Crack Line Research Articles

Mode-III stress intensity factors for two circular inclusions subject to a remote uniform shear load

ABSTRACTAn analytical solution to the antiplane elasticity problem associated with two circular inclusions interacting with a line crack is provided in this article. A series solution for the stress field is derived in an elegant form by using complex variable theory in conjunction with the alternation method. Based on the superposition method, a singular integral equation (SIE) is established from the traction-free condition along the crack surface. After solving the SIE, the mode-III stress intensity factors (SIFs) can be obtained to quantify the singular behavior of the stress field ahead of the crack tips. Numerical results of the SIFs, when a crack is embedded either in the inclusion or in the matrix, are discussed in detail and displayed in graphic form.

Elastic-plastic analysis of the crack surface vicinity under a pair of anti-plane forces applied at an arbitrary point on the crack surface

An elastic-plastic analysis of the mode III crack surface vicinity was performed in an infinitely wide elastic-perfectly plastic plate, in which a pair of anti-plane forces applied at an arbitrary point on the crack surface. The crack line analysis method was used without the traditional small-scale yield condition. The plastic zone length, the plastic zone shape, and the elastic-plastic stress field in the vicinity of the crack surface were obtained analytically. Moreover, the plastic zone lengths in the vicinity of the crack surface and crack line were compared, and it was found that under a pair of anti-plane forces applied at an arbitrary point on the crack surface, the plastic zone length in the vicinity of the crack surface reached its maximum faster than that in the vicinity of the crack line under the same conditions, which indicates the stress state near the crack surface region is more detrimental than that near the crack line region. The variation of plastic zone length with the load position was also studied, and it was shown that when the point forces were closer to the crack tip, the plastic zone length was smaller and the stress state of the crack was more disadvantageous.

Strength Behavior of Bamboo-Reinforced Concrete Slabs

The research work is carried out to determine the load-deflection relationship of bamboo-reinforced concrete slabs subjected to four-point load. Experimental work includes load capacity test, deflection and failure patterns observation of two concrete slabs. Varying percentages of main reinforcement of 20 mm × 10 mm Semantan bamboo were used in the 1100 mm × 500 mm × 100 mm slabs. The slabs were tested to failure under four-point loading. From the testing, it can be said that the maximum load catered by the slab increased with the increase in percentage of bamboo strip reinforcement. As for the crack patterns, it is observed that slab with higher percentage of reinforcement experienced an obvious crack line.

Formulating the in-plane frictional resistances and collapse mechanisms for multi-storey masonry block walls

In this paper a macro-block model accounting for frictional resistances is presented to assess the lateral strength of a multi-storey masonry block wall. The kinematic approach of limit analysis is used to define the load factor causing the onset of rocking-sliding mechanism under in-plane horizontal loading. A dry frictional contact condition is assumed at the rigid block interfaces, according to the Coulomb's law with non-associated flow rule. The key aspect of the proposed approach is the introduction of a criterion to evaluate the contribution of the actual frictional resistances depending on the inclination angle of the crack line. An accurate assessment of the frictional resistances is also obtained by distinguishing two different contributions (the wall own weight and additional vertical loads) and their application points. Hence, a sensitivity analysis is performed with respect to the overloading condition, the friction coefficient, and geometrical parameters such as the shape ratios of the wall and the unit block and the number of rows. The analytical results of the proposed model are also validated against results from other existing macro and micro-block modelling approaches in terms of load factor. The comparison confirms the reliability of the proposed model that allows, with similar results, great simplification of the computational effort with respect to micro-block models.

Theoretical DMT Interpretation in Sensitive Clays

Abstract Closed-form solutions are deduced in the present article for the stresses and displacements generated during installation of the flat dilatometer blade in undrained clay, by assuming that the soil behaves ideally elastic first and elastic-plastic second. In the first case, the installation of the dilatometer is modeled as the expansion of a long elliptical cavity, commencing from a vertical line crack under uniform internal pressure. Computations indicate that the horizontal tangential stress may reach very high negative or tensile values in areas located along the edges of the elliptical cavity. In these areas, the maximum shear stresses also attain very high levels. As a consequence, either fractures or plastic deformations would be expected to develop in such areas. In the second case, the installation of the dilatometer is modeled as the expansion of a long cylindrical cavity, in which the applied pressure is transmitted through an internal hydrostatic core. Outside the core, the clay behaves as a linearly elastic perfectly plastic (Tresca) material. The computed ultimate radial pressures compare well with published data obtained by means of finite element analyses. Finally, the theoretical solutions are applied to field tests carried out in a sensitive clay deposit of eastern Canada. The results show that the clay suffers severe remolding following the insertion of the dilatometer.

Study on Cause Analysis and Treatment Measures of Lining Cracking and Ballast Bed Freezing at Tunnel Portal in Seasonally-Frozen Regions

The purpose of this study is taking the ZEST tunnel of Xilin hot-Ulanhot Railway in Inner Mongolia province of China as an example to investigate the cause and treatment measures of lining cracking and ballast bed freezing at tunnel portal in seasonally-frozen regions. Field investigation method was used to investigate the characteristics of lining cracking and ballast bed freezing in winter. The results show that the longitudinal cracks in the side wall are symmetrical and located in the middle of the wall. The longitudinal cracks have obvious seasonal characteristics, which mainly occur in winter, and the width of cracking was alternatively varied and broadened year by year, of which the process proved to be irreversible. The number of cracks and the width and length of the cracks all have the trend of further development in the last year. Numerical calculation method was used to study the internal force change law of the lining structure of the ZEST tunnel under seasonal frost heaving force. The results show that the lining cracking is mainly caused by the frost heaving force load. Based on the above analysis results, the treatment measures for the frost heave cracking, ballast bed freezing and the leakage of water leakage during the spring thawing period are proposed, the remediation measure proposed is quite effective and the problems such as cracking, ballast bed freezing and water leaking of tunnel lining are completely solved.

Analytical method for determining the durability of fiber reinforced composite materials

The durability of composite materials with metallic and non-metallic matrix can be calculated using both the uniaxial and biaxial loading of the composite, following the wear phenomenon that occurs in these cases. At the same time, this mode of loading of composite material offers multiple ways of analyzing crack resistance, because the wear phenomenon characteristic of these materials is composed of both the wear of the matrix and, in particular, the sliding wear and the crack-breaking behavior of the fibers. This paper proposes to approach the procedure of solving the specific equation systems with regard to the crack resistance, using for this purpose a composite panel with a rectangular surface, with a height w = 60 mm and a thickness t = 18 mm, subjected to loads variables. The model is considered to be loaded under a tension σct (MPa), both above and below the crack line.

Mechanical Properties and Morphology of Epoxy/Graphene Nanocomposite Using Bath Sonication and Tip Sonication

There are different graphene loadings (0, 0.2, 0.4, 0.6, 0.8, and 1.0 vol%) were used in order to study the effect graphene loading using different type of ultrasonication. Two types of ultrasonication: bath and tip sonication were applied in the preparation of epoxy/graphene nanocomposites. Effect of different ultrasonication applied on the mechanical properties and morphology of nanocomposites were investigated. By using tip sonication, epoxy/graphene shown better improvement in the mechanical properties due to direct ultrasonication that generates higher sound pressures and intensity compared to bath sonication which is indirect ultrasonication. Besides, epoxy/graphene nanocomposites prepared using tip sonication exhibits greater fracture toughness where lower intensity and non-uniform sonication effect failed to achieve optimum dispersion of graphene nanoplatelets and also its distribution using bath sonication. Rougher surface with increased deflected crack lines was observed on the samples that prepared using tip sonication further proven that more fracture energy was dissipated which inhibits the propagation of cracks and hence delayed the failure of nanocomposites.

Experimental Study of the Microstructural Evolution of Glauberite and Its Weakening Mechanism under the Effect of Thermal-Hydrological-Chemical Coupling

The microstructures of rock gradually evolve with changes in the external environment. This study focused on the microstructure evolution of glauberite and its weakening mechanism under different leaching conditions. The porosity were used as a characteristic index to study the effect of brine temperature and concentration on crack initiation and propagation in glauberite. The research subjects were specimens of ϕ3 × 10 mm cylindrical glauberite core, obtained from a bedded salt deposit buried more than 1000 m underground in the Yunying salt formation, China. The results showed that when the specimens were immersed in solution at low temperature, due to hydration impurities, cracks appeared spontaneously at the centre of the disc and the solution then penetrated the specimens via these cracks and dissolved the minerals around the crack lines. However, with an increase of temperature, the dissolution rate increased greatly, and crack nucleation and dissolved regions appeared simultaneously. When the specimens were immersed in a sodium chloride solution at the same concentration, the porosity s presented gradual upward trends with a rise in temperature, whereas, when the specimens were immersed in the sodium chloride solution at the same temperature, the porosity tended to decrease with the increase of sodium chloride concentration. In the process of leaching, the hydration of illite, montmorillonite, and the residual skeleton of glauberite led to the expansion of the specimen volume, thereby producing the cracks. The diameter expansion rate and the expansion velocity of the specimen increased with temperature increase, whereas, due to the common-ion effect, the porosity of the specimen decreases with the increase of sodium chloride solution concentration.

Molecular dynamics investigation of mechanical properties of single-layer phagraphene

Phagraphene is a very attractive two-dimensional (2D) full carbon allotrope with very interesting mechanical, electronic, optical, and thermal properties. The objective of this study is to investigate the mechanical properties of this new graphene like 2D material. In this work, mechanical properties of phagraphene have been studied not only in the defect-free form, but also with the critical defect of line cracks, using the classical molecular dynamics simulations. Our study shows that the pristine phagraphene in zigzag direction experience a ductile behavior under uniaxial tensile loading and the nanosheet in this direction are less sensitive to temperature changes as compared to the armchair direction. We studied different crack lengths to explore the influence of defects on the mechanical properties of phagraphene. We also investigated the temperature effect on the mechanical properties of pristine and defective phagraphene. Our classical atomistic simulation results confirm that larger cracks can reduce the strength of the phagraphene. Moreover, it was shown the temperature has a considerable weakening effect on the tensile strength of phagraphene. The results of this study may be useful for the design of nano-devices using the phagraphene.

Effect of crack location on vibration analysis of partially cracked isotropic and FGM micro-plate with non-uniform thickness: An analytical approach

An analytical model is presented for nonlinear vibration analysis of variable thickness, thin isotropic and functionally graded rectangular micro-plate containing a partial crack located within the centre line of the plate. Linear and parabolic thickness variation is considered in one or both the in-plane directions of the plate. The thickness variation is such that the volume of the plate is equal to that of the uniform thickness plate. The continuous line crack is parallel to one of the edges of the plate. The equations of motion are derived using the equilibrium principle based on Classical Plate Theory while the size effect is incorporated using the modified couple stress theory. The partial crack is represented by bending moment and in-plane force according to the simplified line spring model. The effect of in-plane forces is considered by employing the Berger's formulation. The derived governing equation is converted into a cubic nonlinear Duffing equation by employing Galerkin's method. The effect of nonlinearity is established by deriving the frequency response equation for the cracked variable thickness plate using the method of multiple scales. The nonlinear frequency response curves show the phenomenon of bending hardening or softening. The influence of crack length, crack location, internal material length scale parameter, boundary conditions, gradient index, unidirectional and bidirectional taper constant on the fundamental frequency of square plate is demonstrated. Similar to uniform thickness plate, it is found that the presence of crack affects the vibration characteristics of variable thickness plate. When compared to uniform thickness plate, the effect of crack can be reduced by varying the thickness of the plate. Thus, it is concluded that in a given volume, it is better to employ variable thickness plate as far as the vibration characteristics are considered.

Development of the crack-line-update method for two-dimensional piercing simulations

We have developed the crack-line-update method for two-dimensional piercing simulations by a finite element method. This method is combined with a remeshing process involving an outer line and meshing. By using the crack-line-update method, crack lines, which are derived from a stress and strain analysis of the high-damage regions, are added to the outer line in every remeshing step. In this paper, we compare the simulations between the mesh deletion and crack-line-update methods. The crack-line-update method successfully simulated the arresting of cracks during the piercing process, whereas the mesh deletion method could not express such fracture behavior.

A Screw Dipole in Inhomogeneity Interaction with an Elliptical Inhomogeneity Containing a Confocal Crack

The paper is aimed to investigate a theoretical model that a screw dipole inside an elastic elliptical inhomogeneity that containing a confocal line crack under longitudinal shear. The analytic solutions of stress fields of matrix and inhomogeneity, the image force and image torque acting on the center of screw, and the stress intensity factor of line crack tip are obtained by using the complex method of elasticity. Then through the numerical analysis, the effects of the relative shear modulus, the dip angle of screw dipole, the shape of inhomogeneity on image force, image torque and stress intensity factor are discussed in detailed. The result show that both the image force and image torque periodically changes as the dip angle and when the inclusion is hard, the moment of image torque is greatly affected by the material constant and the cracks in the inclusions can enhance the repulsion of the hard matrix to dislocation and weaken the attraction of the soft matrix to dislocations.

Sonic IR crack size estimation using 2D heat diffusion model with arbitrary heat source function along the crack

Over the past decade, sonic infrared (IR) has been gaining rapid popularity in fatigue crack detection. Accuracy and robustness of crack size estimation using existing temperature-based image processing techniques are rather limited due to the absence of analytical solutions describing the heat diffusion around the crack. In this study, a 2D heat diffusion model with an arbitrary heat source function along a crack line is developed to make the technique more practical and capture the random nature of heat generation along the crack. The validity of the forward 2D heat diffusion model is established in close comparison with 2D finite element (FE) results. The validated analytical solution is used as a basis for best-fit analysis to retrieve the arbitrary heat source functions along the crack, which are used to estimate crack sizes. Using the 2D FE simulations with and without random temperature uncertainties, the proposed method delivers high accuracy in estimating crack sizes. Moreover, the accuracy in estimating crack sizes is validated using experimental sonic IR data. This makes it a practical approach to unlock the potential capabilities and limitations of sonic IR inspection technology.

Advanced engineered cementitious composites with combined self-sensing and self-healing functionalities

This study focused on enhancing the self-sensing ability of engineered cementitious composites (ECC) to accurately monitor their cracking behavior and healing performance. The ultimate goal was to develop an advanced smart material that combines self-sensing and self-healing capacities, while preserving the high mechanical and ductility properties of standard ECC. To achieve those features, carbon fibers (CF) and carbon nanotubes (CNT) were added to ECC mixtures in different concentrations. Compressive and flexural strength and mid-span beam deflection capacity testing of sound specimens were performed as part of the mechanical characterization. Recovery rates of flexural properties were assessed on pre-cracked specimens at different healing ages. The combined self-sensing and self-healing capabilities of sound and pre-cracked specimens were evaluated based on electrical resistivity (ER) measurements completed at different moisture states and healing ages. Microstructural analysis was used to investigate outer and inner regions of healed crack lines. Test results showed that mechanical properties, self-healing ability and conductivity of ECC can be improved by incorporating CNFs or CNTs. However, accurate combined self-sensing and self-healing efficiency can only be reached with CNT-based ECCs.

Identification of deep-rooted transverse cracks using Ground Penetrating Radar

Executive summaryTransverse cracking is a surface distress resulting from various mechanisms appearing in the pavement and their occurrence proves improper action of the structure, which, in a long run will be subject to accelerated degradation. The proper evaluation of the progress of cracking is certainly helpful in finding out the origin of this type of damage; therefore, also in the correct selection of the repair technology.The use of GPR (Ground Penetrating Radar) as an auxiliary tool in assessing the structural condition of the pavement in terms of identification of transverse cracking is not a new practice. However, it is still a complicated task due to many external factors which may distort the result or even prevent analysis of data, especially in terms of interpretation of the obtained radar images.This article presents the case study for the practical use of the method of GPR inspection of the transverse cracks structure to analyse the process of restoring transverse cracks in bituminous pavement. This procedure is based on the earlier catalogue of the GPR manifestations of the elements of deep cracking structure and requires precise synchronization of the GPR measurement with cracks observed on the pavement. Explicit manifestations are only visible in expanded cracks, where the zone of material changes in the vicinity of the cracking surface has a width of at least one decimetre. Such defects usually result from the long-lasting operating process, and their presence in the deeper layers of the structure is an evidence of breaking continuity of mechanical consistency of the foundation under the cracking line.

Numerical and experimental investigation on thermal shock failure of Y2O3-coated CVD ZnS infrared windows

Infrared transparent windows on aircraft and missiles can be subjected to extreme aerothermodynamics, which can cause thermal shock failure. Finite element analysis and oxygen–propane flame jet impingement tests were performed to investigate the thermal shock failure of an yttrium oxide-coated chemical vapor deposition (CVD) ZnS infrared window. Good agreement was achieved between the simulation and experimental results, which indicated that thermal shock failure occurs under high temperature differences and thermal stresses. The temperature and stress in the samples increased rapidly in a few seconds and then trended to be stable. The center area of the window surface failed most easily because the maximum temperature and stress both occurred in this area. No delamination of the Y2O3 films occurred during the thermal shock, which indicated good adhesion between the Y2O3 films and CVD ZnS substrate. In the experiment, the center area of the specimen surface was damaged in the form of pits and line cracks.

Numerical algorithm of reinforced concrete lining cracking process for pressure tunnels

PurposeThe cracking of a reinforced concrete lining has a significant influence on the safety and leakage of pressure tunnels. This study aims to develop, validate and apply a numerical algorithm to simulate the lining cracking process during the water-filling period of pressure tunnels.Design/methodology/approachCracks are preset in all lining elements, and the Mohr−Coulomb criterion with a tension cutoff is used in determining whether a preset crack becomes a real crack. The effects of several important factors such as the water pressure on crack surfaces (WPCS) and the heterogeneity of the lining tensile strength are also considered simultaneously.FindingsThe crack number and width increase gradually with the increase in internal water pressure. However, when the pressure reaches a threshold value, the increase in crack width becomes ambiguous. After the lining cracks, the lining displacement distribution is discontinuous and steel bar stress is not uniform. The measured stress of the steel bar is greatly determined by the position of the stress gauge. The WPCS has a significant influence on the lining cracking mechanism and should not be neglected.Originality/valueA reliable algorithm for simulating the lining cracking process is presented by which the crack number and width can be determined directly. The numerical results provide an insight into the development law of lining cracks and show that the WPCS significantly affects the cracking mechanism.

On the Question of Inspecting the Plate with a Crack by the Eddy-Current Method

The problem of how one or several rectilinear cracks intersecting at a point affect eddy-currents and electromotive force (e.m.f.) induced in a current loop has been considered. The loop is located above a nonmagnetic infinite plate, orthogonally to the crack lines. Under these conditions, when the plate is geometrically thin and can be replaced with a conductive surface, the problem is solved analytically. The calculation data, which are illustrated by the graphs of how the e.m.f. depends on the proximity to the crack when the current frequency and loop location height are varied, show that crack’s contribution to the magnetic reaction virtually fades at distances exceeding the sum of the linear loop length and its height. Results of conducted physical experiments prove the adequacy of the developed mathematical model and its applicability to the solution of such problems.

Mechanical responses of pristine and defective C3N nanosheets studied by molecular dynamics simulations

The purpose of this study is to investigate the mechanical properties of a new two-dimensional graphene like material, crystalline carbon nitride with the stoichiometry of C3N. The extraordinary properties of C3N make it an outstanding candidate for a wide variety of applications. In this work, the mechanical properties of C3N nanosheets have been studied not only in the defect-free form, but also with critical defects such as line cracks and notches using molecular dynamics simulations. Different crack lengths and notch diameters were considered to predict the mechanical response at different temperatures under the uniaxial tensile loading. Our simulation results show that larger cracks and notches reduce the strength of the nanosheets. Moreover, it was shown the temperature rise has a weakening effect on the tensile strength of C3N. Our study can provide useful information with respect to the thermo-mechanical properties of pristine and defective graphene like C3N 2D material.