Some elasticity problems in fiber-reinforced composites with imperfect bonds

Özbek, Tuğba

doi:10.1016/0020-7225(69)90085-8

Cited by 25 publications

(9 citation statements)

References 3 publications

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“…In both figures the stress drops more rapidly for smaller values of z. For large values of z, in fact, the axial stress az asymptotically approaches the Lam~ solution given by (15); the limit decreases as rapidly as 1/r. Therefore, for smaller values, it decreases much faster, i.e.…”

Section: 0mentioning

confidence: 80%

“…Moreover,~ this part of the solution also satisfies the stress boundary conditions given by (9) and, of course, the equilibrium condition. Hence, by adding equations (15) to those given by (11) we obtain the complete solution to the Somigliana ring dislocation depicted in Fig. 1, i.e.…”

Section: The Lm6 Problem: the "Homogeneous" Partmentioning

confidence: 99%

“…For example, Erdogan and Ozbek [ 14] and Ozbek and Erdogan [15] provided the formulation for the cylindrical crack in fibermatrix composites in terms of dislocation densities used to model the discontinuity across the crack. Recent works along the same lines have been presented by Kasano et al [ 16,17] for anisotropic materials and by Farris et al [ 18] for isotropic materials.…”

Section: Introductionmentioning

confidence: 99%

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The Somigliana ring dislocation

1992

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Abstrset. A basic elasticity solution applicable to an important class of internal stress problems related, for example, to fiber-matrix composites and spalling of cylindrical coatings is obtained. The basic problem that has been solved is that of the slnsular stress-displacement field resulting from the introduction of a Somigliana ring dislocation in an isotropic linear elastic solid. The Burgers vector of this dislocation has two components, one being normal to the plane of the circular ring dislocation (Vulterra type) and the other being in the radial direction of the ring dislocation everywhere (Somigliana type). The analytical solution, in terms of complete elliptic integrals of the first, second and third kinds, is obtained using the Love stress function and Fourier transform. The results are verified numerically and by examining various limiting cases, including the straight edge dislocation as the radius of the dislocation loop tends to infinity, the orthogonal pair of dipoles as the radius tends to zero, and the Lam~ solution of a cylindrical bar and a cylindrical hole in an infinite medium as the axial location of the dislocation tends to minus infinity. The resulting analytical solution is considered as a step towards evaluating both the extended stress field around and interactions among various three-dimensional defects such as cylindrical cracks, fiber-tips and fiber-matrix debonding. AMS mbjeet ~tioa (19~0): 73S05. List of symbols ~b = Love stress function a, = Radial stress ~o = Transveric stress a~ = Axial stress a,z = Shear stress u = Radial displacement w = Axial displacement z, r = Axial and radial coordinates v = Poisson's ratio G = Shear modulus of elasticity b = Burgers vector b~ --Radial Burgers vector b2 = Axial Burgers vector R = Radius of ~ircular dislocation loop ~ = Fourier transform variable Io, 11 = Modified Bessel functions of the first kind Ko, KI = Modified Bessel functions of the second kind K('), E(.), II(.) = Complete elliptic integrals of the first, second and third kind, respectively. A = 4 × 3 matrix B = 2 × 2 matrix H(') = Heaviside step function 6(') = Dirac delta function

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Section: 0mentioning

confidence: 80%

Section: The Lm6 Problem: the "Homogeneous" Partmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Somigliana ring dislocation

1992

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“…The solution of the wedge problem shown in Figure 8 with r` and without a crack initiating at thi apex will appear elsewhere. The application of the technique described in this section to singular integral equations of the second kind with complex coefficients may be found in [31], [33], [42] and [43]. Extension of the technique to a system of equations in which A, B, and k(x,y) are square matrices is given in [44] and [251. : .…”

Section: Singular Integral Equations Of the Second Kindmentioning

confidence: 99%

Mixed Boundary-value Problems in Mechanics

1978

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“…The initial impetus for this research stems from the work of Erdogan and Ozbek (1969) and Ozbek and Erdogan (1969). There is a limited literature available on the analysis of cylindrical cracks occurring in fiber reinforced composites due to delamination along the fiber matrix interface.…”

Section: Introductionmentioning

confidence: 99%

Cylindrical crack vis a vis parallel crack pair: shielding, energetics and asymptotics

Ramesh

Simha

2008

Int J Fract

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Fibrous materials often contain cylindrical cracks due to delamination along the matrix-fiber interface. It is instructive to analyse a cylindrical crack of length 2a and diameter 2h in a homogeneous medium and compare the results with those for a pair of parallel cracks of length 2a and spacing 2h. The pair of parallel cracks mutually shielding each other is examined here with regard to the variation of stress intensity factors and energetics including the asymptotic limit of a pair of nearly coalescing parallel cracks. A unified formulation for parallel cracks/cylindrical crack based on crack opening displacement (COD) in terms of Chebyshev polynomials is developed. The characteristic variation of stress intensity factors as the cracks approach each other (h → 0) shows that the stress intensity factors vanish for the case of a vanishingly small cylindrical crack but not for the 2D parallel pair of cracks. The 2D case of a pair of collapsing parallel cracks ensures a finite energy release rate asymptoting to that of a single crack. Further research is needed to establish definitive asymptotic bounds for the case of extremely closely spaced cracks on the lines of Hutchinson and Suo (Adv

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Some elasticity problems in fiber-reinforced composites with imperfect bonds

Cited by 25 publications

References 3 publications

The Somigliana ring dislocation

The Somigliana ring dislocation

Mixed Boundary-value Problems in Mechanics

Cylindrical crack vis a vis parallel crack pair: shielding, energetics and asymptotics

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