We study in-plane ruptures on a bimaterial fault governed by a velocity-weakening friction with a regularized normal stress response. Numerical simulations and analytical estimates provide characterization of the ranges of velocity-weakening scales, nucleation lengths and background stresses for which ruptures behave as cracks or pulses, decaying or sustained, bilateral or unilateral. With strongly velocity-weakening friction, ruptures occur under a wide range of conditions as large-scale pulses with a preferred propagation direction, that of slip of the more compliant material. Such ruptures have macroscopic asymmetry manifested by significantly larger seismic potency and propagation distance in the preferred direction, and clearly quantified by the directivity ratio derived from the second order moments of the spatio-temporal distribution of slip rate. The macroscopic rupture asymmetry of the large-scale pulses stems from the difference in the criticality conditions for self-sustained propagation in each rupture direction, induced by the asymmetric normal stress changes operating in bimaterial interfaces. In contrast, crack-like ruptures show macroscopic asymmetry under restrictive conditions. The discussed mechanism is robust with respect to regularization parameters, ranges of stress heterogeneities and a proxy for off-fault yielding and should operate similarly for crustal-scale rupture pulses even in the absence of velocity-weakening. Small-scale pulses, driven by the bimaterial normal stress reduction at the scale of the process zone, can detach from the rupture front of the large-scale pulses that propagate in the preferred direction. However, their occurrence depends on the relaxation scale in the regularization of the normal stress response and their development can be hindered by off-fault yieldin
