Crack dynamics in a nonlinear lattice
Tóm tắt
A discrete two-dimensional square-cell lattice with a steady propagating crack is considered. The lattice particles are connected by massless bonds, which obey a piecewise-linear double- humped stress–strain relation. Initially, Hooke’s law is valid as the first stable branch of the force–elongation diagram; then, as the elongation becomes critical, the transition to the other branch occurs. Further, when the strain reaches the next critical value, the bond breaks. This transition is assumed to occur only in a line of the breaking bonds; the bonds outside the crack line are assumed to be in the initial branch all the time. The formulation relates to the crack propagation with a ‘damage zone’ in front of the crack. An analytical solution is presented that allows to determine the crack speed as a function of the far-field energy release rate, to find the total speed-dependent dissipation, and to estimate the role of the damage zone. The analytical formulation and the solution present a development of the previous ones for the crack and localized phase transition dynamics in linear and bistable-bond lattices.
Từ khóa
Tài liệu tham khảo
Bolotovsky BM, Stolyarov SN (1972) On radiation principles for a medium with dispersion. In: Ginzburg VL, Zel’dovich Ya.B, Leontovich MA, Markov MA, Ritus VI, Sakharov AD, Feinberg EL (eds) Problems for theoretical physics. Nauka, Moscow, pp 267–280 (in Russian)
J Botsis A Chudnovsky (1987) ArticleTitlePulsations of damage during a fast running crack Int J Frac 33 R67–70 Occurrence Handle10.1007/BF00044420
O Braun Y Kivshar (1998) ArticleTitleNonlinear dynamics of a Frenkel–Kontorova dislocation in a one-dimensional crystal Phys Rev V 138 IssueID3A A763–A766
Broberg KB (1999) Cracks and fracture. Academic Press, London, XVI+752pp
J Frenkel T Kontorova (1948) ArticleTitleOn the theory of plastic deformation and twinning Sov Phys 13 1–10
M Marder (2004) ArticleTitleEffects of atoms on brittle fracture Int J Frac 130 517–555 Occurrence Handle10.1023/B:FRAC.0000049501.35598.87
M Marder S Gross (1995) ArticleTitleOrigin of crack tip instabilities J Mech Phys Solids 43 1–48 Occurrence Handle0878.73053 Occurrence Handle1312562 Occurrence Handle10.1016/0022-5096(94)00060-I
LI Slepyan (1981) ArticleTitleDynamics of a crack in a lattice. Sov Phys Doklady 26 538–540 Occurrence Handle0497.73107
LI Slepyan (2000) ArticleTitleDynamic factor in impact, phase transition and fracture J Mech Phy Solids 48 927–960 Occurrence Handle0988.74050 Occurrence Handle1746550 Occurrence Handle10.1016/S0022-5096(99)00061-7
Slepyan LI (2002) Models and phenomena in fracture mechanics. Springer, Berlin, XVII+576pp
LI Slepyan (2005) ArticleTitleCrack in a material-bond lattice J Mech Phys Solids 53 1295–1313 Occurrence Handle2137065 Occurrence Handle10.1016/j.jmps.2005.02.003
LI Slepyan MV Ayzenberg-Stepanenko (2004) ArticleTitleLocalized transition waves in bistable-bond lattices J Mech Phys Solids 52 1447–1479 Occurrence Handle02173563 Occurrence Handle2066217 Occurrence Handle10.1016/j.jmps.2004.01.008
LI Slepyan MV Ayzenberg JP Dempsey (1999) ArticleTitleA lattice model for viscoelastic fracture Mech Time-Dependent Mater 3 159–203 Occurrence Handle10.1023/A:1009846932233