Abstract
In this paper new quantized failure criteria are proposed, also for nanoscale applications. The main theories in the context of the strength of solids, i.e., of brittle fracture, dynamic fracture, fatigue and Weibull Statistics are reconsidered according to the proposed “quantization rules”. The “corresponding principle” is verified and thus the classical theories are found to be the limit cases of the quantized counterparts. As an example, our treatment is applied to very recent experimental results on carbon or WS2 nanotubes and to futurist ultra-nanocrystalline diamond nanowires, for which the tensile, bending and ideal strength are estimated.
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Barber AH, Kaplan-Ashiri I, Cohen SR, Tenne R, Wagner HD (2005b) Stochastic strength of nanotubes: an appraisal of available data. Composite Sci Technol in press
A Carpinteri (1982) ArticleTitleNotch sensitivity in fracture testing of aggregative materials Eng Frac Mech 16 467–481 Occurrence Handle10.1016/0013-7944(82)90127-8
A Carpinteri B Chiaia (1996) ArticleTitleCrack-resistance behavior as a consequence of self-similar fracture topologies Int J Frac 76 327–340
A Carpinteri N Pugno (2002) ArticleTitleOne-, two- and three-dimensional universal laws for fragmentation due to impact and explosion J Appl Mech 69 854–856 Occurrence Handle10.1115/1.1488937
A Carpinteri N Pugno (2004) ArticleTitleSize effects on average and standard deviation values for the mechanical properties of condensed matter: a energy based unified approach Int J Frac 128 253–261 Occurrence Handle10.1023/B:FRAC.0000040988.61253.05
A Carpinteri N Pugno (2005a) ArticleTitleFracture instability and limit strength condition in structures with re-entrant corners Eng Frac Mech 72 1254–1267 Occurrence Handle10.1016/j.engfracmech.2004.09.008
A Carpinteri N Pugno (2005b) ArticleTitleAre the scaling laws on strength of solids related to mechanics or to geometry? Nature Materi 4 421–423 Occurrence Handle10.1038/nmat1408 Occurrence Handle2005NatMa...4..421C
A Carpinteri N Pugno (2005c) ArticleTitleStrength and toughness of micro- and nano-structured materials: unified influence of composition, grain size and structural dimension Rev Advanced Mater Sci J 10 320–324
Cornetti P, Carpinteri A, Pugno N, Taylor D (2005) Finite fracture mechanics: a coupled stress and energy failure criterion. Eng Frac Mech. In press
HD Espinosa et al. (2003) ArticleTitleFracture strength of ultrananocrystalline diamond thin films: identification of Weibull parameters J Appl Phys 94 6076–6084 Occurrence Handle10.1063/1.1613372 Occurrence Handle2003JAP....94.6076E
LB Freund (1990) Dynamic fracture mechanics Cambridge University Press Cambridge, MA Occurrence Handle0712.73072
H Gao B Ji IL Jaeger E Arzt P Fratzl (2003) ArticleTitleMaterials become insensitive to flaws at nanoscale: lesson from Nature Proc Nat Acad Sci USA 100 5597–5600 Occurrence Handle10.1073/pnas.0631609100 Occurrence Handle2003PNAS..100.5597G
AA Griffith (1921) ArticleTitleThe phenomenon of rupture and flow in solids Phil Trans Roy Soc. A221 163–198 Occurrence Handle1921RSPTA.221..163G
D Gruen (1999) ArticleTitleNanocrystalline diamond films Annu Rev Mater Sci 29 211–259 Occurrence Handle10.1146/annurev.matsci.29.1.211
A Kashtanov Yu Petrov (2004) ArticleTitleFractal models in fracture mechanics Int J Frac 128 271–276 Occurrence Handle10.1023/B:FRAC.0000040990.68602.e2
CH Ke N Pugno B Peng HD Espinosa (2005) ArticleTitleExperiments and modeling of carbon nanotube NEMS device J Mech Phys Solids 53 IssueID6 1314–1333 Occurrence Handle10.1016/j.jmps.2005.01.007
D Leguillon (2002) ArticleTitleStrength or toughness? A criterion for crack onset at a notch Eur J Mech A/Solids 21 61–72 Occurrence Handle1061.74047 Occurrence Handle10.1016/S0997-7538(01)01184-6
Morozov NF (1984) Mathematical issues of a crack theory. Nauka, Moscow (in Russian)
NF Morozov YuV Petrov AA Utkin (1990) Dokl Akad Nauk SSSR 313 IssueID2 276
H Murakami (1986) Stress intensity factors handbook Pergamon press Oxford, UK
H Neuber (1958) Theory of notch stresses Springer Berlin Occurrence Handle0962.74002
V Novozhilov (1969) ArticleTitleOn a necessary and sufficient criterion for brittle strength Prik Mat Mek 33 212–222
DM Owen SZ Zhuang AJ Rosakis G Ravichandran (1988) ArticleTitleExperimental determination of dynamic crack initiation and propagation fracture toughness in thin aluminum sheets Int J Frac 90 153–174 Occurrence Handle10.1023/A:1007439301360
Peng B, Espinosa HD (2004) Fracture size effect in ultrananocrystalline diamond—Weibull theory applicability. In: Proceedings of the Int. Mech. Eng. Congress 2004, California, 13–19 November 2004
Petrov YuV (1996) Quantum macromechanics of fracture of solids. Preprint of Inst. for Problems of Mechanical Engineering, Russ. Acad. Sci., St.-Petersburg
YuV Petrov NF Morozov VI Smirnov (2003) ArticleTitleStructural macromechanics approach in dynamics of fracture Fatigue Frac Eng Mater Struct 26 363–372 Occurrence Handle10.1046/j.1460-2695.2003.00602.x
YV Petrov EV Sitnikova (2004) ArticleTitleDynamic cracking resistance of structural materials predicted from impact fracture of an aircraft alloy Tech Phys 49 57–60 Occurrence Handle10.1134/1.1642679
Pugno N (2002) A quantized Griffith’s criterion, Day study of the Italian Group of Fracture on Nanomechanics of Fracture (Communication to the President), 25–26 September 2002, Vigevano, Italy (in Italian)
Pugno N (2004a) Arxiv: cond-mat/0411556, 22 nov
Pugno N (2004b) Dynamics of nanotube based NEMS. XI Int. Congress on Sound and Vibration (N. 283), 5–8 July 2004b, St. Petersburg, Russia
N Pugno (2004c) ArticleTitleNon-linear dynamics of nanotube based NEMS. Transworld Research Network, Special on recent research developments in sound and vibrations 2 197–211
N Pugno (2005) ArticleTitleThe nanoscale strength of Ultra Nano Crystalline Diamond Rev Adv Mater Sci J 10 156–160
N Pugno M Ciavarella P Cornetti A Carpinteri (2005) ArticleTitleA generalized Paris’s law for fatigue crack growth J Mech Phys solids 54 1333–1349 Occurrence Handle10.1016/j.jmps.2006.01.007 Occurrence Handle2006JMPSo..54.1333P
N Pugno B Peng HD Espinosa (2004) ArticleTitlePredictions of strength in MEMS components with defects—A novel experimental-theoretical approach Int J Solids Struct 42 647–661 Occurrence Handle10.1016/j.ijsolstr.2004.06.026
N Pugno R Ruoff (2004) ArticleTitleQuantized fracture mechanics Phil Mag 84 IssueID27 2829–2845 Occurrence Handle10.1080/14786430412331280382
Pugno N, Ruoff R (2006) Nanoscale Weibull Statistcs. J Appl Phys 99:024301/1–4
AA Seweryn (1998) ArticleTitleNon-local stress and strain energy release rate mixed mode fracture initiation and propagation criteria Eng Frac Mech 59 737–760 Occurrence Handle10.1016/S0013-7944(97)00175-6
D Taylor (1999) ArticleTitleGeometrical effects in fatigue: a unified theoretical model Int J fatigue 21 413–420 Occurrence Handle10.1016/S0142-1123(99)00007-9
D Taylor P Cornetti N Pugno (2005) ArticleTitleThe fracture mechanics of finite crack extensions Eng Frac Mech 72 1021–1028 Occurrence Handle10.1016/j.engfracmech.2004.07.001
Weibull W (1939) A statistical theory of the strength of materials. Ingeniörsvetenskapsakademiens, Handlingar, Nr. 151
M-F Yu O Lourie MJ Dyer K Moloni TF Kelly RS Ruoff (2000) ArticleTitleStrength and breaking mechanism of multiwalled carbon nanotubes under tensile load Science 287 637–640 Occurrence Handle10.1126/science.287.5453.637 Occurrence Handle2000Sci...287..637Y
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Pugno, N. New quantized failure criteria: application to nanotubes and nanowires. Int J Fract 141, 313–323 (2006). https://doi.org/10.1007/s10704-006-0082-7
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DOI: https://doi.org/10.1007/s10704-006-0082-7