7.C3 where: tb thickness of inner hull to prevent yielding (mm) C 555 for yield criteria (empirical) Mp mass of meteoroid (grams) VP velocity of meteoroid (km/sec) S separation distance between inner and outer hull (cm) This relation assumes an outer hull thickness that is equivalent to the inner hull thickness .. Using the 500 cm separation between hull and neglecting the shield material, it is found that to prevent yielding of the inner hull both hulls must be 0.1 mm thick. Since the colony's hulls are 40 mm thick, the probability of complete penetration of both hulls is considered negligible. The second criteria to be examined is the probability of outer hull failure due to meteoroid impact. In this case penetration is not necessary for failure, the formation of a critical-sized crack will fail the plate. The major mode of failure is due to a combination of spalling and melting of the impacted material. The impact sends stress waves throughout the hull and if these reach a critical intensity in a minimum of time, spalling of the back surface can occur. On the front surface,the shock waves can cause the internal energy of the hull material to rise to a sufficient level to cause melting of the steel. This change of state in the local impact region will form cracks and may lead to the failure of the plate. Assuming the main cause of failure is the change from the fragment's kinetic energy to thermal energy, it is possible to determine the meteoroid size which will cause immediate failure of an outer hull plate. The affected region has a diameter equal to the plate thickness, and using the heat of fusion of steel at 65 calories/gm and specific heat of steel at .11 cal/gm/°C (7.C3),the following relationships can be obtained.
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