Finite Element Analysis of Interactions of between two cracks in FGM notched Plate under Mechanical Loading

Abstract

The investigation of multiple crack interactions in fracture mechanics is important to predict the safety and reliability of structures. This paper introduces a 2D numerical investigation used to calculate the J-integral of the main crack behavior emanating from a semicircular notch and double semicircular notch and its interaction with another crack which may occur in various positions in titanium /titanium boride functionally graded material (TiB/Ti FGM) plate subjected to tensile mechanical load. Young's modulus of the functionally graded material plate varies along the specimen width (notch radius direction r-FGM) with exponential-law (E-FGM) function. Further, the Poisson's ratio is taken as a constant in normal direction. For this purpose the variations of the material properties are applied at the integration points and at the nodes by implementing a subroutine USDFLD in the ABAQUS software. The variation of the J-integral according to the position, the length, and the angle of rotation of cracks are examined; also the effect of different parameters for double notch FGM plate is investigated as well as the effect of band of FGM within the ceramic plate to reduce Jintegral. According to the numerical analysis, all parameters above played an important role in determining the J-integral.

A New Hybrid Finite Element Method: Electromagnetic Propagation in Bent Waveguides

“…In equation (2) which has the form of a Bessel differential equation, the parameter ϒ, interpreted as a radial propagation constant, is given by:…”

“…where S is the transversal waveguide domain with the outer boundary reduced to the line s d , H (2) ν (ϒr ) is the derivative of the Hankel function with respect to (ϒr ) on s d . The variation of the functional is given by [25]:…”

“…The finite element method (FEM) arose due to the need to solve complex problems [1]. In the beginning the method was applied for mechanical structural analysis, in Civil [2] and Aeronautical Engineering [3]. The FEM is, in our days, one of the most important numerical methods used in simulation in different areas [4], namely in biomedical applications [5], [6], in the optimization [7], design and simulation of electrical, electronic and optical devices [8].…”

Investigations in static response and free vibration of a functionally graded beam resting on elastic foundations

“…Bouchikhi, A. S et al [10] investigated the 2D simulation used to calculate the J-integral of the main crack behavior emanating from a semicircular notch and double semicircular notch and its interaction with another crack which may occur in various positions in (TiB/Ti) FGM plate under mode I. Yassine Khalfi et al [11] developed a refined and simple shear deformation theory for mechanical buckling of composite plate resting on two-parameter Pasternak's foundations. Meftah Kamel [12] presented a finite element method for analyzing the elasto-plastic plate bending problems.…”