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Special Issue Honoring Professor Fazil Erdogan’s Contributions to Mixed Boundary Value Problems of Inhomogeneous and Functionally Graded Materials

Fracture Mechanics of Periodic Multilayers With Different Microstructural Scales and Moduli Contrast

[+] Author and Article Information
Linfeng Chen

 Gilsanz, Murray & Steficek LLP, Structural Engineers, New York, NY 10001

Marek-Jerzy Pindera

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

J. Appl. Mech 75(5), 051109 (Jul 11, 2008) (11 pages) doi:10.1115/1.2936236 History: Received June 20, 2007; Revised September 30, 2007; Published July 11, 2008

In a recent investigation of microstructural effects in finite periodic multilayers, we have shown that under Mode I loading, the crack-opening displacement approaches that of the same crack in an equivalent homogenized material as the microstructure comprised of alternating stiff and soft layers becomes increasingly finer. In contrast, Mode I stress intensity factor asymptotically converges to values that depend on the stiffness of the cracked layer. Preliminary calculation of Mode I strain energy release rate as a function of the microstructural refinement suggested that this may be a better fracture mechanics parameter for assessing fracture toughness of periodic layered media. Herein, we extend the above investigation by considering both Mode I and II loading to study the effect of layer modulus ratio on fracture mechanics parameters as a function of microstructural refinement. The previously introduced concept of partial homogenization of the microstructure sufficiently far from the crack is also pursued in order to gauge its efficiency in correctly capturing fracture mechanics parameters with a minimum of computational effort. The fracture mechanics parameters are shown to be influenced by the local microstructure to an extent that depends on the layer modulus mismatch. An accurate calculation of these parameters requires the retention of several layers adjacent to the affected cracked layer whose number depends on the modulus mismatch and loading mode.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 4

Comparison of the crack-opening displacements under Mode I loading in the actual 2n+1=201 and homogenized multilayers with the elastic moduli layer ratios Eh∕Es=20,10,2: (a) crack in hard layer and (b) crack in soft layer

Grahic Jump Location
Figure 5

(a) Normalized Mode II stress intensity factor KII∕KIIPostma and (b) normalized Mode II strain energy release rate GII∕GIIPostma of the crack embedded in hard (filled symbols) and soft (open symbols) layers as a function of the layer refinement 2n+1 for the elastic moduli ratios Eh∕Es=20,10,2

Grahic Jump Location
Figure 7

(a) Normalized Mode I stress intensity factor KI∕KIdiscrete and (b) normalized Mode I strain energy release rate GI∕GIdiscrete of the crack embedded in a hard (filled symbols) and soft (open symbols) layer as a function of the number of retained layers for the elastic moduli ratios Eh∕Es=20,10,2 and a multilayer with 101 discrete layers

Grahic Jump Location
Figure 8

(a) Normalized Mode II stress intensity factor KII∕KIIdiscrete and (b) normalized Mode II strain energy release rate GII∕GIIdiscrete of the crack embedded in hard (filled symbols) and soft (open symbols) layers as a function of the number of retained layers for the elastic moduli ratios Eh∕Es=20,10,2 and a multilayer with 101 discrete layers

Grahic Jump Location
Figure 1

Periodic multilayers with increasingly finer microstructural scales, constructed with RUCs containing the same proportion of the individual layers (after Hornung (4))

Grahic Jump Location
Figure 2

Geometry of the (2n+1)-layered structure with alternating soft and hard layers weakened by a single centrally positioned crack subjected to tractions applied to the crack faces: (a) fully discrete and (b) partially homogenized microstructures

Grahic Jump Location
Figure 3

(a) Normalized Mode I stress intensity factors KI∕KIPostma and (b) normalized Mode I strain energy release rate GI∕GIPostma of the crack embedded in a hard (filled symbols) and soft (open symbols) layer as a function of the layer refinement 2n+1 for the elastic moduli ratios Eh∕Es=20,10,2

Grahic Jump Location
Figure 6

Comparison of the crack-opening displacements under Mode II loading in the actual 2n+1=201 and homogenized multilayers with the elastic moduli layer ratios Eh∕Es=20,10,2: (a) crack in hard layer and (b) crack in soft layer

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