Intensity Factor Crack Research Articles

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.

Dynamic Thermal Response of Multiple Interface Cracks between a Half-Plane and a Coating Layer under General Transient Temperature Loading.

This paper explores the thermal behavior of multiple interface cracks situated between a half-plane and a thermal coating layer when subjected to transient thermal loading. The temperature distribution is analyzed using the hyperbolic heat conduction theory. In this model, cracks are represented as arrays of thermal dislocations, with densities calculated via Fourier and Laplace transformations. The methodology involves determining the temperature gradient within the uncracked region, and these calculations contribute to formulating a singular integral equation specific to the crack problem. This equation is subsequently utilized to ascertain the dislocation densities at the crack surface, which facilitates the estimation of temperature gradient intensity factors for the interface cracks experiencing transient thermal loading. This paper further explores how the relaxation time, loading parameters, and crack dimensions impact the temperature gradient intensity factors. The results can be used in fracture analysis of structures operating at high temperatures and can also assist in the selection and design of coating materials for specific applications, to minimize the damage caused by temperature loading.

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.

Effect of wood and peanut shell hydrochars on the desiccation cracking characteristics of clayey soils

Soil cracking can significantly alter the water and nutrient migration pathways in the soil, influencing plant growth and development. While biochar usage has effectively addressed soil cracking, the feasibility of using less energy-intensive hydrochars in desiccating soils remains unexplored. This study investigates the impact of wood and peanut shell hydrochars on the desiccation cracking characteristics of clayey soil. A series of controlled environmental laboratory incubations with regular imaging was conducted to determine crack development's dynamic in unamended and hydrochar-amended soils. The results reveal that the addition of wood hydrochar at 2% and 4% dosage reduced the crack intensity factor (CIF) by 22% and 43%, respectively, compared to the unamended control soil. Similarly, the inclusion of peanut shell hydrochar at 2% and 4% lowered the CIF by 22% and 51%, respectively. The presence of hydrophilic groups on the surface of hydrochars, such as O–H, CH, and C–O–C, enhanced the water retention capacity, as confirmed by Fourier-transform infrared analysis. The CIF decrease is attributed to mitigated water evaporation rates, enabled by enhanced water retention within the hydrochar pore spaces. These findings are supported by scanning electron microscopy analyses of the hydrochar morphology. Despite CIF reduction with hydrochar incorporation, the crack length density (CLD) increased across all hydrochar-amended series. In contrast to unamended soil which exhibited pronounced widening of large cracks and extensive inter-pore voids, the incorporation of hydrochar resulted in higher CLD due to the formation of finer interconnecting crack meshes. Consequently, the unamended control soil suffered greater water loss due to heightened evaporation rates. This study sheds new light on the potential of hydrochars in addressing desiccation-induced soil cracking and its implications for water conservation.

Effects of microplastic contamination on the hydraulic, water retention, and desiccation crack properties of a natural clay exposed to leachate

Microplastic (MP) can significantly affect soil behaviour and the ecosystem. This paper presents an experimental study to investigate the effects of MP contamination and leachate exposure on the desiccation cracks, hydraulic conductivity, and water retention properties of the natural black clay. The leachate was from a landfill in Australia. The black clay was incorporated with up to 2.0% MPs by weight (w/w) with diverse dimensions and mixed with water/leachate. The measured properties include saturated hydraulic conductivity (ksat), soil-water characteristic curves, moisture evaporation rates, and crack intensity factors. The results suggest that the inclusion of MPs significantly increases ksat, and this increase is more obvious for soils with larger dimensions and contents of MPs, e.g., ksat of the black clay with 2.0% of 500 μm MP increases significantly by 206% (p < 0.05). The black clay exposed to leachate exhibits a slight increase in ksat due to the low viscosity of leachate. The existence of MPs decreases the residual moisture contents and air-entry pressures, and so does the water retention capacity (v/v %) of the black clay. The exposure to leachate increases the air-entry pressures by 6.0%–15.8% of the clay. The evaporation rates increase with the dimensions and concentrations of MPs. The highest evaporation rate (0.96 g/h) can be observed in samples exposed to 2.0% 500 μm MP with water addition. For all samples, the crack intensity factors increase when MP content is between 0.2% and 1.0% and decreases slightly after that. After being exposed to leachate, the evaporation rates and crack intensity factors of the black clay are decreased by 2.4%–12.6% and 3.6%–13.7%, respectively.

Investigation of optimal surface paste disposal design based on crack intensity

ABSTRACT There are many factors affecting the mechanical and geochemical stability of the surface paste disposal (SPD) method. The most important of these are the cracks occurring during the storage of tailings. The relationship between the volumetric water content (VWC), matrix absorption (MS), and oxygen (O2) values of the paste material are important in the formation of cracks. In this study, surface crack formations of the paste material stored at the laboratory in accordance with 3 different storage methods (cemented and uncemented) were observed during the pour and after the deposition, and crack intensity factor (CIF) was measured. The relationship between CIF with VWC, MS, and O2 parameters was examined. As a result, the CIF value decreases approximately by %75 with cement addition in the lowest and highest layers in the SPD method. In a case receiving the most rain, the crack intensity value of the highest layer was determined to be 3,9% in the Design 3 where cement was used in the lowest and highest layers. In addition, VWC, MS, and O2 levels were 35%, −29 kPa, and 17.5%, respectively, making the paste material more efficient in terms of mechanical and geochemical stability.

Crack development in a physical model of undisturbed expansive soil slope and core sample under wet-dry cycles

Cyclic wetting and drying in expansive soil slopes results in the formation of desiccation cracks and irreversible structural changes which can cause substantial reduction in overall soil strength leading to slope instability. This study investigates the structural and crack development in a physical model of undisturbed expansive clay slope and small core sample subjected to five wet-dry cycles. The surface distribution and vertical extent of cracks in the slope model was measured during the various drying and drying cycles. The crack intensity factor, which quantifies surface cracks increased with increasing wet-dry cycles and became constant in the third cycle. Vertical cracks whose bases are connected by near horizontal cracks or cracks parallel to the slope developed to a maximum depth of 28 cm in the physical model. The shallow depth and orientation of these cracks along the slope may be a contributing factor for the shallow infinite slope failure in expansive soils. In addition, suction and water content measurements were made during various cycles. Changes in suction occurred to a depth of 28 cm, and the maximum suction increased with increasing cycle number. The results also demonstrate boundary and size effects on crack formation.

Analysis of a method to compute mixed-mode stress intensity factors for non-planar cracks in three-dimensions

In this work, we present and prove results underlying a method which uses functionals derived from the interaction integral to approximate the stress intensity factors along a three-dimensional crack front. We first prove that the functionals possess a pair of important properties. The functionals are well-defined and continuous for square-integrable tensor fields, such as the gradient of a finite element solution. Furthermore, the stress intensity factors are representatives of such functionals in a space of functions over the crack front. Our second result is an error estimate for the numerical stress intensity factors computed via our method. The latter property of the functionals provides a recipe for numerical stress intensity factors; we apply the functionals to the gradient of a finite element approximation for a specific set of crack front variations, and we calculate the stress intensity factors by inverting the mass matrix for those variations.

Effect of wetting–drying cycles on the desiccation of tailings pre-dewatered with super absorbent polymer

The main objective of this investigation is to understand the desiccation behaviour of fluid fine tailings (FFT) pre-dewatered with a superabsorbent polymer (SAP) with respect to wetting–drying cycles. Raw FFT (control) and pre-dewatered FFT with SAP were subjected to five cycles of wetting and six cycles of drying. Evaporation was found to be the dominant mechanism in the dewatering of raw FFT, as well as FFT pre-dewatered with SAP. In both cases, the suction developed in each drying cycle was eliminated temporarily by the succeeding wetting cycle. The minimum solids content within the column was found to be around 70%, which corresponded to a vane shear strength of 4.5 kPa. Based on the digital images of the surface, the crack intensity factors of the raw FFT and pre-dewatered FFT were calculated to be 26 and 14%, respectively. Scanning electron microscopy and mercury intrusion porosimetry analyses indicated that the FFT pre-dewatered with SAP after 25 days of evaporation in the second lift exhibited the most compacted texture. The solids content of the FFT pre-dewatered with SAP increased to 98% from an initial 50%. The SAP pre-dewatering method can significantly increase the shear strength of FFT subjected to wetting–drying cycles.

Roles of vetiver roots in desiccation cracking and tensile strengths of near-surface lateritic soil

Desiccation cracking is a major cause of shallow failure of lateritic soil slopes. Knowledge of soil tensile strength helps better understand the cracking behavior of vegetated lateritic soil. This study aims to examine the surficial cracking behavior and tensile strength of remolded lateritic soil containing horizontally arranged vetiver roots. Desiccation cracking tests, root pullout tests and direct tensile tests were performed on lateritic soil considering various porosities, degrees of saturation, and root contents. The mechanism underlying the root reinforcement was analyzed by scanning electron microscopy. The results demonstrate that adding 0.4% grass roots can reduce the crack width and crack intensity factor, and thus mitigate crack developments in lateritic soil. The interfacial shear strength exhibits a decreasing trend with increasing root diameter. As the root content increases from 0% to 1.0%, the tensile strength of lateritic soil increases to reach the peak at a root content of 0.4%-0.5% and then drops greatly. This is why the optimal root content in resisting crack development is about 0.4%. Microscopic tests show that the interfacial shear strength originates from the friction, interlocking force, cementation and capillary force between the rough root surface and surrounding soil particles. A power function-based empirical equation expressed by the root diameter and porosity is proposed to estimate the interfacial shear strength of rooted lateritic soil. Additionally, a semi-theoretical equation of the tensile strength of rooted lateritic soil is deduced based on the tensile strength of soil matrix and the interfacial shear strength between the roots and soil matrix. This equation considers the root content and root diameter distribution and is applicable to the soil of different state parameters (e.g., porosity, degree of saturation and water content). The results could provide insights into the mitigation of desiccation cracking in lateritic soil slopes with root-reinforcement technology.

Determination of mixed-mode stress intensity factors for axial crotch corner cracks at cylindrical vessel to nozzle intersections under internal pressure and nozzle loads

In this study, Stress Intensity Factors (SIF) of quarter circle and semi elliptic cracks at the crotch corner of the intersection between a cylindrical pressure vessel and a radial nozzle have been computed for combinations of the actions of internal pressure and external forces on the nozzle. Until now, practitioners have used simplified solutions for SIFs available from the literature, such as the Newman-Raju equations for the mode I SIF produced by an internal longitudinal semi-elliptical crack in a cylinder, to approximate the SIF produced at a crotch corner crack. These equations do not take into account the effect of the opening of the cylinder for the nozzle and the resulting stress distribution along the cylinder. As a result, there is uncertainty about the validity of using these simplified solutions in engineering critical assessments and a more exact determination of the SIFs for crotch corner cracks would be beneficial.The mode I, II and III stress intensity factors have been determined for crotch corner cracks for a single size of vessel and are presented as a function of variables such as location on the crack front, crack size and aspect ratio (a/c), crack angle with respect to the axis of the vessel, and the magnitude of internal pressure and external forces. The results are presented in graphical form. The study concludes with the recommendation that the analysis be extended to a wider range of vessel and nozzle parameters.

Influence of Geotextile Materials on the Fractal Characteristics of Desiccation Cracking of Soil

In recent years, the irregular cracks formed during the damage evolution of civil engineering materials have been able to be quantitatively described by using fractals. In this study, the fractal characteristics of the desiccation cracking of soil were investigated under different substrate contact and permeability conditions through a natural drying test in the laboratory. Three kinds of base contact conditions of soil, namely, grease, geomembrane, and geotextile, were designed, and two samples for each contact condition, including one parallel sample, were used. The continuous drying experiment was carried out at a constant ambient temperature. The crack morphology under different spacings was analyzed quantitatively using digital image processing technology. The fractal dimensions of three soil substrate contact conditions (grease, geomembranes, and geotextiles) were between 1.238 and 1.93. When the crack network on the soil surface stops developing, the fractal dimensions under the three experimental conditions are 1.88, 1.93 and 1.79, respectively. In the final state of crack development, the crack intensity factor of the sample with grease at the bottom is 2.99% and 4.02% higher than that of the sample with geomembranes and geotextiles at the bottom, respectively. The residual water contents of the samples with bottom contact conditions of grease, geomembrane, and geotextile increase successively, which are 3.12%, 5.76% and 9.71%, respectively. The effects of interface friction and permeability on soil cracking behavior are analyzed, and the evolution characteristics and formation mechanisms of cracks in soil are revealed.

Stress intensity factor assessment for reactor pressure vessel nozzles containing postulated corner cracks

Due to the structural discontinuity of geometry having higher stress concentration, the nozzles may dominate the structural integrity of reactor pressure vessel (RPV) system, even the material radiation embrittlement is insignificant. The nonmandatory Appendix G in Section XI of the ASME Boiler and Pressure Vessel code provides a fracture mechanics-based methodology using magnification factors to calculate the stress intensity factor of reference crack tips as long as the stress distribution through the nozzle section is available. This paper establishes various three-dimensional finite element models of Taiwan domestic RPV nozzles to conduct a series of stress and linear elastic fracture mechanics analyses to estimate the stress intensity factors. The circular and elliptical reference corner cracks with depths of one-fourth and one-tenth thickness of the vessel wall along the 45° path are considered. Two evaluation results using the ASME method and the finite element linear elastic fracture mechanics analysis are compared. It is found that the ASME method produces conservative values of stress intensity factor at crack tips of circular corner cracks but underestimates the elliptical corner cracks. Finally, an adjusted magnification factor formula is proposed to obtain more accurate stress intensity factors for elliptical-shaped nozzle corner cracks.

A novel coupling approach for determination of stress intensity factor for bi-material Reissner plates under bending or twisting

A novel coupling approach is proposed to determine stress intensity factors (SIFs) for interface cracks in bi-material Reissner plates under bending or twisting. The Reissner plate theory is adopted to derive asymptotic solutions around the crack tip and T-spline functions are introduced to establish the model. The approach has two major steps. Firstly, the overall cracked plate is divided into two regions (near and far fields) and is discretized by the T-spline based isogeometric analysis (IGA). Subsequently, the large number of fundamental unknowns of control points in the near field is reduced into a small set of undetermined coefficients of asymptotic solutions obtained by the eigenfunction expansion method. Therefore, explicit expressions of SIFs and singular stress components near the crack tip are obtained simultaneously. A number of numerical examples for various cracks laying at the interface are presented, and are found to be in good agreement with available solutions.

Two-dimensional weight function for the determination of stress intensity factors for semi-elliptical surface cracks in finite-thickness and finite-width plates

In this study, a new two-dimensional (2D) weight function of stress intensity factors (SIFs) for semi-elliptical surface cracks in finite-thickness and finite-width plates subjected to arbitrary stress distributions was proposed. To determine the unknown coefficients in the weight function, parametric three-dimensional finite element (FE) models were developed to obtain the solutions of SIFs. The analysis matrix covers wide ranges of relative crack-length ratios 0.1 ≤ c/W ≤ 0.9, to consider the finite width effect, as well as aspect ratios 0.2 ≤ a/c ≤ 1.0 and relative crack-depth ratios 0.025 ≤ a/T ≤ 0.8. The present weight function was verified against the FE results and the solutions available in the literature. The maximum differences were within 6% for both the surface and deepest points. The proposed 2D weight function can be applied to calculate SIFs and predict the fatigue life of engineering structural components involving surface flaws.

An interaction integral method coupled with special crack tip elements for evaluation of stress intensity factors

Accurate computation of stress intensity factors (SIFs) for two-dimensional cracks by an interaction integral method combined with special crack tip elements is presented in this paper. SIFs are of great importance to fracture mechanics analysis. Due to special variation of displacement around the crack tip and the singularity and near singularity of integrals in interaction integral method, the results obtained by which are affected by the radius of the closed loop. Thus, a general method for singular integrals and nearly singular integrals is applied in the paper. With the interaction integral method coupled with the proposed special crack tip element, more stable and accurate values of the SIFs can be obtained. Numerical examples have demonstrated the effectiveness of the proposed method.

New binary paper/wood industry waste blend for solidification/stabilisation of problematic soil subgrade: macro-micro study

This article presents the potential application of paper/wood industry waste by-products, i.e. lignosulphonate (LS) in conjunction with lime (LM) [i.e. LS-based cementing admixture (LSCA)] to mitigate desiccation induced cracking and mechanical vulnerabilities of expansive soil subgrade. The results showed that the LSCA and lime (LM) significantly ameliorated the soil consistency, subgrade strength characteristics (i.e. California bearing ratio and resilient modulus), and completely mitigated the swelling potential with enhanced resistance against Sr . Moreover, the LSCA and LM notably reduced the 3D-volumetric shrinkage and crack intensity factor (CIF) by 90.1 and 87.4%, respectively. The mineralogical and microstructural analyses manifested that the LSCA induced new cementitious compounds (i.e. hydrates of calcium silicate and calcium aluminate), and substantially enhanced the interlocking among the soil particles compared to the untreated and LS-treated soils. Besides, pavement thickness analyses showed that the LSCA treated subgrade, omits the provision of sand cushion and sub-base course promoting road material conservation.

Weight functions for an array of collinear cracks in an infinite anisotropic elastic plate

Abstract Weight functions are provided for calculating the stress intensity factors for collinear cracks in an infinite anisotropic elastic plate. The number of cracks as well as the length of the cracks are arbitrary. The weight functions are for crack-face loading, which may be non-self-equilibrium. It is shown that for self-equilibrium loading, the weight functions are independent of elastic constants. For non-self-equilibrium loading, however, an additional constant term that is material-dependent appears.

Comparative study on the abilities of different crack parameters to estimate the salinity of soda saline-alkali soil in Songnen Plain, China

Salinity is commonly considered to be the main factor determining the crack extent of clayey soda saline-alkali soil in the Songnen Plain in China. However, there are great variations among different parameters in quantifying the extent of desiccation cracks in salt-affected soil, leading to substantial uncertainty in their abilities to characterize soil salinity. This study aimed to analyze the relationships between different types of crack parameters and the salinity of soil samples to establish optimal prediction models for the electrical conductivity (EC) values. To achieve these objectives, 104 soil samples with different salinity levels were obtained and pre-processed based on a unified standard for binary crack patterns. Thereafter, three common types of crack parameters including the crack intensity factor (CIF); box-counting dimensions under equal-partitions of 2, 3, 5, and 7; and four gray-level co-occurrence matrix (GLCM) texture features were extracted for correlation coefficients with the EC values of the soil samples based on a series of regression analyses. The results indicate that although different types of crack parameters all have a clear correlation with EC, CIF shows a poor relationship with EC values compared to those of the fractal dimensions and the GLCM texture features. The CIF, box-counting fractal dimensions based on 2 equal-partition, and contrast (CON) texture feature were then selected as the most ideal indices to develop exponential regression models for EC estimation. In addition, fitting results from verification work showed that CON was the best predictor of EC (R2 of 0.85), with an accuracy much higher than box-counting dimension based on 2 equal-partition (R2 of 0.68) and CIF (R2 of only 0.56).