excluded. Under this condition, varying the impact velocity while keeping its normal component constant, practically the same crack pattern is obtained (see Fig. \[snap2\]). Thus, the crack propagation and orientation during the fragmentation process solely depends on the normal component of the impact velocity.

Comparing the crack pattern obtained in the simulations to the experimental results [@fra_pattern], we did not find any meridian cracks as they are difficult to detect in two dimensions. The pattern of oblique cracks and secondary cracks has a satisfactory agreement with the experimental results. The simulations confirm that oblique cracks which were observed in experimental investigations [@fra_pattern] develop along the trajectories of maximum compression planes.

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   ![\[snap2\] The reassembled snapshots of normal and oblique impacts at different velocities keeping the normal component constant as $500$cm/sec. The crack patterns are almost same in all cases. (a) $\theta = 90^{\circ}$. (b) $\theta = 75^{\circ}$. (c) $\theta = 60^{\circ}$. (d) $\theta = 45^{\circ}$. ](crack/crack_90_500.ps "fig:"){width="40.00000%"}   ![\[snap2\] The reassembled snapshots of normal and oblique impacts at different velocities keeping the normal component constant as $500$cm/sec. The crack patterns are almost same in all cases. (a) $\theta = 90^{\circ}$. (b) $\theta = 75^{\circ}$. (c) $\theta = 60^{\circ}$. (d) $\theta 