Energy considerations in crack deflection phenomenon in single crystal silicon Article Received: 22 June 2005 Accepted: 27 February 2006 DOI:
Cite this article as: Sherman, D. Int J Fract (2006) 140: 125. doi:10.1007/s10704-006-0048-9 Abstract
Crack deflection in single-crystal brittle occurs when a crack, propagating on one cleavage plane, ‘chooses’, from energy considerations, to continue propagating on another cleavage plane. This phenomenon was identified during dynamic crack propagation experiments of thin, rectangular [0 0 1] single-crystal (SC) silicon specimens subjected to three-point bending (3PB). Specimens with long pre-cracks (hence propagating at a ‘low’ energy and velocity) cleave along the vertical (1 1 0) plane, while the same specimens but with short pre-cracks (and therefore with higher propagation energy and velocity) cleave along the inclined (1 1 1) plane. The same specimens with intermediate pre-crack length show that the crack first propagates on the (1 1 0) plane and then deflects to the (1 1 1) plane. We show that the deflection is due to variations of the material property that resists cracking, Γ, the dynamic cleavage energy, with velocity and crystallographic orientation. We propose selection criteria to explain the deflection: The crack will deflect to the plane with the lowest dynamic cleavage energy. We further suggest that crack deflection is the basic mechanism controlling the way the crack consumes energy while propagating and is the main cause of surface perturbations. The spatial temporal fracture energy along the (1 1 0) cleavage plane is evaluated.
Keywords Dynamic fracture Single-crystal Cleavage Crack deflection Energy dissipation References Be’ery, I, Lev, U, Sherman, D 2003 On the lower limiting velocity of a dynamic crack in brittle solids J Appl Phys 93 2429 2434 CrossRef ADS Google Scholar Cramer, T, Wanner, A, Gumbsch, P 2000 Energy dissipation and path instabilities in dynamic fracture of silicon single crystals Phys Rev Lett 85 788 CrossRef ADS Google Scholar Fawaz, SA 1999 Stress intensity factor solution for part-elliptical through cracks Eng Fracture Mech 63 209 226 CrossRef Google Scholar Freund, LB 1990Dynamic fracture mechanics Cambridge University Press Cambridge MATH Google Scholar Griffith, AA 1920 The phenomena of rupture and flow in solids. The phenomena of rupture and flow in solids Mech Eng A 221 163 198 Google Scholar Hauch, JA, Holland, D, Marder, M, Swinney, H 1999 Dynamic fracture in single crystal silicon Phys Rev Lett 82 3823 3826 CrossRef ADS Google Scholar Irwin, GR 1958 Fracture Flugge, S. eds. Handbuch der Physik Springer Germany 551 Google Scholar Kiciak, A, Glinka, G, Ema, M 1990 Eng Fract Mech. 60 221 238 CrossRef Google Scholar Lawn, B 1993Fracture of brittle solids Cambridge University Press Cambridge, UK Google Scholar Lin, XB, Smith, RA 1999 Finite element analysis of fatigue crack growth of surface cracked plate, Part II: crack shape changes Eng Fract Mech 63 523 540 CrossRef Google Scholar Marder, M, Gross, S 1995 Origin of crack tip instability J Mech Phys Solids 43 1 48 MATH MathSciNet CrossRef Google Scholar Muhlstein, CL, Brown, SB, Ritchie, RO 2001 High-cycle fatigue of single-crystal silicon thin films J Microelectromech Syst 10 593 600 CrossRef Google Scholar Newman, JC, Jr., Raju, IS 1981 An empirical stress intensity factor equation for the surface cracks Eng Fract Mech 15 185 192 CrossRef Google Scholar Pérez, R, Gumbsch, P 2000a Directional anisotropy in the cleavage fracture of silicon Phys Rev Lett 84 5347 CrossRef ADS Google Scholar Pérez, R, Gumbsch, P 2000b An Ab Initio study of the cleavage anisotropy in silicon Acta Mater 48 4517 CrossRef Google Scholar Raju, IS, Newman, JC, Jr. 1979 Stress intensity factors for a wide range of semi-elliptical surface cracks in finite thickness plate Eng Fract Mech 11 817 829 CrossRef Google Scholar Sharon, E, Cohen, G, Fineberg, J 2001 Propagating solitary waves along a rapidly moving crack front. nature 410 68 71 CrossRef ADS Google Scholar sherman, D, Be’ery, I 1998a Nonlinear dynamic rupture in sapphire Phys Rev Lett 80 540 CrossRef ADS Google Scholar Sherman, D, Be’ery, I 1998b Nonlinear analysis of the fracture surface of a single-crystal brittle solid. physica D 119 424 CrossRef ADS Google Scholar Sherman, D, Be’ery, , I, 2000 Fracture mechanisms of sapphire under bending J Mater Sci 35 1283 CrossRef Google Scholar Sherman, D, Be’ery, I 2003a The shape and the energies of a dynamically propagating crack under bending J Mater Res 18 2379 2386 Google Scholar Sherman, D, Be’ery, I 2003b Velocity dependent crack deflection in silicon Scripta Mater 49 551 555 CrossRef Google Scholar Sherman, D, Be’ery, I 2004a Non linear dynamical analysis of crack surface perturbations and their dependence on velocity and direction. physical D 90 177 189 CrossRef ADS Google Scholar Sherman, D, Be’ery, I 2004b ‘From crack deflection to lattice vibrations – macro to atomistic examination of dynamic cleavage fracture’ J Mech Phys Solids 52 1743 1761 CrossRef Google Scholar Sinclair, JE, Lawn, BR 1972 Atomistic study of cracks in diamond-structure crystals P Roy Soc A 329 83 ADS Google Scholar Spence, JCH, Huang, YM, Sankey, O 1993 Lattice trapping and surface reconstruction for silicon cleavage on (111). Ab-Initio quantum molecular dynamics calculation Acta metall Mater 41 2815 2824 CrossRef Google Scholar Stalder, B, Beguelin, P, Kausch, HH 1983 A simple velocity gauge for measuring crack growth Int J Frac 22 47 50 CrossRef Google Scholar Thomson, R, Hsieh, C, Rana, V 1971 Lattice trapping of fracture cracks J Appl Phys 42 3154 CrossRef ADS Google Scholar Copyright information
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