The traditional design approaches of mechanical elements are based on some simple formula taken from theory and adapted by means of empirical coefficients to the case of interest.
Thus, shafts are treated as beam structures and the so called "nominal stress" calculated in this way is corrected by using the "theoretical stress concentration factor", to consider local effects related to the geometry of particular zones (i.e.: fillets to connect sections with different diameters, lubricating holes,….). The theoretical stress concentration factor can be found on tables and in textbooks for the simplest and more common cases, while it has to be determined if the case is new. And, if it is too expansive to obtain by experiments, some values from similar cases are adapted.
This approach is changed with the diffusion of the finite element codes that allow one to obtain accurate values of the stresses without developing complex experiments. The introduction of finite element calculation has permitted the development of new and refined design approaches, based more on the analysis than on simple formulas. But, also in this case the material is considered homogeneous, continuous and without defects.
If we focus our attention on fatigue, the traditional design approach is full of empirical coefficients: the surface coefficient, the dimensional coefficient, the fatigue notch sensitivity that consider in a simple way the influence of complex phenomena on the fatigue behaviour of materials and components. Anyway, also in this case the computational approach considers a perfect, continuous material.
But materials have defects, whose criticality depends on the service conditions, on the environment and on the material sensitivity to their presence.
Surface defects, inclusions and voids, for example, can play an important role in determining the fatigue strength of materials, as they can be considered as a pre-existent crack that is the site where crack propagation starts. Their importance increases for very long durations, since other failure mechanisms are active only for higher applied stresses and the presence of defects becomes critical. And the importance of taking into account defects increases in surface hardened materials, since surface is no more the most critical zone of the element.
The development of design approaches able to take the defects into account is not simple and must be based on Fracture Mechanics concepts, the science that studies the way defects propagate or not.
On this basis an approach called "Defect Tolerant Design" has been developed and allows one to predict if a defect could be dangerous or not. Indeed, the application of this methodology is not easy, since it requires a complete statistical characterization of the defects in the material (their distribution in terms of number and dimensions), but it is successfully used in some important industrial sectors: automotive is one of this and, in particular, springs and bearings are designed taking into account the material defects.
And what about shot peening? Also considering the presence of defects, shot peening is important to improve fatigue strength. As previously written, defects act as pre-existent cracks and shot peening is useful in avoiding crack propagation thanks to the action of the residual stresses induced.
If surface defects are considered, this is even more evident and there are data that show that shot peening can induce an increment of the fatigue limit of more than 50% in elements containing defects with known dimensions. For example, by means of rotating fatigue tests, it was found that the fatigue limit of a gas-nitrided steel with artificially induced surface defects (obtained with electro-erosion in controlled conditions) was doubled.
Also in the case of internal defects, shot peening has a useful effect, since the in-depth residual stress trend can shift the position of a critical defect in the inner layer of material, thus allowing application of a larger stress before failure. From another point of view, if we consider a defect at the same position, the action of shot peening is able to increase the dimension of the critical defect, thus improving the global behaviour of the material.
Anyway, if we want to take full advantage by shot peening elements designed taking into account the presence of defects, the treatment must be set up with opportune parameters, chosen after adequate theoretical and experimental studies.

Shot Peening in the Automotive Industry
by Mario Guagliano
Contributing Editor MFN and
Associate Professor of Technical University of Milan
20156 Milan, Italy
E-mail: mario@mfn.li

Author: Mario Guagliano