Crack Problems Research Articles

An accurate semi-analytical method for the treatment of an eccentric annular crack embedded in an infinite isotropic elastic medium under arbitrary internal pressure

This work provides a semi-analytical method for the calculation of the stress intensity factor (SIF) associated with an internally pressurized eccentric annular crack embedded in an infinite isotropic elastic solid. The inner and outer edges of the crack consist of the circumferences of two eccentric circles and the internal pressure exerted on the crack faces has an arbitrary distribution. Using Somigliana formulation a hypersingular integral equation governing the proposed crack problem is obtained. Next, by the employment of a conformal mapping the considered crack is mapped on to a concentric annular crack. In the mapped domain, with the aids of Fourier expansion of the displacement discontinuity function across the crack faces together with the notion of the Hadamard finite-part integral, the hypersingular integral equation is converted to a system of linear algebraic equations for the unknown constants of the expansion. Upon the determination of these constants, the angular dependent SIFs along both the inner and outer edges of the crack are obtained accurately. The accuracy of the current formulation is showcased through the re-examination of the simple concentric annular crack problems considered previously in the literature. In the presence of eccentricity, the effects of such geometrical parameters as the ratio of the radii of the inner to outer eccentric circular edges of the crack and the normalized eccentricity on the values of the SIFs along both the inner and outer edges of the crack are studied. As it will be seen the material properties of the elastic matrix do not affect the values of SIFs.

Basalt fiber as natural reinforcement to improve the performance of ecological grouting slurry for the conservation of earthen sites

Abstract Grouting material is the core force transfer medium of grouting sealing and anchorage reinforcement methods for cracks in earthen sites; the performance of grouting slurry is the key to affecting the reinforcement effect. To solve the problems of poor flexural strength, easy shrinkage and cracking of existing grouting slurry, using Glutinous Rice Pulp, Calcined Ginger Nuts, and Loess Soil as substrates, and choosing the content and length of basalt fiber (BF) as control variables, 13 groups of specimens were designed by orthogonal test method to explore the influence of mixed fiber on the mobility, shrinkage, compressive, and flexural strength. The microstructure was analyzed by SEM to explain the strengthening mechanism from physical and chemical perspectives. The results show that the mobility decreases linearly with the increase in BF content and length; after mixing BF, the shrinkage rate is significantly reduced, but when the fiber length and content are relatively high, the surface is prone to cracking. The excellent bridging ability of BF can effectively improve the compressive and flexural strength of the specimen. When the fiber length and content are high, the specimen shows certain ductile failure characteristics, and the fracture energy increases more than 10 times.

Water quenching cracking mechanism and prevention of steels

ABSTRACTQuenching is often an essential step in heat treatment of steels for enhancing strength. Water quenching which is low cost and free of pollution risk instead of oil quenching or polymer aqueous solution quenching which is high cost and has high pollution risk will be widely used in heat treatment enterprises. However, the problem of easy cracking of low alloy steels (especially medium carbon low alloy steels) quenched in water has long been a concern for many researchers. The finite element simulation (FES) is used to predict transient stress at cracking position during quenching of an AISI 4140 steel cylinder sample and found that the transient tangential tensile stress at cracking position was only 350 MPa which is smaller than half of the yield strength (775 MPa) of AISI 4140 steel. Such a low tensile stress causing quenching cracking is surprising. To ascertain the underline reasons, a phase-field finite element (PFFE) model is established to investigate the microscopic stress distribution produced by martensitic transformation. The results indicate that the microscopic stress at the junction of the lath martensitic variants in AISI 4140 steel exceeded 800 MPa, and thus such a high microscopic stress is considered as the origin of quenching cracking. By using two examples, our work further clarifies the basic principle of the water–air alternative timed quenching (ATQ) process invented by us as a process suitable for engineering applications with the ability to avoid water quenching cracking and ensure mechanical properties.

Automated fatigue crack detection of orthotropic steel decks using an improved mask region-based convolutional neural network approach

Orthotropic steel decks (OSD) are widely used in the bridge industry, but they are susceptible to fatigue cracking due to various factors such as weld defects, overload traffic, and complicated welded joint configurations. Traditional crack detection methods rely mainly on visual inspection, which is time-consuming and prone to errors. Recently, many crack detection methods based on machine vision have been introduced. However, accurately and effectively detecting fatigue cracks of OSD remains challenging due to the indistinct nature of these cracks compared to the background and their susceptibility to various types of noise. To address these problems, this research proposes an improved Mask Region-based Convolutional Neural Network (Mask R-CNN). The proposed model enhances the feature extraction ability of the original Mask R-CNN by introducing a Convolutional Block Attention Module (CBAM) and Path Augmentation Feature Pyramid Network (PAFPN) into the backbone network. Additionally, a morphological closing operation is performed on the extracted fatigue cracks to address the problem of disjoint cracks. On the basis of crack mask closure, the pixel-wise quantization of cracks was achieved using relevant OpenCV functions. Evaluation on a crack dataset of OSD shows that the proposed model outperforms other methods with precision, recall, average precision (AP), and F1 score of 83.98%, 84.44%, 77.9%, and 84.21%, respectively. In conclusion, the experiment validates that the proposed model can effectively detect, segment, and quantify fatigue cracks of OSD.

Structural detection and reinforcement methods for existing buildings

With the popularity of building construction worldwide, building design, construction technology and quality are faced with inherent deficiencies and may be hit by disasters. Therefore, the diagnosis and reinforcement of building structure has become a major problem to be solved urgently in the current building construction. This paper introduces simple detection methods of different building structures and reinforcement techniques under different conditions. In the part of detection methods, various basic detection methods of normal building structure are studied. Then, a special damage appearance is discussed. Besides the traditional electronic imaging method to detect cracks, a special method is proposed to solve the crack problem, namely Min-Max Gray Level Discrimination (M2GLD). This method can improve the detection accuracy and reduce the influence of human factors. At the same time, several different reinforcement techniques are proposed, including traditional reinforcement techniques and advanced reinforcement techniques. This paper introduces the traditional technology of ancient timber structures and the technology of spraying and external bonding FRP to enhance flexural, shear and compressive strength. This paper can be used as reference for structural inspection and reinforcement of existing buildings.

Determination of Adiabatic Temperature in Hardening Concrete According to Different Standards

The problem of thermal cracking in mass concrete structures still remains unsolved. There are many factors that influence the thermal regime in these concrete structures, the main ones being the type and content of cement in the concrete mixture, the thickness of the concrete layer, and the ambient temperature. However, the most important factor is the cause of the heat generated. Currently, there are a large number of standards and empirical formulas for determining the origin of a heat source using adiabatic equations. This paper provides a comparison of formulas for determining the adiabatic temperature in hardening concrete as the basis for determining the thermal regime in large-sized concrete structures.

Plane and axisymmetric problems of an interfacial crack in a power-law graded material

Plane and axisymmetric problems of interfacial cracks in a power-law graded infinite medium are examined. It is shown that the models are governed by integral equations of Mellin’s convolution type whose kernels are expressed through the hypergeometric function. Exact solutions are derived by the method of orthogonal Jacobi polynomials in a series form and by the Wiener–Hopf method by quadratures. Mode-I stress intensity factors and the associated weight functions for power-law graded materials in the plane and axisymmetric cases are introduced and evaluated. It is shown that, although the displacement jump and the normal traction component have power singularities at the crack tip different from 1/2, the strain energy variation is proportional to the crack length change as in the case of homogeneous materials. A Griffith-type criterion of crack propagation in power-law graded materials is proposed and results of numerical tests are reported.

Analytical solution for contact and crack problem ın homogeneous half-plane

Analytical solution for contact and crack problem ın homogeneous half-plane

Realization of adaptive mesh refinement for phase-field model of thermal fracture within the FEniCS framework

This paper presents an adaptive phase field model for simulating fracture due to coupled interactions (such as thermal quenching and hot cracking in additive manufacturing). The proposed model is implemented in an open-source finite element framework, FEniCS. The model considers spatial variations of the fracture toughness and differential coefficients of thermal shrinkage. Several paradigmatic case studies are addressed to demonstrate the potential of the proposed modeling framework. Specifically, we (a) benchmark our crack predictions for mechanical and thermal boundary condition interactions with the results from alternative numerical methods, (b) accurately reproduce experimentally observed complex crack trajectories due to thermal quenching and hot cracking in additive manufacturing, and (c) demonstrate the ease of extending of the proposed framework to thermal cracking problems in three dimensions. The current implementation provides the basic for an efficient framework for fracture problems due to multi-physical interactions for practical engineers with less programming expertise.

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.

An application of Lobatto–Chebyshev method to a nonhomogeneous plane problem with two cracks

In this manuscript, Lobatto–Chebyshev method, which is an effective collocation method, is applied to a system of singular integral equations, which leads from a nonhomogeneous plane problem. It is assumed that there are two cracks in a nonhomogeneous medium. The problem is formulated in the view of the basics of the elasticity theory and boundary conditions of the problem. By using the method of singular integral equation, the problem is converted to a system of first kind Cauchy type singular integral equations. It is aimed to determine the stress intensity factors (SIFs) of the crack problem. It is seen that Lobatto–Chebyshev quadrature has many advantages in determining SIFs. To verify the validity of the method, the obtained results corresponding to the one crack case are compared with the results in literature.

The Multi-Virtual Crack Closure Technique for three-dimensional interface crack problems

The Virtual Crack Closure Technique (VCCT) is a simple method that was found in the past to produce good results for determining stress intensity factors of cracks in homogeneous bodies and poor results for interface cracks. In recent papers, the VCCT was found to produce excellent results for two-dimensional interface cracks where many elements were used in the virtual crack extension (VCE). This approach is called here the Multi-VCCT. A criterion for the optimal number of elements used in the VCE was also found. Here, the M-VCCT is extended to three-dimensional interface crack problems. Results for three-dimensional problems containing a straight through finite length interface crack and a penny-shaped interface crack are presented. The interfaces include that between two homogeneous and isotropic dissimilar materials, as well as two transversely isotropic materials.

Investigation of stress states around a finite-height crack

This paper is concerned with the analysis of a crack that has a finite-height at its crack tip, loaded under Mode I and II loading. The stress field around the “crack-height” region has been analysed and local Williams’ eigensolutions collocated using the H-integral. Results of the analysis help us to predict which one of the three possible places that fracture failure could occur is most likely, i.e., (1) at the middle plane of the crack tip (collinear with the sharp crack problem), (2) at the “notch corner” or (3) at the intermediate plane between the notch corner and the middle plane (intermediate state). A practical example of an infinite plane with a rectangular shaped crack has also been shown to demonstrate the practical use of the results of this paper.

Dynamic fracture behavior for hole-initiated cracks in functionally graded magneto-electro-elastic bi-materials

In this article, the dynamic fracture behavior of hole-initiated cracks in functionally graded magneto-electro-elastic (FGMEE) bi-materials with exponential variation is studied by Green’s function method, and SH-wave is considered as an external load acting on the bi-materials. The mechanical model of the cracks is constructed through interface-conjunction and crack-deviation techniques, thereby simplifying the crack problem to solving a series of the first kind of Fredholm’s integral equations, from which the dynamic stress intensity factor (DSIF) at the crack tips is expressed. Numerical results clarified the factors that affect the DSIF, including wave number, incident angle, the geometry of the defect, and the gradient of the bi-materials. The accuracy of the present methods is examined by comparing the obtained results with the reference solutions. Compared with previous traditional numerical and analytical methods, the methods proposed in this paper are relatively more effective and applicable, and provide a new perspective for studying the fracture problems of FGMEE materials with more complex defects in practical engineering.

A Boundary-Element Analysis of Crack Problems in Multilayered Elastic Media: A Review

Crack problems in multilayered elastic media have attracted extensive attention for years due to their wide applications in both a theoretical analysis and practical industry. The boundary element method (BEM) is widely chosen among various numerical methods to solve the crack problems. Compared to other numerical methods, such as the phase field method (PFM) or the finite element method (FEM), the BEM ensures satisfying accuracy, broad applicability, and satisfactory efficiency. Therefore, this paper reviews the state-of-the-art progress in a boundary-element analysis of the crack problems in multilayered elastic media by concentrating on implementations of the two branches of the BEM: the displacement discontinuity method (DDM) and the direct method (DM). The review shows limitation of the DDM in applicability at first and subsequently reveals the inapplicability of the conventional DM for the crack problems. After that, the review outlines a pre-treatment that makes the DM applicable for the crack problems and presents a DM-based method that solves the crack problems more efficiently than the conventional DM but still more slowly than the DDM. Then, the review highlights a method that combines the DDM and the DM so that it shares both the efficiency of the DDM and broad applicability of the DM after the pre-treatment, making it a promising candidate for an analysis of the crack problems. In addition, the paper presents numerical examples to demonstrate an even faster approximation with the combined method for a thin layer, which is one of the challenges for hydraulic-fracturing simulation. Finally, the review concludes with a comprehensive summary and an outlook for future study.

Nanosecond laser grooving of water-immersed silicon carbide assisted by high intensity focused ultrasound (HIFU)

Silicon carbide (SiC) is a very important semiconductor and ceramic material with many applications. However, its micromachining is difficult and it is still challenging to achieve a good combination of high quality, productivity and low cost. The corresponding author previously proposed the “ultrasound-assisted water-confined laser micromachining” (UWLM) process, a new machining technology utilizing in-situ ultrasound to improve laser machining of a water-covered workpiece. The author's previous studies show that UWLM based upon a high intensity focused ultrasound (HIFU) transducer is able to produce a relatively high machining rate and quality for metals. Thus, it is natural to guess the HIFU-based UWLM process might also possibly help provide a good solution for SiC micromachining. However, SiC have properties very different from metals. An experimental study is critically needed to confirm whether or not HIFU-based UWLM can still produce a high machining rate and quality for SiC, and overcome additional challenge(s) arising (if any). However, such a study is seldom reported to the authors' knowledge. This paper reports a study on the micro grooving of SiC via the HIFU-based UWLM process. With the conditions in this study, it has been found that UWLM can produce a much better apparent groove quality (i.e., much less recast material and/or debris re-deposition) than the laser machining process in the ambient air, and a much higher machining depth per pulse than the laser machining process in water with no ultrasound. The likely fundamental mechanism is the in-situ cleaning effect due to ultrasound-induced cavitation flow and pressure waves in water. The laser machining process in water with or without ultrasound can produce cracks at relatively low pulse repetition rates (PRRs). Time-resolved pressure measurements in water have been performed to help analyze stress sources causing the cracks. The crack problem appears to be effectively solved by using a relatively high PRR of 5 kHz. One possible major reason is expected to be the inter-pulse thermal accumulation effect at the high PRR, improving workpiece fracture toughness and/or reducing temperature gradients.

Efficient healing of existed cracks in cement via synergistic effects of cement matrix activation and monomer polymerization

The effective repair of existing cracks can prolong the service life of infrastructures, which is of great significance for energy saving and emission reduction. A great deal of research on self-healing cement has been undertaken to efficiently prevent possible future cracking problems in buildings, but these methods do not deal with existing cracks. Herein, the efficient healing of existing cracks is achieved by the synergistic reaction of cement matrix activation and organic polymerization of sodium acrylate (ANa). ANa polymerization was systematically investigated for its effect on stimulated calcium silicate hydrate (C-S-H) and true healing systems in this study. The interconnected porous structure of sodium polyacrylate (PANa) observed during study suggested that ANa had been polymerized successfully under room temperature and the denser short rod-like C-S-H was also formed during the polymerization process. The formation of this organic-inorganic hybrid structure facilitates the rapid healing of existing cracks. When applied to cement, results showed that the compressive strength of specimens with the healing agent SS/PANa recovered 119.99% of its original strength and the micro-cracks of approximately 50 μm were completely sealed after 7-day curing. The ANa in the cracks helps enhance the reactivity of matrix and the polymerization improves the binding ability, forming an organic-inorganic composite network of the PANa and C-S-H. The composition and microstructure of the healed area revealed that the healing products were mainly composed of calcite (CaCO3), calcium hydroxide (CH), C-S-H and PANa.

On an annular crack near an arbitrarily graded interface in FGMs

Annular cracks can be generated during the fabrication of materials and around the pre-existing defects. Previous works on the annular crack problems were most limited to homogenous materials. This paper extends the analysis and examines the axisymmetric problem of a flat mixed-mode annular crack near and parallel to an arbitrarily graded interface in functionally graded materials (FGMs). The crack is modelled as plane circular dislocation loop and an efficient solution for dislocation in FGMs is used to calculate the stress field at the crack plane. The three-parts mixed boundary value problem is solved by a series expansion method. Analytical solutions of the stress intensity factors are obtained. Compared with many other existing analytical treatments to the crack problems in FGMs with the assumption of special gradation, the present method can consider arbitrarily graded shear modulus and Poisson's ratio. It is shown that the present solution can reduce to existing solutions in literatures for annular crack in homogenous materials. Numerical study is conducted to investigate the fracture mechanics of annular crack in FGMs. A practical example of an annular crack in a real Epoxy-Glass FGM with measured data of material properties is also considered.

Scalable manufacturing of the Al-based master composites containing TiB2 and TiC particles and their modification effect on the hot cracking of rapidly solidified Al alloys

This work proposed a scalable manufacturing method for preparing the Al-based master composites containing micrometer-TiB2 and nanometer-TiC particles through molten salt reaction combined with vibration assisted dispersion. The modification effect of the Al-based master composites on the hot cracking and microstructure of 6000 and 7000 series Al alloys with high crack sensitivity during rapid solidification is initially investigated. The results show that the addition of the mixed particles could significantly refine the grains, effectively suppress the hot cracks, and improve the mechanical properties of rapidly solidified Al alloys. Meanwhile, the modification effect of the mixed particles is better than those of the single-phased micrometer-TiB2 particles or nanometer-TiC particles. This scalable and low-cost manufacturing process provides a practical way for preparation of metal matrix composites with low concentration of particles, and proposed a new path to solve the hot cracking problems in the rapid solidification areas such as additive manufacturing.

Finite element study of V-shaped crack-tip fields in a three-dimensional nonlinear strain-limiting elastic body

We study the crack-tip fields in a three-dimensional (3D) plate with a V-shaped crack employing Rajagopal’s theory of elasticity with the strain-limiting effect. The classical linear elastic fracture mechanics (LEFM) theory bears a well-documented inconsistency, i.e., for a static crack problem under the traction-free boundary condition, the LEFM theory predicts singular crack-tip strains. Such results are inconsistent with the constitutive relation derived using the assumption of uniform bound for the strain values. Instead, Rajagopal’s recent theory of elasticity provides implicit constitutive relations between the linearized strain and Cauchy stress in which one can impose an a-priori upper bound for strains. We formulate the strain-limiting theory comprehensively in this article. The linearized strain is expressed as a nonlinear function of the Cauchy stress. The equation for the equilibrium of the linear momentum under a special type of nonlinear constitutive relation reduces to a second-order quasilinear elliptic boundary value problem (BVP). Using a Picard-type linearization and a continuous Galerkin-type finite element technique, we solve several BVPs with tensile and shear displacement loading. The numerical results for the strains, the stresses, the stress intensity factor (SIF), and strain energy density (SED) are obtained for different Poisson values, strain-limiting parametric values, and the V-shaped angles. The growth of the near-tip strains is far less than that of stresses, and the results for both the SIF and SED are also consistent with the results from LEFM. Our work demonstrates that the framework of Rajagopal’s theory of elasticity can provide a basis for developing physically meaningful and mathematically well-posed BVPs to study evolution of cracks, damage, nucleation, or failure in elastic bodies.