Fracture Mechanics of Thin Plates and Shells Under Combined Membrane, Bending, and Twisting Loads

[+] Author and Article Information
Alan T. Zehnder

Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853–1502 e-mail: atz2@cornell.edu

Mark J. Viz

Exponent Failure Analysis Associates, Chicago, IL 60606

Appl. Mech. Rev 58(1), 37-48 (Mar 08, 2005) (12 pages) doi:10.1115/1.1828049 History: Online March 08, 2005
Copyright © 2005 by ASME
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FEM simulation of a crack along a lap joint in a pressurized fuselage. Fuselage bulges out on one side of the lap joint, resulting in crack tip out-of-plane shearing stresses. Courtesy of Dr. V. Britt, formerly NASA Langley Aircraft Structures Branch.
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Membrane, bending, and transverse shear fracture modes for a plate with a straight through crack. Stress intensity factors corresponding to each mode are shown.
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Coordinate system at the tip of a crack in a plate or shell.
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Finite crack at angle β to the loading in an infinite plate. (a) Uniform far field transverse shearing. Moments needed for equilibrium are omitted for clarity. (b) Uniform far-field bending moment.
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Thin, cracked plate, (h/a=0.02), where h is the plate thickness and a is the crack half-length, under symmetric bending. Normal stresses at the surface versus radial distance from the crack as predicted by 3D analysis, Reissner, and Kirchhoff theories. σ0 is the far field surface tensile stress.
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Thin, cracked plate under uniform shear. Midplane shear stresses, σ32yz in figure) and σ12xy in figure) versus distance from the crack tip, along x2=0, as predicted by Kirchhoff theory and 3D FEM analysis. σ0 is the far-field mid-plane shear stress.
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Thin, cracked plate under uniform shear (h/a=0.024,ν=.3). Distributions of the shear stress σ13 through the thickness from 3D finite element analysis at different radial distances from the crack tip.
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Mixed-mode fatigue crack growth rate results. The solid (Hudson 101) and dashed (Viz 7096) lines represent the crack growth rate for pure Mode-I loading. The vertical line indicates the range of crack lengths present in this data when ΔKI=11 ksi in.R=0.7. Data are plotted only for relatively low values of k2.
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Same as Figure 7, for medium range of values of k2.
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Same as Figure 7, for relatively large values of k2.
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Fracture in plates and shells under tension and out-of-plane shearing. (a) The surfaces behind the crack can be in contact, resulting in frictional and normal tractions that shield the crack tip from the full measure of stress variation, reducing crack growth rate. (b) The loss of indexing of mating fracture surfaces due to out-of-plane displacement results in increased normal traction and shear traction due to asperities trying to slide through each other. (c) Cracks often grow on a slant in the orientation shown, resulting in greatly increased out-of-plane shear and normal shielding tractions.
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Mixed-mode fatigue crack growth rate in the absence of crack contact (dashed line) and with contact (solid line connecting points) R=0.1.




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