Stress Intensity Factor Research Articles

Cross-Crack Interaction and Initiation Mechanism Under Hydro-Mechanical Coupling

In this paper, the equation for computing the maximum Stress Intensity Factor (SIF) of cross-crack under hydraulic-mechanical coupling was derived by the dislocation method and the integral equation, and the influence of cross-crack geometric parameters (branch-crack length, pinch angle, inclination angle) on the interacting SIF was analyzed, and its influence law was obtained. Using the maximum shear and tensile SIF ratio criterion as a basis, the fracture criterion of hydraulic-mechanical coupling cross-crack was established, and the initiation process of hydraulic-mechanical coupled red sandstone cross-crack was predicted (including the cross-crack initiation angle, initiation load, and initiation mechanism). Results showed that for cross-crack with the inclination angle fixed ([Formula: see text]), [Formula: see text] of crack tip C decreases slowly. For cross-crack with change of [Formula: see text]. [Formula: see text] of crack tip A increases, and crack tip C decreases with [Formula: see text]. For the cross-crack hydraulic-mechanical coupling test, as the cross-crack angle [Formula: see text] grows, the fracture initiation stress first reduces before increasing. Initiation mechanisms are Mode I fracture and initiation angles are usually negative. The hydraulic-mechanical coupling cross-crack initiation criterion is validated by the experimental findings, which align with the expected outcomes.

Sustainable future of construction: the potential of concrete with basalt mini-bars as reinforcement

The paper concerns the influence of basalt minibars on the subcritical and critical behaviour of test specimens made of concrete with low-emission cement. Low-emission cement produces lower emissions of greenhouse gases and other pollutants than traditional cement. Analyses were conducted on changes in fracture mechanics parameters depending on the content of microfibers in the concrete mix (0, 2, 4, 8 kg/m³), the type of cement used, and the water-to-cement ratio (w/c). It was demonstrated that concrete reinforced with basalt microfibers exhibits increased resistance to crack initiation and propagation. An increase in the stress intensity factor was observed for CEMI 42.5R concretes at w/c=0.5 by 27%, at w/c =0.4 by 62%, and for CEM II 42.5R/A-V concretes at w/c=0.5 by 29%, and at w/c=0.4 by as much as 30%. It was shown that the addition of microfibers to concrete made with low-emission cement significantly increases the mechanical parameters of this material.

The Influence of Residual Stress on Fatigue Crack Growth Rates in Stainless Steel Processed by Different Additive Manufacturing Methods

The Influence of Residual Stress on Fatigue Crack Growth Rates in Stainless Steel Processed by Different Additive Manufacturing Methods

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.

Influence of crack aperture and orientation on the uniaxial compressive behavior of rock

The pre-existing cracks with various geometric and physical properties significantly affect the mechanical behaviors of rock mass. In this study, uniaxial compressive tests are performed on numerical models of specimens containing a single pre-existing crack with different apertures and orientations based on PFC 2D to shed light on the impact of different crack apertures and orientations. The results reveal that the uniaxial peak strength and elastic modulus tend to decrease with increasing apertures, but they tend to increase with increasing inclination angles. Crack apertures can affect the stress intensity factor in the vicinity of the pre-existing crack tips, which further influences the crack initiation and crack type. Furthermore, shear cracks are more prone to occur in a pre-cracked specimen with a larger crack aperture and larger crack orientation. The crack initiation stress and strain initially show a slight decrease until the inclination angle reaches 45°, and then significantly increase with the further increase of angle from 45° to 90°. The microcracks occur earlier and easier when the inclination angle is 45°. As the inclination angle of the pre-existing crack increases, shear-sliding along the crack becomes more prominent, resulting in the formation of coplanar secondary cracks. The macro failure patterns switch from tensile failure to shear failure with increasing crack inclination angle, which is in good agreement with trend lines of displacement in the displacement field.

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.

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.

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