TY - JOUR

T1 - Some surprising phenomena in weak-bond fracture of a triangular lattice

AU - Slepyan, L. I.

AU - Ayzenberg-Stepanenko, M. V.

N1 - Funding Information:
This research was supported by The Israel Science Foundation, Grant No. 28/00-1, and ARO, Grant No. 41363-M.

PY - 2002/8

Y1 - 2002/8

N2 - A semi-infinite crack growing along a straight line in an unbounded triangular-cell lattice and in lattice strips is under examination. Elastic and standard-material viscoelastic lattices are considered. Using the superposition similar to that used for a square-cell lattice (J. Mech. Phys. Solids 48 (2000) 927) an irregular stress distribution is revealed on the crack line in mode II: the strain of the crack-front bond is lower than that of the next bond. A further notable fact about mode II concerns the bonds on the crack line in the lattice strip deformed by a 'rigid machine'. If the alternate bonds, such that are inclined differently than the crack-front bond, are removed, the stresses in the crack-front bond and in the other intact bonds decrease. These facts result in irregular quasi-static and dynamic crack growth. In particular, in a wide range of conditions for mode II, consecutive bond breaking becomes impossible. The most surprising phenomenon is the formation of a binary crack consisting of two branches propagating on the same line. It appears that the consecutive breaking of the right-slope bonds - as one branch of the crack - can proceed at a speed different from that for the left-slope bonds - as another branch. One of these branches can move faster than the other, but with time they can change places. Some irregularities are observed in mode I as well. Under the influence of viscosity, crack growth can be stabilized and crack speed can be low when viscosity is high; however, in mode II irregularities in the crack growth remain. It is found that crack speed is a discontinuous function of the creep and relaxation times.

AB - A semi-infinite crack growing along a straight line in an unbounded triangular-cell lattice and in lattice strips is under examination. Elastic and standard-material viscoelastic lattices are considered. Using the superposition similar to that used for a square-cell lattice (J. Mech. Phys. Solids 48 (2000) 927) an irregular stress distribution is revealed on the crack line in mode II: the strain of the crack-front bond is lower than that of the next bond. A further notable fact about mode II concerns the bonds on the crack line in the lattice strip deformed by a 'rigid machine'. If the alternate bonds, such that are inclined differently than the crack-front bond, are removed, the stresses in the crack-front bond and in the other intact bonds decrease. These facts result in irregular quasi-static and dynamic crack growth. In particular, in a wide range of conditions for mode II, consecutive bond breaking becomes impossible. The most surprising phenomenon is the formation of a binary crack consisting of two branches propagating on the same line. It appears that the consecutive breaking of the right-slope bonds - as one branch of the crack - can proceed at a speed different from that for the left-slope bonds - as another branch. One of these branches can move faster than the other, but with time they can change places. Some irregularities are observed in mode I as well. Under the influence of viscosity, crack growth can be stabilized and crack speed can be low when viscosity is high; however, in mode II irregularities in the crack growth remain. It is found that crack speed is a discontinuous function of the creep and relaxation times.

KW - A. Fracture

KW - B. Viscoelastic lattice

KW - C. Integral transforms

UR - http://www.scopus.com/inward/record.url?scp=0036681301&partnerID=8YFLogxK

U2 - 10.1016/S0022-5096(01)00141-7

DO - 10.1016/S0022-5096(01)00141-7

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AN - SCOPUS:0036681301

SN - 0022-5096

VL - 50

SP - 1591

EP - 1625

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

IS - 8

ER -