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TECHNICAL PAPERS

Cohesive Modeling of Quasi-Static Fracture in Functionally Graded Materials

[+] Author and Article Information
Soma Sekhar Kandula1

Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, 306 Talbot Lab, 104 S. Wright Street Urbana, IL 61801skandula@uiuc.edu

Jorge Abanto-Bueno

Department of Mechanical Engineering, Bradley University, 1501 W. Bradley Avenue Peoria, IL 61625

John Lambros, Philippe H. Geubelle

Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, 306 Talbot Lab, 104 S. Wright Street Urbana, IL 61801

1

To whom correspondence should be addressed.

J. Appl. Mech 73(5), 783-791 (Nov 07, 2005) (9 pages) doi:10.1115/1.2151210 History: Received December 20, 2004; Revised November 07, 2005

A spatially varying cohesive failure model is used to simulate quasi-static fracture in functionally graded polymers. A key aspect of this paper is that all mechanical properties and cohesive parameters entering the analysis are derived experimentally from full-scale fracture tests allowing for a fit of only the shape of the cohesive law to experimental data. The paper also summarizes the semi-implicit implementation of the cohesive model into a cohesive-volumetric finite element framework used to predict the quasi-static crack initiation and subsequent propagation in the presence of material gradients.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Details of the ECO SENT FGM specimens used in the experimental study

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Figure 2

Spatial variation of normalized material properties in the material gradient direction of ECO SENT FGM I (a) and FGM II (b) specimens used in the validation study. The maximum values of the material properties, λmax, are given in Table 1. The dashed vertical lines mark the initial crack-tip location. The symbols represent the experimental data, and the curves correspond to their fit using a piecewise exponential or linear functions defined in the Appendix. The width of the specimen is 150mm, and a0 is the initial crack length.

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Figure 3

DIC technique used in the deformation measurements of a SENT specimen: (a) undeformed state, (b) deformed state, (c) vector plot of the measured in-plane displacement field for the instant shown in (b), and (d) contours of opening displacement comparing measured (dotted-dashed line) and theoretical (solid line) values. In (c) and (d), the x-axis is parallel to the crack line and the crack tip is located at the coordinate origin.

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Figure 4

Fracture resistance (GIc) curves for ECO FGM I and FGM II along with the experimental data (symbols) versus location x. The origin of the coordinate system is defined at the initial crack-tip location.

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Figure 5

(a) Schematic of the CVFE concept, showing a cohesive element introduced between two volumetric elements. The cohesive element is shown its deformed state: originally it has no thickness and the adjacent nodes are superposed. It behaves like distributed nonlinear cohesive springs connecting the adjacent volumetric edges. (b) Schematic of the bilinear cohesive model for mode I. The dashed line shows potential unloading and reloading paths.

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Figure 6

Details of the finite element mesh used in the validation study with the inset showing a close view of the initial crack tip

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Figure 7

Snapshot of a 300h homogeneously UV-irradiated ECO fracture specimen showing the extent of the crazing ahead of the crack tip

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Figure 8

(a) Evolution of the reaction R and crack length Δa curves of FGM I SENT specimen as a function of the applied displacement Uapp for four different values of Sinitial: 0.98, 0.8, 0.7, and 0.6. The close-up of the crack propagation curves is plotted in the inset for clarity. The dashed curves correspond to the experimental measurements. (b) Evolution of the cohesive zone length with Uapp for the same four values of Sinitial.

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Figure 9

Comparison between the numerically predicted crack advance (Δa) and corresponding reaction force (R) curves with the experimentally observed counterparts for five different FGMs used in the sensitivity analysis, as a function of applied displacement (Uapp). A Sinitial value of 0.98 is used in this study.

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Figure 10

Comparison between the numerically predicted crack advance (Δa) and corresponding reaction force (R) curves with the experimentally observed counterparts as a function of the applied displacement (Uapp), assuming a peak separation stress of 0.95σmax(x): (a) ECO FGM I SENT specimen and (b) ECO FGM II SENT specimen.

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Figure 11

COD distribution Δn(x) along the fracture plane normalized with the local critical separation Δnc(x) values computed at the four points of interest, denoted by symbols in the inset, on the reaction versus applied displacement curve for ECO FGM I and with Sinitial of 0.8. The intersection of the curves with the top and bottom horizontal dashed lines mark the crack-tip and the cohesive zone tip locations, respectively.

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