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Research Papers

A Strain Gradient Model for Fracture Prediction in Brittle Materials

[+] Author and Article Information
Jia Li1

LPMTM, CNRS UPR 9001, Université Paris XIII, 99 Avenue Jean-Baptiste Clément, 93430 Villetaneuse, Francejia.li@lpmtm.univ-paris13.fr

1

Corresponding author.

J. Appl. Mech 75(2), 021004 (Feb 20, 2008) (9 pages) doi:10.1115/1.2775498 History: Received September 25, 2006; Revised July 09, 2007; Published February 20, 2008

In this paper, we present a new model to predict the fracture in brittle materials from a geometrical weakness presenting an arbitrary stress concentration. The main idea is to combine the strain gradient elasticity with a cohesive model that includes both the displacement and the rotation jumps between the cohesive surfaces in the separation law. Three material parameters were used in the establishment of the fracture criterion. The first two parameters are the commonly used σc, the ultimate stress, and Gc, the critical energy release rate. The third parameter is the characteristic length l as in most of the strain gradient models. The proposed three-parameter model enables to take the different stress concentration levels into account, thus providing a criterion to predict fractures for any stress concentration, whether it is singular or not. Experimental results were selected to verify the accuracy and efficiency of the criterion. It was shown that the proposed model is physically reasonable, highly accurate, and easy to apply. It can be used in crack initiation prediction of engineering structures made of brittle materials.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Separation laws between cohesive surfaces

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Figure 2

A deformed infinitesimal cohesive element

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Figure 3

Hybrid strain gradient bidimensional elements: (a) a 6-noded element and (b) a height-noded element

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Figure 4

Cohesive element

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Figure 5

A typical mesh of the finite element models

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Figure 6

Predicted critical loads at fracture with different length parameters l

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Figure 7

Predicted critical loads at fracture with different cohesive models

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Figure 8

Predicted critical loads at fracture with different critical strain energy release rates gGc

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Figure 9

Predicted critical loads at fracture with different values of lc(l=0.5mm)

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