Stress Intensity Factor Research Articles

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.

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.

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

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.

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.

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.

Study on the interference mechanism and fracture behavior of penetrating parallel double cracks

The existence of crack groups in structures is objective and inevitable during the process of manufacture and service. In this paper, the interactions between penetrating parallel double cracks are systematically investigated through finite element methods, experimental studies and theoretical analyses, where both the brittle dominant and ductile materials are taken as the research objects. The interactions between cracks are discussed through the interference factors C based on stress intensity factor K, which is related with the relative distance between crack tips. It is found that the fracture behaviors of multiple cracks are associated with all the interference factors at four crack tips. For the alignment double crack, shielding effects at all the crack tips cause the mutually exclusive crack propagations, and then strengthen the critical load of the specimen. For offset double cracks, the inner crack extension directions are attracted to each other, the outer crack extension directions are repelling each other, the critical loads depend on the degree of the attraction or the repelling effect. There exists a relationship between the comprehensive interference factor with all the crack tips included and the loading capacity. For the specimen with multiple surface cracks, the interference effects are also related with the relative distance between crack tips, through which it can be preliminary obtained that the regulations and the effect to the fracture behaviors are similar to those of penetrating cracked specimen, which will be discussed in detail in our next findings. The interference behaviors and critical loads of multiple cracks discussed above also provide an important basis on the coalescence and evaluation of multiple cracks.

Overload-induced anisotropy of fatigue crack growth in laser deposited Ti–6Al–4V alloy

Considering the anisotropy of microstructure of additive manufactured metal materials, quantitative assessment of the anisotropy of fatigue crack growth (FCG) behavior is necessary for structural damage tolerance design and evaluation. This study conducted an experimental and mechanistic investigation of the FCG behavior of the laser metal deposited (LMD) Ti–6Al–4V alloy, focusing on the anisotropy of FCG and the effect of overload on FCG. Both the FCG experiments with constant amplitude loading (CAL) and with a single overload (OL) were performed in different directions. Under CAL, the FCG rate exhibits a bilinear correlation with the stress intensity factor. Before the transition point (ΔKT = 16.9 MPa√m), since the grain boundaries are sparser along the columnar crystal growth direction, the FCG rate in the XY specimen is higher than that in the other directions. When the FCG rate further increases, the hindrance effect of grain boundaries on FCG weakens, and the anisotropy of FCG rates disappears. An interesting new finding is that when an overload is applied after ΔKT, the FCG rates in the XZ and ZX directions become different, and the overload-induced anisotropy increases with the overload ratio (OLR). The difference in FCG rates between the two directions exceeds 23.2% when OLR is 2.5. Based on microscopic and theoretical analysis, it was demonstrated that the overload induces residual strain in front of the crack-tip and enhances FCG resistance. The FCG resistance is positively related to the size of the plastic zone and negatively related to the yield strength in the loading direction.