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.

Using deep learning method to predict dimensionless values of stress intensity factors and T‐stress of edge notch disk bend (ENDB) specimen

AbstractA deep learning (DL) approach is implemented to determine the dimensionless stress intensity factors of mode‐I (YI) and mode‐III (YIII), as well as the normalized T‐stress (T*) of the edge notch disk bend specimen. The deep neural network (DNN) method as the DL approach is used to model the relationship between the geometry parameters of the specimen a/t, S/R, and β as inputs, and YI, YIII, and T* as output variables. To this end, three datasets consisting of 176, 176, and 123 finite element method data points from the previous studies are extracted for YI, YIII, and T*, respectively. The developed DNN models predicted the YI, YIII, and T* with correlations of 0.97003, 0.96918, and 0.97047, respectively. Then partial dependence plot is performed to determine the relationship between YI, YIII, and T* and the geometry parameters, which is useful in predicting and optimizing YI, YIII, and T*.

Isothermal and thermomechanical fatigue crack growth behavior of 316LN stainless steel under load‐ and strain‐controlled modes

AbstractCrack growth tests of 316LN stainless steel under load‐controlled and strain‐controlled thermo‐mechanical fatigue (TMF) loadings at the temperature range of 350°C ~ 550°C were conducted. Moreover, the isothermal fatigue (IF) crack growth tests at the maximum temperature of 550°C were performed for comparison. The differences in IF and TMF crack propagation behavior under different loading conditions were thoroughly discussed, and the underlying mechanisms were revealed by a comprehensive characterization of the deformation state of the crack tip region using digital image correlation (DIC) and electron backscatter diffraction (EBSD) methods. Furthermore, it was found that the EBSD characterization was simply based on a single plane made it difficult to evaluate the complex crack growth behavior. In addition, the limitations of the classical parameter of stress intensity factor under TMF loading were presented.

Cyclic R‐Curve Measurements for Structural Metallic Alloys

Fractures nucleated from defects and subjected to cyclic loading can experience propagation for a range of stress intensity factor ΔK well below the so‐called long crack threshold. This phenomenon is attributed to the development of crack closure mechanisms which may differ from those observed in laboratory tests conducted in accordance with current standards. Cracks originating from material defects require a specific degree of extension to develop the plastic wake, thus achieving a stabilized condition called the long crack threshold. However, in certain materials, this stabilization length can extend up to several millimeters, effectively encompassing a significant portion of the component's fatigue life. Therefore, understanding and quantifying the development of ΔKth with crack extension is important for implementing a reliable assessment procedure based on the fracture mechanics theory. Herein, R‐curve measurements are presented for five distinct structural metallic alloys widely used in various industrial applications. Additionally, the impact of load ratio is investigated, providing a comprehensive analysis of fatigue crack resistance in terms of the R‐curve concept. This study underscores the necessity of ruling new experimental techniques to measure and implement the long crack threshold, thereby ensuring the development of a reliable and robust framework for fatigue assessment.

In situ observation of fatigue crack propagation in soda‐lime glass with initial crack and residual stress induced by Vickers indentation under four‐point bending

AbstractThe present study examined the four‐point bending fatigue properties of glass with an initial crack and residual stress induced by Vickers indentation. The fatigue properties of glass with an initial crack are influenced by the residual stress induced by Vickers indentation. Regardless of the presence of residual stress, the failure time under static fatigue is shorter than that under cyclic fatigue. In the region of a small crack, the fatigue crack aspect ratio for glass is smaller than that for metallic materials. The crack growth rate in glass with an initial crack initially decreases and then increases with an increase in the maximum stress intensity factor, Kmax. To investigate the effect of residual stress on the fatigue crack propagation behavior of soda‐lime glass, the in situ observation of fatigue crack propagation was conducted. Crack closure occurs in glass in which tensile residual stress induced by Vickers indentation was released by annealing.

Effect of crack surface friction on stress intensity factor for double-edge cracked Brazilian disk specimens under parabolic distribution load

The weight function method was employed to derive the closed-form solutions of stress intensity factors (SIFs) for double-edge cracked Brazilian disk (DECBD) specimens subjected to parabolic distribution loads, taking into account the influence of crack surface friction. Additionally, the accuracy and validity of these solutions were discussed in comparison with previous numerical results. Furthermore, the impact of friction coefficient and load distribution angle on SIFs was further investigated. The results indicate that the effect degree of load distribution angle on SIFs is closely correlated with both the loading angle θ and crack length α. Both the mode I and mode II SIFs increase with increasing load distribution angle γ for θ = 15° and α < 0.4. However, when α ≥0.60, the impact of load distribution angle γ on SIFs becomes negligible. Furthermore, the friction between crack surfaces of DECBD specimens significantly affects the dimensionless mode II SIF YII, leading to a decrease in dimensionless mode II SIF YII as the friction coefficient μ increases. Moreover, it further demonstrates that both the relative crack length α and friction coefficient μ play important roles in determining the critical loading angle θIIc for crack sticking. The critical loading angle θIIc for crack sticking increases with an increasing relative crack length; however, an increase in the friction coefficient leads to a reduction of this critical loading angle θIIc.

Multi-crack propagation analysis of double-side welded rib-to-deck joint in orthotropic steel decks

Rib-to-deck welded joints are among the most susceptible to fatigue in orthotropic bridge decks (OSDs). Prior research has primarily examined the stress intensity factor (SIF) and propagation morphology of a solitary fracture at these joints, allocating limited attention to the investigation of the propagation of multiple cracks. This paper presents a methodology for simulating and computing the weld toe magnification factor and the SIF of semi-elliptical surface cracks in innovative double-sided welded rib-to-deck (DWRTD) joints. The intention was to simplify the calculation of the SIF for this fatigue detail. The SIF obtained from the calculation model in combination with a multiple crack coalescence approach resulted in a series of fatigue life prediction models of multiple co-planar semi-elliptical cracks. Compared with the results of fatigue tests on the DWRTD joints, the calculated fatigue life and propagation morphology of multiple cracks from the model showed good agreement. Finally, the parameters were analysed to investigate the effects of crack number, bridge deck thickness, residual stress, and penetration rate. Compared to a single crack, multiple cracks reduced the service life of the bridge deck by approximately 30%. When the bridge deck thickness increases from 12 mm to 20 mm, the nominal stress amplitude near the weld ∆σ decreases by 2.2 times, resulting in a 7-fold increase in crack propagation time. Compared to penetration rate and residual stress, ∆σ is the most crucial factor affecting fatigue propagation life. Therefore, it is suggested to increase the thickness of the bridge deck during design.

Interaction between microcapsules and crack using XFEM and data-driven fracture toughness predictive model

The interaction mechanism between microstructures of materials, including microcrack, inclusion and interface defect, is crucial for studying the microscopic damage of materials. The interaction between microcapsules and cracks in self-healing material is examined using a combination of the extended finite element method (XFEM) and the interaction integral method, which is implemented by a program written in Fortran language. The non-dimensional stress intensity factors (SIFs) of a crack with a single microcapsule, a pair of microcapsules and a cluster of microcapsules are investigated. Moreover, the data-driven fracture toughness predictive model using a genetic programming-based symbolic regression (SR) technique is proposed by training the data from the XFEM program. Results reveal that the non-dimensional SIFs are related to the mechanical property, geometry and interface defect of microcapsule. The influence of microcapsule on the SIF is limited within a distance of five times the microcapsule radius. The predictive model quantifies the contribution of microscopic structures on the macroscopic fracture parameter, highlighting the potential of machine learning in guiding the quantitative design and discovery of high-performance smart materials.

Research on Crack Propagation of Nitrate Ester Plasticized Polyether Propellant: Experiments and Simulation

To understand the fracture properties of the nitrate ester plasticized polyether (NEPE) propellant, single-edge notched tension (SENT) tests were carried out at room temperature (20 °C) under different tensile rates (10–500 mm/min). The mechanical response, crack morphology, evolution path, and crack propagation velocity during the fracture process were studied using a combination of a drawing machine and a high-speed camera. The mode I critical stress intensity factor KIc was calculated to analyze the tensile fracture toughness of the NEPE propellant, and a criterion related to KIc was proposed as a means of determining whether the solid rocket motors can normally work. The experimental results demonstrated that the NEPE propellant exhibited blunting fracture phenomena during crack propagation, resulting in fluctuating crack propagation velocity. The fracture toughness of the NEPE propellant exhibited clear rate dependence. When the tensile rate increased from 10 mm/min to 500 mm/min, the magnitude of the critical stress intensity factor increased by 62.3%. Moreover, numerical studies based on bond-based peridynamic (BBPD) were performed by modeling the fracture process of the NEPE propellant, including the crack propagation speed and the load–displacement curve of the NEPE propellant. The simulation results were then compared with the experiments.

Fracture performance of fiber reinforced geopolymer: Synergetic perspective

It is well-known the hybridization of different types of fibers exaggerates the contribution of mono fiber reinforcement on the mechanical and/or fresh properties of the concrete. Despite this fact, very few researchers have pointed out the synergetic effect of hybrid fibers on the fracture response of the geopolymer concretes. Hence, the present work seeks to extend the current knowledge of material science to cover the synergetic effect of hybrid fibers. To this end, a total of 15 mixtures, including plain matrix were manufactured. Steel, carbon, and glass fibers were incorporated into the mixtures at varying ratios. For the fracture evaluations, the rectangular prisms with the central notches were exposed to a three-point static bending test. Crack formations on the specimen surfaces were recorded through the 2D digital image correlation (DIC) method. Test results were examined in terms of some mechanical and fracture properties of geopolymer composites. Accordingly, the compressive strength, Young's modulus, flexural strength, limit of proportionality, and residual strengths were evaluated as the mechanical properties, while the fracture energy, characteristic length, effective crack length, initial stress intensity factor, and unstable stress intensity factor were considered as the fracture properties. Based on the experimental results, carbon fiber was found to be capable of increasing pre-peak mechanical response, while the steel and glass fibers were useful in improving the post-peak fracture properties of geopolymer concretes. In most cases, similar results were also attained for the hybrid fiber-reinforced concretes.

Modelling Fatigue Crack Growth in High-Density Polyethylene and Acrylonitrile Butadiene Styrene Polymers.

Prior studies into fatigue crack growth (FCG) in fibre-reinforced polymer composites have shown that the two methodologies of Simple-Scaling and the Hartman-Schijve crack growth equation, which is based on relating the FCG rate to the Schwalbe crack driving force, Δκ, were able to account for differences observed in the measured delamination growth curves. The present paper reveals that these two approaches are also able to account for differences seen in plots of the rate of crack growth, da/dt, versus the range of the imposed stress intensity factor, ΔK, associated with fatigue tests on different grades of high-density polyethylene (HDPE) polymers, before and after electron-beam irradiation, and for tests conducted at different R ratios. Also, these studies are successfully extended to consider FCG in an acrylonitrile butadiene styrene (ABS) polymer that is processed using both conventional injection moulding and additive-manufactured (AM) 3D printing.

Experimental research on the fracture of Laminated bamboo lumber using compact tension specimens based on the net section method and digital image correlation technique

This investigation evaluates the significance of thickness (B) and initial crack length-to-width ratio (α) on the fracture toughness of Laminated bamboo lumber (LBL) compact tension (CT) specimens under mode Ⅰ fracture conditions. The digital image correlation (DIC) technique is employed to analyse the result, while the net section method is utilised to determine the critical strain energy release rate (GIc). The fracture mode observed in LBL is characterised as brittle fracture, and the critical stress intensity factor (KIc) of CT specimens achieved a maximum value of 25.58 MPa·mm1/2. The fracture energy, calculated by the net section method, was determined by analysing the crack extension length (ae) of the CT specimen obtained by the DIC technique. This study aims to establish the mathematical connection between GIc, ae, and critical load (PQ) in terms of the strain energy release rate context, which offers an innovative approach to analysing GIc data of CT specimens subjected to mode I fracture. The calculated value for GIc was determined to be 12.18 J/mm2.

Fatigue behaviour and life prediction of self-piercing riveted joints in DP590/AA5754 dissimilar sheets

This paper investigates the fatigue properties of self-piercing riveted joints made by DP590 steel and AA5754 aluminium alloy. The fatigue failure mechanism and fatigue fretting mechanism of the joint were well revealed by analysing the microstructure features of fracture surfaces of sheets and rivets as well as viewing and measuring the distribution and chemical composition of fretting debris. The fatigue life of the joint was also predicted based on the stress intensity factor of the kinked crack of the lower sheet. The results confirmed that two failure modes occurred during fatigue: lower sheet fracture and rivet fracture. During the fatigue failure, cracks appeared in both the lower sheet and the rivets, indicating a competitive relationship between the propagation of cracks in the lower sheet and the rivets. In the range of 40 % and 50 % load level, fatigue crack propagation of the lower sheet is dominant and fracture failure of the lower sheet occurs. Rivet fatigue crack propagation has a significant advantage in the 60 % load range and rivet fracture failure often occurs. It was found that the fatigue failure of the lower sheet is mainly influenced by the main crack, which produces two different morphological sections. Fretting wear of the contact surface was the source of crack initiation, and the fretting debris promoted crack initiation and propagation. Cracks propagate along the width and thickness of the plate, as well as the thickness of the rivet neck. The stress intensity factor range can properly predict the fatigue life of joints.

Fracture of four semi-regular lattices regulated by T-stress in modified boundary layer models

The development of additive manufacturing technology has promoted the rise of various lattice metamaterials, and evaluating their fracture properties is critical for both application and safety. Here, by conducting finite element simulations on four types of elastic-brittle semi-regular lattices (kagome, snub-trihexagonal, elongated-triangular, and snub-square), we indicate that the fracture toughness of lattice metamaterials is not solely determined by the crack-tip singular term, i.e., the critical stress intensity factor, but is also influenced by the non-singular T-stress term. T-stress regulates fracture toughness by modulating geometrical distortions and force-carrying modes of lattice bars around the crack front. This regulation effect depends on the lattice topology and becomes weaker under mixed-mode loading. As the relative density of lattices decreases, T-stress can force elastic buckling of bars around the crack front, which may deteriorate the fracture toughness. Additionally, positive T-stress tends to promote the crack deflection and negative T-stress tends to inhibit. Our results offer new insights into the structure-property relationships in the presence of T-stress, which may contribute to design the geometry of micro/nano-lattice metamaterials.

Finite Element Analysis Study of Buried Crack Defects in B-Sleeve Fillet Welds

Finite Element Analysis Study of Buried Crack Defects in B-Sleeve Fillet Welds

Automatic crack tip localization in enormous DIC images to in-situ characterize high-temperature fatigue crack growth behavior

Digital Image Correlation (DIC), with its advantages of full-field, non-contact and applicability to extreme environments, is a powerful deformation measurement technique to in-situ monitor the high-temperature fatigue crack propagation behavior. For the DIC-based fracture mechanics analyses of cracking, crack tip position in DIC images, which is usually determined visually and manually, plays a significant role. However, the long-term fatigue-DIC experiment at both room-and high-temperatures poses a real challenge due to the huge amount of DIC images, lower image quality at high-temperature, and even the invisibility of cracks. In this paper, a fully automated algorithm for localizing the crack tip is proposed based on the crack tip displacement field and the immune algorithm. Compared to traditional algorithms, it does not necessitate iterative initial values of crack tip location, and permits precise and fast determination of critical fracture mechanics parameters, such as the Stress Intensity Factors (SIFs). The algorithm reliability is validated by both numerical simulation and fatigue testing of nickel-based superalloy GH4169 at room temperature and 650℃. It is shown that crack tip position and SIF values can be precisely and automatically determined within 7 s per image using an ordinary low-cost computer, which significantly improves the analyzing efficiency.

Adaptability and crack resistance effect of continuous fiber anti-crack composite sealing layer

Traditional anti-crack seals are greatly affected by temperature effects and lack adaptability, making them vulnerable under extreme conditions. Therefore, a novel composite sealing layer material for crack prevention was proposed. This material combines fibers with a fine anti-slip wear layer, which is placed on top of the crushed stone layer. Furthermore, the XFEM was utilized to analyze the adaptability and anti-crack effectiveness of the continuous fiber anti-crack composite sealing layer. The conducted experiments revealed that as the cracks in the base pavement widened from 1.0 mm to 2.0 mm, there was an observed increase of 11.4% in stress intensity factor. A variation in the stress intensity factor of 6.3% was observed within the specified range of crack width when the modulus of the continuous fiber anti-crack composite sealing layer was fixed at 300 kPa. These results are of vital importance in comprehending the performance of this material in terms of crack resistance adaptability and its influence on practical applications.

Experimental and numerical assessment of fracture toughness variations in steam boiler components after a long period of operation

This study presents an experimental and numerical assessment of the fracture toughness of steam boiler components, which have been in operation for more than 100,000 h. The materials tested are components of two different parts of a steam turbine unit: the pipeline section that connects the headers with turbines, which is made of 13HMF steel, and the valve chamber section, which is made of L17HMF steel grades. Full-size arc-shaped tension specimens (AT) are employed for the experimental evaluation. AT and single-edge notch tension (SENT) specimens are used for numerical assessment. The finite element method (FEM) formulations are developed and examined in Abaqus, which is set up as a shell model with the specimen thickness designated as the mid-surface for the analysis. The notch is modeled using a contour integral definition based on the maximum energy release rate criterion. The fracture toughness is quantified using the stress intensity factor (KI), and the results are compared. The valve chamber is found to have a higher fracture toughness than the pipeline section. The effect of specimen geometry is also noticeable, and the fracture toughness of SENT and AT specimens are compared. The results are useful in assessing the component’s durability after long operation.

Enhanced fatigue crack propagation resistance of a new Al–Cu–Li alloy via different aging processes

The fatigue crack propagation (FCP) behavior of a new Al–Cu–Li alloy under different aging treatments including T3, T8, and non-isothermal aging (NIA) was investigated. It was detected that the T8-24h sample exhibited the highest FCP resistance and the best mechanical performance. Compared with the T3-40D sample, the crack paths of the T8-24h sample and the C150 (non-isothermal peak-aged) sample were more tortuous and the crack width was narrower. Furthermore, the T8-24 sample had the lowest decreased FCP rate by an order of magnitude at the stress intensity factor (ΔK) of 30 MPa·m1/2. A large number of nano-scale T1 phases were precipitated in the T8-24h sample and their number density was also increased compared with the other sample. The presence of the tiny T1 phase plays a crucial role in impeding crack propagation as it can be sheared by dislocations without accumulating damage. This resulted in a substantial improvement both in the mechanical and fatigue properties of the alloy. Moreover, in the Paris stage of FCP, factors such as the size and concentration of precipitates within the grain and grain boundary play a vital role in determining the extent of crack growth. The results of transmission electron microscopy (TEM) bright field images on grain boundaries (GBs) analysis show that the variations in strength between the grain boundary and intragranular regions have a direct influence on the alloy's susceptibility to fatigue and corrosion resistance.

Mode I fracture propagation and post-peak behavior of sandstone: Insight from AE and DIC observation

Microcracks generated at the crack tip, particularly in quasi-brittle materials such as sandstone, give rise to a non-linear region known as the fracture process zone (FPZ), which cannot be analyzed using linear elastic fracture mechanics (LEFM). To gain insights into the nonlinear fracturing behavior of rock, this study conducted three-point bending experiments on sandstone beams with prefabricated notch. Stable mode-Ⅰ fracture propagation during the post-peak stage was achieved by the monotonic increment of crack mouth opening displacement (CMOD) measured by a clip gauge. The acoustic emission (AE) and digital image correlation (DIC) techniques were utilized to visually track the detailed crack propagation process from both micro and macro perspectives. Nonlinear fracture parameters, including FPZ length, were identified by AE and DIC measurements and compared with the theoretical calculation. A nonlinear fracture criterion relating applied load, equivalent crack length, and stress intensity factor were established, from which the theoretical CMOD-P curve at the post-peak stage were obtained and validated with experimental measurement from MTS machine. The results reveal that microcracks formulating the FPZ materialize in the pre-peak stage, with the majority emerging post-peak to facilitate the propagation of the traction-free crack and FPZ in the loading direction, as evidenced by AE locations and DIC displacement gradient. Throughout the crack propagation process, over 65 % of microcracks are estimated to be tensile mode based on both AF/RA and polarity analysis, aligning with anticipated outcomes from macroscopic three-point bending fracture tests. Energy dissipation primarily occurs within the FPZ to facilitate separation of crack faces, with the dissipated energy region advancing towards the beam boundary. By integrating AE source locations and DIC displacement gradient, the FPZ length of the 3-point-bending sandstone specimens is determined to be lp = 8.1 mm, slightly exceeding the theoretical FPZ lengths calculated by the Irwin model (lp = 7.0 mm) and the Dugdale-Barenblatt model (lp = 7.6 mm). Using a non-linear fracture criterion that incorporates the FPZ and employing the in-time equivalent crack length measured by AE and DIC as an intermediate variable, the theoretical applied load-crack length curve during the post-peak stage is calculated, showing close agreement with load cell measurements with a negligible error of approximately 2 %. Furthermore, the theoretical post-peak CMOD vs. load curve aligns with experimentally obtained results, demonstrating a non-linear crack propagation speed at a constant CMOD rate, wherein crack propagation speed decreases as crack length increases.