Localization, Delocalization, and Compression Fracture in Moderately Thick Transversely Isotropic Bilinear Rings Under External Pressure

[+] Author and Article Information
Reaz A. Chaudhuri

Department of Materials Science & Engineering, University of Utah, Salt Lake City, UT 84112-0560r.chaudhuri@m.cc.utah.edu

J. Eng. Mater. Technol 128(4), 603-610 (Jul 11, 2006) (8 pages) doi:10.1115/1.2345453 History: Received August 10, 2005; Revised July 11, 2006

A fully nonlinear finite element analysis for prediction of localization∕delocalization and compression fracture of moderately thick imperfect transversely isotropic rings, under applied hydrostatic pressure, is presented. The combined effects of modal imperfections, transverse shear∕normal deformation, geometric nonlinearity, and bilinear elastic (a special case of hypoelastic) material property on the emergence of interlaminar shear crippling type instability modes are investigated in detail. An analogy to a soliton (slightly disturbed integrable Hamiltonian system) helps understanding the localization (onset of deformation softening) and delocalization (onset of deformation hardening) phenomena leading to the compression damage∕fracture at the propagation pressure. The primary accomplishment is the (hitherto unavailable) computation of the mode II fracture toughness (stress intensity factor∕energy release rate) and shear damage∕crack bandwidth, under compression, from a nonlinear finite element analysis, using Maxwell’s construction and Griffith’s energy balance approach. Additionally, the shear crippling angle is determined using an analysis, pertaining to the elastic plane strain inextensional deformation of the compressed ring. Finally, the present investigation bridges a gap of three or more orders of magnitude between the macro-mechanics (in the scale of mms and up) and micro-mechanics (in the scale of microns) by taking into account the effects of material and geometric nonlinearities and combining them with the concepts of phase transition via Maxwell construction and Griffith-Irwin fracture mechanics.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

(a) Nomenclature and geometry of an imperfect ring. (b) Shape of a quarter-ring with modal imperfection.

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Figure 2

Bilinear strain hardening material behavior

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Figure 3

Effect of strain hardening parameter, n=E′∕E, on the computed equilibrium paths of a moderately thick (Ri∕h=17.86) ring with modal imperfections (σY∕E=0.0035)

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Figure 4

Variation of (a) normalized peak pressure and (b) normalized deflection at peak pressure, with respect to the inverse hardening parameter, 1∕n=E∕E′

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Figure 5

Maxwell diagram for computation of propagation pressure in a moderately thick ring (Ri∕h=17.86, w0=0.008*Ri, n=0.5)

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Figure 6

Dependence of normalized propagation pressure on log(1∕n)

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Figure 7

Idealization of an initial localized dent or shear damage

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Figure 8

Dependence of (a) maximum mode II stress intensity factor and (b) energy release rate in compression on log(1∕n)

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Figure 9

Variation of normalized shear crack width with respect to the inverse hardening parameter, 1∕n=E∕E′



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