 An experimental scheme is proposed using a trapped ion quantum simulator to observe pre-thermalization and a dynamic phase transition in a one-dimensional x-y spin chain with long range interactions and inhomogeneous lattice spacing, where local physical observables relax to pre-thermal values at an intermediate timescale before completely relaxing to thermal values at much longer time. The physical origin of pre-thermalization is shown to result from a non-trivial structure in the lower half of the energy spectrum, while the dynamic behavior of the system crosses different phases when the interaction range is continuously tuned, indicating the existence of a dynamic phase transition. This article was authored by Zhixian Gong and L. M. Duan.