Stress Intensity Factors For Cracks Research Articles

On the suitability of single-edge notch tension (SENT) testing for assessing hydrogen-assisted cracking susceptibility

Combined experiments and computational modelling are used to increase understanding of the suitability of the Single-Edge Notch Tension (SENT) test for assessing hydrogen embrittlement susceptibility. The SENT tests were designed to provide the mode I threshold stress intensity factor (Kth) for hydrogen-assisted cracking of a C110 steel in two corrosive environments. These were accompanied by hydrogen permeation experiments to relate the environments to the absorbed hydrogen concentrations. A coupled phase-field-based deformation–diffusion-fracture model is then employed to simulate the SENT tests, predicting Kth in good agreement with the experimental results and providing insights into the hydrogen absorption–diffusion–cracking interactions. The suitability of SENT testing and its optimal characteristics (e.g., test duration) are discussed in terms of the various simultaneous active time-dependent phenomena, triaxiality dependencies, and regimes of hydrogen embrittlement susceptibility.

Experimental Study on the Fatigue Crack Propagation Rate of 925A Steel for a Ship Rudder System.

The low-temperature fatigue crack propagation rate of 925A steel, as a rudder steel for polar special ships, has a crucial impact on the evaluation of the fatigue strength of polar ships. The purpose of this article is to study the fatigue crack propagation rate of 925A steel under different low-temperature conditions from room temperature (RT) to -60 °C. The material was subjected to fatigue crack propagation tests and stress intensity factor tests. The experimental tests were conducted according to the Chinese Standard of GB/T6398-2017. The results show that as the temperature decreases, the lifespan of 925A increases. Within a certain stress intensity factor, as the temperature decreases, the fatigue crack propagation rate decreases. At -60 °C, it exhibits ductile fracture; within normal polar temperatures, it can be determined that 925A meets the requirements for low-temperature fatigue crack propagation rates in polar regions. However, in some extreme polar temperatures below -60 °C, preventing brittle failure becomes a key focus of fatigue design. Finally, the fatigue crack propagation behavior at the microscale of 925A steel at low temperatures was described using fracture morphology. The experimental data can provide reference for the design of polar ships to further resist low-temperature fatigue and cold brittle fracture.

Calculation and Discussion for Crack Driving Force of Dissimilar Metal Welded Joint of Nuclear Power Equipment Nozzle and Safe End

This study investigates the effects of the material mechanical properties heterogeneity and strength mismatch variation on crack driving forces for cracks in a dissimilar metal welded joint (DMW) of a reactor pressure vessel inlet nozzle to the safe end. Linear elastic and elastic-plastic analyses are carried out to calculate the stress intensity factor (SIF) and J-integral for cracks in the DMW. The effects of crack locations, crack depths, and strength mismatch factors on the SIF and J-integral are studied. The SIF results obtained by finite element analysis are compared with those obtained by the influence function method adopted in the nuclear power code. Results show that the effect of crack location on the SIF can be ignored. The SIFs calculated by the influence function method for cracks in the DMW are basically reasonable, although its conservatism is slightly insufficient. Moreover, with moving the crack location from the nozzle through buttering and weld metal to the safe end, the J-integral increases. The effect of the crack location and strength mismatch factors on the J-integral is essentially caused by variation of the plastic zone and the material properties of the crack front. The crack sizes affect the level of influence of the crack location and the strength mismatch factors on the J-integral. The J-integral increases with decrease of the strength mismatch factor.

About Measuring the Stress Intensity Factor of Cracks in Curved, Brittle Shells

Most techniques of measuring the stress intensity factor (SIF) in the cracking process assume a crack in a planar medium. Currently, there is no effective approach for curved brittle shells, particularly for non-developable cases, i.e., shapes with non-vanishing Gaussian curvature. This paper introduces a novel approach to obtaining material properties related to fracture by experimentally observing weakly curved surfaces. Based on the DIC record of the displacement field around the crack tip, the truncated Williams expansion is fitted to the data adjusted according to the shallow shell equations. The convergence properties of the method are investigated by comparing experimental data of PMMA cylinders to theoretical and numerical predictions. The applicability of the technique to non-developable surfaces is verified. It is demonstrated that robust convergence requires the number of terms in the Williams expansion exceeding 6. For different geometries, the ratio of the data selection radius and the length of the crack should exceed 0.3.

Multi-domain wavelet boundary element method for calculating two-dimensional stress intensity factors

In order to improve the accuracy of stress intensity factors (SIFs) calculated by traditional boundary element methods (BEM), the multi-domain wavelet boundary element method (WBEM) is proposed. Firstly, by adjusting the nodes of the B-spline wavelet element on the interval, crack-tip elements are constructed. Since B-spline wavelet on the interval (BSWI) has excellent compact support characteristics and is particularly suitable for describing solution domains with large gradient changes, the constructed crack-tip can reduce the numerical oscillation effect near the crack tip. Secondly, the crack-tip elements are implemented into WBEM. And the combination of WBEM and multi-domain technology can effectively handle interface cracks. Thirdly, the crack problem solving strategy based on multi-domain WBEM can directly evaluate the SIFs of cracks. Finally, several numerical examples involving homogeneous media and bi-material models are given to verify that the proposed method is simple and highly accurate.

Mechanical integrity of tubular elements based on strength and fracture criteria during transient CO2 injection

Geological carbon sequestration (GCS) is an essential technology for reducing carbon emissions. Wellbore integrity is crucial to ensure the safety of GCS. During low-temperature carbon dioxide (CO2) injection, the wellbore temperature decreases, causing the tubing and casing to contract, resulting in considerable axial tensile stresses, and making mechanical failure likely. This paper establishes a transient flow model for CO2 injection to predict the temperature and pressure distribution in the wellbore. Then, the strength safety factor of the tubing and casing is calculated using the material strength criteria. Fracture mechanics theory is employed to analyze the risk of crack propagation in defective tubing or casing during CO2 injection. The study indicates that the wellbore temperature near the wellhead is lower as CO2 is injected. Under typical injection conditions, the tubing and casing have high strength safety factors but small crack propagation factors. The stress intensity factor of cracks on the tubing and casing's outer surface is more significant than inner surface defects, posing a higher risk of crack propagation. When the tubing or casing exits a penetrating crack, its propagation safety factor is less than 1, necessitating the avoidance of through-wall cracks. The results guide maintaining wellbore integrity in carbon dioxide geological sequestration engineering.

Size effects in fatigue crack growth in confined volumes: A microbending case study on nanocrystalline nickel

Mechanical size effects are a well known phenomenon when the sample volume is reduced or the characteristic length of the microstructure is changed. While size effects in micropillar compression (smaller is stronger) or due to grain refinement (Hall-Petch) are well understood, this is less so in fracture mechanics. Given this lack of knowledge, the main question addressed in this work is: What happens to the fatigue crack growth properties when extrinsic size effects play a role? To answer this question, nanocrystalline nickel cantilevers, ranging in width from 5 to ▪, were subjected to fatigue crack growth. The crack growth rates and stress intensity factors were calculated and the Paris exponent in the stable crack growth regime was determined. It was found that the results scatter more strongly for the smaller cantilevers compared to the larger cantilevers. Results are interpreted in terms of plastic zone size and ligament size which are found to be critical for small cantilevers.

A Semi-Analytical Solution for the Stress Field and Stress Intensity Factor of Hole-Edge Cracks Using Improved Muskhelishvili Method

A semi-analytical solution is provided to obtain the stress intensity factors (SIFs) of hole-edge cracks with different configurations and the stress fields along the crack propagation direction in an infinite isotropic plane. The complicated solution procedure while using the Muskhelishvili method is improved by expanding an irrational mapping function into an approximate rational function so that singular integral equations could be converted to linear equations. The proposed method used to obtain the SIFs of symmetrical cracks emanating from circular or elliptical holes and a single crack emanating from a circular hole is compared with other methods in the literature. The results show that this method is universal and accurate for hole-edge cracks. In addition, the effects of the lengths of the asymmetrical cracks and the ratio of the semi-axes of the elliptical hole ([Formula: see text]/[Formula: see text] on the SIFs are studied, which have not been previously reported.

SIF formula based on exact SIF distribution for semi‐elliptical surface cracks subjected to mode I, II, III uniform loading

AbstractThe stress intensity factor (SIF) distribution of a semi‐elliptical surface crack is often used for evaluating the fatigue strength of structures. Virtually exact distributions of SIFs can be provided along the crack front by solving the hypersingular integral equation of the body force method. In this paper, to create a very accurate SIF variation formula, the elliptical crack SIF solutions , , are used and the SIF ratios , , are mainly focused. Paying attention to the corner point singularity, by applying the least squares method to the ratio , in the whole range of parametric angle , and formulas can be proposed. Instead, formula can be proposed by applying the method of least squares to the ratio of in the range but applying directly to in the range . In this way, all of formulas proposed in this paper provide the SIFs with better than 1.0% accuracy.

Efficient technique for evaluation of three-dimensional elastic–plastic fracture mechanics parameters based on equivalent distributed stress concept

This study proposes an efficient technique for the evaluation of the elastic–plastic fracture mechanics (EPFM) parameters of three-dimensional (3D) cracks based on the modified crack cohesive force (CCF) model. In the current method, the 3D crack’s EPFM parameters are analyzed by applying the pseudo crack face traction (CFT) to a two-dimensional (2D) center crack in an infinite plate. This pseudo traction is called the equivalent distributed stress (EDS). The EDS to be applied on the 2D center crack is determined in a manner that reproduces the relationship between crack length and stress intensity factor (SIF) of the intended 3D crack. Once EDS is determined, EPFM parameters for 3D cracks can be obtained instantly by using the center crack’s analytical closed-form solutions. This approach can compute the 3D crack’s EPFM parameters in dramatically less computation time than 3D finite element (FE) analysis. The effectiveness of the proposed method is validated by comparing the EPFM parameters of a 3D penny-shape crack obtained from this method against the reference analytical solutions and numerical FE analysis results. The parameters determined by the present method show excellent agreement with the reference solutions.

Double inclined cracks overlapping effect on mixed stress intensity factors using XFEM object-oriented implementation

The object of research is the Mixed Mode Stress Intensity Factor (MMSIF) of a two-dimensional (2D) plate. With the emergence of modern technologies and advanced innovations which contribute to the development and improvement of the design, implementation and management of construction projects, it has become easier. However, it is very difficult to manufacture components free from unavoidable defects, such as cracks, which lead to material deterioration and ultimately shorten its service life. Based on the process of local enrichment region using partition of unity concept, the extended finite element method (XFEM) has overcome the limitations of the standard FEM method in terms of modeling and numerical simulation of discontinuities (cracks) while gaining its general advantages. This makes XFEM a powerful and widely used digital tool in recent years. One of the most frequently raised problems in the discontinuities field (cracks) is the phenomenon of juxtaposition of multiple cracks in a cracked isotropic plate, which must be studied to determine the extent of its effect on the crack stress intensity factor in order to obtain higher safety reliability. On this basis, an improved object-oriented programming (OOP) with extended finite elements was used because of its great importance and well-known benefits. In this paper, the MMSIF of a 2D plate is determined to show the effect of the out-of-phase orientation of the angle, as well as the effect of the juxtaposition of two inclined cracks. As a result of the research, it is shown that, the convergence between the results obtained in this study with those reported in the literature, and to theoretical values is remarkable, and their close agreement was noted. In the future, based on the object-oriented approach characteristics represented by flexibility, scalability, and modularity, which were explained in this research, this proposed approach can be enriched to include heterogeneous materials modeling, whether linear or nonlinear, crack propagation in dynamics, in addition to Complex 3D industrial problems.

Analytical Solution of Ice–Rock-Model Stress Field and Stress Intensity Factors in Inhomogeneous Media

The stress distribution and fracture parameter calibration of ice–rock models are important aspects of studying rock properties at high altitudes and latitudes. However, progress in ice–rock modeling has been slow and singular, and it is limited due to the discrete nature of rocks and the applicability of fracture mechanics. In this study, a circular inhomogeneous ice–rock model is proposed for the first time, and a method is provided for calculating the stress field of the model under biaxial loading. A method for calculating the single-crack stress intensity factor of the model subjected to biaxial compressive loading is also provided. The novelty of this work is that the inhomogeneous ice–rock model is treated as a superposition of two models, namely, a circular pore plate and circular ice, according to the superposition principle. The key is that the stress field distribution law of the ice–rock model is obtained based on the basis of the displacement continuity of the ice–rock interface. The analytical and approximate solutions of the stress intensity factor of a single crack were also obtained by considering the normal phase effect of the crack surface and combining the stress distribution law of the ice–rock model. Comparison with the CAE method was made to verify the correctness of the stress field and stress intensity factor calculation methods. The evolution laws of lateral pressure coefficients, the elastic modulus ratio of ice and rock on the stress field, and the stress intensity factor were analyzed. The effects of lateral pressure coefficients, elastic modulus ratios, and crack distributions on the failure modes were investigated using the extended finite element method (XFEM). This study can provide a theoretical basis for the evaluation of mechanical properties and prediction of the failure modes of frozen rock bodies.

Study on Stress Intensity Factor of Girth Weld with Crack Defects

In order to study the safety performance of the girth weld with cracks in the pressure vessel in use, based on fracture mechanics, this paper adopts ABAQUS and FRANC3D joint simulation to calculate the crack tip stress intensity factor(SIF). The influence of crack location, length and depth on the stress intensity factor of crack tip is analyzed. The results show that the crack SIF at different crack locations (inner crack > buried crack > outside crack) increases with the increase of crack length and increases with the increase of crack depth.

Estimation of stress intensity factor for surface cracks in the firtree groove structure of turbine disk using pool-based active learning with Gaussian Process Regression

Estimation of stress intensity factor for surface cracks in the firtree groove structure of turbine disk using pool-based active learning with Gaussian Process Regression

A fast approach for predicting stress intensity factors in tortuous cracks under mixed-mode loading

Realistic crack morphologies are generally sinuous rather than straight, which brings a great challenge to capture accurately the stress intensity factors at the crack tip. In this paper, a fast approximation method for predicting stress intensity factors in tortuous cracks under mixed-mode loading is proposed in terms of geometry simplification and semi-theoretical calculation. First, the finite element results show that the main and branch two-segment crack geometry approximation possesses a good capability of predicting the stress intensity factors of tortuous cracks under mixed-mode loading, whereas the simplification strategy of one straight crack cannot characterize the crack tip field of sinuous cracks. Then, an efficient semi-theoretical estimation approach is proposed to obtain the stress intensity factors of the branch crack from those of the main crack, which is validated to further reduce the computational time, resulting in a two-step accelerated operation. Moreover, the effect of main crack offset is also discussed and some recommendations are given to ensure accurate predictions within an acceptable margin of error for microstructural design or other application purposes.

Analysis of electrode crack propagation in solid oxide fuel cell with pre-crack

The mechanical performance of solid oxide fuel cell is one of the main factors limiting its commercialization process. In order to reduce the degree of crack propagation during the cooling process and improve the stability and durability of the cell, the finite element analysis is conducted on a three-dimensional model of solid oxide fuel cell containing pre-cracks. Utilizing the extended finite element method (XFEM) and fracture theory, considering the stress distribution, length and maximum width after crack propagation and deflection angle of crack as criteria, this paper investigates the influence of various parameters, including working temperature, material properties, pre-crack angle and pre-crack location, on pre-crack propagation behavior and proposes a solution to improve the stability of the cell based on material optimization and structural optimization. Set a pre-crack at the left boundary of the anode to analyze the influence of different operating conditions on the propagation of anode cracks in the cell. The correctness of finite element simulation is verified by comparing the simulation results and theoretical results of crack stress intensity factors in the same model. From the comprehensive analysis of the thermal stress of the cell, the crack length and maximum width after pre-crack propagation, and the two deflection angles of crack propagation, it can be seen that within the selected parameters, in order to ensure the stability of the cell and inhibit the degree of crack propagation, the operating temperature of the cell should not be lower than 1023 K, and the coefficient of thermal expansion of anode should be less than 12.50×10<sup>-6</sup> K<sup>-1</sup>. In addition, when the pre-crack angle is 45° or the pre-crack is 0.45mm away from the bottom of anode, the maximum width after crack propagation is the smallest, and the propagation path is the most predictable. In this case, the cell is affected by the smallest crack range and the highest stability. This research provides a guidance for suppressing crack propagation in solid oxide fuel cell, improving the lifetime and promoting the commercialization process of fuel cell.

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

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

A Meso-Macro Method of Evaluating Water Content Effect on Direct Tensile Fracture in Brittle Rocks

Tensile stress is one of the primary forms of loading triggering the fracture in brittle rocks. Water content strongly affects the fracture process induced by meso-crack extension under the direct tensile loading of brittle rocks. Due to limitation of current equipments, the experiment of direct tensile fracture considering water content effect of brittle rocks is hardly implemented. Furthermore, the meso-macro model simultaneously considering the influence of water content and tensile loading on fracture behaviours of brittle rocks is also rarely studied. This paper proposes a meso-macro mechanical model to evaluate the water content effect on the fracture process under direct tensile loading of brittle rocks. This model is developed by combining the suggested model of meso-crack extension under direct tensile loading, the correlation of macroscopic strain and meso-crack extension, and considering the effect of water content on fracture toughness KIC and initial damage D0. This meso-macro model is linking the development process of meso-crack initiation, extension and coalescence to macroscopic fracture. The axial stress-strain curves during progressive tensile fracture under different water contents were studied, and the rationality of the suggested theoretical model was validated by the test results. The influences of water content on the relation between wing crack length and axial stress, the relation between wing crack length and stress intensity factor KI, crack initiation stress, peak stress, and elastic modulus were analyzed. The influences of the model parameter β and the initial crack angle φ on the peak stress and crack initiation stress under the different water contents are also discussed.

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

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

Estimation of the stress intensity factor of an interface crack by the scattered SH-far field

The diffraction of the plane elastic SH-wave from a semi-infinite interface crack on junction of two elastic semi-infinite media is studied. The crack is modelled by the mathematical cut with no stress on its faces. The displacement and the stress fields are continuous outside of the crack. The wave diffraction problem is reduced to the solution of the mixed boundary value problem for Helmholtz equation. We search the solution which satisfies the Neumann boundary condition on the crack faces and the continuity condition for the stress and displacement fields outside of the crack. The radiation condition at the infinity and the Meixners condition at the crack tip must be also satisfied. Using the Fourier integral transform, the mixed boundary value problem is reduced to the Wiener-Hopf functional equation which is valid in the given strip of regularity in the complex plane. The method of factorization and decomposition, as well as the Liouvilles theorem, are used to solve this equation. Its kernel function is factorized and represented as a product of two split functions that are regular in the overlapping half-planes. These ones allow for the simple poles outside of the regularity regions. The solution of the Wiener-Hopf equation is presented in analytical form. The scattered displacement field is found for an arbitrary frequency and sounding angle by applying an inverse Fourier integral transform to the solution. The asympŹtotic formula for the stress intensity factor (SIF) at the crack tip is obtained. The correlation between complex amplitude of the SH-wave far scattered displacement field and the SIF caused by this field is obtained for an arbitrary radiation angle, frequency and medium parameters. This allows us to express the SIF through the amplitude of the far field if the radiation frequency, sounding angle as well as the physical characteristics of materials are known. It is shown that in the plane that is normal to the tip of the crack the ratio of SIF for the given junction and two fixed values of the sounding angle or two sounding frequencies is proportional to the ratio of the scattered fields. It is found that under above mentioned condition the proportionality rate does not depend on material properties. The obtained relations can be applied for estimation of the SIF with changing frequency and sounding angle.