## 1 Introduction  
In modern engineering applications, various techniques are employed to enhance the durability of components under pressure and increase safety levels. One of these techniques is autofrettage, a crucial manufacturing process that involves subjecting a cylinder to high internal pressure, inducing plastic deformation. Upon pressure release, the cylinder's material attempts to revert to its original shape, resulting in beneficial residual compressive stresses within and residual tensile stresses outside the cylinder. These residual stresses enhance the cylinder's ability to withstand higher pressures by reducing material stress. Hydraulic autofrettage, utilizing fluid pressure, and mechanical autofrettage, employing mandrels, are the two primary methods used to enhance the pressure-bearing capacity and fatigue life of cylinders. Widely adopted across industries like aerospace, automotive, and pressure vessel manufacturing, autofrettage significantly improves the durability and safety of high-pressure components [1; 2; 3; 4; 5; 6; 7]. The most significant factors that can affect the residual stress field obtained from hydraulic autofrettage are autofrettage pressure, wall thickness, and material properties [8]. The variability of these factors can create a high level of variability in the residual stress response. Therefore, knowing the sensitivity of the residual stress response obtained from the autofrettage process to these factors is crucial in the design of pressure vessels. [PERSON] et al. utilized the complex variable finite element method to compute the sensitivity of the residual stress field obtained from autofrettage applied to a thick-walled spherical pressure vessel to material parameters and autofrettage pressure. According to the results obtained, it was observed that the most influential parameter on residual stresses is the autofrettage pressure, while the yield stress stands out as the most influential among material parameters [8]. In the production process of a component resistant to high pressure, machining is often required after the autofrettage process. Machining is employed to achieve specific manufacturing tolerances in components such as the piston-cylinder pair of a high-pressure pump. Additionally, it can be applied to the outer surface of a firearm barrel to lighten the barrel in regions where the internal pressure of the barrel is low or to create grooves on the inner bore to impart a rotational motion to the bullet. As a result of these processes, some of the beneficial residual stresses created by the autofrettage process are lost, and a new residual stress distribution is formed in the cylinder wall. This affects the load-bearing capacity of the component during service. Therefore, determining the residual stress loss caused by the machining process is crucial for accurately estimating the pressure-carrying capacity of the designed cylinder [9; 10]. [PERSON] et al. examined the residual stress fields resulting from internal and external material removal operations applied to a thick-walled autofretaged cylinder for materials exhibiting both the Bauschinger effect and those that do not show it [11]. [PERSON] et al. developed an analytical model for calculating the new residual stress field resulting from the internal, external, and combined processing of a firearm barrel after autofrettage. The model treats partially autofretaged and fully autofrettaged barrels separately. Additionally, in this study, they validated the analytical model developed with finite element analysis [12]. [PERSON] et al. investigated the effect of material removal on residual stress using an analytical method that accounts for the material's true unloading behavior [13]. [PERSON] et al. examined the effect of internal and external machining on residual stress using the finite element method. The results indicated that the maximum circumferential stress was more sensitive to internal machining than external machining and that material removal did not alter the elastic-plastic interface [14].