Fracture analysis of a functionally graded interfacial zone under plane deformation (original) (raw)
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Journal of Applied Mechanics, 2008
A Mode-III crack problem in a functionally graded material modeled by anisotropic strain-gradient elasticity theory is solved by the integral equation method. The gradient elasticity theory has two material characteristic lengths ᐉ and ᐉЈ, which are responsible for volumetric and surface strain-gradient terms, respectively. The governing differential equation of the problem is derived assuming that the shear modulus G is a function of x, i.e., G ϭ G͑x͒ ϭ G 0 e x , where G 0 and  are material constants. A hypersingular integrodifferential equation is derived and discretized by means of the collocation method and a Chebyshev polynomial expansion. Numerical results are given in terms of the crack opening displacements, strains, and stresses with various combinations of the parameters ᐉ, ᐉЈ, and . Formulas for the stress intensity factors, K III , are derived and numerical results are provided.
Journal of Applied Mechanics, 2003
A Mode-III crack problem in a functionally graded material modeled by anisotropic strain-gradient elasticity theory is solved by the integral equation method. The gradient elasticity theory has two material characteristic lengths ᐉ and ᐉЈ, which are responsible for volumetric and surface strain-gradient terms, respectively. The governing differential equation of the problem is derived assuming that the shear modulus G is a function of x, i.e., G ϭ G͑x͒ ϭ G 0 e x , where G 0 and  are material constants. A hypersingular integrodifferential equation is derived and discretized by means of the collocation method and a Chebyshev polynomial expansion. Numerical results are given in terms of the crack opening displacements, strains, and stresses with various combinations of the parameters ᐉ, ᐉЈ, and . Formulas for the stress intensity factors, K III , are derived and numerical results are provided.
International journal for numerical …, 2003
The interaction integral is a conservation integral that relies on two admissible mechanical states for evaluating mixed-mode stress intensity factors (SIFs). The present paper extends this integral to functionally graded materials in which the material properties are determined by means of either continuum functions (e.g. exponentially graded materials) or micromechanics models (e.g. self-consistent, Mori-Tanaka, or three-phase model). In the latter case, there is no closed-form expression for the material-property variation, and thus several quantities, such as the explicit derivative of the strain energy density, need to be evaluated numerically (this leads to several implications in the numerical implementation). The SIFs are determined using conservation integrals involving known auxiliary solutions. The choice of such auxiliary ÿelds and their implications on the solution procedure are discussed in detail. The computational implementation is done using the ÿnite element method and thus the interaction energy contour integral is converted to an equivalent domain integral over a ÿnite region surrounding the crack tip. Several examples are given which show that the proposed method is convenient, accurate, and computationally e cient. integral for two admissible states (actual and auxiliary ÿelds) of an elastic solid. The analysis requires evaluation of the integral along a suitably selected path surrounding the crack tip (far-ÿeld).
Engineering Fracture Mechanics, 1998
In this paper, the dynamic anti-plane crack problem of two dissimilar homogeneous piezoelectric materials bonded through a functionally graded interfacial region is considered. Integral transforms are employed to reduce the problem to Cauchy singular integral equations. Numerical results illustrate the effect of the loading combination parameter k, material property distribution and crack configuration on the dynamic stress and electric displacement intensity factors. It is found that the presence of the dynamic electric field could impede of enhance the crack propagation depending on the time elapsed and the direction of applied electric impact.
1999
The driving forces for a generally oriented crack embedded in a Functionally Graded strip sandwiched between two half planes are analyzed using singular integral equations with Cauchy kernels, and integrated using Lobatto-Chebyshev collocation. Mixed-mode Stress Intensity Factors (SIF) and Strain Energy Release Rates (SERR) are calculated. The Stress Intensity Factors are compared for accuracy with previously published results. Parametric studies are conducted for various non-homogeneity ratios, crack lengths, crack orientation and thickness of the strip. It is shown that the SERR is more complete and should be used for crack propagation analysis.
Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 2017
Dynamic stress intensity factors are important parameters in the dynamic fracture behavior of a cracked body. In this paper, an interaction integral method is utilized to compute the mixed-mode dynamic stress intensity factors of three-dimensional functionally graded material solids. Using a proper definition of actual and auxiliary fields, a new formulation and application of the interaction integral is proposed, which is independent of the derivatives of the material properties. ABAQUS finite element package is applied to analyze the functionally graded material cracked bodies. Accordingly, a user material subroutine is written for implementing the continuous variation of the material properties. Temperature was used as an additional variable to consider the variation of density. A research code is developed to compute the interaction integral. This code is then validated by solving some homogeneous and functionally graded material problems. Furthermore, the effect of the material...
Elastodynamic analysis of a functionally graded half-plane with multiple sub-surface cracks
Acta Mechanica Solida Sinica, 2012
The stress fields are obtained for a functionally graded half-plane containing a Volterra screw dislocation. The elastic shear modulus of the medium is considered to vary exponentially. The dislocation solution is utilized to formulate integral equations for the half-plane weakened by multiple smooth cracks under anti-plane deformation. The integral equations are of Cauchy singular type at the location of dislocation which are solved numerically. Several examples are solved and the stress intensity factors are obtained.
Functionally Graded Plate Fracture Analysis Using the Field Boundary Element Method
2021
This paper describes the Field Boundary Element Method (FBEM) applied to the fracture analysis of a 2D rectangular plate made of Functionally Graded Material (FGM) to calculate Mode I Stress Intensity Factor (SIF). The case study of this Field Boundary Element Method is the transversely isotropic plane plate. Its material presents an exponential variation of the elasticity tensor depending on a scalar function of position, i.e., the elastic tensor results from multiplying a scalar function by a constant taken as a reference. Several examples using a parametric representation of the structural response show the suitability of the method that constitutes a Stress Intensity Factor evaluation of Functionally Graded Materials plane plates even in the case of more complex geometries.
A model for graded materials with application to cracks
International Journal of Fracture, 2003
Stress intensity factors are calculated for long plane cracks with one tip interacting with a region of graded material characteristics. The material outside the region is considered to be homogeneous. The analysis is based on assumed small differences in stiffness in the entire body. The linear extent of the body is assumed to be large compared with that of the graded region. The crack tip, including the graded region, is assumed embedded in a square-root singular stress field. The stress intensity factor is given by a singular integral. Solutions are presented for rectangular regions with elastic gradient parallel to the crack plane. The limiting case of infinite strip is solved analytically, leading to a very simple expression. Further, a fundamental case is considered, allowing the solution for arbitrary variation of the material properties to be represented by Fourier's series expansion. The solution is compared with numerical results for finite changes of modulus of elasticity and is shown to have a surprisingly large range of validity. If an error of 5% is tolerated, modulus of elasticity may drop by around 40% or increase with around 60%.