Line Spring Model and Its Applications to Part-Through Crack Problems in Plates and Shells

The line spring model is described and extended to cover the problem of interaction of multiple internal and surface cracks in plates and shells. The shape functions for various related crack geometries obtained from the plane strain solution and the results of some multiple crack problems are presented. The problems considered include coplanar surface cracks on the same or opposite sides of a plate, nonsymmetrically located coplanar internal elliptic cracks, and in a very limited way the surface and corner cracks in a plate of finite width and a surface crack in a cylindrical shell with fixed end

Reconstruction of Crack Cluster in the Rectangular Domain by Ultrasonic Waves

In the present article we study the reconstruction problem for clusters of linear cracks inside a rectangular domain. The parameters to be reconstructed are the number of cracks and the size and slope of each defect. The scanning is performed by a single ultrasonic transducer placed at a certain boundary point. The input data, used for the reconstruction algorithm, is taken as measured oscillation amplitudes over an array of chosen boundary points. The proposed numerical algorithm is tested on some examples with multiple clusters of cracks whose position and geometry are known a priori

On utilization of elliptical rings in assessing cracking tendency of concrete

A new experimental method by utilizing elliptical rings to replace circular rings recommended by ASTM and AASHTO was explored for assessing cracking potential of concrete and other cement-based materials under restrained condition. A series of thin and thick elliptical concrete rings were tested alongside circular ones until cracking. Cracking age, position, and propagation were carefully examined. It is found that thin elliptical rings with appropriate geometry can initiate cracks quicker than circular ones, which is desirable for accelerating the ring test. However, thick elliptical rings seem not to exhibit a desirable geometry effect of accelerating ring test compared with circular ones. There were multiple visible cracks that occurred in an elliptical ring and some cracks were initiated but did not propagate through the ring wall. In comparison, there was only one crack in the circular rings. Finally, the features of multiple cracks in restrained elliptical rings were examined and their impact on interpreting elliptical ring test results was elaborated. © 2014 4th International Conference on the Durability of Concrete Structures

A new empirical model to predict stress intensity factor for double interacting surface cracks located in hollow cylinder

Fracture in cylinders is one of the most popular types of failure. Owing to the impact of production processes, nondestructive testing, and severe operational conditions, etc., cracks exist. The cracks could be detected in single or multiple form, where multiple cracks considered among the significant concerns that cylinders expected to experience. This is because in the existence of multiple neighboring cracks, crack interaction can take place between cracks and accelerates fracture process and lead to a catastrophic failure. Consequently, this study focuses on the problem of double interacting surface cracks located on external and internal surfaces of a hollow cylinder and oriented into parallel and non-coplanar parallel cracks configuration. Stress Intensity Factor (SIFs) has been chosen as the driving force to define the crack interaction. The SIFs have been analyzed for a wide variety of crack geometry, and cylinder type as well as separation distances utilizing finite element software Ansys under different types of mechanical loadings. Based on the analysis results, an empirical mathematical model was produced to predict the SIFs for double parallel cracks using the SIFs for a single crack, for thick and thin cylinders, separately. The empirical model was verified in terms of performance evaluation metrics, which exhibited prediction error less than 5%. Also, it is shown that crack interaction influence for parallel cracks demonstrated by shielding interaction influence only, while both shielding, and amplification impacts produced for non-coplanar cracks. The crack separation distance (horizontal and angular) between the cracks displayed substantial influence on interaction since it exhibited the ability to convert the interaction behavior from shielding to amplification impact (for angular). The presented results in this research serve the literature database since SIFs for a wide variety of cracks geometry have been introduced under different types of loading. Besides, the proposed mathematical model could be used easily and confidently as it displayed a high rate of accuracy

Experimental analysis of 3D cracking in drying soils using ground-penetrating radar

This paper describes the capabilities of a novel technique to investigate crack formation and propagation in drying soils. The technique is a relatively simple, non-destructive indirect technique using a ground-penetrating-radar (GPR) system to detect cracks that form and propagate inside a soil specimen during desiccation. Although GPR devices have been used for multiple applications, their use in soils for the detection of small desiccation cracks has not been demonstrated yet. The experiment and the methodology used to test the accuracy of a small compact commercial GPR device for crack identification are described. The main objective was to identify what type of signals and what crack width and separation between them can be detected using the GPR device. The results indicate that cracks of 1 or 2mm wide can be detected depending on its position and shape, whereas sub-millimeter cracks are undetectable with the currently existing devices in the market. Regardless of this limitation, the GPR method can be useful to find time-related bounds of when the cracks appear, to point at their location and sometimes at the separation between two of them. Detection of cracks with origin at the bottom or within the specimen was accomplished with this system. Distances of 5 cm or more between cracks can be detected and measured, as well, with accuracy.Peer ReviewedPostprint (author's final draft

Effect of thermal cycling frequency on the durability of Yb-Gd-Y-based thermal barrier coatings

The effects of thermal cycling frequency and buffer layer on the crack generation and thermal fatigue behaviors of Yb–Gd–Y-stabilized zirconia (YGYZ)-based thermal barrier coatings (TBCs) were investigated through thermally graded mechanical fatigue (TGMF) test. TGMF tests with low- (period of 10 min) and high-frequency (period of 2 min) cycling were performed at 1100 °C with a 60 MPa tensile load. Different cycling frequencies in TGMF test generate two kinds of crack propagation modes. The sample with low-frequency cycling condition shows penetration cracks in the YGYZ top coat, and multiple narrow vertical cracks are generated in high-frequency cycling. To enhance the thermomechanical properties, different buffer layers were introduced into the TBC systems, which were deposited with the regular (RP) or high-purity 8 wt% yttria stabilized zirconia (HP-YSZ) feedstock. The purity of the feedstock powder used for preparing the buffer layer affected the fracture behavior, showing a better thermal durability for the TBCs with the HP-YSZ in both frequency test conditions. A finite element model is developed, which takes creep effect into account due to thermal cycling. The model shows the high stresses at the interfaces between different layers due to differential thermal expansion. The failure mechanisms of YGYZ-based TBCs in TGMF test are also proposed. The vertical cracks are preferentially created, and then the vertical and horizontal cracks will be propagated when the vertical cracks are impeded by pores and micro-cracks

The p-Laplace equation in domains with multiple crack section via pencil operators

The p-Laplace equation \n \cdot (|\n u|^n \n u)=0 \whereA n>0, in a bounded domain \O \subset \re^2, with inhomogeneous Dirichlet conditions on the smooth boundary \p \O is considered. In addition, there is a finite collection of curves \Gamma = \Gamma_1\cup...\cup\Gamma_m \subset \O, \quad \{on which we assume homogeneous Dirichlet boundary conditions} \quad u=0, modeling a multiple crack formation, focusing at the origin 0 \in \O. This makes the above quasilinear elliptic problem overdetermined. Possible types of the behaviour of solution $u(x,y)$ at the tip 0 of such admissible multiple cracks, being a "singularity" point, are described, on the basis of blow-up scaling techniques and a "nonlinear eigenvalue problem". Typical types of admissible cracks are shown to be governed by nodal sets of a countable family of nonlinear eigenfunctions, which are obtained via branching from harmonic polynomials that occur for $n=0$. Using a combination of analytic and numerical methods, saddle-node bifurcations in $n$ are shown to occur for those nonlinear eigenvalues/eigenfunctions.Comment: arXiv admin note: substantial text overlap with arXiv:1310.065

Vibration analysis of beam with multiple cracks

The present work deals with the free vibration analysis of a cracked beam with multiple transverse cracks using finite element method. In this analysis, an ‘overall additional flexibility matrix’, instead of the ‘local additional flexibility matrix’ is added to the flexibility matrix of the corresponding intact beam element to obtain the total flexibility matrix, and from there the result is compared with previous studies. The natural frequencies of free vibration of the beam with multiple cracks are computed. It is observed that with increase in number of cracks the natural frequencies decreases. The effect of cracks is more pronounced when the cracks are near to the fixed end than free end. The natural frequency decreases with increase in relative crack depth

Application of local and non-local approaches to multiple fatigue crack initiation and propagation

Fatigue strength conditions presented in terms of normalized equivalent stress functionals defined on loading processes are used to unite the stages of material damage with fatigue crack initiation and multiple crack propagation under arbitrary loading history. Examples of employing the local form of the functionals associated with the Palmgren-Miner linear damage accumulation rule and the power-type S–N diagram to a periodic crack system are given and shortcomings of the local approach are pointed out. A non-local approach free from the shortcomings is described. Equations for curvilinear crack growth rate vectors taking into account the whole damage history ahead of the crack are presented for multiple cracks under mixed-mode loadin