Stress value after elastic-plastic loading, elastic loading, and unloading.Įquations (7) and (9) have been defined as variables and compared to the solution computed in COMSOL Multiphysics. It is worth noting that the residual stresses obtained may also be found by subtracting the elastic curve (green) from the elastic-perfectly plastic curve (blue). The red curve represents the residual stresses after one loading-unloading cycle. According to the blue curve, COMSOL Multiphysics results match perfectly with this value. The beam is fixed at the left-hand side and a bending moment is applied on the free end.īased on the beam theory, it turns out that the bending moment is constant in this case and the stress can be written as: Let’s consider the following slender beam with a rectangular cross section, depth a, and width b. These types of analyses also help you discover the optimal amount of material to be used for their reliability or the most suitable shape that needs to be designed, in order to avoid malfunctions and failures. Only through qualitative and quantitative analysis of these stresses is it possible to determine the most suitable machining processes for a given application.

For instance, brittle materials, such as glass in smartphone screens, are often manufactured so that compressive residual stresses are induced on the surface to avoid crack-tip propagation.įor these reasons, residual stresses play an important role in mechanical projects as a whole. Although residual stresses may alter the performance, or even lead to the failure of manufactured products, some applications actually rely on them. Indeed, uncontrolled residual stresses may cause a structure to fail prematurely. These will influence the part’s fatigue, failure, and even corrosion behaviors.

During the manufacturing process of a mechanical part, residual stresses will be introduced. Residual stresses are self-equilibrating stresses that remain after performing the unloading of an elastic-plastic structure. Then, we will introduce a sheet metal forming model. First, we will explain how they can be computed and interpreted in a bending beam example with or without work hardening. Today, we will introduce the concept of residual stresses in structural mechanics and find out how to compute them by taking the example of a deep metal drawing process.

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