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.
1.
Broberg
, K. B.
, 1999, Cracks and Fracture
, Academic Press
, San Diego
.2.
Fineberg
, J.
, Gross
, S. P.
, Marder
, M.
, and Swinney
, H. L.
, 1991, “Instability in Dynamic Fracture
,” Phys. Rev. Lett.
0031-9007, 67
(4
), pp. 457
–460
.3.
Marder
, M.
, and Gross
, S.
, 1995, “Origin of Crack Tip Instabilities
,” J. Am. Soc. Mass Spectrom.
1044-0305, 43
(1
), pp. 1
–48
.4.
Abraham
, F. F.
, Brodbeck
, D.
, Rudge
, W. E.
, and Xu
, X.
, 1997, “A Molecular Dynamics Investigation of Rapid Fracture Mechanics
,” J. Am. Soc. Mass Spectrom.
1044-0305, 45
(8
), pp. 1595
–1619
.5.
Abraham
, F. F.
, Brodbeck
, D.
, Rudge
, W. E.
, Broughton
, J. Q.
, Schneider
, D.
, Land
, B.
, Lifka
, D.
, Gerner
, J.
, Rosenkrantz
, M.
, Skovira
, J.
, and Gao
, H.
, 1998, “Ab Initio Dynamics of Rapid Fracture
,” Modell. Simul. Mater. Sci. Eng.
0965-0393, 6
, pp. 639
–670
.6.
Holland
, D.
, and Marder
, M. P.
, 1998, “Ideal Brittle Fracture of Silicon Studied With Molecular Dynamics
,” Phys. Rev. Lett.
0031-9007, 80
(4
), pp. 746
–749
.7.
Slepyan
, L. I.
, Ayzenberg-Stepanenko
, M. V.
, and Dempsey
, J. P.
, 1999, “A Lattice Model for Viscoelastic Fracture
,” Mech. Time-Depend. Mater.
1385-2000, 3
, pp. 159
–203
.8.
Abraham
, F. F.
, and Gao
, H.
, 2000, “How Fast Can Cracks Propagate?
” Phys. Rev. Lett.
0031-9007, 84
(14
), pp. 3113
–3116
.9.
Abraham
, F. F.
, 2001, “The Atomic Dynamic of Fracture
,” J. Am. Soc. Mass Spectrom.
1044-0305, 49
, pp. 2095
–2111
.10.
Swadener
, J. G.
, Baskes
, M. I.
, and Nastasi
, M.
, 2002, “Molecular Dynamics Simulation of Brittle Fracture in Silicon
,” Phys. Rev. Lett.
0031-9007, 89
(8
), Ad. No. 085503
.11.
Slattery
, J. C.
, Oh
, E.-S.
, and Fu
, K.
, 2004, “Extension of Continuum Mechanics to the Nanoscale
,” Chem. Eng. Sci.
0009-2509, 59
, pp. 4621
–4635
.12.
Fu
, K.
, Robinson
, R. L.
, and Slattery
, J. C.
, 2004, “An Analysis of Supercritical Adsorption in the Context of Continuum Mechanics
,” Chem. Eng. Sci.
0009-2509, 59
, pp. 801
–808
.13.
Tadmor
, E. B.
, Philips
, R.
, and Ortiz
, M.
, 1996, “Mixed Atomistic and Continuum Models of Deformation in Solids
,” Langmuir
0743-7463, 12
, pp. 4529
–4534
.14.
Shenoy
, V. B.
, Miller
, R.
, Tadmor
, E. B.
, Philips
, R.
, and Ortiz
, M.
, 1998, “Quasicontinuum Models of Interfacial Structure and Deformation
,” Phys. Rev. Lett.
0031-9007, 80
(4
), pp. 742
–745
.15.
Knap
, J.
, and Ortiz
, M.
, 2001, “An Analysis of the Quasicontinuum Method
,” J. Mech. Phys. Solids
0022-5096, 49
(9
), pp. 1899
–1923
.16.
Xiao
, S. P.
, and Belytschko
, T.
, 2004, “A Bridging Domain Method for Coupling Continua With Molecular Dynamics
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 193
, pp. 1645
–1669
.17.
Hein
, P.
, 1914, “Untersuchungen Über den Kritischen Zustand
,” Z. Phys. Chem.
0942-9352, 86
, pp. 385
–410
.18.
Winkler
, C. A.
, and Maass
, O.
, 1933, “Density Discontinuities at the Critical Temperature
,” Can. J. Res.
0366-6581, 9
, pp. 613
–629
.19.
Maass
, O.
, 1938, “Changes in the Liquid State in the Critical Temperature Region
,” Chem. Rev. (Washington, D.C.)
0009-2665, 23
, pp. 17
–28
.20.
McIntosh
, R. L.
, Dacey
, J. R.
, and Maass
, O.
, 1939, “Pressure, Volume, Temperature Relations of Ethylene in the Critical Region II
,” Can. J. Res. Sect. B
, 17
, pp. 241
–250
.21.
Palmer
, H. B.
, 1952, “Schlieren Optical Studies of the Critical Region of Pure Substances
,” Ph.D. thesis, University of Wisconsin, Wisconsin.22.
Slattery
, J. C.
, 1990, Interfacial Transport Phenomena
, Springer-Verlag
, New York
.23.
Hamaker
, H. C.
, 1937, “The London-Van der Waals Attraction Between Spherical Particles
,” Physica (Utrecht)
0031-8914, 4
, pp. 1058
–1072
.24.
Lifshitz
, E. M.
, 1956, “The Theory of Molecular Attractive Forces Between Solids
,” Sov. Phys. JETP
0038-5646, 2
, pp. 73
–83
.25.
Israelachvili
, J. N.
, 1991, Intermolecular and Surface Forces
, Academic Press
, London
.26.
Westergaard
, H. M.
, 1934, “Stresses at a Crack, Size of the Crack and the Bending of Reinforced Concrete
,” Proc. Am. Concrete Inst.
, 30
, pp. 93
–102
.27.
Westergaard
, H. M.
, 1937, “Bearing Pressures and Cracks
,” J. Appl. Mech.
0021-8936, 6
, pp. A.49
–A.53
.28.
Williams
, M. L.
, 1957, “On the Stress Distribution at the Base of a Stationary Crack
,” J. Appl. Mech.
0021-8936, 24
, pp. 109
–114
.29.
Williams
, M. L.
, 1959, “The Stresses Around a Fault or Crack in Dissimilar Media
,” Bull. Seismol. Soc. Am.
0037-1106, 49
, pp. 199
–204
.30.
Hirschfelder
, J. O.
, Curtiss
, C. F.
, and Bird
, R. B.
, 1954, Molecular Theory of Gases and Liquids
, Wiley
, New York
, corrected with notes added, 1964.31.
Israelachvili
, J. N.
, 1973, “Van der Waals Dispersion Force Contribution to Works of Adhesion and Contact Angles on Basis of Macroscopic Theory
,” J. Chem. Soc., Faraday Trans. 2
0300-9238, 69
, pp. 1729
–1738
.Copyright © 2006
by American Society of Mechanical Engineers
You do not currently have access to this content.