This article focused on the stress analysis of an edge crack in a thin hallow rotating functionally graded material (FGM) disk. The disk is assumed to be isotropic with exponentially varying elastic modulus in the radial direction. A comprehensive study is carried out for various combinations of the crack length and orientation with the different gradation of materials. The effect of non-uniform coefficient of thermal expansion on the distribution of stress intensity factor is also studied. The results which are normalized for the advantage of non-dimensional analysis show that the material gradation, the crack orientation and the crack length have significant influence on the amount of stress intensity factors.

In this paper, a continuous model for flexural vibration of beams with an edge crack perpendicular to the neutral plane has been developed. The model assumes that the displacement field is a superposition of the classical Euler-Bernoulli beam's displacement and of a displacement due to the crack. The additional displacement is assumed to be a product between a function of time and an exponential function of space. The unknown functions and parameters are determined based on the zero stress conditions at the crack faces and the concept of J-integral from fracture mechanics. The governing equation of motion for the beam has been obtained using the Hamilton principle and solved using a modified Galerkin method. The results have been compared with finite element results and an excellent agreement is observed.

In this paper, buckling of simply supported column with an edge crack is investigated numerically and analytically. Four different scenarios of damage severities are applied to a column, Open crack assumption and the effect of closing crack in stability of the column which depends on position and size of cracks, are numerically compared. crack surfaces contact is modeled with GAP element using SAP2000. For analytical solution, transfer matrix method, combined with fundamental solutions of the intact columns is used to obtain the capacity of slender prismatic columns. The stiffness of the cracked section is modeled by a massless rotational spring and governing equations are obtained explicitly for simply supported column from second-order determinant. As expected results show that the effect of a closing crack in presence of compressive load may lead to an increment in buckling load depending on crack depth and position. For the first time, a dimensionless formulation based on numerical results is presented in this study. Proposed formula predicts increment effect of closing crack in buckling results of a notched column.

In the current research work, the problem of fracture mechanics in a plate with a central hole under tensile loading is studied. The stress intensity factors are calculated for a finite plate containing two symmetrical hole-edge cracks. The problem is solved by two different methods, namely the finite element method and the FRANC software analysis. At first the finite element method is used and by writing a program in MATLAB software the stress intensity factors at the crack tips are calculated. The same problem is then reanalyzed with the Franc software and the results are compared. The effects of various factors such as the hole diameter, crack length and crack angle have been investigated on stress intensity factors. The results show that for small crack lengths, the effect of cracks length is more than that of the hole diameter on variation of normalized stress intensity factors, while it is the opposite for large crack lengths, the effect of hole diameter is more than that of the cracks length on variation of normalized stress intensity factors.

The aerospace and automotive industries widely use composite materials due to their weight-to-strength ratios. One of the most significant problems with composites is repair and maintenance. This study attempts to repair glass epoxy composites. The repair process involves two stages: 1)optimization of the position of the hole and 2) repair work. To optimize the repair techniques, two distinct holes were performed: 1) at the center of the specimen and 2) at the edges of the specimen. As a result, the hole drilled at the center gives higher strength than the hole drilled at the edges. After the optimization, samples were repaired with a single hole in the center and peak loads of 60% and 90%. The cracked and delaminated areas were repaired with epoxy/hardener. The repaired samples were subjected to a three-point bending test, and the results were compared with the Neat GFRP samples. The results show that the curves of the repaired samples aligned with both the post and the residual flexural strength. The residual flexural strength of the 60% and 90% peak-loaded repaired samples retains about 47% and 76%, respectively.

This paper explores the lateral vibration behavior of a micro cantilever beam with an Open edge crack under axial load using the modified strain gradient theory (MSGT). A concentrated mass, incorporating its rotational inertia, is positioned at the beam's free end. The Open edge crack is represented using the Dirac delta function. By employing MSGT, Hamilton's principle, and the Dirac delta function, the governing equations for system motion and relevant boundary conditions are derived to examine the size-dependence effects. Analytical solutions for the first and second natural frequencies of the cracked cantilever beam are provided, and validated through finite element modeling. The study further investigates the impact of various system parameters, including material length scale parameters, crack depth, crack location, cantilever beam length, axial load, and the presence of the concentrated mass, on the natural frequencies. The findings demonstrate that the crack depth, crack location, and material length scale parameters considerably influence the lateral vibration characteristics of the system. Notably, increasing the values of l_i/h from 0 to 0.25 leads to an approximate 40% rise in the natural frequency.