Stress Intensity Factors For Cracks Research Articles

Failure Prediction of an Airfoil-Type Crack in Thermoelectric Coupling Materials

Airfoil-type cracks with curved surfaces and sharp tips are frequently encountered in modern engineering applications and the aerospace industry. However, such cracks significantly threaten structures due to stress concentration and further cause damage. This study investigates the theoretical analysis and failure prediction of airfoil-type cracks within thermoelectric coupling materials under the interaction of remote mechanical loads, heat flux and electric current density. By employing complex variable theory, conformal mapping methods, and the analytic continuation theorem, the full-field stress and stress intensity factors of an airfoil-type crack were determined under three different loading conditions. The results indicate that when the airfoil-shaped crack tip is subjected to horizontal compression, vertical tensile mechanical load, and both heat flux and current density parallel to the crack, the crack tip would reach a dangerous state. Additionally, the full-field stress distribution reveals stress concentration around the crack tip, which explains variations in SIFs under different external forces and shape factors. Four critical situations suppressing crack propagation under mixed loading conditions are proposed. Furthermore, using an acrylic plate and bismuth telluride alloy as examples, the critical values of external loading for the mixed-mode fracture are determined based on the strain energy density criterion. These critical values can be used to predict failure initiation, thus reducing the risk of structural failure due to airfoil cracks within thermoelectric coupling materials.

Strength analysis due to thermal loading and tensile loading when metals are bonded by heat-curing adhesives

Heat-curing adhesives are widely used after being cured by heating to a temperature higher than room temperature. To evaluate the adhesive strength, therefore, it is necessary to consider both the thermal stress generated during heat curing and external loads such as tensile stress. Butt joint specimens are essential for evaluating tensile adhesive strength but also thermal strength. The interfacial strength can be discussed from the stress intensity factor (SIF) of a fictitious edge interfacial crack assumed at the interface end. This is because the SIF is controlled by the intensity of singular stress field (ISSF) at the crack-free interface end and a constant term associated with the thermal load. In this paper, a useful thermal SIF solution is proposed by superposing the SIF under tensile stress and the SIF under uniform interface stress associated with thermal loading. This general SIF expression provided under arbitrary material combination can be applied for predicting the tensile strength σc and critical temperature change ΔT without performing new FEM calculations. The usefulness of the expression is confirmed through the adhesive strength of Aluminum/Epoxy butt joint experimentally obtained. Once the critical SIF K1C can be obtained from the tensile strength σc and the temperature change ΔT, the adhesive strength can be expressed asK1C = constant of an assumed fictitious interface, and this can be used to predict critical σc for various temperature change ΔT and for various adhesive bondline thickness h.

Study on the Stress Intensity Factor of Tilt Crack on the Inner Surface of Pipeline

Abstract Cracking is one of the key factors jeopardizing the safe operation of pipelines, and Stress Intensity Factor (SIF) is an important parameter for evaluating the degree of crack danger. Cracks on engineering pipelines often appear in irregular patterns. In this paper, with FRANC3D crack analysis software, SIFs of the circumferential tilt cracks and axial tile cracks on the inner wall surface of a pipe under internal pressure were studied with concentration on the effects of the crack tilt angles. Mode I stress intensity factor weakening effect KI/K0 was defined and influences of the crack tilt angle, pipe and crack size on KI/K0 were investigated. With enough simulation results, empirical formulas for calculating the Mode I SIF for the circumferential or axial tilt crack were obtained by modifying the formulas for calculating the SIF of the crack in AMSE FFS-1.

Stress intensity factor models using mechanics-guided decomposition and symbolic regression

The finite element method can be used to compute accurate stress intensity factors (SIFs) for cracks with complex geometries and boundary conditions. In contrast, handbook solutions act as surrogate SIF models that provide significantly faster evaluation times. However, the development of conventional surrogate SIF models relies on manual development based on low-order parameterizations. This limits surrogate model accuracy and generalizability. In this paper, we develop a framework for the automated development of mechanics-guided handbook SIF solutions by using interpretable machine learning via genetic programming for symbolic regression (GPSR). Formalizing the mechanics-based approach of Raju and Newman, SIF training data is decomposed into multiple subsets. This decomposition enables parallel GPSR model development of subfunctions, each of which accounts for specific geometrical corrections with respect to a known analytical model. Using this mechanics-based approach with GPSR allows for equations to be learned with improved accuracy and reduced complexity relative to the Raju Newman equations while maintaining the inherent interpretability of mathematical expressions. In this paper, we present equations that match the complexity of the Raju Newman equations while having reduced error, as well as equations with similar errors and reduced complexity.

3D analysis of crack propagation in nuclear graphite using DVC coupled with finite element analysis

The initiation and propagation of cracks within nuclear graphite components compromise the lifespan of advanced gas-cooled reactors and even lead to safety incidents. A thorough understanding of fracture properties in nuclear graphite is crucial for the effective management and design of graphite structural components. In this work, an in-situ test of a double cleavage drilled compression (DCDC) specimen was conducted using X-ray tomographic imaging to fully analyze the 3D crack propagation behavior in IG-11 nuclear graphite. “Subvolume Splitting” digital volume correlation (SS-DVC) was employed to accurately quantify the displacement fields surrounding the crack. The entire 3D crack propagation and crack surface around the crack front were precisely captured through 3D imaging processing of the gray level residual (GLR) field. Additionally, crack opening displacements (CODs) and stress intensity factors (SIFs) were determined using finite element (FE) analysis with extended finite element method (XFEM). Experimental results indicate that although mode I crack remains predominant throughout the whole process, complex crack propagation exists around the crack front. The utilization of irregular crack surfaces in FE analysis helps to obtain refined displacement fields and accurate SIFs of the crack front. This work provides comprehensive insights into crack propagation and reveals the influence of complex crack morphology on SIF calculations, facilitating accurate prediction of structural integrity and rational design of graphite components.

Stress Intensity Factor of Surface Cracks in the Tubing of High-Temperature and High-Pressure Deep Wells

Stress Intensity Factor of Surface Cracks in the Tubing of High-Temperature and High-Pressure Deep Wells

Damage behavior of the surrounding medium caused by different blast-induced dynamic and static loadings

The combination of the dynamic action of explosion stress wave and the static action of explosion gas expansion is what primarily drives rock-breaking blasting, and their different intensities lead to different blasting effects. Therefore, experiments were conducted to explore the damage behaviour of the surrounding medium caused by different blast-induced dynamic and static loadings using digital laser Schlieren and digital laser dynamic caustic systems. The results were as follows: In the air medium, when the explosives detonated, TATP (triacetone triperoxide) had the strongest quasi-static effect, and the highest velocity explosion shock wave and products compared with those of NHN (nickel hydrazine nitrate) and DDNP (diazodinitrophenol). Part of the TATP explosion product was ahead of the shock wave front, whereas for NHN and DDNP, their explosion products were behind the propagation of the shock wave front. The highest pressure peak of TATP was the result of the combined action of the shock wave and explosion product impacting the sensor. In the solid medium, NHN, the explosive with the strongest dynamic load, had the strongest stress wave and highest stress intensity factor peak of the main crack. The velocity reached the peak value at the early stage of propagation, and the dynamic action had a dominant effect on the cracking of the crack; the stronger the dynamic action, the higher the crack initiation energy. The stress intensity factor and propagation rate of the main crack of TATP with the strongest quasi-static effect decreased slower than those of the other explosives; therefore, the main crack propagation time and length were the longest. After cracking, the quasi-static effect dominated the process of crack propagation, where the stronger the quasi-static effect, the longer duration of the driving force of crack propagation. The research results provide a basis for customising explosives for different functions in practical engineering and realising the fine and efficient utilisation of explosion energy.

Stress intensity factor analysis for multiple cracks in orthotropic steel decks rib-to-floorbeam weld details under vehicles loading

In recent years, it has been found that multiple cracks coexist in the existing steel bridge orthotropic steel decks (OSDs) longitudinal rib-to-floorbeam (RF) details. The synergistic expansion mechanism of multiple cracks in the orthotropic steel bridge deck panel is still unclear. This paper proposes a multiscale extension finite element method based on ABAQUS and FRANC 3D interactive technology to simulate the fatigue crack propagation behavior of steel bridge RF details under dynamic vehicle loading. The effectiveness of this method is verified by comparing experimental data. The crack propagation behavior of longitudinal rib weld toes, transverse diaphragm weld toes, and transverse diaphragm arc notches is studied, and the influence of fatigue crack length and angle on the initial crack stress intensity factor (SIF) of adjacent details is discussed.

Dissipation during crack growth in a viscoelastic material from a cohesive model for a finite specimen

AbstractIn the present paper, we extend results recently given by Ciavarella et al. (J Mech Phys Solids 169:105096, 2022) to show some actual calculations of the viscoelastic dissipation in a crack propagation at constant speed in a finite size specimen. It is usually believed that the cohesive models introduced by Knauss and Schapery and the dissipation-based theories introduced by de Gennes and Persson-Brener give very similar results for steady state crack propagation in viscoelastic materials, where usually only the asymptotic singular field is used for the stress. We show however that dissipation and the energy balance never reach a steady state, despite the constant propagation crack rate and stress intensity factor. Our loading protocol permits a rigorous solution, and implies a short phase with constant specimen elongation rate, but then possibly a very long phase of constant or decreasing elongation, which differs from typical experiments. For the external work we are therefore unable to use the de Gennes and Persson-Brener theories which suggested that the increase of effective fracture energy would go up to the ratio of instantaneous to relaxed modulus, at very fast rates. We show viscoelastic dissipation is in general a transient quantity, which can vary by orders of magnitude while the stress intensity factor is kept constant, and is largely affected by dissipation in the bulk rather than at the crack tip. The total work to break a specimen apart is found also to be possibly arbitrarily large for quite a large range of intermediate crack growth rates.

A Novel Analysis of the Size Effect on Stress Intensity Factor for Center and Edge Cracks in Tension by the Net-Section Mechanics

A Novel Analysis of the Size Effect on Stress Intensity Factor for Center and Edge Cracks in Tension by the Net-Section Mechanics

Mixed-mode fracture analysis of CORC cables with double-edge cracks under tension and torsion

The Conductor on round core (CORC) refers to a circular cable that is helically wound with rare-earth-barium-copper-oxide ((RE)BCO) high-temperature superconducting (HTS) tapes. This type of cable finds extensive applications in large superconducting magnets. However, the mechanical–electrical performance of CORC cables is hindered by microscopic edge cracks that occur during the mechanical slitting process of HTS tapes. In this paper, the mixed-mode stress intensity factor (SIF) of cracks in CORC cables under different loading conditions is investigated using the extended finite element method (XFEM). The design variables of CORC cables are optimized by considering the effect of various factors such as the crack parameter, the winding angle, the core radius, and the Poisson’s ratio of the winding core on the SIF. The results indicate that the impact of each factor on the mixed-mode SIF varies depending on the loading mode. Notably, the influence of the winding angle on the SIF is particularly significant and intricate. In the case of tensile loading, a smaller winding angle proves advantageous in impeding crack propagation. Conversely, the most dangerous winding angle for torsional loads is 45°. The divergence of these effects can be indirectly indicated by theoretical solutions regarding the tape strain along the helix direction. For the cases examined, the results have shown that the crack propagation path is independent of these factors, and the direction of propagation is perpendicular to the edge of the tape.

Influence of load ratio on fatigue life assessment of AZ31B magnesium alloy under different temperatures

First ever fatigue crack growth experiments were conducted under various load ratios (R = 0.1 to 0.8) at 300 K, and (R = 0.1, 0.3, 0.5, and 0.7) at 327 K and 473 K, respectively, on AZ31B magnesium alloy. The results reveal that temperature-dependent variations in both fatigue crack growth rates and stress intensity factor ranges (ΔK) across different load ratios. It was found that at relatively higher load ratio (R = 0.8) leads to a lower ΔK = 8.0287 MPa√m and a lower load ratio (R = 0.1) result in a higher ΔK = 15.5981 MPa√m, indicating that the material undergoes fatigue crack propagation at a higher level of stress intensity factor range at room temperature. A slower crack propagation was seen at higher load ratio (R = 0.8), whereas lower load ratio (R = 0.1) exhibits faster crack growth at 300 K. Similarly, crack growth generally increases at higher temperatures (i.e., 373 K and 473 K). The fatigue life of the magnesium alloy AZ31B increased from 12,410 to 87,031 cycles at 300 K, 9,620 to 32,667 cycles at 373 K, and 9,140 to 30,143 cycles at 473 K as the load ratio increases. The average fatigue life decreases to 59 % and 63 % as the temperature is varied from 300 K through 373 K to 473 K. The fractographic and surface roughness carried out by field emission scanning electron microscopy and 3D-Profilometer respectively, illustrate that roughness of fracture surfaces correlates with an increase in the fatigue crack growth rate for a specific value of ΔK.

Finite Element Analysis based Stress Intensity Factor Solutions for Surface Cracks

The stress intensity concept is important in termsof crack extension as critical values of the stress intensityfactors govern crack initiation. Therefore, the present workdetermines stress intensity factors for semielliptical shallowand deep surface cracks as a function of parametric angle,crack depth, and aspect ratio for tension and bending loads.The stress intensity factors are obtained from a threedimensional finite-element analysis of semielliptical surfacecracks in finite plates subjected independently to tensionand bending loads under elastic conditions. The obtainedstress intensity factor is used to predict the crack growthunder linear elastic conditions. Results show that the stressintensity factor varies along the crack front for shallow anddeep cracks. At the deepest point in bending and tension thestress intensity factor increases as the ratio of the crackdepth to the crack length at surface decreases. However, atthe free surface the stress intensity factor becomesmaximum when the crack depth equals crack length. Asurface crack in tension loading is predicted to break thewall thickness with a relatively small amount of crackgrowth at surface. While in bending the crack breaksthrough with large amount of crack growth in the widthdirection.

Calculation of Stress Intensity Factor for Annular Double Cracks on Inner Surface of Pipeline

Calculation of Stress Intensity Factor for Annular Double Cracks on Inner Surface of Pipeline

Contact problem for an interface crack under action of a moving punch

Nowadays coatings are used in many applications to reduce contact friction, reduce energy losses, improve wear and pitting resistance, and so on in various machine parts. In some cases, coating applications are limited due to coating delamination. The latter is caused by a crack growth due to cyclic loading along a coating interface with the substrate. This paper is focused on modeling and analyzing the behavior of interface cracks between a coating and a substrate. A flat rigid punch subjected to normal and tangential loading is slowly moving along the solid surface. The solid is represented by an elastic half-plane covered by two elastic layers bonded to each other and to the substrate. The elastic materials of the coatings and the substrate are homogeneous but different. The thickness of the layer adjacent to the substrate is considered to be (significantly) smaller than the one above it. This thin layer plays the role of the interface between the other one and the substrate. The interface layer has a crack parallel to its surface and located in the middle of it. The crack surfaces are free from friction and can partially open/close or completely open/close. Some numerical results for the crack stress intensity factors and other solution parameters are presented for cracks small and comparable in size with the punch contact region.

Interaction Assessment of Stress Intensity Factors of Surface Cracks on Thick Cylinders under Tension Force and Bending Moment

From an engineering perspective, hollow cylinders have various applications in the industry due to their strength, versatility, and geometric properties, making them vital for various applications in diverse industries. Therefore, it could be seen in many aspects such as fluid conveyance, manufacturing and fabrication, rotating machinery, structural components, storage, and pressure vessels. As it is well-known fracture is the most dominant type of failure in cylinders that is caused by defects or flaws. With time, these cracks (flaws) may extend and lead to a tragic failure, posing significant risks to both the nearby environment and humans. Moreover, crack cooperation which is known as (crack interaction) represents a chief apprehension, where cooperation or interaction may accelerate the crack growth and cause unpredictable failure. In this work, a wide variety of crack configurations were examined to quantify the interaction of double-interacting surface cracks located on a thick cylinder numerically via ANSYS software. The Stress Intensity Factor (SIFs) has been utilized as a driving force to describe the crack interaction. The results found that crack interaction influenced both cracks by the same rate, and SIFs distributed along the crack front by the same style as that of a single crack. Also, an inversely proportional relationship has been found between the crack interaction and the separation distance between the cracks. It is possible to conclude that the crack interaction of double interacting cracks exhibited a shielding effect, where SIFs for the case of double cracks were less than those of single crack.

Experimental study on decoupled charge blasting-induced crack propagation with parabolic shaped charge

In this study, a new parabolic shaped charge structure is proposed to realize bidirectional blasting in coal mines. To examine the fracture characteristics of rock mass induced by shaped charge structure under explosion load, a dynamic caustic experimental system is adopted. Further, the blasting-induced damage distribution characteristics of rock mass caused by different decoupling coefficients are investigated. Using polymethyl methacrylate (PMMA) as the experimental material, a two-dimensional model is established. AUTODYN, an explicit dynamics simulation program, is used to examine the initial crack generation process under shaped charge blasting. The stress wave propagation rule and the relationship between blasting damage and decoupling coefficient are explored. The results show that the parabolic shaped charge structure can control the explosion energy distribution and reduce the surrounding rock damage. When the decoupling coefficient is 2, the main crack length is optimum. During the crack propagation process, the growth rate and stress intensity factor of the main crack of the specimen show an oscillatory downward trend. Two stress concentration points are generated on either side near the main crack, forming the initial crack. When the decoupling coefficient is less than 2, long cracks exist in both the shaped and non-shaped charged directions, and the energy gathering effect is poor. When the decoupling coefficient is greater than 2, the energy gathering effect is obvious, but the main crack length is shorter.

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.

Computational Analysis of Predicting Stress Intensity Factor Using Hdmr Technique

The present research focused to develop meta-model (MM) as a low-cost substitute for the Finite Element Method (FEM), to forecast the Stress Intensity Factor (SIF) of a semi-elliptic crack propagating. Multi-linear regression (MLR) based MM is developed for predicting the crack propagation. Three parameters—Root Mean Square Error (RMSE), Maximum Absolute Error (AAE), and Average Absolute Error—are examined to compare the MM's precision (AAE).

Analytical solution to stress intensity factors of cracks on both sides of a triangular hole in an infinite plate

This paper presents an analytical solution for determining the stress intensity factors (SIFs) of double-sided cracks emanating from a triangular hole in an infinite plate. A conformal function is introduced, which can be applied to these cracks, and the SIFs are analytically derived using the Muskhelishvili method. By combining the Schwarz-Christoffel integral with the conformal transformation for cracks originating from circular holes, a mapping function for the cracked triangular hole is presented. The accuracy of the SIF at the single right-sided crack of the triangular hole is validated using finite element method (FEM) and compared with existing references. This study investigates the influence of biaxial loading factors and lengths of cracks on SIFs. The SIF of the hole-edge crack is related to the structure from which the crack emanates. This analytical approach provides a reliable solution for calculating SIFs of double-sided cracks emanating from a triangular hole.