Crack Plane Research Articles

ELASTIC TRANSVERSAL-ISOTROPIC SPACE WITH TWO UNIAXIAL PARALLEL CIRCULAR CRACKS AND ASSOCIATED PROBLEMS OF BASICITY

In the paper a problem of the stress state in a transversely isotropic space with two parallel circular cracks, the centers of which are located on the axis of anisotropy of the space, is investigated. A constant normal load acts on the crack planes. The problem is solved by the generalized Fourier method. For this purpose, systems of compressed spheroidal coordinates are introduced, the origins of which are connected to the centers of cracks. The general solution of the problem is constructed in the form of series based on axisymmetric variants of the general vector solutions of the system of equations of equilibrium of a transversely isotropic body in spheroidal coordinates, which were previously constructed by one of the authors of the paper. To implement the method, it is further generalized to compressed spheroidal coordinate systems with origins shifted along the axis. For this purpose, new addition theorems for basic vector displacements of transversally isotropic bodies in the above-mentioned coordinate systems are obtained. After applying the generalized Fourier method, the problem is reduced to an infinite system of linear algebraic equations. It is proved that under certain geometrical and mechanical conditions the operator of the system is a Fredholm operator. The reduction method is used for the numerical solution of the system. Graphs of normal stresses in the plane of one of the cracks outside its boundaries, as well as values of stress intensity factor at the top of the crack for different geometric parameters of the cracks, are obtained. The obtained results agree with the known value of the stress intensity factor in the problem with one crack. The practical convergence of the reduction method is studied.
 As an important related problem, the problem of proving the basicity of a general axisymmetric set of external solutions of the system of equilibrium equations of a transversally isotropic body whose boundary is described in compressed spheroidal coordinates is considered. The key problem here is obtaining subtle estimates from below of the modulus of the determinant of the first boundary value problem. As a corollary of the obtained result, several important estimates from the theory of special functions are derived, in which Legendre functions of the second kind from a purely imaginary argument appear.

In-situ microtomography image segmentation for characterizing strain-hardening cementitious composites under tension using machine learning

The application of machine learning and computer vision in microtomography provides new opportunities to directly analyze the microstructural evolutions of strain-hardening cementitious composites (SHCC) under tensile load, especially the strain-hardening process. For the first time, a state-of-the-art machine-learning pipeline combined with digital volume correlation for automated microtomography segmentation analysis (MSA) was developed to separate different components and quantify the in-situ 3D morphological properties of the fibers and pore networks imaged with in-situ synchrotron X-ray computed microtomography. Strain localization and crack initiation were observed around the interconnected pores where strain localized instead of the weakest cross-section defined by the fiber distribution and porosity. Fibers reinforced the crack planes through fiber debonding, bridging, bending, stretching, and orientation redistribution, which contributed to the crack width control and ductility of SHCC in the experiment. This work is essential to understand the progressive damage mechanisms of SHCC and help refine the characterization, modeling, and design of the composite using a bottom-up approach.

Crack Initiation Mechanism of AISI 4340 Steel for High‐Cycle Torsional Fatigue Loading

The nucleation of microstructural fatigue cracks in AISI 4340 steel is investigated. The pre‐electropolished specimen is employed for the observation of the very early stage of fatigue crack initiation correlated with the microstructure. It is found that there are precipitate‐free zones (PFZs) around the lath and packet boundary, and the strength of PFZ is lower than that of the lath due to the lack of second‐phase strengthening. Therefore, the fatigue crack would first initiate within the PFZ. Besides, the initiated crack plane usually is the maximum shear stress plane. However, the MnS inclusions would cause stress concentration so that the lath boundary (LB) deviating from the maximum shear stress plane could also have sufficient driving force to crack. In contrast, when the LB is vertical to the cracked MnS inclusion, it would prevent the crack from propagating into the matrix because of the anisotropy of lath martensite. The effects of the stress concentration caused by the MnS inclusion on the maximum deviation angle and the S‐N curve are discussed.

Thermal convection in rapid 3D extension of a planar crack

Thermal convection in rapid 3D extension of a planar crack

Fracture analysis of a curved crack in a piezoelectric plane under general thermal loading

The mixed-mode problem of a cracked piezoelectric plane subjected to a general in-plane thermal load is considered. The crack is modeled as distributed thermo-mechanical dislocations with unknown density which are determined by using the Fourier transform method. Furthermore, stress, electric displacement, and heat flux in the intact plane, under thermal load are obtained. These solutions are used to construct singular integral equations in the piezoelectric plane with an arc-shaped crack under thermo-mechanical loading. The integral equations are solved numerically to obtain dislocation density functions on a crack surface. These functions are used to determine field intensity factors for the crack. Finally, the effect of the crack length, the radius of the crack, and distance from the temperature disturbance is investigated under different loading conditions.

Elastic-Wave Scattering by a Plane Crack: Application of Flaw Detection

Elastic-Wave Scattering by a Plane Crack: Application of Flaw Detection

Study on Fatigue Behavior of Orthotropic Steel Bridge Deck that Considers Corrosion Effects

As a widely used deck system of long-span bridges, the U rib–diaphragm connection in orthotropic steel bridge deck (OSBD) is prone to fatigue cracking under repeated vehicle loads, and the corrosion medium will accelerate the fatigue cracking. To study the influence of corrosion on the fatigue properties of bridges and the fatigue crack propagation law, the three-dimensional (3D) corrosion morphologies of typical OBSD components under different mass loss rates (w) were obtained by the cellular automata (CA) corrosion model. The, the CA model could reflect the electrochemical metal (Me) corrosion. Then, based on AutoCAD, Rhinoceros, and ABAQUS, the solid model of a U rib–diaphragm connection with surface pits was obtained in ABAQUS. Finally, a multiscale finite-element (FE) model of a long-span bridge with millimeter-scale corrosion pits and cracks was established. The stress intensity factors at crack tips and dynamic fatigue crack propagation at the U rib–diaphragm connection were studied by the extended finite-element method (XFEM), and the difference in fatigue crack propagation life and cumulative energy release rate under different wwere investigated. The results showed that compared with the method of uniform thickness reduction to characterize corrosion effects, the ultimate bearing capacity that was obtained by the CA corrosion model was more consistent with the experimental results. Compared with when the corrosion effects were not considered, when the wof the U rib was 6%, 8%, and 10%, the peak stress intensity factor (KI) of the crack initiation at the weld toe of the U rib increased by 32%, 49%, and 86% and the fatigue growth life of the U rib–diaphragm was reduced by 6.5%, 18.9%, and 50%, respectively. According to the cumulative energy release rate of the crack initiation at the weld toe of the U rib, the crack was a composite crack that was dominated by the opening model crack, supplemented by the in-plane shear model crack and the antiplane shear model crack.

Research on Crack Width Measurement Based on Binocular Vision and Improved DeeplabV3+

Crack width is the main manifestation of concrete material deterioration. To measure the crack information quickly and conveniently, a non-contact measurement method of concrete planar structure crack based on binocular vision is proposed. Firstly, an improved DeeplabV3+ semantic segmentation model is proposed, which uses L-MobileNetV2 as the backbone feature extraction network, adopts IDAM structure to extract high-level semantic information, introduces ECA attention mechanism, and optimizes the loss function of the model to achieve high-precision segmentation of crack areas. Secondly, the plane space coordinate equation of the concrete structure was constructed based on the principle of binocular vision and SIFT feature point matching, and the crack width was calculated by combining the segmented image. Finally, to verify the performance of the above method, a measurement test platform was built. The experimental results show that the RMSE of the crack measurement by using the algorithm is less than 0.2 mm, and the error rate is less than 4%, which has stable accuracy in different measurement angles. It solves the problem of fast and convenient measurement of the crack width of concrete planar structures in an outdoor environment.

Study on in-plane double-crack propagation in the rib-to-deck welded toe of steel-bridge

The fatigue problem of two in-plane cracks in rib-to-deck welded toe of orthotropic steel bridge decks is an important issue. Traditionally, related work focuses on single-crack propagation in these joints; however, many practical observations have shown that the initial weld cracks of structures are characterized by multiple cracks in a small range. Thus, the main goal of this paper is to investigate the mechanism of and guidelines for in-plane double-crack propagation in rib-to-deck welded toe of orthotropic steel bridge decks. In this paper, the rib-to-deck welded toes in the orthotropic steel deck of the Anqing Yangtze River Bridge are taken as the background. Based on extended finite element method theory, single-crack propagation theory and the multiple-crack coalescence law, the stress intensity factors at the crack tip are calculated by the interaction integral method, and the propagation directions are determined using the maximum energy release rate (Merr) criterion. The whole process of in-plane double-crack propagation, coalescence and failure in rib-to-deck welded toe of long-span steel bridge decks and their fatigue life are simulated according to the principle of an equivalent crack front. Meanwhile, the most unfavorable conditions of cracking parameters are determined by changing the spacing and shape ratio of the two cracks. Then, the fatigue loading experiment is carried out on equal proportion specimens under appropriate cracking parameters. The results reveal the whole process of in-plane double-crack propagation in rib-to-deck welded toe of orthotropic steel bridge decks, and the verification shows that experimental results agree well with the simulation results.

Mixed-mode I/II fracture performances of glued laminated bamboo in the in-plane longitudinal direction

Considering that glued laminated bamboo components usually fail because of the longitudinal cracks under combined tensile/shear loading, mixed-mode I/II fracture tests were conducted on two kinds of glued laminated bamboo boards in the in-plane longitudinal direction by Arcan test method: laminated bamboo lumber (LBL) with thick-layer unidirectional-arranged bamboo strips and glued laminated bamboo (glubam) with thin-layer bidirectional-arranged bamboo strips. on the basis of Wu criterion for mixed mode fracture of wood, the mixed-mode I/II fracture envelops of LBL and glubam are constructed by curve fittings on the calculated fracture toughness components and the pure mode-I and mode-II fracture toughness. The results show that the small quantity of transverse bamboo fibers change the fracture mode in the in-plane longitudinal direction from short and quick matrix-dominated brittle failure of LBL specimens into long and slow fiber and matrix-dominated quasi-ductile failure of glubam specimens. In response to the in-plane longitudinal crack, only 1:4 of transverse fibers to longitudinal fibers can provide about 6 times of the pure mode-I fracture toughness, 1.4 times of the pure mode-II fracture toughness and more than 6.5 times of the area within the mixed-mode I/II fracture envelope.

Binocular video-based 3D reconstruction and length quantification of cracks in concrete structures

In the past few years, image-based methods for crack inspection have been developed to reduce the cost of the manual crack inspection. However, current image-based methods usually obtain only localized planar crack detection results, while global location and three-dimensional (3D) geometric information of the crack is desired to evaluate the whole structure. In addition, automatic quantification of the actual sizes of all cracks in the global structure is a challenge to overcome. To address these issues, this paper develops an automated 3D reconstruction and length quantification framework for cracks in concrete structures based on binocular videos. In the proposed framework, a crack semantic 3D reconstruction method, combined with binocular visual simultaneous localization and mapping (VSLAM) and a high-performance segmentation network, is first proposed to achieve accurate crack 3D characterization and global localization. A 3D crack quantification method based on point cloud processing is also developed to accurately identify individual cracks on the global structure and quantify their lengths. Field tests are conducted on a concrete bridge to demonstrate the automated inspection framework, which shows high efficiency and practicability. The accuracy of crack detection and quantification of the proposed method is also validated against the results of manual inspection.

Study on numerical simulation method of viscosity time-varying slurry diffusion law

In this study, finite element and finite difference methods were used for numerical calculations. The law of slurry diffusion in the inclined plane cracks is summarized in this study. Further, the equation describing the diffusion of slurry with time-varying viscosity in the plane fracture with dip angle was derived, and the mathematical model of slurry diffusion control equation and improved entropy clustering algorithm were developed. Thus, the law of slurry diffusion with time-varying viscosity in an inclined plane fractured rock mass was studied in detail, and the control equation obtained was modified to improve the prediction accuracy of diffusion of slurry with time-varying viscosity. By applying the model to actual working conditions, the results highlighted that the improved entropy clustering algorithm could more accurately describe the relationship between the factors influencing slurry diffusion and the slurry diffusion radius. The improved entropy clustering algorithm model can adjust the weights of the factors influencing the slurry diffusion in the diffusion control equation, which leads to a more flexible and more accurate slurry diffusion control equation.

Crystallographic analysis of slip system activation in bimodal Ti–6Al–3Nb–2Zr–1Mo alloy under various dwell-fatigue loadings

The microscopic deformation behavior is always been of significant interest in revealing the mechanism of the dwell fatigue effect. This study systematically characterized the deformation system activation in Ti–6Al–3Nb–2Zr–1Mo (Ti6321) alloy using in situ tensile and quasi-in situ dwell fatigue tests. The critical resolved shear stresses of the basal and prismatic slip systems in the Ti6321alloy were first calculated using the slip trace analysis method. The study demonstrated that, under dwell fatigue, basal and prismatic slips consist of major microscopic deformation modes. Most of the slip deformation occurred rapidly during the early stage of dwell fatigue and was independent of the dwell loading. The basal slip was found to be the predominant slip mode regardless of the dwell conditions. The results suggested that the elastic anisotropy of the hexagonal-closed-packed (HCP) structure could lead to heterogeneous microscopic stress, thus activating more basal slip activities. Such activities were found to participate in the crack initiation through two unique cracking modes: basal plane crack and (0001) twist boundary crack.

Fracture analysis of multiple curved cracks in an orthotropic FGM coating bonded to an orthotropic substrate layer

In this paper, based on the distribution dislocation technique (DDT), multiple curved cracks placed in an orthotropic FGM layer bonded to an orthotropic layer and also interface cracks are considered. With the use of integration of Fourier transform the problem is reduced to a system of Cauchy-type singular integral equations which are solved numerically to compute the dislocation density on the surfaces of the cracks. The distribution dislocation is a powerful method to calculate accurate solutions to plane crack problems; especially this method is very good for solutions of curved crack patterns. Hence this technique allows considering any number of embedded and edge cracks with arbitrary curved shape and also interface cracks. Many numerical examples are given to validate our results with available analytical, finite element and experimental methods. The primary objective of this paper is to investigate the effects of the interaction of multiple curved cracks, the shape of crack, material orthotropy, nonhomogeneity parameters, the thickness ratios and the crack length on the modes I and II SIFs and energy release rate. Numerical results show that the normalized energy release rate and modes I/II SIFs decreasing with the both of the stiffness ratio of the coating and the nonhomogeneity parameter.

Static Response of Circular Cavities With a Non-Radial Crack Subject to Antiplane Stress

Abstract Tunnels, pipelines, and other subterranean circular cavities are common components of modern infrastructure. In addition, seismic activities are common in many areas with pipelines, which may put these structures under unknown risk of fracture. A particular risk case of interest can be characterized as a plane strain problem with a circular cavity and crack in an infinite plane under antiplane stress. Antiplane, i.e., mode III, loading has seen less study relative to modes I and II due to the lower risk factor in structures that are especially vulnerable to fracture (e.g., in the automotive and aerospace industries), and the increase in complexity compared to modes I and II. The work here further explores this phenomenon on circular cavities, and particularly, the effect of non-radial cracks on the stress intensity factor via a parametric study. The study introduces a semi-analytical method and also uses commercial finite element software to further expand on the investigation.

Fracture behavior of B2 phase matrix of Ti2AlNb-based alloy with microcracks of different orientations

The influence mechanism of crack orientation on B2 phase crack propagation behavior under cyclic loading is studied by using the meta-atom molecular dynamics (MAMD) method, and the simulation results are compared and verified based on the theory of linear elastic fracture mechanics. According to the different propagation speed of crack in B2 phase matrix, the crack propagation process can be divided into three stages: elastic stage, rapid propagation stage and slow propagation stage. The toughness or brittleness of the crack mainly depends on the competition between the cleavage fracture of the atomic bond and the plastic slip at the crack tip. The crack propagation behavior is obviously orientation dependent. Orientation I and orientation II expand in the form of ductile fracture. Orientation III shows obvious brittleness and expands in the form of cleavage fracture. Orientation IV (Orientation I-IV represent the four angles between the crack plane and the crystal orientation) shows both ductile fracture and brittle cleavage fracture. The defects and stress concentration at the crack tip provide a driving force for martensitic nucleation, and the hcp phase produced by martensitic transformation effectively increases the toughness of the crack. The simulation results of molecular dynamics are basically consistent with the theoretical prediction of linear elastic fracture mechanics. This suggests that the variation of the orientation could tune the crack tip plasticity and toughening in B2 phase matrix.

Method of fundamental solution using Erdogan's solution: Static and dynamic

This paper developed the method of Erdogan`s fundamental solution (MFS) for a 2D in-plane crack problem with static and dynamic loads. The analytical solutions with complex variables with a pair of static concentrated force in a cracked infinite domain were derived by Erdogan in 1965. Based on the Erdogan's fundamental solutions, the MFS is extended to 2D elasticity under static and dynamic loads. The Laplace transform technique and the Durbin inversion technique are adopted for a dynamic case to determine the time-dependent variables. The domain integrals are obtained numerically with both Constant Cell Method (CCM) and Finite Block Method (FBM). The accuracy and convergence of the MFS are demonstrated by four numerical examples. Comparisons have been implemented with both analytical solutions and the finite element method.

In-Plane Crack Rotation Behavior of Reinforced Concrete Panels

In-Plane Crack Rotation Behavior of Reinforced Concrete Panels

Highly stable and strain-insensitive metal film conductors via manipulating strain distribution.

Metal film-based stretchable conductors are essential elements of flexible electronics for wearable, biomedical, and robotic applications, which require strain-insensitive high conductivity over a wide strain range and excellent cyclic stability. However, they suffer from serious electrical failure under monotonic and cyclic tensile loading at a small strain due to the uncontrolled film cracking behavior. Here, we propose a novel in-plane crack control strategy of engineering hierarchical microstructures to achieve outstanding electromechanical performance via harnessing the strain distribution in metal films. The wrinkles delay the crack initiation at undercuts which should be the most vulnerable sites during the stretching process. The surface protrusions/grooves/undercuts inhibit the crack propagation because of the effective strain redistribution. In addition, hierarchical microstructures significantly improve cyclic stability due to the strong interfacial adhesion and stable crack patterns. The metal film-based conductors exhibit ultrahigh strain-insensitive conductivity (1.7 × 107 S m-1), negligible resistance change (ΔR/R0 = 0.007) over an ultra-wide strain range (>200%), and excellent cyclic strain durability (>15 000 cycles at 100% strain). A range of metal films was explored to establish the universality of this strategy, including ductile copper and silver, as well as brittle molybdenum and high entropy alloy. We demonstrate the strain-insensitive electrical functionality of a metal film-based conductor in a flexible light-emitting diode circuit.

Revelation of microcracks as tooth structural element by X-ray tomography and machine learning

Although teeth microcracks (MCs) have long been considered more of an aesthetic problem, their exact role in the structure of a tooth and impact on its functionality is still unknown. The aim of this study was to reveal the possibilities of an X-ray micro-computed tomography (muCT) in combination with convolutional neural network (CNN) assisted voxel classification and volume segmentation for three-dimensional (3D) qualitative analysis of tooth microstructure and verify this approach with four extracted human premolars. Samples were scanned using a muCT instrument (Xradia 520 Versa; ZEISS) and segmented with CNN to identify enamel, dentin, and cracks. A new CNN image segmentation model was trained based on “Multiclass semantic segmentation using DeepLabV3+” example and was implemented with “TensorFlow”. The technique which was used allowed 3D characterization of all MCs of a tooth, regardless of the volume of the tooth in which they begin and extend, and the evaluation of the arrangement of cracks and their structural features. The proposed method revealed an intricate star-shaped network of MCs covering most of the inner tooth, and the main crack planes in all samples were arranged radially in two almost perpendicular directions, suggesting that the cracks could be considered as a planar structure.