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TECHNICAL PAPERS

# A Theory of Fracture Based Upon an Extension of Continuum Mechanics to the Nanoscale

[+] Author and Article Information
Eun-Suok Oh

Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843-3368

Jay R. Walton

Department of Mathematics, Texas A&M University, College Station, TX 77843-3368jwalton@math.tamu.edu

John C. Slattery

Texas A&M University, College Station, TX 77843-3368

See the recent treatise by Broberg (1), for example, for an overview of much of these developments.

J. Appl. Mech 73(5), 792-798 (Nov 23, 2005) (7 pages) doi:10.1115/1.2166651 History: Received December 22, 2004; Revised November 23, 2005

## Abstract

A theory of fracture is presented that is based upon an extension of continuum mechanics to the nanoscale through the incorporation of long-range intermolecular forces which correct bulk material descriptions near interfaces. The surface energy on crack surfaces, which is given in terms of the long-range intermolecular forces, plays an important role in an expression for the stress distribution near the crack tip. It is observed through numerical simulation that the incorporation of these long-range intermolecular forces removes the square-root stress singularity predicted by classical linear elastic fracture mechanics.

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## Figures

Figure 1

Schematic of Mode I fracture of phase C in phase A

Figure 2

δ is the distance separating the two phases A and C, corresponding physically to the sum of the effective radii of the A and C molecules or the effective distance between molecules of A and C ((11), p. 4623). The dividing surface h(x) is located halfway between the two phases.

Figure 3

Dimensionless crack configurations h⋆ for different σ0⋆ and δ⋆⋆. Here we have used E=100GPa, δ=0.2nm(11,25,31) and a=10nm.

Figure 4

Dimensionless surface energy γ⋆ for σ0⋆=10−4 and δ⋆⋆=2.50. Here we have used E=100GPa, δ=0.2nm(11,25,31), and a=10nm.

Figure 5

Dimensionless stress distribution T22(I,bulk)⋆ on the fracture axis for σ0⋆=10−4 and δ⋆⋆=2.50. Here we have used E=100GPa, δ=0.2nm(11,25,31), and a=10nm; r* indicates the distance from the crack tip.

## Errata

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