The formation of a one-dimensional residual stress field in the neighbourhood of a cylindrical defect in the continuity of an elastoplastic medium

On the Residual Stresses in the Vicinity of a Cylindrical Discontinuity in a Viscoelastoplastic Material

“…4). Although the numerical calculations performed in the present study and in [1] used different models, their results differ quantitatively only slightly. This work was supported by the Russian Foundation for Basic Research (Grant No.…”

“…The manifestation of viscous properties in the deformation stage preceding plastic flow or in the unloading stage is less obvious. Below, we consider exactly this case, assuming, as in [1], that the plastic flow is ideal. We note that the displacements of points of the medium being deformed in the vicinity of the discontinuity are commensurable with the defect size; therefore the assumption of small strains cannot be used.…”

“…The formation of a residual stress field in the vicinity of a cylindrical discontinuity has been previously considered for the model of large elastoplastic strains [1]. It turned out that the assumption of an ideal nature of plastic flow and allowance for only the elastic properties of the material during its deformation before plastic flow and during unloading are responsible for the adjustability of the defect to cyclic loads.…”

“…One of the goals of the present study is to compare the results obtained with the results of solution of the problem in question for the model of an ideal elastoplastic medium. As noted above, this problem is considered in [1] using the model of large elastoplastic strains proposed in [2]. Therefore, the given mathematical model is chosen as the basis for the construction of further modeling relations.…”

“…Figure 1 gives the variation in the boundary of the defect during loading. Figure 2 shows the difference in the defect size for unloading between the case of an ideal elastoplastic medium [1] (the solid curve in Figs. 2-4) and with allowance for viscosity during elastic deformation and during unloading (the dashed curve in Figs.…”