Values Of Stress Intensity Factor 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.

Plastic zones for ductile layer sandwiched between two different substrates

This study is an extension of previously developed models of plasticity occurring in the vicinity of ​​a longitudinal crack in a thin elastic-plastic layer sandwiched between two identical, ideally elastic substrates: Varias–Suo–Shih [1], Rogowski-Molski [2], and Rogowski [3]. The solution presented in the current study describes the plastic zone size problem in a thin constrained layer bonded to two different substrates. A well-known two-term K-T Williams [4] stress solution for interfacial cracks is used to obtain the plastic zone size. A new equation with coefficients dependent on the layer and substrate material properties was obtained, allowing for the calculation of the plastic zone size in the thin ductile layer based on the values of the complex stress intensity factor K and T-stresses. The proposed model is tested for several arbitrarily selected interfacial crack geometries, load conditions, bonding layers, and substrate material properties. Because of the complicated oscillatory description of the local stress field, the final solution of the mathematical equation is obtained numerically, ignoring a small zone of intense stress oscillations near the crack tip. Good agreement is obtained between the results from the proposed model and the FEM results in terms of quantity and quality. A novel approach may be utilized in the future as a method for estimating the parameter of fracture criterion for bonded joints.

Consideration of the effects of frost heave force and train loads on the cracks and propagation pattern of ballastless track slabs in cold regions

The construction of ballastless railway tracks in cold regions is susceptible to frost heave forces, which may particularly impact the stability of track slab cracks and lead to crack propagation. In this paper, the frost heave tests are conducted on the concrete specimens with prefabricated cracks to observe the evolution of the frost heave force within the cracks. The frost heave force is subsequently applied to the finite element model of the concrete specimens to calculate the stress intensity factors (SIFs). In addition, the CRTS III ballastless track model is established to investigate the crack propagation patterns under frost heave and train loads. The results show that the frost heave force in concrete cracks during freezing and thawing is divided into five stages, which produces two peaks of frost heave force. Train loading caused the SIFs of the crack tips to open and close alternately and to rise significantly under the coupling effect of frost heave load. The SIF increases approximately linearly with crack width and is higher for transverse cracks than for longitudinal cracks. Small size cracks do not possess sufficient SIF values to exceed fracture toughness, implying no crack propagation. However, as the crack width is constantly increasing, the SIF will eventually exceed the fracture toughness. Therefore, strict control over track slab's crack width is necessary for CRTS III ballastless tracks.

Evaluation of RPV closure head penetration integrity considering fitting and residual stresses

To ensure the structure integrity of the Reactor Pressure Vessel (RPV), the main challenge is the embrittlement of beltline material. However, the stress is more complex for the regions of Closure Head Penetration (CHP). Feedback of leakage at the CHP has been found during in-service inspection. Although the detailed mechanical evaluation of the RPV head and the CHP has been carried out by many international institutions, there are limited studies to concern structure integrity of CHP tube. The systematic analysis of the influence of material strength matching, assemble stress, the Welding Residual (WR) stress and work pressure load on the fracture is also limited. In this paper, the systematic influence of these factors is analyzed, and the distribution characteristics of Stress Intensity Factor (SIF) and the crack propagation characteristics are studied. The 2D model and accurate 3D model are carried out using the finite element method. The results show that the WR stress on the outer surface of the CHP and the area adjacent to the weld is larger than the yield strength of the material. There is a gap between the RPV and the upper part of the CHP. The attenuation rate of the WR stress in the outlet direction of RPV is lower than that in the inlet direction, so cracks are more likely to occur in the out of direction. The influence of WR stress on the circumferential stress distribution and fracture parameters in the wall thickness direction of CHP is bigger than the influence of assemble load and design condition load. However, the overall stress of CHP is low. The SIF values along the crack front have an asymmetric distribution, and the SIF value is very small. As the fatigue crack propagation life is much longer than the assumed limit in the design lifetime, the risk of fracture and crack fatigue propagation caused by mechanical stress is low.

Influence of solid solution treatment on fatigue crack propagation behavior in the thickness direction of 2519A aluminum alloy thick plates

2519A aluminum alloy thick plates have excellent applications in the military industry due to their superior ballistic resistance and fatigue properties. However, the delamination cracking along the thickness direction of this alloy hinders its further utilization. To address this issue and enhance the fatigue properties of this alloy, the effect of single-stage solid solution treatment (SST) and two-stage solid solution treatment (DST) on the fatigue crack propagation (FCP) behavior in the thickness direction of the alloy was investigated. Compared to the optimum SST, the volume fraction of the secondary phase of the alloy was reduced by 28.6% after DST. The precipitated phases were finer with more uniform distribution, and the volume fraction and number density of the precipitation increased by 47% and 30%, respectively. The DST resulted in a lower fatigue crack growth rate (FCGR) and an increase of 2.92% in the critical stress intensity factor value (ΔKcr). The crack propagation mode of the alloy after SST was inter/transgranular crack propagation, while it was transgranular after DST. The aspect ratio of grain and the number of secondary phases in the alloy decrease after DST. Meanwhile, the grain boundary (GB) precipitation phase spacing, the precipitation-free zone (PFZ) width, and the spacing between the secondary phases increase. These changes result in decreased crack sources in the alloy and reduced the bridging effect of secondary phases on fatigue cracks, thus improving the fatigue performance of the alloy.

The effect of loading rate on mixed mode I/II fracture behavior of adhesively bonded joints: Experimental and numerical approach

In this study, the use of a modified Arcan fixture to investigate the fracture behavior of adhesively bonded Al/Al joints has been discussed under rate-dependent loading in various loading conditions (mode I, mode II, and mixed mode (I/II)). It was observed that the testing speed has a significant effect on the fracture properties of the joints, especially in pure mode, II. The results indicated that failure load was increased for all three loading modes and an increase was also observed for strain energy release rate at all loading conditions. The critical fracture loads obtained from the experimental tests were used to calculate the values of the critical stress intensity factors and strain energy release rates for loading modes I, II, and mixed mode I/II at different loading rates by using the finite element method. It was shown that the values of strain energy release rate for loading mode II were higher than mode I and mixed mode at all loading speeds. Finally, scanning electron microscope analyses (SEM) were used to investigate the effects of loading speed on the failure surfaces of the adhesive in microstructural scales and it was shown that at low loading rates, the number of crazes that cause failure in the adhesive layer increases.

Experimental and numerical failure mechanism evaluation of anisotropic rocks using extended finite element method

Rocks often show an anisotropic behavior due to microcracks, mineral-based structure, and unequal in-situ stresses. The crack tip's stress intensity factors (SIFs) that control rock failure heavily depend on anisotropy. Given the significance of extensive research to identify the effects of anisotropy on the mechanical behavior and strength of rocks, numerical modeling is considered an essential method in designing structures and analyzing their stability. This study experimentally and numerically evaluated the effects of the bedding angle, initial crack angle with the loading axis, crack length, and anisotropy ratio on the stress intensity factor of transversely isotropic rocks via the extended finite element method (XFEM). Cracked chevron-notched Brazilian disks (CCNBDs) were fabricated from phyllite under the International Society for Rock Mechanics (ISRM) standards and tested at different initial crack lengths and angles for validation. The XFEM approach was then used to predict toughness and crack propagation path in the tested and new specimens with varying ratios of anisotropy and bedding angles (ψ = 0, 30, 45, 60, and 90°). The results demonstrated that with the increase of the anisotropy ratio, in equal crack length and initial angle, the absolute value of the SIFs have larger values. In addition, with the increase of crack length, the first and second modes of SIF increased, which indicates the failure of the specimen at lower loads. Also, bedding angle is effective on the stress intensity factors and this effect becomes more intense as the crack length increases. Finally, the anisotropy properties not only affect the values of SIFs, but also can change the angle at which the specimen experiences pure mode I or mode II.

Stress intensity factors and full-field stresses for a hypocycloid-type crack within a thermo-elastic material

This study focuses on the failure analysis of a hypocycloid-type crack within a thermo-elastic material. Employing the conformal mapping method, analytical continuation theorem, and principle of superposition, the explicit general solution for stress intensity factors (SIFs) associated with an arbitrary-edged hypocycloid-type crack is determined analytically under the influence of remote homogeneous heat flux and mechanical load. The superposition method combines stress functions and SIFs for two distinct loading conditions. The outcomes of the normalized SIFs are affected by the magnitude and orientation of the heat flux and mechanical load. A full-field stress distribution is provided to account for variations in SIFs. Certain combinations of loads lead to maximum SIF values, rendering the system highly vulnerable to damage, while two specific scenarios inhibit crack propagation, thereby reducing the risk of structural failure.

Unusual Fatigue Crack Growth Behavior of Long Cracks at Low Stress Intensity Factor Ranges.

In this article, we characterize and review the unusual lack of threshold in fatigue crack growth (FCG) behavior for some alloys at low values of stress intensity factor ranges ΔK and its implications to damage-tolerant design approaches. This unusual behavior was first observed by Marci in 1996 in IMI 834 alloy. Conventional applications of linear elastic fracture mechanics to FCG analysis at constant R-ratio (or Kmax) assumes that (da/dN) decreases monotonically with decreasing ΔK and approaches the threshold value of ΔKth with (da/dN) ≤ 10-7 mm/cycle for a given R (or Kmax). However, instead of ΔK threshold behavior, some materials exhibit plateau or acceleration in da/dN rate with decreasing ΔK for long cracks tested in both constant R and Kmax conditions. This unusual (da/dN)-ΔK behavior is only observed experimentally but not understood and represents a challenge to scientists and engineers to model the safe fatigue life prediction of structures under low amplitude vibrating loads.

Effect of support friction on pure mode I, II, and III fracture toughness of cement concrete tested with edge-notched disc bend specimen

In this paper, the effect of friction on the interactions between the supports and test specimen is investigated in the fracture tests under pure mode I, pure mode II, and pure mode III loadings. 3D finite element analyses are performed on the ENDB (edge-notched disc bend) specimen by modeling the friction at the interactions, and SIFs (stress intensity factors) are computed. The results show that friction affects the values of SIFs significantly. Next, mode I, mode II, and mode III fracture tests are performed on the ENDB specimens made of concrete by using three different supports including the R (roller), RG (roller-in-groove), and F (fixed)-supports. Based on the results, mode I, mode II, and mode III fracture toughness are considerably dependent on the type of supports. Such that the F-supports and R-supports show the highest and lowest values of the fracture toughness, respectively due to having the highest and lowest friction coefficients at the interactions. Finally, the friction coefficients at the interactions are computed for the mode I, mode II, and mode III loadings using the FE and experimental data. Accordingly, mode I fracture tests of the concrete are more sensitive to the friction coefficient at the interactions than the mode II and mode III ones.

Numerical investigation of thermal fatigue crack growth behavior in SAC305 BGA solder joints

PurposeThis study aims to investigate the reliability issues of microvoid cracks in solder joint packages exposed to thermal cycling fatigue.Design/methodology/approachThe specimens are subjected to JEDEC preconditioning level 1 (85 °C/85%RH/168 h) with five times reflow at 270°C. This is followed by thermal cycling from 0°C to 100°C, per IPC-7351B standards. The specimens' cross-sections are inspected for crack growth and propagation under backscattered scanning electronic microscopy. The decoupled thermomechanical simulation technique is applied to investigate the thermal fatigue behavior. The impacts of crack length on the stress and fatigue behavior of the package are investigated.FindingsCracks are initiated from the ball grid array corner of the solder joint, propagating through the transverse section of the solder ball. The crack growth increases continuously up to 0.25-mm crack length, then slows down afterward. The J-integral and stress intensity factor (SIF) values at the crack tip decrease with increased crack length. Before 0.15-mm crack length, J-integral and SIF reduce slightly with crack length and are comparatively higher, resulting in a rapid increase in crack mouth opening displacement (CMOD). Beyond 0.25-mm crack length, the values significantly decline, that there is not much possibility of crack growth, resulting in a negligible change in CMOD value. This explains the crack growth arrest obtained after 0.25-mm crack length.Practical implicationsThis work's contribution is expected to reduce the additional manufacturing cost and lead time incurred in investigating reliability issues in solder joints.Originality/valueThe work investigates crack propagation mechanisms of microvoid cracks in solder joints exposed to moisture and thermal fatigue, which is still limited in the literature. The parametric variation of the crack length on stress and fatigue characteristics of solder joints, which has never been conducted, is also studied.

Stress Intensity Factor equations for incipient transverse external annular eccentric cracks contained in a shaft under bending

One of the most common failures in rotating machines is the apparition and propagation of fatigue cracks in one of its main elements: the shafts. These cracks can cause catastrophic failures and lead to costly maintenance or repair processes. Most of the studies in relation to cracks contained in shafts have focused on straight or elliptical transverse cracks. However, although it is less common, the shaft breaks also occur with cracks whose fronts are approximately circumferential, that are more difficult to analyze. These cracks are transverse with circular shape that extend over a complete circumference and that have a certain eccentricity. This work presents the equations that provide the value of the Stress Intensity Factor (SIF) of an incipient crack with circumferential shape contained in a shaft subjected to bending, along the front, as a function of the characteristics of the crack, size and eccentricity. For this, an exhaustive numerical study has been carried out, using the Finite Element Method (FEM), to determine the SIF value along the circumferential front for different sizes and eccentricities of the annular crack.

Deterministic Stress Intensity Factor of a Railway Axle under Adverse Running Condition

Although railway axles are a crucial part of railway vehicles, they are susceptible to long-term failure because of repeated loads. The aim of this research is to investigate the stress intensity factor (SIF) of a surface elliptical crack on a high-speed railway axle under various operating conditions. The study employs numerical analysis to explore the impact of press-fitting, rotary bending, stable and adverse running conditions on the SIF solutions. The main findings demonstrate that adverse running conditions, such as the press-fitting force, asymmetric vehicle weight, lateral force and wheel-rail contact force, can significantly increase the SIF values and result in axle failure. The press-fitting effect and rotary bending also have a significant impact on the SIF values, highlighting their importance in the railway axle design and analysis. The outcome of this research emphasizes the significance of accurately estimating SIF values to ensure the safe and reliable performance of railway axles in adverse operating conditions.

An accurate semi-analytical method for the treatment of an eccentric annular crack embedded in an infinite isotropic elastic medium under arbitrary internal pressure

This work provides a semi-analytical method for the calculation of the stress intensity factor (SIF) associated with an internally pressurized eccentric annular crack embedded in an infinite isotropic elastic solid. The inner and outer edges of the crack consist of the circumferences of two eccentric circles and the internal pressure exerted on the crack faces has an arbitrary distribution. Using Somigliana formulation a hypersingular integral equation governing the proposed crack problem is obtained. Next, by the employment of a conformal mapping the considered crack is mapped on to a concentric annular crack. In the mapped domain, with the aids of Fourier expansion of the displacement discontinuity function across the crack faces together with the notion of the Hadamard finite-part integral, the hypersingular integral equation is converted to a system of linear algebraic equations for the unknown constants of the expansion. Upon the determination of these constants, the angular dependent SIFs along both the inner and outer edges of the crack are obtained accurately. The accuracy of the current formulation is showcased through the re-examination of the simple concentric annular crack problems considered previously in the literature. In the presence of eccentricity, the effects of such geometrical parameters as the ratio of the radii of the inner to outer eccentric circular edges of the crack and the normalized eccentricity on the values of the SIFs along both the inner and outer edges of the crack are studied. As it will be seen the material properties of the elastic matrix do not affect the values of SIFs.

A two-dimensional inverse crack tip element for shape sensing and structural health monitoring

inverse Finite Element Method (iFEM) is a powerful tool for shape sensing and structural health monitoring of marine structures and has several advantages with respect to some other existing approaches. However, current iFEM formulation is not suitable for marine structures having pre-existing cracks due to stress singularities at the crack tip. In this study, a two-dimensional inverse crack tip element formulation is presented. The element is suitable for thin structures under in-plane loading conditions. The inverse crack tip element allows determination of Stress Intensity factor values at the crack tip. To validate the accuracy and demonstrate the capability of the inverse crack tip element, six different numerical cases are considered for different geometry, loading and boundary conditions. iFEM analysis results are compared with regular finite element analysis results as the reference solution and very good agreement is observed between the two solutions demonstrating the capability of the current iFEM approach.

The influence of recycled asphalt pavement materials on low and intermediate fracture behavior of asphalt concrete (AC) after exposing to different thawing and freezing periods

The effects of compaction process, mixture type and environmental conditions on mode I cracking resistance of asphalt concrete (AC) materials was investigated experimentally. To do that, a large number of edge notched disc bend specimens containing 0, 25 and 50% recycled asphalt mixture (RAP) material and exposed to different numbers of thawing and freezing cycles (0 to 10 cycles) were fractured. The critical values of stress intensity factor and fracture energy indexes were obtained for the AC mixtures at three test temperatures of −25, 0 and + 25 °C. Based on the results, the fracture resistance capacity of the AC mixture was decreased by increasing the RAP content, number of thawing/freezing cycles and decreasing the test temperature. The effect of thawing/freezing cycles on decreasing the cracking resistance was more pronounced for the first cycles and the variations of fracture toughness and fracture energy values with the numbers of thawing/freezing cycles showed a plateau form for higher numbers of cycles. The fracture curves of the tested samples manufactured using the Gyratory compaction method was upper than the related curves of samples made by Marshall compaction method. The sensitivity of fracture results (i.e., gradient of reduction in the fracture resistance versus freeze/thaw cycles) became low by increasing the test temperature.

Prediction of pipeline fatigue crack propagation under rockfall impact based on multilayer perceptron

Recently, the artificial intelligence technologies have been widely used in the field of pipeline integrity management. When crossing mountains, pipelines would inevitably encounter rockfall impact, which will potentially affect the growth of crack. However, previous research barely investigated the effect of sudden rockfall impact on health management of pipelines with fatigue cracks. To overcome this limitation, a novel crack propagation prediction algorithm based is proposed for pipelines subjected to rockfall impact. The stress intensity factor (SIF) rockfall impact ratio is introduced to describe the interaction effect of rockfall on the fatigue crack of pipelines. And the dynamic SIF values are acquired by finite element modeling (FEM) where 354 models with different parameters are analyzed. To more accurately forecast the crack growth under the rockfall impact, a method integrates multilayer perceptron (MLP) with Paris’ law is proposed based on the above reliable database. Two parameters impacting the performance of the network including the number of neurons in the hidden layer and the hidden layer's activation function are evaluated and network with the most precise prediction results is selected. Quantitative analyses are performed for key factors including rockfall mass, impact velocity, impact position and crack size. The prediction results using dynamic SIF values are compared with the static ones to indicate the effect of rockfall on the crack propagation. The proposed method is valuable to support decision-making in pipeline reliability assessment and integrity management.

Fracture analysis in 2D plane strain problems for composite materials containing hard inclusions and voids using an extended consecutive-interpolation quadrilateral element

This paper investigates fracture mechanics in particle-reinforced composites by using the extended finite element method enhanced by the consecutive-interpolation quadrilateral element. These composite materials have discontinuous boundaries such as cracks, voids, holes, and soft inclusions. And the extended consecutive-interpolation quadrilateral element (XCQ4) is employed to model these boundaries in two-dimensional linear elastic deformation problems. XCQ4 combines the enrichment functions in the traditional extended finite element method with the consecutive interpolation on a 4-node quadrilateral element. This element uses both nodal values and averaged nodal gradients as interpolated conditions. In fracture analysis, the stress intensity factors (SIFs) are important parameters that must be defined. In this study, the values of SIFs at the crack tips are evaluated with the help of the interaction integrals approach. The obtained numerical results are compared with other reliable results showing high accuracy and convergence rate of the XCQ4 element.

Computing the stress intensity factor range for fatigue crack growth testing at 20 kHz

AbstractInertia and damping influence the values of the stress intensity factors (SIFs) at high‐frequency loading and they must be included in computations. In the present study, different dynamic simulation procedures were carried out for two types of specimen geometries and the achieved SIF values were compared. Fast computation procedures such as harmonic modal analysis and direct steady‐state analysis were compared to the computationally expensive transient dynamic analysis. Two different methods for calculating the SIF, the J‐integral and the crack tip opening displacement (CTOD) methods, were applied and compared and the results showed a near perfect agreement in calculation of the mode I SIF. The Rayleigh damping model was introduced into the dynamic computation to investigate its effect and the results revealed a clear effect on the SIF at 20 kHz frequency. The fast direct steady‐state analysis showed good agreement to both harmonic modal and transient analysis with the different damping values used and is, after this study, the recommended procedure.

Prediction of the durability of a plate with a through crack taking into account biaxial constraints of deformations along the front of a normal rupture crack

A methodology for evaluating the durability of plate elements of structures taking into account biaxial constraints of deformations along the front of a normal rupture crack (Mode I crack) is presented. The absence of the available literature data in which the prediction of the crack growth is carried out using Txx- and Tzz-stresses which are non-singular terms in the Williams expansion for stresses at the crack tip is noted. The calculation of the fatigue crack growth rate is based on the Paris equation in which the range of the effective SIF is used instead of the range of the usual stress intensity factor (SIF). In this case, the expression for the effective SIF includes Txx- and Tzz-stresses in addition to the usual SIF. This approach provides taking into account, for example, the thickness of the plate for predicting the durability, which is impossible when only the SIF and Txx-stresses are used. The formula for the effective SIF is derived proceeding from the assumption that tangential stresses in the pre-fracture zone are equal to the local strength of the material. In this case, the size of the pre-fracture zone and the local strength of the material are determined taking into account Txx- and Tzz-stresses. The numerical simulation is based on the proprietary finite-element program which allows calculating Txx- and Tzz-stresses at the front of a through crack in a plate subjected to cyclic uniaxial and biaxial tension. It is shown that nonsingular Txx-stresses primarily describe the effect of biaxial loading on the survivability, whereas Tzz-stresses describe the effect of the plate thickness on the survivability. It is shown that with increasing thic kness of the plate the value of the effective SIF increases due to the increased constraint along the crack front, thus increasing the crack growth rate and decreasing the survivability. With an increase in the stress ratio R, under the condition of a constant stress range, the maximum effective SIF reaches the critical value equal to the fracture toughness much faster thus reducing the durability. It is shown that for uniaxial cyclic tension, the durability predicted by the proposed methodology is higher than that in the classical approach, when the conventional SIF is used in the Paris equation. For biaxial cyclic tension of a plate, an increase in stresses directed parallel to the crack banks leads to an increase of crack front constraints and therefore to a decrease in the durability compared to the classical approach. In other words, the classical theory does not always provide a conservative estimate of the durability, which indicates the expediency of using the developed method for calculating the durability taking into account biaxial constraints of deformations along the crack front.