  We consider a class of separately convex phase field energies employed in
fracture mechanics, featuring non-interpenetration and a general softening
behavior. We analyze the time-discrete evolutions generated by a staggered
minimization scheme, where fracture irreversibility is modeled by a
monotonicity constraint on the phase field variable. After recasting the
staggered scheme by means of gradient flows, we characterize the
time-continuous limits of the discrete solutions in terms of balanced viscosity
evolutions, parametrized by their arc-length with respect to the L2-norm (for
the phase field) and the H1-norm (for the displacement field). By a careful
study of the energy balance we deduce that time-continuous evolutions may still
exhibit an alternate behavior in discontinuity times.
