We investigate the strongly correlated ion dynamics and the degree of coupling achievable in the evolution of freely expanding ultracold neutral plasmas. We demonstrate that the ionic Coulomb coupling parameter $Gamma_{rm i}$ increases considerably in later stages of the expansion, reaching the strongly coupled regime despite the well-known initial drop of $Gamma_{rm i}$ to order unity due to disorder-induced heating. Furthermore, we formulate a suitable measure of correlation and show th at $Gamma_{rm i}$ calculated from the ionic temperature and density reflects the degree of order in the system if it is sufficiently close to a quasisteady state. At later times, however, the expansion of the plasma cloud becomes faster than the relaxation of correlations, and the system does not reach thermodynamic equilibrium anymore.
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