×

zbMATH — the first resource for mathematics

Steady-state mode I cracks in a viscoelastic triangular lattice. (English) Zbl 1116.74419
Summary: We construct exact solutions for Mode I steady-state cracks in an ideally brittle viscoelastic triangular lattice model. Our analytic solutions for the infinite lattice are compared to numerical results for finite width systems. The issues we address include the crack velocity versus driving curve as well as the onset of additional bond breaking, signaling the emergence of complex spatio-temporal behavior. Somewhat surprisingly, the critical velocity for this transition becomes a decreasing function of the dissipation for sufficiently large values thereof. Lastly, we briefly discuss the possible relevance of our findings for experiments on mode I crack instabilities.

MSC:
74R20 Anelastic fracture and damage
74A45 Theories of fracture and damage
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abraham, F.F.; Brodbeck, D.; Rafey, R.A.; Rudge, W.E., Instability dynamics of fracture—a computer-simulation investigation, Phys. rev. lett., 73, 2, 272-275, (1994)
[2] Barenblatt, G.I., The formation of equilibrium cracks during brittle fracture: general ideas and hypothesis, axially symmetric cracks, Appl. math. mech., 23, 622-636, (1959) · Zbl 0095.39202
[3] Cramer, T.; Wanner, A.; Gumbsch, P., Dynamic fracture of Glass and single crystalline silicon, Z. metallkd, 90, 675-686, (1999)
[4] Cramer, T.; Wanner, A.; Gumbsch, P., Energy dissipation and path instabilities in dynamic fracture of silicon single crystals, Phys. rev. lett., 85, 4, 788-791, (2000)
[5] Field, J.E., Brittle fracture: its study and application, Contemp. phys., 12, 1-13, (1971)
[6] Fineberg, J.; Gross, S.P.; Marder, M.; Swinney, H.L., Instability in dynamic fracture, Phys. rev. lett., 67, 4, 457-460, (1991)
[7] Fineberg, J.; Gross, S.P.; Marder, M.; Swinney, H.L., Instability in the propagation of fast cracks, Phys. rev. B, 45, 10, 5146-5154, (1992)
[8] Fineberg, J.; Marder, M., Instability in dynamic fracture, Phys. rep., 313, 1-2, 1-108, (1999)
[9] Gumbsch, P.; Zhou, S.J.; Holian, B.L., Molecular dynamics investigation of dynamic crack stability, Phys. rev. B, 55, 6, 3445-3455, (1997)
[10] Hauch, J.A.; Holland, D.; Marder, M.P.; Swinney, H.L., Dynamic fracture in single crystal silicon, Phys. rev. lett., 82, 19, 3823-3826, (1999)
[11] Holland, D.; Marder, M., Ideal brittle fracture of silicon studied with molecular dynamics, Phys. rev. lett., 80, 4, 746-749, (1997)
[12] Holland, D.; Marder, M., Erratum: ideal brittle fracture of silicon studied with molecular dynamics, Phys. rev. lett., 81, 18, 4029, (1998)
[13] Kessler, D.A., Steady-state cracks in viscoelastic lattice models II, Phys. rev. E, 61, 3, 2348-2360, (2000)
[14] Kessler, D.A.; Levine, H., Steady-state cracks in viscoelastic lattice models, Phys. rev. E, 59, 5, 5154-5164, (1998)
[15] Kessler, D.A.; Levine, H., Arrested cracks in nonlinear lattice models of brittle fracture, Phys. rev. E, 60, 6, 7569-7571, (1999)
[16] Kessler, D.A., Levine, H., 2001. Nonlinear lattice models of viscoelastic mode-III fracture. Phys. Rev. E 63 (1) No. 016118/1-9.
[17] Kulamekhtova, Sh.A., Saraikin, V.A., Slepyan, L.I., 1984. Plane problem of a crack in a lattice. Izv. AN SSSR. Mekh. Tverd. Tela 19 (3) 112-118 [Mech. Solids 19 (3), 102-108].
[18] Langer, J.S., Models of crack propagation, Phys. rev. E, 46, 6, 3123-3131, (1992)
[19] Langer, J.S.; Lobkovsky, A.E., Critical examination of cohesive-zone models in the theory of dynamic fracture, Jpsp, 46, 9, 1521-1556, (1998) · Zbl 0971.74009
[20] Marder, M.; Gross, S.P., Origin of crack tip instabilities, J. mech. phys. solids, 43, 1, 1-48, (1995) · Zbl 0878.73053
[21] Marder, M.; Liu, X., Instability in lattice fracture, Phys. rev. lett., 71, 15, 2417-2420, (1993)
[22] Omeltchenko, A.; Yu, J.; Kalia, R.K.; Vashishta, P., Crack front propagation and fracture in a graphite sheet: a molecular-dynamics study on parallel computers, Phys. rev. lett., 78, 11, 2148-2151, (1997)
[23] Pechenik, L., 2000. Pattern formation and nonlinear dynamics in nonequilibrium physical systems. Ph.D. Thesis, UCSD, 2000.
[24] Pla, O.; Guinea, F.; Louis, E.; Ghasias, S.V.; Sander, L.M., Viscous effects in brittle fracture, Phys. rev. B, 57, 22, R13,981-R13,984, (1998)
[25] Sander, L.M.; Ghasias, S.V., Thermal noise and the branching threshold in brittle fracture, Phys. rev. lett., 83, 10, 1994-1997, (1999)
[26] Sharon, E.; Gross, S.P.; Fineberg, J., Local crack branching as a mechanism for instability in dynamic fracture, Phys. rev. lett., 74, 25, 5096-5099, (1995)
[27] Sharon, E.; Gross, S.P.; Fineberg, J., Energy dissipation in dynamic fracture, Phys. rev. lett., 76, 12, 2117-2120, (1996)
[28] Slepyan, L.I., 1981. Dynamics of a crack in a lattice. Dokl. Akad. Nauk SSSR 258 (1-3) 561-564 [Sov. Phys.-Dokl. 26 (5), 538-540]. · Zbl 0497.73107
[29] Slepyan, L.I., 1982. The relation between the solutions of mixed dynamical problems for a continuous elastic medium and a lattice. Dokl. Akad. Nauk SSSR 266 (1-3), 581-584 [Sov. Phys.-Dokl. 27 (9), 771-772]. · Zbl 0541.73115
[30] Slepyan, L.I., Ayzenburg-Stepanenko, M.V., Dempsey, J.P., 1999. Mech. Time-Dependent Mater. 3, 159-203.
[31] Thomson, R., The physics of fracture, Solid state phys., 39, 1-29, (1986)
[32] Yoffe, E.H., The moving griffith crack, Philos. mag., 42, 7, 739-750, (1951) · Zbl 0043.23504
[33] Zhou, S.J.; Beazley, D.M.; Lomdahl, P.S.; Holian, B.L., Large-scale molecular dynamics simulations of three-dimensional ductile failure, Phys. rev. lett., 78, 3, 479-482, (1997)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.