In structure of rocks, there are a number of pores, joints and small Cracks which called discontinuities. Studies showed that these discontinuities propagate under load and emit acoustic wave (signals). Acoustic emission (AE) method is used to study these signals. In AE method, a rock sample is loaded and a number of sensors are placed around it. Then during the loading test by growing the Cracks signals emit and collecting by sensors. By collecting and analyzing these signals in the frequency dimension, mechanism of Crack propagation could be studied. In this research, frequency bandwidth of the waves emitted from a rock sample under increasing load has been investigated. Data which obtained from an experiment on rock sample have been used for study. A sample of granite with dimensions of 1*3*6 inches was subjected to uniaxial loading. A code was written to change the data and executed in MATLAB. By execution the code, initially, raw data is transmitted into domain-time signals. Then, time-amplitude dimension signals converted to the frequency dimension using wavelet transform. Analyses were carried out with outputs of code and in form of diagrams and figures are presented. Analysis showed that by elapse of time and Crack growth in the experiment, there was an inverse relationship between the length of the growing Crack and frequency bandwidth of the emitted wave, and the frequency bandwidth decreased.

Turbomachinery, specially gas turbines and axial compressors, play an important and vital role in energy producing and transmission industries. Thus, probable defects must be detected and measured in a timely manner, in order to prevent expensive costs of repair and maintenance. In this paper, a gas turbine blade-disc connection model, that is one of the most important and sensitive gas turbine parts, has been inspected using phased array ultrasonic non-destructive testing method. In manufactured mockup specimen, a Crack with 4 and 8 millimeters length, has been created in two steps, followed by the length effect study on inspection results. Comparison of acquired signals in different angles for each Crack length with acquired signals got from the healthy model in the same angles, has been employed for Crack sizing purposes. The increase in the amplitude of Crack reflected signals and the decrease in the amplitude of signals related to the wall behind the Crack versus increase in the inspection angle, in ultrasonic phased array testing, has been utilized for extracting a novel feature for Crack length estimation. Experimental results show that it is possible to evaluate the Crack length in the complicated fir-tree geometry of the disc connection area to the blade, with the amount of error less than 10%, using the extracted feature.

Mode I fracture toughness (KIC) is one of the most important parameters in fracture mechanics, which represents the ability of a material containing a pre-existing defect to resist tensile failure. In this paper, the Crack length effect on the mode I fracture toughness of an isotropic homogeneous material was investigated. For this purpose, several disc shaped PPMA samples were loaded in pure tension by performing pseudo-compact tension (pCT) tests. Digital image correlation (DIC) method was utilized to assess and monitor the distribution of the deformation field during the tests. DIC results were also used to compare the effect of Crack length on the deformation field variation in samples. Very good agreement was found between the KIC values estimated in this study and those reported in the past for the similar material,indicating that the pCT method is convenient for the assessment of KIC. The experimental results also show that the initial Crack length has a tangible impact on KIC, although the magnitude of its influence is closely related to material structure and type. According to the tests results, an increase in the initial Crack length leads to increase the ultimate displacement at failure point, decrease the maximum load and the amount of absorbed energy until the moment of failure, and finally decrease the mode I fracture toughness of the material. Results of this study show that the pCT method configuration is useful for testing PMMA and may be useful for testing other materials suitable amenable of molding such as mortar, concrete and ceramics. According to the comparison of the results, in the optimum range of sample diameter, about 50 mm, the initial Crack length is suggested between 11. 5 to 15. 5 mm for the PMMA.

The term hydraulic fracturing expresses process of beginning and expanding the Crack in the rock that caused by hydraulic pressure exerted by the fluid which is a way for assessing state of tensions in the ground and increase the efficiency of oil reservoirs. In this study, by carring out laboratory test, the effect of the geometry of Cracking created in the wall of the well is investigated on hydraulic fracture pressure. This investigation is important because the companies that perform the hydraulic fracture are always trying to decrease cost of pump purchase. So pressure investigation can be useful in selecting suitable pump. For testing, a series cylindrical and hollow samples with a 73 mm external diameter, 25 mm inner diameter and 150 mm height are provided. In these samples, artificial Cracks were created and the effect of length, height and Crack thickness on hydraulic pressure was investigated. These tests are carried out for several different modes that in each series one of the parameters is changed and two other parameters are fixed and the effect of each parameters on the hydraulic fracture pressure is investigated. For the production of cylindrical samples, a mold was made to prepare Cracked sample. The experimental results indicate that hydralic fracturing pressure linearly decreases with a increasing in the length and height of the Crack. This pressure nonlinearly decreases with a increasing in the Crack width. Also, Crack length have more effect than Crack height on the hydraulic fracture pressure and is also greater than the Crack width.

SummaryGeomechanical properties of some sedimentary and metamorphic rocks are important because they are anisotropic.  These properties affect on stability of rock construction. In this research, the changes in the stress intensity factor in anisotropic rock have been investigated based on the changes in the Crack angle with the loading axis and anisotropy ratio. In this research, the finite element method and ABAQUS software are used because of their ability to simulate anisotropic rock. The CCNBD disc sample was used according to the standards of ISRM. It concluded that the stress intensity factor is dependent on the anisotropy ratio, layering angle, and Crack length and pure tension (mode one) does not necessarily occur at a zero-Crack angle with the loading axis (β=0), and this angle is completely affected by the layering angles (Ѱ).Introduction Investigating the behavior of rock under load and determining its mechanical properties are important to designing rock structures. The importance increases when the rock is anisotropic. In the design two mechanical properties; the first rock strength and the second deformation should be considered. The anisotropy rocks require the simultaneous investigation of the resistance behavior and the failure mechanism [1]. A rock is called anisotropic when the value of mechanical properties is different in two different directions. Fracture toughness is the critical stress intensity factor of a sharp Crack where propagation of the Crack suddenly becomes rapid and unlimited [2].For materials that have linear elastic behavior, this property is usually expressed in terms of a quantity called the critical value of the stress intensity factor. This parameter is indicated by the symbol K [3] In this research, the main question is to investigate the changes in the stress intensity factor in anisotropic rocks by changing the angle of the Crack with the loading axis, anisotropy ratio, Crack length, and layering angle.Methodology and ApproachesFor investigation of research question numerical method was considered. The software used Abaqus finite element(FEM) [4]. Abaqus is a set of powerful engineering simulation programs based on the FEM and can solve a wide range of problems from a relatively simple linear analysis to very complex nonlinear analysis. The rock sample was an anisotropic Phyllite belonging to the abutment of the Azad Dam in Kurdistan and the mechanical properties of the sample were taken from Abadat (2013) [5]. CCNBD disk numerical models (D=54 mm and t=30 mm) of Phyllite according to the standard of the International Society of Rock Mechanics (ISRM) with anisotropy ratio (E/E'=1.8 and E/E'=4) in different layering angles (ψ=0-30°-45°-60°-75°-90°) and in different Crack angles with loading extension (β) and in different Crack lengths (a=12-24-36 mm) were built and executed by Abaqus. After execution, the Abacus determined the stress intensity factor of each model, and data were collected and analyzed.Results and ConclusionsSensitivity analysis by variation of four parameters which were anisotropy ratio, different layering angles, different Crack angles with loading extension, and different Crack lengths was carried out. 180 models were built and executed by Abacus software. Three parameters were kept constant the last was changed and the stress intensity factor was evaluated. Figures 2, 3, and 4 show the effect of the anisotropy ratio variation on the angle of the Crack with the loading axis in the pure tensile (mode one), pure shear (mode two), and mixed-mode in the Crack length of 12 mm respectively.1- Variations of layer angle (ψ), Crack angle with loading axis (β), Crack length(a), and change of anisotropy ratio have a noticeable effect on the values of the stress intensity factor.2- In different Crack lengths and in different anisotropy ratios, for a constant layering angle, the stress intensity factor of tensile mode is maximum at β=0 and minimum at β=90° and the stress intensity factor of shear mode is minimum at β=0 and β=90̊ and maximum at β between 30̊-40̊.3- Mode one(pure tensile) in different angles of layering does not necessarily occur at a zero-degree angle with the loading axis (β=0) and this angle is completely affected by the angles of layering (Ѱ).4- According to the results in different layering angles and in different anisotropy ratios, the β angle is different, so that the pure tensile in the layering angle of 30° and the anisotropy ratio equal to 4 occur in β =6°. However, this value is equal to 2° for the anisotropy ratio equal to 1.8

Seismic behavior in concrete weights due to the need to increase the safety of dams during earthquakes has been very much considered in recent years. Most concrete dams are exposed to Cracking damage. These Cracks are created by various factors such as operation, concrete treatment, volumetric changes in concrete mass, loads, etc., and the possible expansion of these Cracks may reduce the efficiency, failure and instability of such dams. The use of fracture mechanics as a new method for estimating the instability and durability of concrete dams has been recommended in world-renowned journals and papers. Due to the sensitivity of the subject of Crack-erosion in concrete dams, as well as considering that in the past the behavior of the Gotvand dam was not investigated due to trapping, this study examined the behavior of the Gotvand Regulatory Dam due to trapping Has been. Abkhus software is used to model this research. Parameters that are considered as variables include the length of the variable for the Cracks and the Crack angle. In the case of the effect of the Crack angle, the results indicate that the worst case for the dam section is to leave a negative angle. The horizontal displacement value for the-30 degree angle is 0. 031 m and is 0. 025 m for Cracking at an angle of +30 degrees. Also, the increase in the length of the Crack increased the amount of displacement, tension and rebound response in the dam. Maximum reciprocating photo in a model with a length of 200 cm, with a Crack angle of +45, is 4% higher than the model with a gap of 30 cm and equal to 1. 78E+8 of Newton.

The elements of the concrete structure are most frequently affected by Cracking. Crack detection is essential to ensure safety and performance during its service life. Cracks do not have a regular shape, in order to achieve the exact dimensions of the Crack; the general mathematical formulae are by no means applicable. The authors have proposed a new method which aims to measure the Crack dimensions of the concrete by utilizing digital image processing technique. A new algorithm has been defined in MATLAB. The acquired data has been analyzed to obtain the most precise results. Here both the length and width of the Crack are obtained from image processing by removing background noise for the accuracy of measurement. A semi-automatic methodology is adapted to measure the Crack length and Crack width. The applicability of the program is verified with the past literature works.

To ensure the rail transportations safety, evaluation of fatigue behavior of the rail steel is necessary. High cycle fatigue behavior of a rail steel was the subject of investigation in this research using fracture mechanics. Finite element method (FEM) was used for analyzing the distribution of the stresses on the rail, exerted by the external load. FEM analysis showed that the maximum longitudinal stresses occurred on the railhead. To find out about the relation of Crack growth with its critical size, and to estimate its lifetime, the behavior of transverse Cracks to rail direction was studied using damage tolerance concept. It revealed that transverse Crack growth initially occurred slowly, but it accelerated once the Crack size became larger. Residual service life was calculated for defective segments of the rails. In addition, allowable Crack size for different non-destructive testing intervals was determined; the allowable Crack size decreased as the NDT intervals increased.