Reply to “Comment on ‘Mechanics of tidally driven fractures in Europa's ice shell’ ”

Abstract

Both Lee et al. and Qin et al. consider propagation of a surface initiated tensile crack oriented vertically in an ice sheet of finite thickness with gravitational overburden. Lee et al. assume the crack walls are always in contact and bear normal stress from overburden. In this closed crack scenario, overburden stress increases linearly with depth just as in an ice half-space. Crack walls cannot sustain tension, so the effect of far field tension is concentrated in the material below the crack walls. This leads to the deep crack penetrations of Lee et al. Qin et al., however, assume an open crack scenario. They inappropriately apply normal stress to open crack walls which are exposed to vacuum and so physically cannot sustain a normal stress [Timoshenko, S.P., Goodier, J.N., 1970. Theory of Elasticity, third ed. McGraw–Hill, New York, p. 191]. Since this inappropriate normal stress is horizontally oriented it has the effect of artificially concentrating compressive stress in the material below the open crack. The severely limited crack propagation depths of Qin et al. result from this inappropriate boundary condition on an open crack wall.