Cycloid crack sequences on Europa: Relationship to stress history and constraints on growth mechanics based on cusp angles

The original model developed to explain cycloidal cracks on Europa interprets cycloids as tensile fractures that grow in a curved path in response to the constantly rotating diurnal tidal stress field. Cusps form when a new cycloid crack segment propagates at an angle to the first in response to a rotation of the principal tidal stress orientation during a period of no crack growth. A recent revised model states that a cycloid cusp forms through the creation of a secondary fracture called a tailcrack at the tip of an existing cycloid segment during shearing motion induced by the rotating tidal stress field. As the tailcrack propagates away from the cusp, it becomes the next cycloid segment in the chain. The qualitative tailcrack model uniquely accounts for the normal and shear stresses that mechanically must resolve onto the tip of an existing cycloid segment at the instant of cusp formation. In this work, we provide a quantitative framework and test of the hitherto purely conceptual tailcrack model. We first present a relative age sequence inferred from geologic mapping of multiply cross-cutting cycloids in Europa's trailing hemisphere and place this into the context of the global stress history. The age sequence requires a cumulative minimum of 630° of shell reorientation due to nonsynchronous rotation to account for the observed range of orientations of cycloids of different ages. We determined the back-rotated longitudes of formation of two cycloid chain examples and used mathematical modeling of europan tidal stresses to show that the tailcrack model for cusp formation is not only viable, but places constraints on the overall development of a cycloid chain by controlling the timing of cusp development within Europa's orbit. For all cusps analyzed, the exact ratio of resolved shear to normal stress required to form the cusp angles by a process of tailcracking, as governed by the principles of linear elastic fracture mechanics, is produced at the tip of a shearing cycloid segment during Europa's orbit. Cusp formation occurs after the point in the orbit at which the maximum tensile principal tidal stress occurs, implying that tensile tidal stresses are not directly responsible for cusp development. Instead, cusps develop when a tailcrack forms at the tip of a cycloid segment in response to the highly perturbed stress field induced during concomitant opening and shearing at the tip of the cycloid segment.