Axsiymmetric crack problem in bonded materials with a graded interfacial region

Öztürk, Murat; Erdoğan, F.

doi:10.1016/0020-7683(95)00034-8

Cited by 125 publications

(64 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In an attempt to address the issues pertaining to fracture analysis of bonded media with such transitional interfacial properties, a series of solutions to certain crack problems was obtained by Erdogan and his associates [Delae and Erdogan 1988;Ozturk and Erdogan 1996].…”

Section: Introductionmentioning

confidence: 99%

The nonlocal theory solution of a mode-I crack in functionally graded materials subjected to harmonic stress waves

Zhou

Liang

2006

JOMMS

View full text Add to dashboard Cite

In this paper, the dynamic behavior of a finite crack in functionally graded materials subjected to harmonic stress waves is investigated by means of nonlocal theory. The traditional concepts of nonlocal theory are extended to solve the dynamic fracture problem of functionally graded materials. To overcome mathematical difficulties, a one-dimensional nonlocal kernel is used instead of a twodimensional one for the dynamic problem to obtain the stress fields near the crack tips. To make the analysis tractable, it is assumed that the shear modulus and the material density vary exponentially and vertically with respect to the crack. Using the Fourier transform and defining the jumps of the displacements across the crack surfaces as the unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Unlike classical elasticity solutions, it is found that no stress singularities are present near crack tips. Numerical examples are provided to show the effects of the crack length, the parameter describing the functionally graded materials, the frequency of the incident waves, the lattice parameter of the materials and the material constants upon the dynamic stress fields near crack tips.

show abstract

Section: Introductionmentioning

confidence: 99%

The nonlocal theory solution of a mode-I crack in functionally graded materials subjected to harmonic stress waves

Zhou

Liang

2006

JOMMS

View full text Add to dashboard Cite

show abstract

“…Similar to the treatment of the crack problem for isotropic non-homogeneous materials in Refs. [2,3], we assume the material properties are described as follow:…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…In an attempt to address the issues pertaining to the fracture analysis of bonded media with such transitional interfacial properties, a series of solutions to certain crack problems were obtained by Erdogan and his associates [2,3] . To our best knowledge, only a few open literature studied the multiple-crack problems in functionally graded materials [4]- [7] .…”

Section: Introductionmentioning

confidence: 99%

Multiple Parallel Symmetric Mode-III Cracks in a Functionally Graded Material Plane

Yang

2009

JMMP

View full text Add to dashboard Cite

In this paper, the basic solutions of multiple parallel symmetric finite length cracks in a functionally graded material plane subjected to anti-plane shear stress loading were studied by the Schmidt method. The problem was formulated through Fourier transform into dual integral equations, respectively, in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. The results show that the stress intensity factors at the crack tips depend on the crack lengths, spacing of the cracks and the functionally graded parameter. It is also revealed that the crack shielding effect presents in functionally graded materials.

show abstract

“…However, the numerical evaluation of the integrals in these studies is fraught with complete regularization of the kernels by ignoring the logarithmic singularities and thus the convergence difficulty. Therefore, logarithmic singularities have to be taken into account in the numerical analysis as suggested by Ozturk and Erdogan [1996].…”

Section: Introductionmentioning

confidence: 99%

Hypersingular integral equations for the solution of penny-shaped interface crack problems

Kilic

Madenci

2007

JOMMS

View full text Add to dashboard Cite

Based on the theory of elasticity, previous analytical solutions concerning a penny-shaped interface crack employ the derivative of the crack surface opening displacements as the primary unknowns, thus leading to singular integral equations with Cauchy-type singularity. The solutions to the resulting integral equations permit only the determination of stress intensity factors and energy release rate, and do not directly provide crack opening and sliding displacements. However, the crack opening and sliding displacements are physically more meaningful and readily validated against the finite element analysis predictions and experimental measurements. Therefore, the present study employs crack opening and sliding as primary unknowns, rather than their derivatives, and the resulting integral equations include logarithmic-, Cauchy-, and Hadamard-type singularities. The solution to these singular integral equations permits the determination of not only the complex stress intensity factors but also the crack opening displacements.

show abstract

Axsiymmetric crack problem in bonded materials with a graded interfacial region

Cited by 125 publications

References 22 publications

The nonlocal theory solution of a mode-I crack in functionally graded materials subjected to harmonic stress waves

The nonlocal theory solution of a mode-I crack in functionally graded materials subjected to harmonic stress waves

Multiple Parallel Symmetric Mode-III Cracks in a Functionally Graded Material Plane

Hypersingular integral equations for the solution of penny-shaped interface crack problems

Contact Info

Product

Resources

About