Stress Intensity Factor Research Articles

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.

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.

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.

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.

Nanocomposite fracture analysis: Aligned Fe3O4-GNP nanoplatelets’ effects on KIC, GIC, CTODc, and fracture mechanisms in epoxy matrices

Epoxy nanocomposites are crucial in aerospace, enhancing structural performance, reducing weight, and improving fuel efficiency across various applications. They ensure safety, reliability, and optimal performance in critical aerospace systems. Optimizing fracture properties like crack growth resistance (KIC), critical stress intensity factor (GIC), and critical crack tip opening displacement (CTODc), is vital for safety, durability, and innovation, especially in epoxy nanocomposites under extreme conditions. This study examines how random Graphene Nanoplatelets (GNP) and aligned Fe3O4-GNP nanoplatelets impact the fracture resistance of epoxy nanocomposites. It analyzes various fracture properties and crack propagation mechanisms following ASTM D5045-99 standards for CT specimen toughness tests using a COD gauge, focusing on nanoparticle alignment and wt% loading effects. Neat epoxy has a KIC of 0.94 MPa m1/2, increasing to 1.20 with 0.600 wt% GNP. Aligned Fe3O4-GNP peaks at 1.49. the baseline GIC starts at 209 J/m2 and rises to 301 J/m2 with 0.600 wt% GNP, and notably to 419J/m2 with aligned Fe3O4-GNP. Aligned Fe3O4-GNP significantly enhances fracture properties by modifying stress distribution at primary crack fronts through mechanisms such as deflection, branching, and twisting. These findings offer crucial insights for improving epoxy nanocomposites in aerospace, ensuring increased safety, reliability, and performance in critical components.

Instantaneous thermal fracture behaviors of a bimaterial with a penny-shaped interface crack via generalized fractional heat transfer

In the high-temperature environment, a larger thermal expansion mismatch of a bimaterial leads to marked thermal stresses and interface crack growth. In this paper, a generalized fractional heat conduction model is used to determine the instantaneous thermal fracture behaviors of a bimaterial interface crack. An axisymmetric thermoelastic problem is solved with the aid of Goodier's thermoelastic displacement potential and Love's potential functions. A mixed initial-boundary value problem is then converted to a singular integral equation of second kind by using the Hankel and Laplace integral transforms. Numerical results of the intensity factors of heat flux and thermal stresses are evaluated using Stehfest's Laplace inversion scheme. The influence of fractional kernel functions with power and exponential law are analyzed, respectively, for aluminum-steel and steel-epoxy, respectively. The thermal stress intensity factors exhibit more wave-like behaviors based on Riemann-Liouville and Atangana-Baleanu models which is different from Caputo-Fabrizio and the complete diffusion model.

Development of a Method for Determining the Residual Life of Structural Elements with Cracks Under the Action of Load and Corrosive Environment, as well as the Application of Corrosion Inhibitors to Enhance It

A developed method for determining the lifespan of structural elements with large-scale cracks of complex geometry under the influence of long-term static loads and corrosive environments. The method is based on an appropriate computational model, which relies on the first law of thermodynamics for the elementary act of local failure (crack propagation), some fundamental principles of physical chemistry, as well as the basic principles of fracture mechanics. The advantages of this method over existing ones are substantiated. The application of the method is demonstrated through examples involving the determination of the residual life of such structural elements as torsion and a pipe with small cracks made of 45KhN2MFA steel (tempered at 470 K and 725 K) under the influence of long-term static loading and distilled water. As the cracks are considered small, we have constructed a computational model in terms of deformation parameters, including a well-known counterpart in fracture mechanics, crack opening at the crack tip δt. At the same time, based on available experimental data from the literature, it is substantiated that the application of existing linear fracture mechanics methods in stress intensity factors KI for implementing the mentioned problems, the application of existing linear fracture mechanics methods is inappropriate. To determine the residual life of structural elements using this method, it is necessary to have kinetic diagrams in coordinates of the growth rate of small cracks and the crack opening at the crack tip, which means V ∼ δt. These diagrams are constructed here using the provided formulas for determining δt and diagrams are constructed here using the provided formulas and known experimental data for 45KhN2MFA steel under the influence of distilled water and static tension. Using the mentioned method, the residual lifespans of the torsion and the pipe were calculated under the influence of long-term static loading and distilled water. Additionally, the effectiveness of water solutions of well-known inorganic corrosion inhibitors on the residual lifespan of the mentioned structural elements was verified through calculations. It was found that the residual lifespan effectively characterizes the performance of corrosion inhibitors, which can be applied in engineering practice.

Crack propagation simulation and overload fatigue life prediction via enhanced physics-informed neural networks

The fatigue crack growth simulation and life prediction of structures are implemented in this paper based on the physics-informed neural networks (PINNs). Firstly, the enhanced PINNs are proposed by introducing the crack tip asymptotic displacement fields, so that the crack tip stress intensity factors can be calculated accurately even when the number of collocation points is small and the distribution grid is regular. The enhanced PINNs essentially transform the solution of elastic body containing crack into the optimization of minimizing the constructed loss functions, and can invert the fracture parameters. Then, an automatic crack propagation simulation method is developed based on the enhanced PINNs. The network architecture and the overall node distribution can be unchanged during the crack propagation process, and only new crack surfaces need to be processed and corresponding loss functions need to be modified. Because the nodal refinement around crack-tip is not required, this simulation method is convenient and can accurately predict the mixed-mode crack propagation path. Finally, the fatigue crack growth life algorithm considering overload is developed, where the effect of each overload can be captured by the cycle-by-cycle method. Based on this algorithm, the retardation behavior can be characterized and the fatigue life of structure under the load spectrum with periodic overloads can be accurately predicted. The sufficient examples are given to verify the feasibility and accuracy of the method proposed in this paper.