Finite element modeling (FEM) of machining-induced residual stresses (RS) takes place over two consecutive steps; a cutting step and a relaxation step. In the latter, the workpiece is left to cool down after deactivating all external loads. The current work focuses on the relaxation step, and how different strain components, material plasticity and workpiece edge deflections affect the final state of different RS components. First, a 2D arbitrary-Lagrangian-Eulerian (ALE) plane strain thermo-mechanical explicit model was used to simulate dry orthogonal cutting. After that, the relaxation process was modeled using three approaches; 1) the classical approach, 2) a new approach that is first presented here, and 3) a modified approach that was developed earlier by the current author. In the classical approach, the same exact machined workpiece is relaxed, considering all stress / strain components and material plasticity. On the other hand, the new approach uses a pure elastic 1D thermal relaxation model, in the cutting direction, and assumes that the workpiece edges normal to the cutting direction remain so. The differences between the RS predicted by the new and classical approaches reflected the combined effects of the examined parameters. The role of each parameter was isolated using three different versions of the modified approach. The current findings confirmed that, for orthogonal cutting, the stress relaxation process can be considered as a 1D pure elastic thermal relaxation process. Also, the workpiece edges normal to the cutting direction deflect during relaxation, contributing to the final state of RS.