Fracture analysis of marble specimens with a hole under uniaxial compression by digital image correlation

Introduction. Preface. 1. Nonlinear Theory of Circular Cylindrical Shells. 2. Buckling of Circular Shells Under Fundamental Loads. 3. Postbuckling Behavior of Circular Cylindrical Shells Under Fundamental Loads. 4. Initial Postbuckling and Imperfection Sensitivity Under Fundamental Loads. 5. Buckling and Postbuckling of Circular Cylindrical Shells Under Combined Loads. 6. Buckling and Postbuckling of Partially Liquid-Filled Circular Cylindrical Shells Under Fundamental Loads. References.

Elastic stability of circular cylindrical shells

The cracks in a rock tend to initiate, propagate, and coalesce under loading. Based on the digital image correlation (DIC) method, uniaxial compression tests are carried out on rock-like specimens with various arrangements of two parallel cracks. The full-field strain and failure features of the rock-like materials are observed and analysis by a self-developed code. Two process zones are defined according to the differences between the shear strain field and the tensile strain field: a shear process zone and a tensile process zone. The following results are obtained in this study. (1) Three coalescence modes can be observed using the DIC method: a shear coalescence mode, a tensile coalescence mode, and a mixed coalescence mode. (2) At the microscopic level, the bridge angle and crack arrangement affect the formation of the process zone; at the macroscopic level, they determine the crack propagation path and the failure mode. (3) The peak strength of the rock-like specimen is related to the crack inclination angle and the bridge angle. (4) Numerical modeling by the expanded distinct element method and the strain strength criterion simulates the different coalescence modes of the experimental study efficiently.

Cracking Processes and Coalescence Modes in Rock-Like Specimens with Two Parallel Pre-existing Cracks

A uniaxial compression test was conducted with a servo loading apparatus to study the failure of a rock-like specimen with a pre-existing single flaw. The evolution of cracks was monitored with digital image correlation technology and simulated with the expanded distinct element method based on the strain strength criterion. The concentration and evolution of the principal strain field were found to be consistent with the initiation, propagation, and coalescence of cracks. As the inclination angle increased, the position of the maximum principal strain concentration changed from within the flaw to the flaw tips, and the distribution of the horizontal displacement field changed from symmetric to antisymmetric. The initiation stress and peak strength were affected by the inclination angle; they were minimum when the inclination angle was 60°. As the inclination angle increased, the failure mode of the specimens transformed from mostly tensile failure to mostly shear failure.

Failure characteristics of rock-like materials with single flaws under uniaxial compression

Indentation-induced cracking may have many implications in rock drilling and cutting processes. In the present work, cyclic indentation tests have been conducted on Yunnan sandstones to investigate the deformation and failure process. Deformation fields on the sample surface have been obtained via the digital image correlation (DIC) technique. It has been found that the macroscopic force–indentation curve exhibits hysteresis and the residual displacements increase during the loading–unloading cycles. Furthermore, a median crack has been observed to nucleate, running almost parallel to the loading axis when the indentation force amounts to a critical value. Such a crack always results in the final failure of the sandstone samples. Experimental analysis reveals the deformation and failure mechanism of sandstone during cyclic indentation. By the DIC technique, the displacement distribution along the crack surface can be easily calculated and, hence, the fracture parameters, such as crack opening displacement and fracture toughness.

Experimental Analysis on Deformation Evolution and Crack Propagation of Rock Under Cyclic Indentation

The failure strength model of brittle materials with a pre-existing open-hole defect is proposed in this paper. A modified Sammis–Ashby model is deduced, in which it can be used to calculate the peak strength of brittle materials. It shows the law between peak strength σp and independent variable μ, which is the ratio of open-hole radius (a) to half-width of the specimen (t). Moreover, numerical and experimental investigations on failure process of rock-like materials with an open-hole imperfection were carried out. In the experiments, 3D-digital image correlation method, an optical technique which utilises the full-field and non-contact measurement, was employed. A progressive elastic damage method realistic failure process analysis (RFPA) was used in the numerical investigation to inspect and verify the modified model and simulate the failure process. The investigation finds that there are good correlations between the experimental, numerical and theoretical results. Moreover, because of the influences of boundary conditions, shear failure type was obtained both experimentally and numerically.

Study on Failure Characteristic of Rock-Like Materials With an Open-Hole Under Uniaxial Compression

Study on single crack propagation and damage evolution mechanism of rock-like materials under uniaxial compression

The problem of buckling stability is very important in thin-walled cylindrical shell structure. In order to investigate the buckling phenomena, digital image correlation (DIC) method was applied in this experiment. The specimens have a thickness of 0.131mm and the ratio of external diameter (R0) to thickness (H) R0/H is 252. Due to its curved and thin walled elements, measurement of displacement and strains by using the traditional methods is difficult, because there is not enough space for sticking necessary torsion gauges to measure the out-of-plane behaviour, even if it is possible, the rigidity of the gauge itself will have an effect on the buckling strength. However, by using the optical image correlation method, the problem is solved. DIC method is an optical instrument which utilizes the full-field and non-contact measurement to gauge the three-dimensional displacement and strains on materials and structural parts. In this paper three dimensional digital image correlation system is applied to observe the buckling generation process in details and make a record of the surface displacement during the compression test by using two high resolution digital cameras, then the test data are analyzed and compared by a special correlation technique which can determine the surface displacements of cylindrical shells and it is shown in colour contour in full-field region. The buckling strengths obtained by the theoretical and experimental methods are compared and discussed in this paper. The experimental study shows that the buckling strength of theoretical value is much higher than that of experimental one, because the buckling strength is highly dependent on the imperfections.

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Visualization of Buckling on Thin-walled Cylindrical Shell by Digital Image Correlation Method

An approximate method is used for analyzing the free vibration problem of isotropic and anisotropic right triangular plates with various aspect-ratios and variable thickness. In this paper, a right triangular plate is considered as a kind of equivalent rectangular plate with point supports. Therefore, the free vibration characteristics of any triangular plate can be obtained by analyzing the equivalent rectangular plate. The differential equations of the equivalent rectangular plate with point supports are established based on the first-order shear deformation theory. By transforming the differential equations into integral equations and using numerical integration, the solutions of the partial differential equation can be obtained in discrete form. The Green function, which is the discrete solution for the deflection, is introduced to obtain the characteristic equation of the free vibration. Frequencies and mode shapes are shown for some triangular plates with various aspect-ratio and variable thickness. The effects of boundary conditions and the fibre orientation on the frequency parameters are considered. The efficiency and accuracy of the numerical solutions by the present method are investigated.

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Chihiro Morita

Papers

Study on Failure Characteristic of Rock-Like Materials With an Open-Hole Under Uniaxial Compression

Study on single crack propagation and damage evolution mechanism of rock-like materials under uniaxial compression

Visualization of Buckling on Thin-walled Cylindrical Shell by Digital Image Correlation Method

Free Vibration Analysis of Anisotropic Right Triangular Plates

Free Vibration Analysis of Square Plates Resting on Non-homogeneous Elastic Foundations