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TECHNICAL PAPERS

Plane Analysis of Finite Multilayered Media With Multiple Aligned Cracks—Part II: Numerical Results

[+] Author and Article Information
Linfeng Chen, Marek-Jerzy Pindera

Civil Engineering Department, University of Virginia, Charlottesville, VA 22904-4742

J. Appl. Mech 74(1), 144-160 (Apr 01, 2006) (17 pages) doi:10.1115/1.2201889 History: Received December 18, 2005; Revised April 01, 2006

In Part I of this paper, elasticity solutions were developed for finite multilayered domains, weakened by aligned cracks, that are in a state of generalized plane deformation under two types of end constraints. In Part II we address computational aspects of the developed solution methodology that must be implemented numerically, and present new fundamental results that are relevant to modern technologically important applications involving defect criticality of multilayers. The computational aspects include discussion of the various parameters that influence the accuracy with which numerical results are generated and subsequent verification by a comparison with previously reported results in the limit, as the in-plane dimensions become very large and layer anisotropy vanishes. The present solution quantifies the thus far undocumented effects of finite dimensions, crack location, and material anisotropy due to a unidirectional fiber-reinforced layer’s orientation on Mode I, II, and III stress intensity factors in composite multilayers with single and multiple interacting cracks under different loading and boundary conditions. These effects may have significant impact on defect criticality of advanced multilayered structures when cracks are in close proximity to vertical and horizontal boundaries.

Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Convergence of the A11m(αβ) and A12m(αβ) elements with the harmonic number m for a two-layer unidirectional graphite/epoxy laminate with three fiber rotations about the z axis and increasingly thinner top layers characterized by μ=h1∕H=0.5, 0.01 (top and bottom)

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Figure 2

Surface plot of Ω(x,x′) in the nondimensionalized space

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Figure 3

Convergence of Chebyshev polynomial coefficients used in approximating the crack opening displacements of two collinear cracks with different separation distances in an infinite isotropic plate under pure Mode I loading

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Figure 4

Surface plots of the h11(pq)(x,x′) elements for the three normalized separation distances rd∕2a=0.1, 0.01, 0.001 (top, middle and bottom): (a)-(c) two collinear crack interaction; (d)-(f) single crack interaction with vertical boundary

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Figure 5

Effective moduli of the graphite/epoxy unidirectional composite as a function of the fiber rotation angle θ about the z axis

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Figure 6

Repeating unit cell of a transversely isotropic graphite/epoxy unidirectional composite with 65% fiber content used in the FVDAM calculation of the homogenized elastic properties. The hexagonal fiber arrangement in the 2−3 plane ensures transverse isotropy in this plane.

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Figure 7

Elements of the matrix B¯α* of the graphite/epoxy unidirectional composite as a function of the fiber rotation angle θ about the z axis

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Figure 8

Geometry of the single-crack problem, showing the geometric parameters used in the numerical study

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Figure 9

Normalized Mode I stress intensity factor KI∕KI∞ as a function of the fiber rotation angle θ for a square plate with a centrally positioned crack of increasingly larger crack lengths characterized by the ratios η=L∕2a=100, 5, 1.2

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Figure 10

Normalized Mode I stress intensity factor KI∕KI∞ as a function of the ratio η=L∕2a for a rectangular plate with a centrally positioned crack and the rotation angle θ=90deg characterized by the ratios ρ=H∕L=1.0, 0.5, 0.2, 0.1

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Figure 11

Normalized Mode I, II and III stress intensity factors KI∕KI∞, KII∕KI∞, KIII∕KI∞ as a function of the fiber rotation angle θ for a square plate with a centrally positioned crack increasingly closer to the upper surface, demonstrating the effect of the crack tip interaction with vertical boundaries controlled by the η ratio for (a)-(c)η=L∕2a=100; (d)-(f)η=L∕2a=1.2

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Figure 12

Geometry of the interacting two-crack problem

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Figure 13

Normalized Mode I, II and III stress intensity factors KI∕KI∞, KII∕KI∞, KIII∕KI∞ at the inner and outer tips of two collinear cracks separated by the normalized distance rd∕2a=0.1 at increasingly closer normalized distances μ=h1∕H to the upper surface of a large square plate (η=L∕2a=100) as a function of the fiber rotation angle θ

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Figure 14

Normalized Mode I stress intensity factor KI∕KI∞ at the inner and outer tips of two collinear cracks centrally positioned (μ=h1∕H=0.5) in a large square plate with the rotation angle θ=90deg as a function of the normalized distance rd∕2a

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Figure 15

Normalized stress intensity factors KI∕KI∞, KII∕KI∞ and KIII∕KI∞ at the inner tips of two horizontal cracks that are offset by ϕ=45deg in the middle of a plate as a function of the fiber rotation angle θ, illustrating the effects of: (a)-(c) normalized separation distance ri∕2a=0.1,0.2 for a large square plate with η=L∕2a=100; (d)-(e) plate aspect ratio ρ=H∕L=0.2, 0.5, 1.0 for the separation distance rd∕2a=0.1 and a smaller plate with (η=L∕2a=5).

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Figure 16

Geometry of the layered configurations with vertically situated multiple cracks: (a) vertically stacked cracks in single column; (b) diagonally stacked cracks in an echelon array

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Figure 17

Normalized stress intensity factors KI∕KIper and KII∕KIper at the tips of vertically stacked cracks at different distances from the top surface of rectangular layers with the fiber rotation angles θ=0deg, 90deg subjected to a uniform external pressure. The normalized vertical crack spacing is d∕2a=0.5 and the crack-to-layer length ratio is η=L∕2a=10.

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Figure 18

Normalized stress intensity factors KI∕KI10, KII∕KI10 and KIII∕KI10 at the tips of diagonally stacked cracks at different distances from the top surface of rectangular layers subjected to a uniform vertical displacement as a function of the fiber rotation angle θ: (a)-(c) spatially uniform θ; (d)-(f) functionally graded θ. The normalized vertical crack spacing is d∕2a=0.5, and the crack-to-layer length ratio is η=L∕2a=30

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