Prediction Method of Crack Propagation Path in Plate with Hole by Singular Integral Equation

In this study, crack path simulation was conducted based on a singular integral equation formulated by a continuous distributed dislocation technique. The problem investigated in this study was to predict the propagation path of a crack moving in an infinite elastic plate with a circular hole, under uniform tensile loading. In order to perform this prediction, a probing method was developed to search for a crack moving direction where the mode II stress intensity factor would be almost zero, enabling the crack to automatically extend in that direction. Some cases for different locations of an initial straight crack were simulated using the program developed.

Download Full-text

Study on Prediction of Propagation Path of Crack Interacting with Inclusion by Singular Integral Equation

The Proceedings of the Materials and Mechanics Conference ◽

10.1299/jsmemm.2018.os0832 ◽

2018 ◽

Vol 2018 (0) ◽

pp. OS0832

Author(s):

Masayuki ARAI ◽

Kazuki YOSHIDA

Keyword(s):

Integral Equation ◽

Singular Integral Equation ◽

Singular Integral ◽

Propagation Path

Download Full-text

An Alternative Technique to Evaluate Crack Propagation Path in Hyperelastic Materials

Tire Science and Technology ◽

10.2346/1.3684484 ◽

2012 ◽

Vol 40 (1) ◽

pp. 42-58 ◽

Cited By ~ 6

Author(s):

R. R. M. Ozelo ◽

P. Sollero ◽

A. L. A. Costa

Keyword(s):

Constitutive Model ◽

Crack Propagation ◽

Experimental Tests ◽

Growth Direction ◽

Propagation Path ◽

J Integral ◽

Alternative Technique ◽

Crack Propagation Path ◽

Hyperelastic Materials ◽

Material Constitutive Model

Abstract REFERENCE: R. R. M. Ozelo, P. Sollero, and A. L. A. Costa, “An Alternative Technique to Evaluate Crack Propagation Path in Hyperelastic Materials,” Tire Science and Technology, TSTCA, Vol. 40, No. 1, January–March 2012, pp. 42–58. ABSTRACT: The analysis of crack propagation in tires aims to provide safety and reliable life prediction. Tire materials are usually nonlinear and present a hyperelastic behavior. Therefore, the use of nonlinear fracture mechanics theory and a hyperelastic material constitutive model are necessary. The material constitutive model used in this work is the Mooney–Rivlin. There are many techniques available to evaluate the crack propagation path in linear elastic materials and estimate the growth direction. However, most of these techniques are not applicable to hyperelastic materials. This paper presents an alternative technique for modeling crack propagation in hyperelastic materials, based in the J-Integral, to evaluate the crack path. The J-Integral is an energy-based parameter and is applicable to nonlinear materials. The technique was applied using abaqus software and compared to experimental tests.

Download Full-text

Approximate Solution Of A Singular Integral Equation With A Multiplicative Cauchy Kernel In The Half-Plane

Computational Methods in Applied Mathematics ◽

10.2478/cmam-2008-0010 ◽

2008 ◽

Vol 8 (2) ◽

pp. 143-154 ◽

Cited By ~ 1

Author(s):

P. KARCZMAREK

Keyword(s):

Integral Equation ◽

Approximate Solution ◽

Singular Integral Equation ◽

Half Plane ◽

Singular Integral ◽

Trigonometric Polynomials ◽

Cauchy Kernel

AbstractIn this paper, Jacobi and trigonometric polynomials are used to con-struct the approximate solution of a singular integral equation with multiplicative Cauchy kernel in the half-plane.

Download Full-text

A semianalytical and finite-element solution to the unbonded contact between a frictionless layer and an FGM-coated half-plane

Mathematics and Mechanics of Solids ◽

10.1177/1081286517744600 ◽

2017 ◽

Vol 24 (2) ◽

pp. 448-464 ◽

Cited By ~ 7

Author(s):

Jie Yan ◽

Changwen Mi ◽

Zhixin Liu

Keyword(s):

Integral Equation ◽

Finite Element ◽

Singular Integral Equation ◽

Contact Problem ◽

Singular Integral ◽

Material Properties ◽

Elastic Layer ◽

Coated Substrate ◽

Receding Contact ◽

Contact Size

In this work, we examine the receding contact between a homogeneous elastic layer and a half-plane substrate reinforced by a functionally graded coating. The material properties of the coating are allowed to vary exponentially along its thickness. A distributed traction load applied over a finite segment of the layer surface presses the layer and the coated substrate against each other. It is further assumed that the receding contact between the layer and the coated substrate is frictionless. In the absence of body forces, Fourier integral transforms are used to convert the governing equations and boundary conditions of the plane receding contact problem into a singular integral equation with the contact pressure and contact size as unknowns. Gauss–Chebyshev quadrature is subsequently employed to discretize both the singular integral equation and the force equilibrium condition at the contact interface. An iterative algorithm based on the method of steepest descent has been proposed to numerically solve the system of algebraic equations, which is linear for the contact pressure but nonlinear for the contact size. Extensive case studies are performed with respect to the coating inhomogeneity parameter, geometric parameters, material properties, and the extent of the indentation load. As a result of the indentation, the elastic layer remains in contact with the coated substrate over only a finite interval. Exterior to this region, the layer and the coated substrate lose contact. Nonetheless, the receding contact size is always larger than that of the indentation traction. To validate the theoretical solution, we have also developed a finite-element model to solve the same receding contact problem. Numerical results of finite-element modeling and theoretical development are compared in detail for a number of parametric studies and are found to agree very well with each other.

Download Full-text