Stress Intensity Factor Solutions Research Articles

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.

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.

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.

Analytical modeling and simulations of dynamic mode-III fracture in pre-stressed dry sandy elastic continuum

A mathematical model has been developed to investigate the SIF (stress intensity factor) and COD (crack opening displacement) for the propagation of mode-III fracture influenced by propagating SH-wave in a pre-stressed dry sandy elastic continuum. The Wiener-Hopf mathematical method along with the Fourier integral transform (FIT) technique have been successively implemented to obtain the solution of the boundary value problem associated with the mathematical model. Furthermore, the closed form solutions of SIF and COD for non-static and static conditions of mode-III fracture have been obtained, and are found to be in well agreement with the existing results present in the literature. The sound effects of various affecting parameters viz. horizontal and vertical (compressive/tensile) pre-stresses, crack depth, and crack velocity on SIF and COD have been explored. In order to delineate the influences of these aforementioned parameters on SIF and COD graphically, numerical simulation has been accomplished.

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.

On the validity of the Tada stress intensity factor solution for the single edge notch tension specimen with pinned ends

The validity of the Tada stress intensity factor (KTada) for pinned-ends single edge notch tension [SEN(T)] specimens is assessed via a combined experimental-modeling approach. Analysis of fatigue crack growth rate reductions during constant-ΔKTada loading demonstrates that specific combinations of alloy stiffness, geometry, and loading result in the true K deviating below KTada. Geometrically non-linear, 3-dimensional finite element calculations confirm mild-to-strong influences of these parameters, which are not captured by KTada. Most existing pinned SEN(T) data are found to use parameters where KTada is not significantly reduced, but the present results underscore the need for a more broadly applicable K solution.

Stress intensity factors and full-field stresses for a hypocycloid-type crack within a thermo-elastic material

This study focuses on the failure analysis of a hypocycloid-type crack within a thermo-elastic material. Employing the conformal mapping method, analytical continuation theorem, and principle of superposition, the explicit general solution for stress intensity factors (SIFs) associated with an arbitrary-edged hypocycloid-type crack is determined analytically under the influence of remote homogeneous heat flux and mechanical load. The superposition method combines stress functions and SIFs for two distinct loading conditions. The outcomes of the normalized SIFs are affected by the magnitude and orientation of the heat flux and mechanical load. A full-field stress distribution is provided to account for variations in SIFs. Certain combinations of loads lead to maximum SIF values, rendering the system highly vulnerable to damage, while two specific scenarios inhibit crack propagation, thereby reducing the risk of structural failure.

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.

Numerical solution of stress intensity factor in an infinite plate containing parallel double cracks under compression and shear

The Fredholm integral equation method and the superposition principle are applied to solve the equations for the problems of collinear double cracks and non-collinear parallel double cracks in an infinite plate under compression and shear. The numerical solutions of the proposed method are verified by the analytical solutions of the elliptic integral method. Then the effects of geometrical position of two cracks and friction of crack face on the interaction between two cracks are investigated, and the calculated results of stress intensity factors at the tips of parallel double cracks under compression and shear are provided. The influences of crack spacing, crack half-length ratio and rock-bridge dip angle on the distribution of perturbation stress on the crack face are discussed, which are not reported previously.

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.

General point load weight function for semi-elliptical surface cracks in round bars

Offshore mooring chains are continuously subjected to cyclic environmental loadings, resulting in fatigue cracks that always develop at the surface and grow across the circular cross-sections. To analyse the fatigue crack growth in a mooring chain based on a fracture mechanics-based approach, the evaluation of stress intensity factors (SIFs) of surface cracks in the chain segments becomes essential. A general point load weight function of SIFs for semi-elliptical surface cracks in straight and curved round bars was derived in this study. Parametric three-dimensional finite element (FE) models were developed to calculate the SIF solutions for determining the unknown parameters in the weight function. The analysis matrix covered wide ranges of aspect ratios 0.1 ≤ a/c ≤ 2.0, relative crack depths 0.03 ≤ a/D ≤ 0.6 and relative bar curvatures 0.0 ≤ D/Ri ≤ 1.5. The developed weight function was verified against the solutions available in the literature and FE results, indicating good accuracy. The proposed weight function can be used in SIF calculation and remaining fatigue life prediction of surface cracked round bar components under complex stress distributions, such as chain links.

Analytical solutions for the plane thermoelastic problem of a nano-open crack in one-dimensional hexagonal quasicrystal non-periodic plane

As a stable material at high temperatures, the presence of cracks and other defects greatly reduces the performance of quasicrystals (QCs). The plane thermoelastic problem of one-dimensional hexagonal quasicrystals (1DHQ) non-periodic plane containing a nano-open crack is analyzed using surface elasticity theory. The closed form solutions are obtained to describe the thermoelastic field corresponding to the nano-crack by the Fourier integral transformation technique. The analytical solutions of the thermal stress intensity factors (TSIFs) and the strain energy density factor (SEDF) at the crack tip are derived explicitly. The influence of the applied loads, the surface effects and the multi-field coupling effects on the TSIFs and SEDF are discussed. The numerical results reveal that the surface effects have an obvious impact on TSIFs with small applied loads, and the surface effects will inhibit the propagation of nano-open cracks. The research results of this study provide some reliable theoretical references for the development of nano-QCs.

Effect of compressive residual stress and press fitting on residual life assessment of deep-rolled EA4T steel railway axles

Deep rolling surface strengthening is an effective way to introduce compressive residual stress (CRS) along the railway axle, which can improve the fatigue resistance of the material. The CRS field was rebuilt adopting the proportional-integral (PI) iteration method and the unit pressure method (UPM) to study the fatigue cracking behavior of deep-rolled EA4T railway axles. The remaining life prediction model and the stress intensity factor (SIF) solution method were then validated using simulations and testing with small-sized specimens. The remaining life of the EA4T railway axle was then calculated by applying a realistic vertical load spectrum. The results showed that CRS prevented crack propagation, enhanced the critical propagation size of railway axle cracks, and prolonged the remaining life of the axle. Additionally, the remaining life of the axle may not support the following maintenance period if a crack with an extendable size emerges at the unloading groove of the railway axle. This work provides a theoretical basis for the optimization of the non-destructive testing (NDT) interval of deep-rolled EA4T railway axles.

Stress Intensity Factor Solutions for Eccentric Annular External Cracks in Notched Round Bars under Tensile Loading

In this paper, stress intensity factor (SIF) solutions of eccentric annular external cracks in elliptical notched round bars under tension loading have been obtained from 3D finite element analysis, along with their relation to the energy release rate obtained with the J-integral contour. The analysis variables have been the ligament diameter, its eccentricity, and the elliptical notch aspect ratio. The maximum SIF increases with the ligament eccentricity, the presence of the notch (compared to when the bar is smooth), and the elliptical notch axial semi-axis (for the same notch depth); it decreases with the ligament diameter. For external cracks, eccentricity induces bending of the bar subjected to tensile loading, which can produce partial and full contact of the crack surface, relevant phenomena in terms of the SIF value at the different points of the crack front.

Role of crack offset and loading condition on fracture behavior of wire specimen

Accurate stress intensity factor (SIF) solutions for cylindrical specimens with varied wire aspect ratios, crack aspect ratio, relative crack depth and crack offset are required to evaluate the fracture toughness of high strength yet brittle rods, cables, fibres and wire specimens. The mode I geometric factor (GF) solutions of various crack configurations in a cylindrical fracture specimen in tension have been determined using linear elastic fracture mechanics in earlier studies. In the present study, finite element analysis (FEA) was used to compute these as a function crack offset and wire aspect ratios for two different boundary conditions-constrained and unconstrained. In constrained loading condition, the GF was seen to decrease significantly with crack offset for wires at lower aspect ratio in all the 3 crack curvatures – concave, straight and convex. GF stabilized as the wire aspect ratio was increased beyond 40. In unconstrained loading the GF values were independent of the wire aspect ratio and crack offset for the 3 crack curvatures.

Anti-plane fracture behavior of n nano-cracks emanating from a magnetoelectrically semi-permeable regular n-polygon nano-hole in magnetoelectroelastic materials

Based on Gurtin–Murdoch surface/interface model and complex potential theory, by constructing a new conformal mapping function, the fracture behavior on n nano-cracks emanating from a n-polygon nano-hole under far-field anti-plane mechanical load, inplane electrical load and magnetic load is studied. The analytical solutions of stress intensity factor, electric displacement intensity factor and magnetic induction intensity factor at the crack tip are given under the boundary conditions of magnetoelectrically semi-permeable. In addition, numerical examples show that when considering the surface effect, the stress field intensity factor, electric displacement intensity factor and magnetic induction intensity factor have obvious size-dependence. The results of this paper show that when the defect size increases to a certain extent, the influence of the surface effect begins to decrease, and finally tends to the results of classical elastic theory.

Mixed mode stress intensity factors of single edge cracked/notched plates under different boundary conditions using strain energy approach

This paper presents the mixed mode I/II stress intensity factors (SIFs) of slanted cracks/notches under tension loading. A two-dimensional finite element analysis (FEA) was employed using the ABAQUS program. Based on the literature survey, there is a lack of solutions for SIFs of slanted cracks in plane stress plates. The strain energy approach (SEA) was adopted to analyze the notched cases. Mode I and II SIFs are derived via the SEA method from the strain energy computed using the FEA technique. The results show excellent agreement with other researchers' work. The key contribution of the present paper is the presentation of the effect of the crack/notch length to plate width ratio on the mode I and II SIFs of a slant-edge-cracked/notched plate under different boundary conditions. Sets of new data of mode I and II SIFs are provided herein in tabular and graphical formats.

Stress Intensity Factor (SIF) Solutions and Fatigue Crack Paths in Eccentric Circumferentially Cracked Round Bar (CCRB) in Tension

In this paper, a numerical modeling was developed to study (on the basis of the Paris law) the fatigue propagation paths of eccentric external (outer) cracks in circumferentially cracked round bars (CCRB) subjected to a cyclic type of loading in the form of either remote tensile loading or imposed axial displacement. Results show how the eccentricity (in relation to the wire axis) of the circular resistant ligament increases with the growth of outer circumferential cracks by subcritical fatigue mechanisms. This phenomenon is more pronounced when the solicitation consists of a remote tensile loading than when it is an axial displacement, when the initial eccentricity of the ligament increases (for a given initial diameter), and when the Paris exponent characteristic of the material rises. The paper also analyzes in depth the different situations regarding contact between crack faces during subcritical cyclic fatigue propagation, covering a wide range of cases including no contact, partial contact, and full contact depending on the ligament diameter (during the process of fatigue crack advance) and the relative eccentricity of the annular crack that loses its axial symmetry in relation to the round bar (cylinder) axis. In addition to the fatigue crack path study, closed-form stress intensity factor (SIF) solutions for the considered geometry (a cylinder with an outer annular crack) are provided in the form of third-degree polynomial expressions as a function of the ligament diameter and the crack eccentricity (both in dimensionless terms).

Semi-empirical formulas on notch stress field and SIF of orthotropic V-shaped thin plate with initial crack under tensile-bending loads

For orthotropic materials, the solution of notch stress field and stress intensity factor (SIF) is not only related to crack opening angle, crack depth, notch length, geometric parameters, but also obviously influenced by material characteristics and constitutive relation. On the basis of isotropic notch stress field and SIF theoretical formula, a series of multi-parameter models of orthotropic materials were constructed and fitted. The effects of notch depth, crack length, the ratio of notch depth to plate width, opening angle and mechanical properties of composite materials on geometric correction coefficient YI are systematically analyzed. On this basis, a semi-empirical formula of YI is put forward by combining stress field analysis and multi-parameter fitting. The semi-empirical formula is further verified with finite element method, traditional formula and various composite materials. The numerical results show that the simple formula proposed in this paper has higher prediction accuracy. Finally, the proposed formula is extended to the solution of notch stress field and geometric correction coefficient for V-notch-cracked plate under bending load, tension-bending complex loads.

Stress intensity factor solution for single-edge cracked tension specimen considering grips bending effects

Stress intensity factor solution for single-edge cracked tension specimen considering grips bending effects