How do applied stresses and residual stresses interact?

It is not always easy to estimate the effect of residual stresses during the design phase. It is generally known that residual stresses can significantly influence the service life of components. For this reason, processes such as deep rolling, machine hammer peening, and shot peening are used repeatedly. They generate the necessary compressive residual stresses in the subsurface area and are thus largely responsible for extending the service life of a dynamically loaded component. However, it is still difficult for design departments to take this into account in their calculations. In the following, we will explain how an initial rough estimate can be made and how residual stresses actually affect dynamic strength.

Residual stresses are internal stresses in the structure

First, we need to understand what residual stresses actually are. Residual stresses are stresses in the microstructure of a component that are present even when no external forces, torques, or temperature gradients are acting on the component, i.e., when the component is completely free of any load. They can occur anywhere in the manufacturing chain and are the result of mechanical and thermal loads during the individual manufacturing steps. For example, so-called casting stresses can arise during casting because the component cools at different rates in different areas. They can arise during machining due to the strong thermo-mechanical stresses caused by the cutting edge, or they can be generated specifically by means of mechanical solidification processes.

As with residual stresses, intrinsic stresses are generally divided into tensile and compressive stresses. Tensile stresses are described mathematically by a positive figure, while compressive stresses are described by a negative figure. In general terms, it can be said that compressive stresses extend the service life of components, while tensile stresses shorten it. 

The reason for this is the initiation of cracks by stress peaks. If the tensile stress in one part in a component is too great, a crack will form at this point. Initially, this crack is small, but it grows larger and larger with further loading until the component finally fails. In simple terms, tensile residual stresses pull on the crack, causing it to grow faster. Compressive residual stresses counteract crack propagation and thus slow down crack growth.

Superposition of load stresses and residual stresses

Like all stresses, residual stresses can also be superimposed with load stresses. This can be done by simple superposition. In other words, the load and residual stresses are simply added together. The result is then a resulting stress. We can easily understand this using the example of a uniaxial stress state, i.e., a bar. If a uniaxial tensile stress of s_load = 600 MPa is applied to this component and it has no residual stress, then the resulting stress is still s_res = 600 MPa. If, on the other hand, the bar is subjected to a compressive residual stress of s_ESP = -200 MPa in the same direction, then mathematically the 200 MPa is subtracted from the 600 MPa and the resulting stress is s_Res = 400 MPa. A bar that would fail at 550 MPa, for example, could therefore be used in the second case, but not in the first case. This explains the effect of residual stresses in a comprehensible way.

But what about a multi-axial stress state? Here, of course, the concept must be applied to the entire stress tensor. In this case, the corresponding residual stress values must be used for each component of the stress tensor. For example, in the x-direction, the principal stress of s_(x) must be calculated with the principal stresses in the x-direction. If this is done for all components as well as the shear stresses, the result is a complete stress tensor with principal stresses [1].

In order to estimate the effect on strength, the concepts of equivalent stress can be applied. This compresses the stress tensor to a single stress value and allows it to be compared with the strength characteristics from the stress-strain diagram. 

Of course, the method presented here is not a complete service life assessment, and further calculations or tests must always be carried out to estimate dynamic strength. However, the method presented here allows the effect of residual stresses to be roughly estimated. Effects such as additional strengthening of the microstructure or residual stress reduction during loading are not taken into account, however.