  We consider second order phase field functionals, in the continuum setting,
and their discretization with isogeometric tensor product B-splines. We prove
that these functionals, continuum and discrete, $\Gamma$-converge to a brittle
fracture energy, defined in the space $GSBD^2$. In particular, in the
isogeometric setting, since the projection operator is not Lagrangian (i.e.,
interpolatory) a special construction is needed in order to guarantee that
recovery sequences take values in $[0,1]$; convergence holds, as expected, if
$h = o (\varepsilon)$, being $h$ the size of the physical mesh and
$\varepsilon$ the internal length in the phase field energy.
