Author(s): Zdenek P. Bazant; Walter P. Murphy
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Abstract: Propagation of bending fracture along a floating sea ice plate, representing an elastic plate on elastic foundation, is analyzed in the sense of linear elastic fracture mechanics (LEFM), assuming the entire plate thickness to be fractured all the way to the fracture tip. The analysis focuses on the size effect. Two specific problems are solved in an idealized form: steady state propagation of thermal bending fracture and vertical penetration of an object through the plate. In both problems it is found that the nominal strength (equivalent to the critical temperature difference in the first problem) decreases as (thickness) ^-3/8. In the thermal problem, the (-3/8) -power law is exact (under the hypotheses of the analysis), while in the penetration problem it is only approximate, approached asymptotically for large sizes. This (-3/8) -power law differs from that known for two-dimensional or axisymmetric LEFM, in which the nominal strength scales as (size) ^-1/2; the difference is caused by the presence of a characteristic length for bending disturbance decay along the plate. An in-plane compressive force makes the size effect stronger than (thickness) ^-3/8, and an in-plane tensile force makes it weaker. Creep and propagation rate effects are approximately taken into account in the thermal problem, and so is the effect of in-plane forces on bending. A numerical example shows that the temperature changes occurring in the Arctic suffice, according to the present theory, to produce bending fractures. Such fractures might serve to initiate the formation of leads of open water, pressure ridges and rafting.
Year: 1992