Semi-infinite Crack Research Articles

Evaluation of the strain energy during the interaction between micro-crack and semi-infinite crack in a brittle material

The main goal of this research is to evaluate the strain energy in a brittle material during the interaction of the semi-infinite crack with a neighboring micro-crack. The problem is formulated by considering a cracked thin plate having a micro-crack that rotates around itself and around the semi-infinite crack whose the cracked plate is subjected to a uniform load under mode I. During the interaction between the semi-infinite crack and micro-crack, the strain energy and stress field can be generated at the crack tip of semi-infinite crack. The theoretical analysis of this interaction is treated mathematically by the complex potentials functions. It is shown that the positioning of the micro-crack relative to the semi-infinite crack leads to amplification, reduction and absorption of the strain energy at the crack-tip. The theoretical results agree with those found numerically.

Thermal characterization of vertical interface by scanning photothermal radiometry.

In this work, scanning photothermal radiometry is used for imaging and to characterize a submicron crack. From the thermal images, the evolution of the crack is mapped in the space with micrometer resolution. A vertical contact interface at the steel-steel junction is used to represent a micro-crack with a thickness less than 0.5μm. The thermal quadrupole approach is used to model the heat transfer within the semi-infinite vertical crack. Then, using the phase mapping and that calculated from the model, the estimation of both the equivalent thermal boundary resistance of the interface and the average interface thickness was done.

The Green's functions of two-dimensional piezoelectric quasicrystal semi-infinite crack and finite crack

This paper investigates the interactions of a semi-infinite crack / finite crack with multiple loadings in a two-dimensional piezoelectric quasicrystal under different boundary conditions. Utilizing the Stroh formalism and conformal mapping, Green's functions of generalized displacements and stresses are obtained for two general cases: a semi-infinite crack and a finite crack subject to free-free or fixed-fixed boundary conditions. The stress and electric displacement intensity factors at the crack tip and the image forces on how dislocations are affected by the crack surfaces are given explicitly. The results are analyzed and compared with special cases documented in the scholarly literature. At the same time, the effects of the Burgers vector components on the generalized stresses and image forces numerically illustrate as well as the impacts of line forces on generalized stress intensity factors.

Full field crack solutions in anti-plane flexoelectricity

In flexoelectric materials, strain gradients can induce electrical polarization. However, internal defects such as cracks profoundly affect the electromechanical coupling properties of flexoelectric solids. In particular, anti-plane cracks involve less physical fields, which are easier to study. In this study, we present a comprehensive and innovative investigation of the anti-plane crack problems in flexoelectric materials, including semi-infinite and finite-length anti-plane cracks. For the first time, we formulate a full-field solution for semi-infinite anti-plane cracks in flexoelectric media by applying the Wiener–Hopf technique. Furthermore, the collocation method and the Chebyshev polynomial expansion are used for the first time to derive the full-field hypersingular integral equation solution for finite-length anti-plane cracks in flexoelectric solids. In addition, a comparative analysis between the full-field and asymptotic solutions for semi-infinite cracks is performed, shedding light on the discrepancies in the representation of the electromechanical coupling behavior near the crack tip. The mixed finite element method is used to compare with the full-field solutions of finite-length cracks. The agreement between the numerical results and the full-field solutions demonstrates the rigor of our study. This research advances the knowledge of defects in flexoelectricity and provides significant insight into relevant failure mechanisms.

Numerical study on ultrasonic detection of cracks in metallic structures with variable cross-sectional thickness

The metal structures are widely used in aerospace engineering, especially in joints and spars. The safety of these parts is important to ensure the safe service of the whole structures. The ultrasonic wave is a traditional technique to detect cracks in metals. However, it is usually difficult to find all the cracks because of its difficulty in variable directions of the crack and the irregular shapes of the metals. This paper aims to address the challenge of detecting cracks in metallic structures with varying cross-sectional thicknesses using ultrasonic methods. The research investigates the behavior of ultrasonic longitudinal and transverse waves as they propagate through aluminum plates with variable cross sections. Additionally, it examines how cracks in different orientations influence these wave types. The theoretical analyses are performed which explore the reflection of oblique incidence waves and the diffraction of ultrasonic waves when they encounter semi-infinite cracks. Subsequently, numerical simulations are performed to validate the theoretical findings and to detect both horizontal and vertical cracks within metal plates of varying cross-sectional thicknesses. The findings indicate that both longitudinal and transverse waves are effective in identifying the location of damage caused by horizontal cracks. However, when it comes to vertical cracks, only transverse waves are successful in detecting their precise location. From the research of this paper, transverse ultrasonic wave is suggested to detect cracks in metal structures with irregular cross sections.

Propagation of semi-infinite crack in an initially stressed dry sandy medium impacted by shear wave

Propagation of semi-infinite crack in an initially stressed dry sandy medium impacted by shear wave

Wiener–Hopf method to solve the anti-plane problem of moving semi-infinite crack in orthotropic composite materials

This paper contains the solution to the problem of a semi-infinite moving crack situated in an orthotropic strip bonded between two identical strips. The crack moves with a constant velocity, and the surface is under shear wave disturbance. We first examine the equations of elasticity, which include equilibrium equations and stress and displacement constitutive relations with the model-specific continuity and boundary conditions. Using the Fourier integral transform, the standard form for the Wiener–Hopf (W-H) equation is obtained, which is solved using the W-H method. The analytical expressions for the considered crack problem have been obtained for stress intensity factor (SIF), normalized stress intensity factor (NSIF), and stress magnification factor (SMF). The behavior of NSIF has been graphically presented for particular cases of composite materials for different crack propagation velocities and various depth ratios of the strips. The novelty of this paper lies in the analytic solutions using the W-H method for the semi-infinite moving crack problem under the influence of anti-plane shear waves. The pictorial presentations of normalized SIF clearly show their dependency on strip depths, crack propagation velocities and elastic constants.

Estimation of the stress intensity factor of an interface crack by the scattered SH-far field

The diffraction of the plane elastic SH-wave from a semi-infinite interface crack on junction of two elastic semi-infinite media is studied. The crack is modelled by the mathematical cut with no stress on its faces. The displacement and the stress fields are continuous outside of the crack. The wave diffraction problem is reduced to the solution of the mixed boundary value problem for Helmholtz equation. We search the solution which satisfies the Neumann boundary condition on the crack faces and the continuity condition for the stress and displacement fields outside of the crack. The radiation condition at the infinity and the Meixners condition at the crack tip must be also satisfied. Using the Fourier integral transform, the mixed boundary value problem is reduced to the Wiener-Hopf functional equation which is valid in the given strip of regularity in the complex plane. The method of factorization and decomposition, as well as the Liouvilles theorem, are used to solve this equation. Its kernel function is factorized and represented as a product of two split functions that are regular in the overlapping half-planes. These ones allow for the simple poles outside of the regularity regions. The solution of the Wiener-Hopf equation is presented in analytical form. The scattered displacement field is found for an arbitrary frequency and sounding angle by applying an inverse Fourier integral transform to the solution. The asympŹtotic formula for the stress intensity factor (SIF) at the crack tip is obtained. The correlation between complex amplitude of the SH-wave far scattered displacement field and the SIF caused by this field is obtained for an arbitrary radiation angle, frequency and medium parameters. This allows us to express the SIF through the amplitude of the far field if the radiation frequency, sounding angle as well as the physical characteristics of materials are known. It is shown that in the plane that is normal to the tip of the crack the ratio of SIF for the given junction and two fixed values of the sounding angle or two sounding frequencies is proportional to the ratio of the scattered fields. It is found that under above mentioned condition the proportionality rate does not depend on material properties. The obtained relations can be applied for estimation of the SIF with changing frequency and sounding angle.

Crack length directivity effects on guided-wave acoustic emission: Numerical investigation of radiation patterns

This paper investigates the effect of a finite-sized crack surface on acoustic emission (AE) generated at the crack tip in a thin metallic plate using a 3D time-domain finite element model. Directivity effects on the first arrivals are of particular focus, and the AE is interpreted in terms of a guided mode decomposition. Crack lengths from 0–10 plate thicknesses are studied, in addition to a semi-infinite crack surface, for frequency content in the neighborhood of 0.1–0.4 MHz-mm. Far-field radiation patterns for the fundamental symmetric (S0) and shear horizontal (SH0) guided modes are measured as a function of crack length. The results show an increase in radiation behind the crack tip for both modes and across all considered crack lengths. The surface wave traveling along the crack length appears to be one of the main drivers behind this increase, due to mode conversion after reaching the opposite end of the crack. However, a similar increase is also observed for the semi-infinite crack case, in which there is no mode conversion (the opposite end of the crack is never reached). A radiation offset (RO) metric is introduced to capture this behavior. Parametric studies of the RO across center frequency and bandwidth are presented. Findings suggest that this metric may be of use for AE-based crack length estimation.

A mechanical model for thin sheet straight cutting in the presence of an elastic support

We study the mechanics of sheet straight cutting in terms of a linear elastic fracture mechanics (LEFM) problem for a infinite thin elastic Kirchhoff plate partly supported by a Winkler foundation. The plate features a semi-infinite crack that is located at the edge of the supported zone and that is subjected to shear and bending loads, representing the action of the cutting tool (e.g. scissors blades). The fact that the plate is only partly supported by the foundation significantly complicates the analysis for it creates a non-symmetric framework, both locally and globally. Yet, a semi-analytical solution is obtained through casting the matrix Wiener–Hopf problem in terms of a pair of convolution integral equations defined on a semi-infinite domain. Stress intensity factors (SIFs) are obtained which converge to the known limits for a symmetric and skew-symmetric free plate. This analysis reveals the fundamental role played by the support in affecting the SIFs in an opposing manner, by enhancing/decreasing the symmetric/skew-symmetric components. Consequently, changing the support stiffness is capable of shifting the failure mechanism, from bending to shear. This observation may be taken advantage of when cutting materials which are more sensitive to either of these failure mechanisms. Also, it proves that the role of the support cannot be neglected when developing mechanical models of any cutting process.

Anisotropy and magnetoelasticity effects on the propagation of the SH-wave-induced semi-infinite crack in a magnetoelastic orthotropic medium

The crux of the present study is to investigate semi-infinite crack propagation in magnetoelastic strip influenced by propagating SH-wave under orthotropic geometrical configurations. The Wiener-Hopf (WH) technique and two-sided Fourier integral transforms (FIT) are applied in the proposed analytical model. A closed-form expression of the stress intensity factor (SIF) has been established for the constant concentrated force. The SIF in a magnetoelastic orthotropic strip is shown to be significantly affected by the crack length and crack speed, medium anisotropy, and magnetoelastic parameter. The proposed model is compared to the case of a magnetoelastic isotropic strip in order to demonstrate the effect of orthotropy as well as other anomalies. Among other observations, it is noted that regardless of whether orthotropy exists in the strip or not, the value of the SIF rises along with the crack speed until it reaches its maximum, at which point it rapidly declines.

Analytical study on the propagation of semi-infinite crack due to SH-wave in pre-stressed magnetoelastic orthotropic strip

This study deals with the propagation of semi-infinite crack impacted by SH-wave propagation in a pre-stressed magnetoelastic orthotropic strip (PMOS). The proposed analytical model makes use of the Wiener-Hopf (WH) approach and two-sided Fourier integral transforms (FIT). The exact formulation of the stress intensity factor (SIF) for constant concentrated force (CCF) has been established in closed form. The effect of influencing factors, including the crack length, crack speed, magnetoelastic parameter, horizontal compressive pre-stress (HCP)/horizontal tensile pre-stress (HTP), vertical compressive pre-stress (VCP)/vertical tensile pre-stress (VTP), and anisotropy parameter on the SIF in the considered strip has been unraveled. The proposed model is compared with the case of a pre-stressed magnetoelastic isotropic strip (PMIS) and some peculiarities, along with the influence of orthotropy have been reported. The significant results reported in the present manuscript reveal that magnetoelasticity and pre-stress is a prominent factor impacting crack propagation in elastic material with orthotropy configuration properties and has a significant impact on the SIF, which has not been taken into account in the existing literature on the subject of fracture mechanics. The present investigation helps with structural and reliability analysis, fracture propagation, material durability and failure of engineering structures.

Crack tip solution for Mode III cracks in spring interfaces

Considering an infinite linear elastic isotropic solid in antiplane shear, the Mode III crack-tip solution for a semi-infinite crack located in a straight spring interface is systematically studied for the first time. A new analytic expression for this crack-tip solution is given in the form of a double asymptotic series of the main and the so-called associated shadow terms. It is shown that the series of the shadow terms associated with a main term is infinite, and all shadow terms include logarithmic terms. Thus, although the interface tractions are bounded, the linear elastic solution at this crack-tip has a logarithmic stress singularity which is comprehensively analysed. Noteworthy, the character of this stress singularity is very different from the well-known square root singularity at the crack tip in the classical fracture mechanics. A key advantage of the present approach is its simplicity, as only elementary mathematical tools are employed, and also its easy implementation in a computer algebra software. The latter fact is very relevant because the expressions of higher-order shadow terms become increasingly complicated, so their generation by a computer code becomes crucial. The present results allow the implementation of new enriched or singular crack-tip finite elements for such cracks, and the automatic generation of analytic solutions for benchmark problems for testing the finite-element codes using these special elements. Such codes can be applied to efficient numerical modelling of interface cracks, e.g., in adhesively bonded joints with a thin adhesive layer.

Limit Equilibrium of a Piecewise Homogeneous Plane with Small-Scale Interfacial Shear Cracks at a Corner Point in the Presence of a Loaded Internal Semi-Infinite Crack

Limit Equilibrium of a Piecewise Homogeneous Plane with Small-Scale Interfacial Shear Cracks at a Corner Point in the Presence of a Loaded Internal Semi-Infinite Crack

Mechanical analysis of the interaction between a semi-infinite Griffith crack and its coplanar plastic zone

This paper presents the complete analytical solution of the equilibrium conditions between a dislocation pile-up and a loaded crack. Contrary to previous models, the image distributions (forces) are included in this calculation. Their influence on the effective stress intensity factor, on the dislocation nucleation conditions and on the criteria for crack propagation are underlined. In semi-brittle materials the size of the dislocation free zone is controlled by material characteristics, as expected from the literature. However, in ductile materials its size is controlled by a mathematical limitation resulting from introduction of image forces. If plastic deformation takes place, the Griffith criteria must be modified by adding additional work required to separate dislocations from their images to the surface energy and the plastic work done to develop the plastic zone. A detailed analysis of the stress distribution inside and outside the pile-up is presented. Within the plastic zone the total stress is not constant while outside and close to the limits a square root variation with distance is noticed. RésuméCet article présente la solution analytique complète des conditions d’équilibre d’un empilement de dislocations en présence d’une fissure chargée. Les effets des distributions (forces) image sont inclus, contrairement aux modèles disponibles dans la littérature. Leur influence sur le facteur d’intensité des contraintes effectif, sur les conditions de nucléation des dislocations et sur le critère de propagation de la fissure est soulignée. L’hypothèse d’une enclave élastique dont la taille est fixée par les caractéristiques physiques de la matière n’est valable que pour les matériaux semifragiles ; elle est limitée par une condition mathématique induite par les forces images dans le cas des matériaux ductiles. En présence de déformation plastique, le critère de Griffith doit être modifié par l’adjonction à l’énergie de surface et au travail plastique d’un travail additionnel effectué lors de la séparation des dislocations et de leurs images. Une analyse détaillée de la répartition des contraintes dans et hors de l’empilement est présentée. A l’intérieur de la zone plastique la contrainte totale n’est pas constante. A l’extérieur, à proximité de ses limites, elle varie comme la racine carrée de la distance

Detachment of a Rigid Flat Punch from a Viscoelastic Material

We show that the detachment of a flat punch from a viscoelastic substrate has a relatively simple behaviour, framed between the Kendall’s elastic solution at the relaxed modulus and at the instantaneous modulus, and the cohesive strength limit. We find hardly any dependence of the pull-off force on the details of the loading process, including maximum indentation at preload and loading rate, resulting much simpler than the case of a spherical punch. Pull-off force peaks at the highest speeds of unloading, when energy dissipation is negligible, which seems to be in contrast with what suggested by the theories originated by de Gennes of viscoelastic semi-infinite crack propagation which associated enhanced work of adhesion to dissipation.Graphical abstract

Contact of the Faces of an Interface Semiinfinite Crack

We consider the equilibrium of two rigidly connected elastic half planes made of different materials, containing a semiinfinite crack on their interface, and subjected to the action of normal and tangential concentrated forces applied to the crack faces. We take into account the friction contact of the crack faces near the crack tip and at a certain distance from the tip. The solution of integral equation of the analyzed problem is obtained in the closed form with the help of the Wiener–Hopf method. We determined the boundaries of contact zones between the crack faces and the distributions of stresses in these zones and on the interface of half planes outside the crack.

Contact Problem for a Semi-Infinite Interface Crack in a Piecewise-Homogeneous Strip

Contact Problem for a Semi-Infinite Interface Crack in a Piecewise-Homogeneous Strip

Wedge acoustic waves in a fluid-filled crack

The existence of wedge acoustic modes of a special fluidic type in solids is demonstrated using the ray theory of slow Krauklis-wave propagation in a fluid-filled wedge-shaped crack. It is found that the phase velocities of the modes at small crack opening angles are proportional to the square root of the angle. The number of localized modes in the semi-infinite crack model is not limited.

Issue Information

International Journal of Applied Glass ScienceVolume 14, Issue 1 p. 1-2 ISSUE INFORMATIONFree Access Issue Information First published: 02 December 2022 https://doi.org/10.1111/ijag.16586AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Graphical Abstract Cover Photograph: (a) Snapshot of molecular model of a 0.1Na2O-0.9SiO2 sodium silicate glass structure with a loaded slit crack simulated with the ReaxFF forcefield. Bonds along a half plane (depicted with a dashed line) were severed to create the initial slit crack. The displacements of atoms in an outer annulus were prescribed by an external boundary condition to generate far-field loading conditions. Atom colors: Si (yellow), O (red), Na (blue). (b) The same sodium silicate molecule model demonstrating the radial displacement field generated by the far field loading conditions. As the distance from the crack tip increases so does the total displacement, consistent the classical linear elastic fracture mechanics continuum solution for a semi-infinite slit crack under mode I loading. Volume14, Issue1Special Issue: Glasses for tomorrowJanuary 2023Pages 1-2 RelatedInformation