Stress Intensity Factor Research Articles

DoE-based modeling of cracked 3D orthotropic panels with stiffeners

This study uses the Design of Experiments (DoE) technique to develop analytical formulations for the stress intensity factor and other non-singular variables near the crack front of a stiffener-reinforced three-dimensional orthotropic panel. The method employs a 52 fractional factorial design, effectively reducing the number of finite element simulations required. The input variables consist of four parameters, each with five levels, which directly affect the process responses. The statistical analysis is performed using the Ellistat software, which offers powerful tools for Design of Experiments (DoE) and incorporates specialized algebraic-statistical approaches. These techniques are utilized for analysing the outcomes and formulating a mathematical model of the cracking characteristics for panels that are strengthened with five stiffeners. The findings of the analysis of variance (ANOVA) indicate strong statistical significance for all tested models, hence verifying their validity based on statistical evaluation criteria. In addition, the residual analysis demonstrates a normal distribution, which strengthens the reliability of the underlying models and fulfils a vital requirement for numerous statistical analyses. The analytical formulations that come from this study have enormous potential for practical use in the field of engineering, specifically for structures that are orthotropic and feature cracks. This study signifies a notable progress in integrating numerical simulation, statistical analysis, and mathematical modelling to develop pragmatic and dependable analytical instruments for the examination of intricate systems.

Application of J-integral to adhesive contact under general plane loading for rolling resistance

In the present work, a mechanical model for two-dimensional non-slipping adhesive contact between dissimilar elastic solids under general loading, namely, normal forces, tangential forces and moments is proposed. The general solutions are obtained analytically with the stresses at the contact edges exhibiting oscillatory singularity, similar to those at a bimaterial interface crack. The well-known J-integral under the current context is analyzed. Its application under the selected integration contour readily gives the relationship between the stress intensity factors and energy release rates at the contact edges. With the results rolling adhesion between two solids with parabolic profiles is considered further. The applied moment can be directly determined by the difference in energy release rates at the trailing and leading edges and hence the rolling resistance even for adhesive contact with cohesive zones. These results provide the foundation for understanding some tribological phenomena associated with adhesion.

A closed form expression of stress intensity factor for an arbitrarily shaped planar crack in 3-D under tensile loading

A closed-form equation was developed in this work to quantify the stress intensity factor (SIF) along an arbitrarily shaped planar crack under mode-I loading by substituting the ellipse-related parameters in Irwin’s solution with geometry-related parameters fi of the crack. This allowed incorporation of the local crack curvature effect on SIF at each discrete point along the crack front and its relative weighted contribution to SIF of the neighboring crack point i, where either stress concentration or shielding took place, into computation of the SIF distribution along the crack front. Good agreement was obtained between the KI values derived in the current work and previous numerical simulation-based studies. The current method could capture the KI distributions for surface and embedded cracks having the same shape, with their maximum values being consistent with Murakami’s area method. This solution of KI allows for highly efficient calculation of ΔKI for quantification of the 3D growth behaviors of a fatigue crack with a complex shape, paving the way for studying the statistical nature of short fatigue crack growth.

Study on the influence of slit pipe wall thickness on the rock breaking effect of slit charge explosion

AbstractIn this study, the influence of slit pipe wall thickness on shaped charge blasting efficiency was investigated. The influence of different slit pipe wall thicknesses on the dynamic behavior of slotted charge blasting was analyzed by a combination of experimental observations and numerical simulations. Polymethyl methacrylate (PMMA) was used as a rock simulation material to prepare slit pipes with different slit pipe wall thicknesses (0.5, 1.0, and 1.5 mm). A dynamic caustics system is used to capture the crack propagation process. ANSYS/LS‐DYNA was used for the numerical simulation analysis. The experimental results show that there is a positive correlation between the slit pipe wall thickness and the crack propagation length, velocity, and dynamic stress intensity factor. With increasing slit pipe wall thickness, the directional propagation and energy concentration ability of cracks are significantly improved, but an increase in the slit pipe wall thickness will also promote the propagation of secondary cracks. In addition, the numerical simulation results support the experimental observations and reveal the existence of an optimal slit pipe wall thickness that can maximize the blasting efficiency while maintaining structural integrity. This study not only deepens the understanding of the physical laws of the blasting process but also provides a practical reference for the optimal design of slotted charges in engineering applications.

Propagation Effect Analysis of Existing Cracks in Box Girder Bridges Based on the Criterion of Compound Crack Propagation

Cracking in concrete box girder bridges will have a significant impact on the safety and durability of the structure, and many box girder bridges which are in service have undergone varying degrees of cracking. Currently, the safety design of actual bridge projects place an emphasis on the stress or the load value of a cross section at the limit value specified in the code for safety control. This design method assumes that the member itself is of uniform and continuous material and is internally undamaged. However, the bridge structure is more or less cracked to varying degrees during the period from casting to construction to operation of the concrete members. In this paper, a finite element computational model of a three-span prestressed concrete box girder bridge with existing cracks is established based on the fracture mechanics theory, and the critical parameters of crack extension are introduced to evaluate the extension state of cracks. At the same time, the extended stability of the existing cracks of the box girder bridge is analyzed by considering the temperature effect, vehicle loading, and prestressing loss, and the sensitivity of crack extension under each working condition is investigated. The results show that, with the increase in crack length and depth, the crack expansion is promoted, but the effect is relatively small, and the maximum stress intensity factor is only 6.48 MPa mm1/2. Under the multi-factor coupling effect, the cracks show a composite crack expansion dominated by type I cracks, the longitudinal cracks of the existing base plate are in a stable state, the maximum value of the crack expansion critical parameter of the vertical cracks of the webs reaches 1.087, and there is a tendency to expand locally. The maximum value of the critical parameter for crack extension of the vertical crack in the web plate reaches 1.087, and there is a tendency towards local expansion. The crack extension evaluation criteria proposed in this paper have a certain reference value for crack extension research on similar concrete box girder bridges and provide a scientific basis for the optimized design of similar bridges.

Plastic Limit Pressure and Stress Intensity Factor for Cracked Elbow Containing Axial Semi-Elliptical Part-Through Crack

The aim of this study is to provide a solution for the plastic limit pressure and stress intensity factor of the elbows containing a part-through axial semi-elliptical crack by considering various crack sizes. The supporting system and loading conditions of the pipeline are described. The critical part of the observed pipeline was isolated for analysis and subjected to various sizes of semi-elliptical cracks. By performing numerical analysis, results were obtained for crack dimension ratios of c/a, and depth/thickness ratios of a/t. The obtained results include plastic limit pressure and stress intensity factor. The results were analyzed with a symbolic regression algorithm, and closed-form solutions for the limit pressure and stress intensity factor were proposed. To validate pipeline integrity, the Structural Integrity Assessment Procedure (SINTAP) was applied, and the FAD (Failure Assessment Diagram) was generated for cracks below the FAD function. The failure pressure was calculated by determining the points where the loading paths intersect the FAD function.

Numerical Fatigue Crack Growth on Compact Tension Specimens under Mode I and Mixed-Mode (I+II) Loading.

This study focused on standard Compact Tension (CT) specimens and two loading modes during the numerical analyses carried out, namely: pure mode I and mixed-mode loading (Modes I+II). Numerical stress intensity factors, KI, were calculated using Abaqus® 2022 and compared with those given analytically under pure mode I loading, showing very good agreement. Additionally, KI, KII, and KIII results obtained from Abaqus® were presented for mixed-mode loading, analyzing crack growth and variation through the thickness of the CT specimen. Moreover, fatigue crack growth simulations under mode I loading were conducted on standard CT specimens using the Extended Finite Element Method (XFEM) and the Paris Law parameters of an AISI 316L stainless steel. It was shown that XFEM effectively determines crack propagation direction and growth, provided that an appropriate mesh is implemented.

Analysis of high temperature and strain amplitude effects on low cycle fatigue behavior of pitting corroded killed E350 BR structural steel

High-tension structural steels are prone to accelerated fatigue damage from pitting corrosion and high-temperature. Despite adverse effects, research on their low cycle fatigue (LCF) behavior is limited. Specifically, studies analyzing temperature-dependent pit sensitivity effects, considering pit-related material’s susceptibility to surface topographic features variation and stress concentration are lacking. This study conducts LCF tests on pitting corroded killed E350 BR structural steel at multiple strain amplitudes and high temperatures. It develops temperature-dependent parameters, such as the cyclic softening pit sensitivity factor, suitable for integration into existing approaches like total cyclic plastic strain energy density (CPSED), power-law, average strain energy density (SED), Coffin-Manson, and pit stress intensity factor (pit-SIF). Further, it proposes multiple linear regression-based prediction models relating total CPSED and average SED with strain amplitude and temperature. Corroded specimens show higher plastic deformation and reduced peak stress, fatigue life, and total CPSED compared to uncorroded ones. The developed parameters, integrated with average SED approach, predicts LCF life within an error band of ±1.5, while power-law relationship reduces it to ±1.2. Moreover, pit-SIF approach estimates fatigue life within an error band of ±1.5. The findings provide critical knowledge for enhanced component design, leading to structural safety, performance, and fire resilience.

A crack in a confocal elliptical inhomogeneity embedded in an infinite matrix subjected to uniform heat flux

We derive a series-form analytical solution to the thermoelastic problem of an insulated and traction-free crack in a confocal elliptical isotropic elastic inhomogeneity embedded in an infinite isotropic elastic matrix subjected to uniform remote heat flux. Using complex variable techniques such as conformal mapping, analytic continuation and Laurent series expansions, the original thermoelastic problem is reduced to an infinite system of linear algebraic equations, the solution of which will yield the mode I and mode II stress intensity factors at the crack tip. An exact closed-form solution is derived when the inhomogeneity and the matrix have identical shear moduli. Detailed numerical results are presented to demonstrate the series-form and closed-form solutions with an emphasis on the particular case of a vanishingly thin inhomogeneity.

Fracture toughness and fatigue crack growth in DMLS Co-Cr-Mo alloy: Unraveling the role of scanning strategies

Co-Cr-Mo alloy is crucial for biomedical implants and aerospace components. These parts often exhibit a high level of geometric intricacy. Direct metal laser sintering (DMLS) is ideal for these complex parts. In DMLS, choosing the right scanning strategies is vital, as it significantly affects the fatigue fracture behavior of the printed components. Thus, the present study investigates the effect of different scanning strategies (stripe, meander, and chessboard) on the fracture toughness and fatigue crack growth behavior of DMLS printed Co-Cr-Mo alloy. For each scanning strategy, fatigue crack growth tests have been performed to evaluate the threshold stress intensity factor and Paris law constants. To corroborate the obtained experimental results, microstructure analyses have been performed using electron backscattered diffraction. Further, failure mechanisms have been identified from fractographs obtained using field emission scanning electron microscopy. It is evident from the obtained test results that scanning strategies caused significant variation in fracture toughness and fatigue crack growth behavior. The stripe scanning strategy has exhibited higher resistance to fracture and fatigue crack growth. However, delayed crack initiation has been observed in the case of the chessboard scanning strategy. The present study provide the background for better selection of scanning strategies to mitigate fatigue fracture in DMLS-printed Co-Cr-Mo alloy designed for specific applications.

Evaluation of crack initiation load of silica glass surfaces formed during subcritical crack growth

AbstractThe crack initiation load of freshly fractured surfaces for silica glass was evaluated with ball indentation. The fracture surfaces were formed during subcritical crack growth in the regions I, II, and III of the stress intensity factor (KI)—crack velocity (V) curve. From the KI–V curve, we linked the obtained fracture surfaces with the ones in the regions I, II, and III. It was found that the crack‐forming probability was the lowest for the fracture surface formed in the region III of the KI–V curve. In order to understand the controlling factors of the crack formation, some properties which are topography, relative nonbridging oxygens (NBO), hydrogen concentrations, and Si–O three‐ or four‐membered ring structures, of the fracture surfaces were measured by atomic force microscopy, X‐ray photoelectron spectroscopy, dynamic secondary ion mass spectroscopy, and Raman spectroscopy, respectively. No distinct difference in NBO and hydrogen concentrations nor the ring structures were found among the fracture surfaces formed in different regions in the KI–V curve. The peak‐to‐valley height of the fracture surface, however, decreased with increasing crack velocity. It is concluded that the roughness or topography of the freshly fractured surface is one of the controlling factors which reduce the intrinsic strength of silica glass.

Wave scattering in a cracked exponentially graded magnetoelectroelastic half‐plane

AbstractAn exponentially graded with respect to depth magnetoelectroelastic (MEE) half‐plane containing two line or curvilinear cracks under time‐harmonic SH wave is studied. The defined mechanical problem is described by boundary integral equations (BIEs) along the cracks boundaries. The computational tool based on the non‐hypersingular traction boundary integral equation method (BIEM) is developed, verified and inserted in numerical simulations. It is based on the analytically derived Green's function and free‐field wave motion solution for exponentially graded MEE half‐plane. The dependence of the generalized stress intensity factors (SIFs) on the material gradient parameters, on the dynamic load characteristics, on the cracks position and their shape, on the dynamic interaction between cracks and between them and half‐plane boundary is numerically analyzed.

Assessment of internal defects in flush ground butt welds in marine structures

In this paper, acceptance criteria of internal planar defects for the highest design S-N curve for surface ground butt welds in fatigue design standards has been assessed based on fatigue tests of tethers containing internal defects. The results from crack growth analysis from defects placed close to the surface are compared with test data from constant amplitude testing of tethers with circumferential welds that includes flaws or small planar defects close to the surface. Floating structures and support structures are subjected to variable loads and the calculated response leads to a long-term stress range distribution with many small stress ranges. This means that if the cracks are small, the resulting stress intensity may be less than the threshold stress intensity factor and the crack does not grow for this stress cycle, or it grows at a reduced crack growth rate in the near threshold region. A methodology to account for this is presented based on a two-parameter Weibull long-term stress range distribution that is representative for load response of floating structures and for support structures for wind turbines. It is shown that the threshold value and the reduced crack growth rate in the near threshold region for small internal defect heights can be used to lift the fatigue test data from constant amplitude testing to be in better correspondence with a higher S-N curve when considering an actual long-term loading.

Evaluation of Mixed-Mode Stress Intensity Factors Using a Small Punch Specimen with a Circular Crack: Preliminary Experiment and an Estimation of Stress Intensity Factors

Evaluation of Mixed-Mode Stress Intensity Factors Using a Small Punch Specimen with a Circular Crack: Preliminary Experiment and an Estimation of Stress Intensity Factors

Tough Cortical Bone-Inspired Tubular Architected Cement-Based Material with Disorder.

Cortical bone is a tough biological material composed of tube-like osteons embedded in the organic matrix surrounded by weak interfaces known as cement lines. The cement lines provide a microstructurally preferable crack path, hence triggering in-plane crack deflection around osteons due to cement line-crack interaction. Inspired by this toughening mechanism and facilitated by a hybrid (3D-printing/casting) process, the study engineers architected tubular cement-based materials with the stepwise cracking toughening mechanism, that enables a non-brittle fracture. Using experimental and theoretical approaches, the study demonstrates the competition between tube size and shape on stress intensity factor from which engineering stepwise cracking can emerge. Two competing mechanisms, both positively and negatively affected by the growing tube size, arise to significantly enhance the overall fracture toughness by up to 5.6-fold compared to the monolithic brittle counterpart without sacrificing the specific strength. This is enabled by crack-tube interaction and engineering the tube size, shape, and orientation, which promotes rising resistance-curves (R-curve). "Disorder" curves and statistical mechanics parameters are proposed for the first time to quantitatively characterize the degree of disorder for describing the representation of the architected arrangement of materials in lieu of otherwise inadequate "periodicity" classification and misperceiveddisorder parameters (perturbation and Voronoi tessellation methods).

Evaluating a Stochastic Singularity Level in a V-Notch Isotropic Domain Due to Randomness in Material Properties

Abstract The singular level of a v-notched isotropic domain is crucial as it relates to the domain’s stress intensity factor (SIF), which is essential for failure prediction. Typically, the singular level is calculated using deterministic material properties (like mean values), but this can misrepresent the severity of the singularity. The singular level’s accuracy is influenced by the stochastic nature of material properties, particularly Poisson’s ratio. This paper presents a stochastic approximation of eigenvalues for an isotropic v-notched domain with stochastic material properties. While both Young’s modulus and Poisson’s ratio are independent stochastic variables, only the stochasticity of Poisson’s ratio affects the eigenvalues. The generalized polynomial chaos method is applied to these stochastic eigenvalues, resulting in a polynomial approximation based on the domain’s stochastic Poisson ratio. The polynomial’s deterministic constants are derived from eigenvalues computed using chosen deterministic material properties according to the stochastic properties of Young’s modulus and Poisson’s ratio. A numerical example illustrates the stochastic approximation of the first two eigenvalues, showing fast convergence as the number of polynomials increases. Results are validated against the Monte Carlo method, highlighting the importance of stochastic approximation in accurately predicting the singular level, which may be more severe than expected when using deterministic approximations. These findings have significant practical implications, as they underscore the need to consider stochastic material properties in structural design and failure prediction.

Investigation of the fracture characteristics of mixed-mode I/III crack by using two kinds of sandstone specimens

This study aims to identify specimens that are more suitable for examining the failure properties of I/III mixed-mode cracks under static loads. We employed single-edge notched bending (SENB) and edge-notched disc bending (ENDB) specimens, and used ABAQUS finite element method software to calculate the stress intensity factors for modes I and III at various crack inclination angles θ. Fracture toughness was tested using three-point bending experiments on two types of sandstone specimens. The evolution of mixed-mode I/III fracture morphology and failure patterns was investigated with a monocular microscope. Additionally, the evolution of the strain field and crack tip opening displacement was analyzed using the digital image correlation method. Our findings indicate that the fracture toughness of the ENDB specimens surpassed that of the SENB specimens. The effective fracture toughness of both SENB and ENDB specimens initially increased with crack inclination angle θ but then decreased. The fracture mode correlated with energy release; the energy release rate of the ENDB specimens exceeded that of the SENB specimens, making the former more brittle. For SENB specimens, crack initiation was primarily intergranular, while ENDB specimens exhibited predominantly transgranular fractures. The crack initiation moments for both specimen types increased with higher crack inclination angles. Furthermore, at the same crack inclination angle, ENDB specimens cracked earlier than SENB specimens.

Prediction model of fatigue crack propagation life of corroded steel plate considering pit characteristics

Pitting corrosion notably increases stress concentration, thus accelerating fatigue crack initiation and propagation at the pit base. This research quantifies the relationship between pit dimensions and fatigue crack development by introducing crack extension ratios (γa​ and γc)​. Employing a series of finite element models, the influence of pit characteristics on the stress intensity factor (K) at the crack tip is assessed. Based on these assessments, a formula for computing the K-value is proposed. Furthermore, a two-stage fatigue life prediction model for both partial and complete penetration is developed using the Paris equation. Results indicate that pits substantially affect the K-value during partial penetration. Specifically, as γa approaches zero, the K-value approaches zero, and as γa approaches one, it aligns with the K-value of a semi-elliptical surface crack. Conversely, in the complete penetration phase, the influence of the pit on the K-value is negligible, and the K-value can be calculated according to the plate with a central penetrating crack. Experimental validation confirms that the model generally maintains a prediction error within 10%.

Investigation on mixed mode I/II crack propagation in nitrate ester plasticized polyether propellant: Experimental and numerical study

The fracture of solid propellant is predominantly attributed to the existence of mixed mode cracks, so it is essential to investigate the the fracture behavior of solid propellant with mixed mode I/II crack. This paper presents fracture characteristics of nitrate ester plasticized polyether (NEPE) propellant under different crack inclination angles (β = 30°–90°). Based on the combination of a drawing machine and a high-speed camera, the mechanical response, crack propagation velocity and crack-path morphology were investigated. The critical equivalent stress intensity factor Keqc was calculated to assess the fracture toughness of the NEPE propellant, and a potential simplified criterion related to the stress intensity factor was proposed. The experimental results demonstrated that the NEPE propellant with mixed mode I/II crack exhibited blunting fracture phenomena during crack propagation, resulting in fluctuating crack propagation velocity. As the crack inclination angle decreases, the fracture toughness of the NEPE propellant increases and then decreases, and the value of Keqc reaches its maximum at β = 45°. Furthermore, numerical studies based on bond-based peridynamic (BBPD) were performed by modeling the crack propagation process of the NEPE propellant, including the crack phase field diagram and the load–displacement curve of the NEPE propellant. The simulation results were then compared with the experiments.

Structural Integrity Analysis of Marine Dynamic Cables: Water Trees and Fatigue

Abstract Offshore power cables are typically designed to have a service life of around 25 years. A pattern is emerging where these cables only last 10 years or even as little as two. The main consensus as to why the service life is so short is due to a combination of fatigue and fretting/wear damages of the copper conductors and water treeing in the insulation material. This study presents a method that can be used to analyze the structural integrity of dynamic subsea power cables and estimate their service life determined by the factors above. The numerical simulation models developed and used to carry out global and local fatigue analyses of dynamic subsea power cables are presented, together with methods and models for assessing fretting, wear, and growth of water tree defects. A methodology for structural integrity assessment that includes all these factors is proposed. A dynamic subsea power cable connected to a wave energy converter is used as the case study for comparison of the service life when these factors are considered compared to when, e.g., the growth of water trees is excluded. A numerical sensitivity analysis demonstrates that the value of the seawater's electrical conductivity and the insulation material's threshold stress-intensity factor greatly influence the cable's service life.