Nanomechanics of Defects in Solids

Advances in Applied Mechanics

Volumn 36, Issue C, 1998, Pages

  Ortiz, Michael ^a   Phillips, Rob ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b Brown University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77956688585     PISSN: 00652156     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0065-2156(08)70184-4     Document Type: Article

References (149)

1. Abraham F.F., and Broughton J.Q. Pulsed melting of silicon (111) and (100) surfaces simulated by molecular dynamics. Phys. Rev. Lett. 56 7 (1986) 734-737
2. Abraham F.F., Schneider D., Land B.D.L., Skovira J., Gerner J., and Rosenkrantz M. Instability dynamics in the 3-dimensional fracture-an atomistic simulation. J. Mech. Phys. Solids 45 9 (1997) 1461-1471
3. Acioli P.H. Review of quantum Monte Carlo methods and their applications. Theochem J. Molecular Structure 394 2-3 (1997) 75-85
4. Ackland G.J., Tichy G., Vilek V., and Finnis M.W. Simple n-body potentials for the noble metals and nickel. Philos. Mag. A 56 6 (1987) 735-756
5. Akgun I. Phonon dispersion in Cu-Zn alloy. Acta Phys. Polon. A 84 6 (1993) 1055-1058
6. Alexander H. Dislocations in covalent crystals. In: Nabarro F.R.N. (Ed). Dislocations in Solids 7 (1986), North-Holland, Amsterdam 114-234
7. Argon A.S. Brittle to ductile transition in cleavage fracture. Acta Metallurgica 35 (1987) 185-196
8. Babuska I., Vitasek E., and Kroupa F. Some applications of the discrete Fourier transform to problems of crystal lattice deformation. I, II. Czechoslovak J. Phys. B 10 (1960)
9. Bacon D.J., Barnett D.M., and Scattergood R.O. Anisotropic continuum theory of lattice defects. Progr. Material Sci. 23 (1979) 51-262
10. Ball J.M., and James R.D. Fine phase mixtures as minimizers of energy. Arch. Rational Mech. Anal. 100 (1987) 13-52
11. Barnett D.M., and Swanger L.A. The elastic energy of a straight dislocation in an infinite anisotropic elastic medium. Phys. Status Solidi B 48 (1971) 419-428
12. Baskes M.I., and Johnson R. Modified embedded atom potentials for HCP metals. Modelling and Simulation in Materials Science and Engineering 2 (1994) 147-163
13. Baskes M.I., Angelo J.E., and Bisson C.L. Atomistic calculations of composite interfaces. Modelling and Simulation in Materials Science and Engineering 2 3A (1994) 505-518
14. Baskes M.I., Hoagland R.G., and Needleman A. Summary report-computational issues in the mechanical behavior of metals and intermetallics. Materials Sci. Engrg. A 159 (1992) 1-34
15. M.I. Baskes R.G. Hoagland T. Tsuji (1997). An atomistic study of the strength of an extended dislocation barrier (in preparation)
16. Baskes M.I., Nelson J., and Wright A.F. Semi-empirical modified embedded atom potentials for silicon and germanium (1989), Sandia National Laboratories, Livermore, CA Technical Report SAND89-8496
17. Beltz G.E., and Rice J.R. Dislocation nucleation versus cleavage decohesion at crack tips. In: Lowe T.C., Rollett A.D., Follansbee P.S., and Daehn G.S. (Eds). Modeling the Deformation of Crystalline Solids: Physical Theory, Application and Experimental Comparisons (1991), TSM-AIME, Warrendale, PA 457-480
18. Belytschko T., and Tabbara M. H-adaptive finite element methods for dynamic problems, with emphasis on localization. Internat. J. Numer. Methods Engrg. 36 (1993) 4245-4265
19. Born M., and Huang K. Dynamical Theory of Crystal Lattices. (1954), Oxford Univ. Press, London
20. Bourret A., Desseaux J., and Renault A. Core structure of the lomer dislocation in germanium and silicon. Philos. Mag. A 45 1 (1982) 1-20
21. Boyer L.L., and Hardy J.R. Lattice statics applied to screw dislocations in cubic crystals. Philos. Mag. 24 (1971) 647-671
22. Brede M., and Haasen P. The brittle-to-ductile transition in doped silicon as a model substance. Acta Metallurgies 36 (1988) 2003-2018
23. Brede M., Hsia K.J., and Argon A.S. Brittle crack propagation in silicon single crystals. J. Appl. Phys. 70 (1991) 758-771
24. Bulatov V.V., Yip S., and Argon A.S. Atomic modes of dislocation mobility in silicon. Philos. Mag. A 72 (1995) 453-496
25. Bullough R., and Tewary V.K. Lattice theory of dislocations. In: Nabarro F.R.N. (Ed). Dislocations in Solids 2 (1979), North-Holland, Amsterdam 1-65
26. Carlsson A.E. Beyond pair potentials in elemental transition metals and semiconductors. Solid State Phys. 43 (1990) 1-91
27. Celli V. Screw dislocation in crystals with diamond structure. J. Phys. Chem. Solids 19 1/2 (1961) 100-104
28. Chaikin P.M., and Lubensky T.C. Principles of Condensed Matter Physics. (1995), Cambridge Univ. Press
29. Chantasiriwan S., and Milstein F. Higher-order elasticity of cubic metals in the embedded-atom method. Phys. Rev. B 53 21 (1996) 14080-14088
30. Chiao Y.-H., and Clarke D.R. Direct observation of dislocation emission from crack tips in silicon at high temperatures. Acta Metallurgica 47 (1989) 203-219
31. Chipot M., and Kinderlehrer D. Equilibrium configurations of crystals. Arch. Rational Mech. Anal. 103 (1988) 237-277
32. Chu C., and James R.D. Analysis of microstructures in Cu-14%-Al-3.9%-Ni by energy minimization. J. Physique IV 5 C8 (1995) 143-149
33. Clark W.A.T., Wagoner R.H., Zhen Z.Y., Lee T.C., Robertson I.M., and Birnbaum H.K. On the criteria for slip transmission across interfaces in polycrystals. Scripta Metallurgica Materialia 26 (1992) 203-206
34. Clark W.A.T., Wise C.E., Shen Z., and Wagoner R.H. The use of the transmission electron microscope in analyzing slip propagation across interfaces. Ultramicroscopy 30 (1989) 76-89
35. Cottrell A.H. Dislocations and Plastic Flow in Crystals. (1953), Oxford Univ. Press
36. Dacorogna B. Direct Methods in the Calculus of Variations. (1989), Springer-Verlag, New York
37. Nabarro F.R.N. Dislocations in a simple cubic lattice. Proc. Roy. Soc. London Ser. A 59 (1947) 256
38. 3V measured by inelastic scattering and cryogenic calorimetry. Philos. Mag. B 75 (1997) 681-699
39. 3V. Philos. Mag. B 18 (1997) 21-23
40. 3V. Phys. Rev. B 55 (1997) 2903-2911
41. Nandedkar A.S., and Narayan J. Atomic structure of dislocations in silicon, germanium and diamond. Philos. Mag. A 61 6 (1990) 873-891
42. Needleman A. A continuum model for void nucleation by inclusion debonding. J. Appl. Mech. 54 (1987) 525-531
43. Needleman A. An analysis of decohesion along an imperfect interface. Internal. J. Fracture 42 (1990) 21-40
44. Needleman A. An analysis of tensile decohesion along an interface. J. Mech. Phys. Solids 38 3 (1990) 289-324
45. Oh D.J., and Johnson R.A. Simple embedded atom model for FCC and hcp metals. J. Materials Res. 3 3 (1988) 471-478
46. Ortiz M., and Pandolfi A. A class of cohesive elements for the simulation of three-dimensional crack propagation. Internat. J. Numer. Methods Engrg. (1998) (in press)
47. Ourmazd A. The electrical properties of dislocations in semiconductors. Contemp. Phys. 25 3 (1984) 251-268
48. 2 ordered alloys. Acta Metallurgica 32 (1984) 435-448
49. Peierls R.E. The size of a dislocation. Proc. Roy. Soc. London Ser. A 52 (1940) 34
50. Pettifor D.G. Bonding and Structure of Molecules and Solids. (1995), Clarendon Press, Oxford
51. Rice J.R. Conserved integrals and energetic forces. In: Miller K.J. (Ed). Fundamentals of Deformation and Fracture (1985), Cambridge Univ. Press
52. Rice J.R. Tensile crack tip fields in elastic ideally plastic crystals. Mech. Materials 6 (1987) 317-335
53. Rice J.R. Dislocation nucleation from a crack tip: an analysis based on the Peierls concept. J. Mech. Phys. Solids 40 (1992) 235-271
54. Rice J.R., and Beltz G.E. The activation energy for dislocation nucleation at a crack. J. Mech. Phys. Solids 42 (1994) 333-360
55. Rice J.R., Beltz G.E., and Sun Y. Peierls framework for dislocation nucleation from a crack tip. In: Argon A.S. (Ed). Topics in Fracture and Fatigue (1992), Springer-Verlag, Berlin 1-58
56. Robertson I.M. Phonon dispersion curves for ordered, partially ordered and disordered iron-aluminum alloys. J. Phys. Condensed Matter 3 (1991) 8181-8194
57. Rose J.H., Ferrante J., and Smith J.R. Universal binding energy curves for metals and bimetallic interfaces. Phys. Rev. Lett. 47 9 (1981) 675-678
58. Samuels J., and Roberts S.G. The brittle-ductile transition in silicon. 1. Experiments. Proc. Roy. Soc. London Ser. A 421 (1989) 1-24
59. Saxena S.K., Agrawal R.M., and Rathore R.P.S. Temperature dependent elastic and lattice dynamical behavior of solids. Phys. Status Solidi B 192 (1995) 45-52
60. Schöck G., and Püschl W. The formation of dislocation loops at crack tips in 3 dimensions. Philos. Mag. A 64 (1991) 931-949
61. Sengupta S. Lattice Theory of Elastic Constants. (1988), Trans Tech Publications, Aedermannsdorf, Switzerland
62. Shenoy V.B., Miller R., Tadmor E.B., Phillips R., and Ortiz M. Quasicontinuum models of interfacial structure and deformation. Phys. Rev. Lett. 80 4 (1998) 742-745
63. Hölzer A., and Siems R. A lattice theory model for peierls-energy calculation. In: Simmons J.A., de Witt R., and Bullough R. (Eds). Fundamental Aspects of Dislocation Theory 317 (1970), U.S. National Bureau of Standards 291-298
64. Hornstra J. Dislocations in the diamond lattice. J. Phys. Chem. Solids 5 (1958) 129-141
65. Hsia K.J., and Argon A.S. Experimental study of the mechanisms of brittle-to-ductile transition of cleavage fracture in Si single crystals. Materials Sci. Engrg. A 176 (1994) 111-119
66. Hughes T.J.R. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. (1987), Prentice-Hall., Englewood Cliffs, NJ
67. Kanzaki H. Point defects in face-centred cubic lattice-distortion around defects. J. Phys. Chem. Solids 2 (1957) 24-36
68. Kaxiras E., and Duesbery M.S. Free energies of generalized stacking faults in Si and implications for the brittle-ductile transition. Phys. Rev. Lett. 70 (1993) 3752-3755
69. Kear B.H., and Wilsdorf G.F. Trans. Metallurgical Soc. AIME 224 (1962) 382
70. Khantha M., Pope D.P., and Vitek V. Cooperative generation of dislocation loops and the brittle-to-ductile transition. Materials Sci. Engrg. A 234 (1997) 629-632
71. Knap J. Surface stress effects on dislocation nucleation processes (1997), Arizona State University, Tempe, Arizona Ph.D. thesis
72. Kohlhoff S., Gumbsch P., and Fischmeister H.F. Crack propagation in b.c.c. crystals studied with a combined finite-element and atomistic model. Philos. Mag. A 64 (1991) 851-878
73. Kohn R.V., and Muller S. Branching of twins near an austenite-twinned-martensite interface. Philos. Mag. A 66 (1992) 697-715
74. Landman U., Luedtke W.D., Barnett R.N., Cleveland C.L., Ribarsky M.V., Arnold E., Ramesh S., Baumgart H., Martinez A., and Khan B. Faceting at the silicon (100) crystal-melting interface: theory and experiment. Phys. Rev. Lett. 56 2 (1986) 155-158
75. Lee T.C., Robertson I.M., and Birnbaum H.K. An in-situ transmission electron microscope deformation study of the slip transfer mechanisms in metals. Metallurgical Trans. A 21 (1990) 2437-2447
76. Lubliner J. Plasticity Theory. (1990), Macmillan, New York
77. Maradudin A.A. Screw dislocations and discrete elastic theory. J. Phys. Chem. Solids 9 (1958) 1-20
78. Marsden J.E., and Hughes T.J.R. Mathematical Foundations of Elasticity. (1983), Prentice-Hall, Englewood Cliffs, NJ
79. Martin J.W., and Doherty R.D. Stability of Microstructure in Metallic Systems. (1976), Cambridge Univ. Press
80. Miller R., and Phillips R. Critical analysis of local constitutive models for slip and decohesion. Philos. Mag. A 73 4 (1996) 803-827
81. Miller R., Phillips R., Beltz G., and Ortiz M. A non-local formulation of the Peierls dislocation model. J. Mech. Phys. Solids (1998) (in press)
82. Miller R., Tadmor E.B., Phillips R., and Ortiz M. Quasicontinuum simulation of fracture at the atomic scale. Modelling and Simulation in Materials Science and Engineering (1998) (in press)
83. Mills M.J., Daw M.S., and Foiles S.M. High-resolution transmission electron microscopy studies of dislocation cores in metals and intermetallic compounds. Ultramicroscopy 56 (1994) 79-93
84. Milstein F. Crystal elasticity. In: Hopkins H.G., and Sewell M.J. (Eds). Mechanics of Solids (1982), Pergamon, Oxford 417-452
85. Milstein F., Fang H.E., Gong X.Y., and Rasky D.J. Bifurcations in cubic crystals under hydrostatic pressure. Solid State Commun. 99 11 (1996) 807-811
86. Movchan A.B., Bullough R., and Willis J.R. Stability of a dislocation-discrete model. European J. Appl. Math. (1998) To appear
87. Mura T. Micromechanics of Defects in Solids. (1987), Kluwer Academic, Boston
88. Musgrave M.J.P. Crystal Acoustics: Introduction to the Study of Elastic Waves and Vibrations in Crystals. (1970), Holden-Day, San Francisco
89. Nabarro F.R.N. Dislocations in a simple cubic lattice. Proc. Roy. Soc. London Ser. A 59 (1947) 256
90. 3V measured by inelastic scattering and cryogenic calorimetry. Philos. Mag. B 75 (1997) 681-699
91. 3V. Philos. Mag. B 18 (1997) 21-23
92. 3V. Phys. Rev. B 55 (1997) 2903-2911
93. Nandedkar A.S., and Narayan J. Atomic structure of dislocations in silicon, germanium and diamond. Philos. Mag. A 61 6 (1990) 873-891
94. Needleman A. A continuum model for void nucleation by inclusion debonding. J. Appl. Mech. 54 (1987) 525-531
95. Needleman A. An analysis of decohesion along an imperfect interface. Internal. J. Fracture 42 (1990) 21-40
96. Needleman A. An analysis of tensile decohesion along an interface. J. Mech. Phys. Solids 38 3 (1990) 289-324
97. Oh D.J., and Johnson R.A. Simple embedded atom model for FCC and hcp metals. J. Materials Res. 3 3 (1988) 471-478
98. Ortiz M., and Pandolfi A. A class of cohesive elements for the simulation of three-dimensional crack propagation. Internat. J. Numer. Methods Engrg. (1998) (in press)
99. Ourmazd A. The electrical properties of dislocations in semiconductors. Contemp. Phys. 25 3 (1984) 251-268
100. 2 ordered alloys. Acta Metallurgica 32 (1984) 435-448
101. Peierls R.E. The size of a dislocation. Proc. Roy. Soc. London Ser. A 52 (1940) 34
102. Pettifor D.G. Bonding and Structure of Molecules and Solids. (1995), Clarendon Press, Oxford
103. Rice J.R. Conserved integrals and energetic forces. In: Miller K.J. (Ed). Fundamentals of Deformation and Fracture (1985), Cambridge Univ. Press
104. Rice J.R. Tensile crack tip fields in elastic ideally plastic crystals. Mech. Materials 6 (1987) 317-335
105. Rice J.R. Dislocation nucleation from a crack tip: an analysis based on the Peierls concept. J. Mech. Phys. Solids 40 (1992) 235-271
106. Rice J.R., and Beltz G.E. The activation energy for dislocation nucleation at a crack. J. Mech. Phys. Solids 42 (1994) 333-360
107. Rice J.R., Beltz G.E., and Sun Y. Peierls framework for dislocation nucleation from a crack tip. In: Argon A.S. (Ed). Topics in Fracture and Fatigue (1992), Springer-Verlag, Berlin 1-58
108. Robertson I.M. Phonon dispersion curves for ordered, partially ordered and disordered iron-aluminum alloys. J. Phys. Condensed Matter 3 (1991) 8181-8194
109. Rose J.H., Ferrante J., and Smith J.R. Universal binding energy curves for metals and bimetallic interfaces. Phys. Rev. Lett. 47 9 (1981) 675-678
110. Samuels J., and Roberts S.G. The brittle-ductile transition in silicon. 1. Experiments. Proc. Roy. Soc. London Ser. A 421 (1989) 1-24
111. Saxena S.K., Agrawal R.M., and Rathore R.P.S. Temperature dependent elastic and lattice dynamical behavior of solids. Phys. Status Solidi B 192 (1995) 45-52
112. Schöck G., and Püschl W. The formation of dislocation loops at crack tips in 3 dimensions. Philos. Mag. A 64 (1991) 931-949
113. Sengupta S. Lattice Theory of Elastic Constants. (1988), Trans Tech Publications, Aedermannsdorf, Switzerland
114. Shenoy V.B., Miller R., Tadmor E.B., Phillips R., and Ortiz M. Quasicontinuum models of interfacial structure and deformation. Phys. Rev. Lett. 80 4 (1998) 742-745
115. Shenoy V.B., Miller R., Tadmor E.B., Rodney D., Phillips R., and Ortiz M. An adaptive finite element approach to atomic-scale mechanics-the quasicontinuum method. J. Mech. Phys. Solids. (1998) To appear
116. Simmons G., and Wang H. Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook. (1971), MIT Press, Cambridge, MA
117. Sinclair J.E. Improved atomistic model of a BCC dislocation core. J. Appl. Phys. 42 13 (1971) 5321-5329
118. Sinclair J.E., Gehlen P.C., Hoagland R.G., and Hirth J.P. Flexible boundary conditions and non-linear geometric effects in atomic dislocation modeling. J. Appl. Phys. 49 7 (1978) 3890-3897
119. Stillinger F.H., and Weber T.A. Computer simulation of local order in condensed phases of silicon. Phys. Rev. B 31 8 (1985) 5262-5271
120. St John C. The brittle-to-ductile transition in pre-cleaved silicon single crystals. Philos. Mag. 32 (1975) 1193-1212
121. Stoneham A.M., Torres V.T.B., Masri P.M., and Schober H.R. Interatomic potentials in semiconductors and their validity for defect calculations. Philos. Mag. A 58 1 (1988) 93-106
122. Stroud A.H. Approximate Calculation of Multiple Integrals. (1971), Prentice-Hall, Englewood Cliffs, NJ
123. Sun Y.M., Beltz G.E., and Rice J.R. Estimates from atomic models of tension-shear coupling in dislocation nucleation from a crack tip. Materials Sci. Engrg. A 170 1-2 (1993) 67-85
124. 3Al and Ni. In: Johnson L.A., Pope D.T., and Stiegler J.O. (Eds). High-Temperature Ordered Intermetallic Alloys 213 (1991), Materials Research Society 243-248
125. Sutton A.P., and Balluffi R.W. Interfaces in Crystalline Materials. (1995), Clarendon Press, Oxford
126. Tadmor E.B., Ortiz M., and Phillips R. Mixed atomistic and continuum models of deformation in solids. Langmuir 12 (1996) 4529-4534
127. Tadmor E.B., Phillips R., and Ortiz M. Quasicontinuum analysis of defects in solids. Philos. Mag. 73 (1996) 1529-1563
128. Tan T.Y. Atomic modelling of homogeneous nucleation of dislocations from condensation of point defects in silicon. Philos. Mag. A 44 1 (1981) 101-125
129. Tewary V.K. Green-function method for lattice statics. Adv. in Phys. 22 (1973) 757-810
130. Thomson R., Zhou S.J., Carlsson A.E., and Tewary V.K. Lattice imperfections studied by use of lattice Green's functions. Phys. Rev. B 46 17 (1992) 10613-10622
131. Trampenau J., Petty W., and Herzig C. Temperature dependence of the lattice dynamics of chromium. Phys. Rev. B 47 6 (1993) 3132-3137
132. Tuszynski J.A., Dixon J.M., and Grundland A.M. Nonlinear field theories and non-Gaussian fluctuations for near-critical many-body systems. Fortschr. Phys. 42 Suppl. 41 (1994) 301-337
133. Veyssiere P. Dislocation core effects in plasticity. Rev. Phys. Appl. 23 (1988) 431-443
134. Vitek V. Interactomic forces in relation to the theory of dislocations. Philos. Mag. A 58 1 (1988) 193-212
135. Vitek V. Structure of dislocation cores in metallic materials and its impact on their plastic behavior. Progr. Material Sci. 36 (1992) 1-27
136. Wei S., and Chou M.Y. Ab initio calculation of force constants and full phonon dispersions. Phys. Rev. Lett. 69 19 (1992) 2799-2802
137. Wolf D., and Yip S. Materials Interfaces. (1992), Chapman and Hall, New York
138. Xu G., Argon A.S., and Ortiz M. Nucleation of dislocations from crack tips under mixed modes of loading: implications for brittle vs. ductile behavior of crystals. Philos. Mag. 72 (1995) 415-451
139. Xu G., Argon A.S., and Ortiz M. Critical configurations for dislocation nucleation. Philos. Mag. 75 2 (1997) 341-367
140. Xu W., and Moriarty J.A. Atomistic simulation of ideal shear strength, point defects and screw dislocations in BCC transition metals: Mo as a prototype. Phys. Rev. B 54 10 (1996) 6941-6951
141. Xu G., and Ortiz M. A variational boundary integral method for the analysis of 3-D cracks of arbitrary geometry modeled as continuous distributions of dislocation loops. Internat. J. Numer. Methods Engrg. 36 (1993) 3675-3701
142. 2 lattice, stability and structure. Philos. Mag. 43 (1981) 1027
143. Yang W., Tan H., and Guo T. Evolution of crack-tip process zones. Modelling Simulation Materials Sci. Engrg. 2 3A (1994) 767-781
144. Zanzotto G. The Cauchy-Born hypothesis, nonlinear elasticity and mechanical twinning in crystals. Acta Cryst. 52 6 (1996) 839-849
145. Zbib H.M., Rhee M., and Hirth J.P. On plastic deformation and the dynamics of 3d dislocations. Internat Int. J. Mech. Sci. 40 2-3 (1998) 113-127
146. Zielinski P. A valence potential model of surface effects in stressed diamond-like crystals. J. Phys. Condensed Matter 3 (1991) 2299-2308
147. Zielinski W., Huang H., Venakataraman S., and Gerberich W.W. Dislocation distribution under a microindentation into an iron-silicon single crystal. Philos. Mag. 72 5 (1995) 1221-1237
148. Zienkiewicz O.C., and Taylor R.L. The Finite Element Method. Vol. 1: Basic Formulation and Linear Problems. (1989), McGraw-Hill, London
149. Zienkiewicz O.C., and Zhu J.Z. A simple error estimator and adaptive procedure for practical engineering analysis. Internal. J. Numer. Methods Engrg. 24 (1987)