Dimensionless Crack Length Research Articles

Damage Tolerance of a Sandwich Panel Containing a Cracked Square Lattice Core

The fracture response of a sandwich panel, with a center-cracked core made from an elastic-brittle square lattice, is explored by finite element simulations and simple analytical models. First, predictions are given for the unnotched strength of the sandwiched core and for the fracture toughness of the lattice under remote tension, remote compression, or remote shear. It is assumed that the lattice fails when the local stress in the cell wall attains the tensile or compressive strength of the solid, or when local buckling occurs. Failure maps are then constructed for a cracked sandwich panel, with axes given by a dimensionless crack length and dimensionless height of the sandwich core. The shear strength of the cracked sandwich panel is examined in detail. The precise form of the failure map for shear loading depends upon the tensile failure strain of the solid and upon the relative density of the lattice. The relevance of the shear failure map to lattices made from a wide range of engineering materials is illustrated through material-property charts. An extension of the method to cyclic loading is discussed.

Stress field in a crack on the interface of materials irradiated with SH-waves

On the basis of the solution of the problem of diffraction of a field of plane SH-waves on a crack located on the interface of materials obtained by the authors earlier, we deduce asymptotic expressions for the stress intensity factors at the crack tips. The dependences of the stress intensity factors on the dimensionless crack length, the angle of incidence of the plane wave, and the mechanical and physical properties of the materials are investigated. The possibility of appearance of singularities of the stress intensity factors near the remote crack tip (relative to the source of radiation) for the tangential and critical angles of irradiation is demonstrated. It is shown that, for the critical angles of incidence, these singularities can appear only in perfect materials and that, in the presence of losses, the increase in the stress intensity factors is bounded. It is also demonstrated that the indicated effects are caused by the diffraction interaction of SH-waves with the crack tips.

A dimensionless multi-size finite element model of a rolling contact fatigue crack

Considerations which should be taken in approaching a rolling contact fatigue (RCF) crack growth problem must cover the variety of possible configurations of geometrical parameters, material properties and loading conditions. The great variety of configurations occurring in engineering practice is probably a reason to the difficulties, which are usually encountered in finding the complete data concerning any particular problem from the discussed field. The purpose of the paper is to introduce a concept of a dimensionless multi-size finite element (FE) model, which can reduce the number of necessary models for a given problem of RCF. This concept is explained on the basis of the 2D version, in which the size of the crack is represented only by its length and the real contact load is applied in the form of traveling theoretical Hertz’ pressure. Such a model assures the possibility of using only one FE mesh for analyzing a number of RCF crack lengths under moving contact load. The multi size feature of the model consists in introducing the two parameters of geometrical similarity to the 2D contact problem, i.e. the crack slope angle and the ratio of crack length to the half width of the theoretical Hertz’ contact patch being called further the dimensionless crack length. These two parameters are sufficient for identifying the considered case. In the conventional approach, each crack length requires building a separate FE model, which can be used to determine the linear elastic fracture mechanics (LEFM) stress intensity factors (SIF) histories. This is very costly, time consuming and laborious, especially in 3D modeling. In the presented approach, the model of the member containing the crack is only one, whilst the different dimensionless crack lengths are realised by means of changing the contact patch instead of the crack length itself. The model was tested and the results obtained are in a good agreement with that obtained conventionally. Additionally, the functionality of the model was presented in conducting several series of analyses for the two crack slopes 15 and 20° and the range of the dimensionless crack lengths from 0.5 to 15. On the basis of the results, the critical dimensionless crack lengths were determined, for which the crack tip is exposed to the highest ranges of the Modes I and II SIFs.

Use of double edge-cracked Brazilian disk geometry for compression-shear fracture investigation of rock

A new specimen geometry—the double edge-cracked Brazilian disk and a relevant fracture analysis by weight function method are proposed for the investigation of rock fracture caused by compression-shear loading. Not only can the mixed mode fracture with any ratio of KI/KII be achieved, but also the pure mode II crack extension can be obtained. The combined mode fracture analysis for this geometry shows that diametral compression in the farfield can induce a compression-shear stress state in the singular stress field ahead of crack tips. Experimental investigations conducted on marble specimens show that the pure mode II crack extension can be obtained when the dimensionless crack length a>0.7 and the inclined crack angle 5°⩽ϕ⩽40°. Normalized mode I and mode II stress intensity factors decrease from −0.45 and 2.47 at ϕ=5° to −1.65 and 1.52 at ϕ=40°, respectively. The strains at three points of specimen are also measured in order to investigate the influence of stress singularity on initial crack extension. The results show that the principal orientations of strain at three points are very stable in the loading process. The derived formulae are quite explicit, and the specimen geometry is easy to fabricate and convenient to achieve the pure mode II crack extension. Therefore, it can hopefully be used to obtain mode II fracture toughness of rock.

Experimental and numerical analysis of vibrating cracked plates at resonant frequencies

Owing to the advantages of noncontact and fullfield measurement, an optical system called the amplitude fluctuation electronic speckle pattern interferometry (AFESPI) method with an out-of-plane setup is employed to investigate the vibration of a cantilever square plate with a crack emanating from one edge. Based on the fact that clear fringe patterns will be shown by the AFESPI method only at resonant frequencies, both the resonant frequencies and the vibration mode shapes can be obtained experimentally at the same time. Three different crack locations will be discussed in detail in this study. One is parallel to the clamped edge, and the other two are perpendicular to the clamped edge. The numerical finite element calculations are compared with the experimental results, and good agreement is obtained for resonant frequencies and mode shapes. The influences of crack locations and lengths on the vibration behavior of the clamped cantilever plate are studied in terms of the dimensionless frequency parameter (λ 2) versus crack length ratio (a/L). The authors find that if the crack face displacements are out of phase, a large value of stress intensity factor may be induced, and the cracked plate will be dangerous from the fracture mechanics point of view. However, there are some resonant frequencies for which the crack face displacements are completely in phase, causing a zero stress intensity factor, and the cracked plate will be safe.

VIBRATION OF CRACKED CIRCULAR PLATES AT RESONANCE FREQUENCIES

It is well known that the presence of cracks will affect the dynamic characteristics of the vibrating plate. Such a problem is complicated because it combines the field of vibration analysis and fracture mechanics. In this study, an optical system called the AF-ESPI method with the out-of-plane displacement measurement is employed to investigate the vibration characteristics of a free circular plate with a radial crack emanating from the edge. The boundary conditions along the circular edge are free. As compared with the film recording and optical reconstruction procedures used for holographic interferometry, the interferometric fringes of AF-ESPI are produced instantly by a video recording system. Based on the fact that clear fringe patterns will appear only at resonant frequencies, both resonant frequencies and corresponding mode shapes can be obtained experimentally at the same time by the proposed AF-ESPI method. Numerical finite element calculations are also performed and the results are compared with the experimental measurements. Good agreements are obtained for both results. The vibrating mode shapes obtained in this study can be classified into two types, symmetric and antisymmetric modes with respect to the crack line. The influence of crack length on resonant frequencies is also investigated in terms of the dimensionless frequency parameter (λ2) versus crack length ratio (a/D). We find that if the crack face displacement is out of phase, i.e., the antisymmetric type, a large value of stress intensity factor may be induced and the cracked circular plate will be dangerous, from the fracture mechanics point of view. However, there are some resonant frequencies for which the crack face displacements are completely in phase, i.e., the symmetric type, which yields a zero stress intensity factor and the cracked plate will be safe.

Size effects in concrete fracture – Part II: Analysis of test results

This paper presents an analysis of the extensive experimental program aimed at assessing the influence of maximum aggregate size and specimen size on the fracture properties of concrete. Concrete specimens used were prepared with varying aggregate sizes of 4.75, 9.5, 19, 38, and 76 mm. Approximately 250 specimens varying in dimension and maximum aggregate size were tested to accomplish the objectives of the study. Every specimen was subjected to the quasi-static cyclic loading at a rate of 0.125 mm/min (0.005 in./min) leading to a controlled crack growth. The test results were presented in the form of load-crack mouth opening displacement curves, compliance data, surface measured crack length and crack trajectories as well as calculated crack length, critical energy release rate, and fracture toughness (G 1). There is a well pronounced general trend observed: G 1 increases with crack length (R-curve behavior). For geometrically similar specimens, where the shape and all dimensionless parameters are the same, the R-curve for the larger specimens is noticeably higher than that for the smaller ones. For a fixed specimen size, G 1 increases with an increase in the aggregate size (fracture surface roughness). For the same maximum aggregate size specimens, the apparent toughness increases with specimen size. It was clear that the rate of increase in G 1, with respect to an increase of the dimensionless crack length (the crack length normalized by the specimen width), increases with both specimen size and maximum aggregate size increase. The crack trajectory deviates from the rectilinear path more in the specimens with larger aggregate sizes. Fracture surfaces in concrete with larger aggregate size exhibit higher roughness than that for smaller aggregate sizes. For completely similar specimens, the crack tortuosity is greater for the larger size specimens. The crack path is random, i.e., there are no two identical specimens that exhibit the same fracture path, however, there are distinct and well reproducible statistical features of crack trajectories in similar specimens. Bridging and other forms of crack face interactions that are the most probable causes of high toughness, were more pronounced in the specimens with larger maximum size aggregates.

Study on the Behavior of a Center Crack under Thermal Impact by the Dislocation Theory

This paper investigated plane strain stress intensity factors caused by thermal impact on a center-crack strip. The crack was aligned perpendicularly to the strip boundary. The problem was analysed by determining the dislocation density function in the singular integral equations formulated by the dislocation theory. Under the abrupt temperature change along the edge, the center crack behaved as a mode I crack due to the symmetric geometry. The value of maximum stress intensity factor monotonically increased until the ratio of dimensionless crack length approached to about 0.3, followed by gradual decrease. As a result, a critical corresponding crack length was determined.

Fracture toughness of some British rocks by diametral loading of discs

Results of fracture toughness tests on five types of rock, as determined by diametral loading of discs, are presented. Results indicate that the fracture toughness ‘K 1’ is independent of crack length and dimensionless crack length but depends upon width to diameter ratio of the specimens. The effect of the width to diameter ratio on fracture toughness was examined in detail and a minimum ratio of 0.8 is recommended.

An experimental K-analysis on the fatigue crack near the interface where plate thickness varies discontinuously —Thin to thick type

The characteristics of fatigue crack propagation behavior near the thickness interface were examined for 6061 T6 aluminium specimens. A series of thin to thick type various thickness specimens was prepared. Fatigue tests were performed under load control in tension-tension. Correction factor of the stress intensity factors (SIF) for various thickness specimens was introduced as the form of F( α, β) where α was a dimensionless crack length and β was the thickness ratio. These correction factors were determined experimentally by means of linear elastic fracture mechanics concepts.

Asymptotic Evaluation of a Combined Stress-Intensity Factor for a Pressurized Cylindrical Shell Containing a Longitudinal Crack

Sanders’ path-independent energy-release-rate integral I for a cracked shallow shell is used to compute the asymptotic form of the combined stress-intensity factor for a pressurized elastically isotropic cylindrical shell containing a longitudinal crack. The combined stress-intensity factor is expressible in terms of the conventional stretching and bending stress-intensity factors and is a function of Poisson’s ratio v and a dimensionless crack length λ. When λ is small the shell is nearly flat and when λ is large the shell is very thin. Asymptotic formulas for I when λ is small or large are obtained. A numerical solution for λ = 0(1) is also obtained.

Sanders’ Energy-Release Rate Integral for Arbitrarily Loaded Shallow Shells and Its Asymptotic Evaluation for a Cracked Cylinder

Sanders’ path-independent, energy-release rate integral I is specialized to an arbitrarily loaded shallow shell containing a stress-free void, assuming linear theory. Two forms of I are given. When the void is a crack, one form reduces to integrals over circles of vanishing radius centered at the tips and is expressible in terms of bending and stretching stressintensity factors. The other form reduces to an integral along the crack. For an elastically isotropic cylindrical shell containing a longitudinal crack and subject to a uniform bending stress at large distances from the crack, the dimensionless form of I depends on Poisson’s ratio v and a dimensionless crack length λ. When λ is small the shell is nearly flat; when λ is large the shell is very thin. An asymptotic formula is obtained for I as λ → ∞. This is done by reducing the boundary-value problem to a coupled set of singular integral equations, scaling, taking the limit as λ → ∞ to obtain inner and outer integral equations, solving the outer equations analytically, and, finally, evaluating I along the crack where the outer solutions dominate. As the evaluation of I does not require an explicit solution of the inner integral equations, an apparently intractible coupled Wiener-Hopf problem is evaded.

Stress-Intensity Factors for Very Short Cracks in Arbitrary Pressurized Shells

A pressurized, shallow, elastically isotropic shell containing a crack is considered. The crack is assumed to lie along a line of curvature of the midsurface. The equations governing the essentially equivalent residual problem, in which the only external load is a uniform normal stress along the faces of the crack, are reduced via Fourier transforms to two coupled singular integral equations. The solutions of these equations depend on three parameters: λ, a dimensionless crack length, κ, the dimensionless Gaussian curvature of the midsurface at the center of the crack, and ν, Poisson’s ratio. Perturbation solutions for small values of λ are obtained by expanding the kernels of the integral equations in series. Explicit formulas for stretching and bending stress-intensity factors are obtained. These represent the first-order corrections due to curvature effects of the well-known flat plate results. The connection with the work of Copley and Sanders for cylindrical shells and Folias for spherical and cylindrical shells is indicated.