) criterion - are employed to predict fracture direction and critical load. The outcomes exhibit good correspondence between experimental critical loads and theoretical predictions.

Fatigue Analysis of a Cracked Shaft: a Finite Element Modeling Approach

Shafts are typically used in sophisticated mechanisms and machinery which highly depend on shafts for rotatory motion which could lead to the failure. In today’s contemporary, damages caused by cracking on mechanical components and structures have increased, causing crack and structural failure. The failure could be examined by the calculation of stress intensity factor (SIF). Once the shaft reaches the critical SIF (SIFIC), the flaw is initiated and has a potential to propagate upon loading. Typically, the flaw would spread in many patterns and tenders to the formation and initiation of different types of cracks. Thus, the objective of this research work is to analyse fatigue cracked shafts. Prediction of crack growth via SIF calculation. SIF is usually adapted to predict the stress intensity near the crack tip where crack propagation occurs. Thus, SIF is used to study and analyse the cracked surface in relation to crack initiation and propagation. The SIF is calculated through finite element method (FEM) since the FEM is capable simulating complex geometry. The SIF is calculated based on the deformation in FEM calculation. The results show the predicted crack propagation and SIF calculation. It is crucial to study the resistance of cracked shafts towards cyclic loading for maintenance preceding and retirement of the structure.

Analytical study of CFRP strengthening steel plates with a semi-elliptical surface crack

Flaws and defects are unavoidable in the manufacturing process of steel members. Surface cracks are a common type of defect in steel structures that can introduce fatigue failure under cyclic loading. In this study, stress analysis of carbon fiber reinforced polymer (CFRP) repaired specimens with a semi-elliptical surface crack was conducted by theoretical analysis. The analysis was used to calculate stress intensity factors at crack tips. Finite element analysis was carried out to verify the proposed equations considering CFRP strengthening. Both single-sided and double-sided strengthening methods were considered. Thereafter, a modified Paris Law model was adopted to predict fatigue crack propagation life. Several parameters, which are crack aspect ratio, crack depth ratio, layers of CFRP, CFRP width and stress range are considered to analyze their influence on fatigue life. It was found that the augmentation of crack aspect ratio, layers of CFRP and CFRP width can significantly increase fatigue crack propagation life of repaired specimens. Furthermore, single-sided repairing on cracked side is better than double-sided repairing.

Fatigue Crack Growth Analysis in Modified Compact Tension Specimen with Varying Stress Ratios: A Finite Element Study

In this study, the primary objective is to analyze fatigue crack propagation in linear elastic fracture mechanics using the SMART crack growth module in the ANSYS Workbench, employing the finite element method. The investigation encompasses several crucial steps, including the computation of stress intensity factors (SIFs), determination of crack paths, and estimation of remaining fatigue life. To thoroughly understand crack behavior under various loading conditions, a wide range of stress ratios, ranging from R = 0.1 to R = 0.9, is considered. The research findings highlight the significant impact of the stress ratio on the equivalent range of SIFs, fatigue life cycles, and distribution of deformation. As the stress ratio increases, there is a consistent reduction in the magnitude of the equivalent range of stress intensity factor. Additionally, a reciprocal relationship is observed between the level of X-directional deformation and the number of cycles to failure. This indicates that components experiencing lower levels of deformation tend to exhibit longer fatigue life cycles, as evidenced by the specimens studied. To verify the findings, the computational results are matched with the crack paths and fatigue life data obtained from both experimental and numerical sources available in the open literature. The extensive comparison carried out reveals a remarkable level of agreement between the computed outcomes and both the experimental and numerical results.

Fracture behavior of superconductor REBCO tapes with multiple edge cracks under electromagnetic force

It is often necessary to narrow wide tapes through a slitting process in applications of the second-generation high-temperature superconductor REBa2Cu3O7-x (REBCO, RE = rare earth) tapes. However, this results in some random length edge cracks appearing on the slit edge and extending at certain angles towards the center of the tape. In this paper, we proposed a randomly distributed multiple-edge crack model to investigate the fracture mechanism of the superconducting tape under electromagnetic force due to high magnetic fields and current density (∼10 T and ∼ 1010A/m2). The electromagnetic body force distributions within the superconducting tape, incorporating multiple edge cracks, are simulated based on the H-formulation. Then a fracture analysis is conducted under the combined loading of tensile and electromagnetic forces, with the numerical calculation of stress intensity factors (SIFs) using the J-integral method. To validate the model's accuracy, we compare the body force distribution caused by an edge crack and the SIFs of edge cracks under uniform tension with existing results. Detailed analyses are undertaken to explore the impacts of electromagnetic body force non-uniformity, interactions between neighboring cracks, and the stochastic nature of geometrical parameters (length, angle, and spacing) on the fracture behavior under an alternating magnetic field. Numerical results indicate that non-uniform electromagnetic body forces arising from defects are a critical factor in crack propagation. Furthermore, the randomness of the geometrical parameters amplifies the interactions between some of the neighboring cracks, causing the tendency of the tape containing random edge cracks to fracture. Therefore, it is advisable to avoid random cracks with substantial length, angle, and spacing during the mechanical slitting process.

Fracture mechanics investigation for 2D orthotropic materials by using ordinary state-based peridynamics

Fracture behaviors of orthotropic plates are studied by using ordinary state-based peridynamic (OSPD) theory. Based on OSPD, a novel nonlocal formulation of interaction integral is proposed by considering the material orthogonality for the fracture parameter evaluation. By employing peridynamic differential operator, the partial differential terms in the formulation can be transformed into corresponding spatial integral form, which contributes to the calculations of stress intensity factors within the framework of OSPD. It has built up a relationship between classical theory and peridynamic theory. Static and dynamic fracture parameters are carefully evaluated. The crack propagation directions are predicted by prototype microelastic brittle (PMB) criterion in OSPD and maximum circumferential stress (MCS) criterion in classical theory. Several pre-cracked plates with orthotropic material are examined, and results are validated by comparing against the reference solutions. The relationship between fiber orientation and crack inclined angle are also examined. Meanwhile, the crack inclination determined by PMB criterion and MCS criterion are compared and discussed. Accuracy of the peridynamic orthotropic model and proposed nonlocal interaction integral are discussed in detail.

General point load weight function for semi-elliptical surface cracks in round bars

Offshore mooring chains are continuously subjected to cyclic environmental loadings, resulting in fatigue cracks that always develop at the surface and grow across the circular cross-sections. To analyse the fatigue crack growth in a mooring chain based on a fracture mechanics-based approach, the evaluation of stress intensity factors (SIFs) of surface cracks in the chain segments becomes essential. A general point load weight function of SIFs for semi-elliptical surface cracks in straight and curved round bars was derived in this study. Parametric three-dimensional finite element (FE) models were developed to calculate the SIF solutions for determining the unknown parameters in the weight function. The analysis matrix covered wide ranges of aspect ratios 0.1 ≤ a/c ≤ 2.0, relative crack depths 0.03 ≤ a/D ≤ 0.6 and relative bar curvatures 0.0 ≤ D/Ri ≤ 1.5. The developed weight function was verified against the solutions available in the literature and FE results, indicating good accuracy. The proposed weight function can be used in SIF calculation and remaining fatigue life prediction of surface cracked round bar components under complex stress distributions, such as chain links.

Stress intensity factors analysis for crack around film cooling holes in Ni-based single crystal with contour integral method

PurposeThis paper aims to provide SIF calculation method for engineering application.Design/methodology/approachIn this paper, the stress intensity factors (SIFs) calculation method is applied to the anisotropic Ni-based single crystal film cooling holes (FCHs) structure.FindingsBased on contour integral, the anisotropic SIFs analysis finite element method (FEM) in Ni-based single crystal is proposed. The applicability and mesh independence of the method is assessed by comparing the calculated SIFs using mode of plate with an edge crack. Anisotropic SIFs can be calculated with excellent accuracy using the finite element contour integral approach. Then, the effect of crystal orientation and FCHs interference on the anisotropic SIFs is clarified. The SIFs of FCH edge crack in the [011] orientated Ni-based single crystal increases faster than the other two orientations. And the SIF of horizontal interference FCHs edge crack is also larger than that of the inclined interference one.Originality/valueThe SIFs of the FCH edge crack in the turbine air-cooled blade are innovatively computed using the sub-model method. Both the Mode I and II SIFs of FCHs edge crack in blade increase with crack growing.

A new semi-analytic method for calculating the thermal–mechanical coupling stress intensity factor of interfacial crack

The interfacial crack thermal–mechanical coupling stress intensity factor (SIF) calculation plays an important role in anti-cracking design and safety assessment of compressed air energy storage (CAES) multi-layer cavern. In current SIF calculation method, there is no consideration of thermal–mechanical coupling effect caused by the difference between the singularity of stress field (λ) and temperature field (λT). In this study, a new semi-analytic method for calculating the thermal–mechanical coupling SIF of interfacial crack is established based on a new thermal–mechanical coupling Williams expansion for the cases of both insulated and constant temperature. The singularity index of temperature field at the crack-tip is dependent on the material parameters (heat conduction coefficient ki) for the crack perpendicular to and terminated at the interface, but independent on the material parameters (ki) for the crack located at the interface. The larger the difference of bi-material's heat conduction coefficient (ki), the larger the value of stress field when the crack is located on the side of larger Young's modulus (Ei) or on the side of lower ki. The semi-analytic method is degenerately verified by available literature results (without thermal–mechanical coupling term) and completely verified by finite element results (with thermal–mechanical coupling term), which can provide a theoretical basis for anti-cracking optimal design of CAES multi-layer caverns under thermal–mechanical loading condition.

Discontinuous quarter-point boundary elements revisited: Computation of T-stress in two-dimensional cracked components

This paper analyzes the use of discontinuous quarter-point quadratic elements in a dual or hypersingular boundary element context to compute the T-stress for cracked 2-D isotropic components. The performance of this approach has been demonstrated in the past for stress intensity factors (SIFs) computation and, herein, it is revisited to assess its adequacy for T-stress evaluation. To this end, novel direct extrapolation formulas that determine the T-stress from the computed nodal displacements at the collocation nodes of the discontinuous quarter-point element are proposed, and their accuracy and effectiveness is satisfactorily tested by several numerical examples involving 2-D cracked Carbon NanoTube (CNT) reinforced composites. SIFs extrapolated from the computed nodal crack opening displacements and T-stress evaluated from the computed stresses at internal points (close to the crack-tip) are also presented for completeness. The proposed techniques are a valid and easy-to-implement alternative to the interaction integral approaches when determining SIFs and T-stress.