**1. Definition of residual stresses and their relevance**

Residual stresses (RS) are stresses present inside the materials and the structures even in absence of any applied external load. Residual stresses arise as a consequence of the complex sequence of steps starting from the material production, through machining, to final joining of subparts allowing manufacturing the final component [1]. Each production stage, in fact, such as casting, forming, joining, cutting, grinding, polishing, welding, heat treating, and so on, contributes to modify the pre-existing state of stress, and all of them add their specific contribution to determine the final residual stress field in the manufactured part [2].

Knowledge, control, and modification of the level of RS inside a given material or part become of capital importance by taking into consideration that residual stresses can impact greatly on the mechanical strength of the material, on its dimensional correspondence to design specifications, as well as on the corrosion resistance and on the fatigue life and durability of the part. It is well-known, for example, that tensile RS play a relevant role in reducing the fatigue life of the component so that several specific stress relaxation treatments have been developed in order to mitigate or eliminate their presence [3]. On the other side, the presence of a compressive stress field can have positive effects, and, due to this reason, some processes such as shot peening or laser shock peening have been developed to allow their introduction.

With respect to the recent past, it can be observed that mechanical designers have, nowadays, a greater awareness about the necessity to take into account also the presence of residual stress in their project. Relevance of RS, in fact, is now well assessed not only at academic level but also on the industrial side. At the same time, the multiplication and the evolution of the production techniques, the appearance of new disruptive manufacturing processes such as the additive manufacturing, the availability of more and more performing surface treatment techniques, the introduction of new coating technologies, and the request for increasingly better performing components result in a demand for more updated methods for residual stress evaluation.

The main aim of this book is to provide the reader with an overview of the principal challenges that research in terms of residual stress evaluation is currently facing including current limitations and potential future developments. At the same time, the reader will have an overview of the different materials, production technologies, and fields of applications where interest in RS evaluation is of capital importance but at the same time still not conveniently fulfilled by traditional and consolidated approaches.
