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Some surprising phenomena in weak-bond fracture of a triangular lattice. (English) Zbl 1116.74321
Summary: 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, No. 5, 927-960 (2000; Zbl 0988.74050)] 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.

MSC:
74A45 Theories of fracture and damage
74R99 Fracture and damage
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