  The directed flow of identified particles can serve as a sensitive tool for
investigating the interactions during initial and final states in heavy ion
collisions. This study examines the rapidity-odd directed flow ($v_{1}$) and
its slope ($dv_{1}/dy$) for $\pi^{\pm}$, $K^{\pm}$, p, and $\bar{\mathrm p}$ in
Au+Au collisions at different collision centralities and beam energies
($\sqrt{s_{\mathrm NN}}$ = 7.7, 11.5, 14.5, 19.6, 27, and 39 GeV) using the
UrQMD model. We investigate the impact of late-stage hadronic interactions on
charge dependent $v_{1}(y)$ and its slope by modifying the duration of the
hadronic cascade lifetime ($\tau$). The energy dependence of $dv_{1}/dy$ for p
($\bar{\mathrm p}$) exhibits distinct pattern compared to $\pi^{\pm}$ and
$K^{\pm}$. Notably, we observe a change in the sign reversal position of proton
$dv_{1}/dy$ at different beam energies with varying $\tau$ in central and
mid-central collisions. Moreover, the difference in $dv_{1}/dy$ between
positively and negatively charged hadrons ($\Delta dv_{1}/dy$) demonstrates a
stark centrality dependence for different particle species. The deuteron
displays a significant increase in $dv_{1}/dy$ with increasing $\tau$ compared
to p and n. This investigation underscores the importance of considering the
temporal evolution and duration of the hadronic phase when interpreting the
sign reversal, charge splitting of $v_{1}$ and light nuclei formation at lower
RHIC energies.
