Interplay between tension and shearing: Relevance to crack growth on Europa

Europa's icy shell experiences a temporally and spatially variable stress field due to the diurnal effects of an eccentric orbit and long-term shell reorientation relative to the core. The stresses have resulted in ubiquitous fracturing of the ice shell with multiple fracture episodes and orientations. The fractures have typically been assumed to provide a proxy for the pattern of paleostress trajectories based on the assumption that the fractures form purely by tensile failure. However, the rapidly changing nature of the stress tensor during crack growth results in shear stresses being resolved onto the crack, particularly if crack growth is staggered. In such cases, continued growth must occur in a direction dictated by the ratio of shear-to-normal stress at the crack tip (a combination of shearing and tension), resulting in mixed-mode I-II cracks in fracture mechanics terminology. The implications of this dual growth mode are illustrated by cuspate cracks called cycloids. Cusps represent periods of no crack growth during which time principal stresses rotate. The normal and shear stresses that resolve from the tidal stress field onto the arrested cycloid tip vary sinusoidally (albeit out of phase), dependent on the crack orientation. When a critical ratio of shear-to-normal stress is achieved, a cusp develops with an angle dictated by this ratio. The range of cusp angles present on Europa indicates that the critical ratio is site-dependent, and appears to be higher for cycloid segments with greater curvatures. For cycloids examined in this study, the critical ratio occurs past the point in the orbit where the tensile stress is maximized, implying that tension alone is insufficient to initiate continued growth of the arrested crack. Instead, a combination of shearing and tension is crucial to jump-starting an arrested cycloid chain by creating a crack-tip stress concentration that forces the development of a cusp.

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