AbstractAssessment of Residual Stresses in Quasi‐statically and Cyclically Loaded MaterialsThe actual knowledge of residual stresses is extremely extensive (see e.g. [1–8]). Nevertheless, in many cases, the consequences of residual stresses on the mechanical behaviour of materials are still qualitatively assessed by experience. This fact is mainly due to the great expense which is necessary to obtain sufficient quantitative information concerning residual stresses in technical parts. Without such data, however, it is not possible to assess residual stress states objectively.In modern materials technology, residual stresses are usually applied in a twofold manner. On the one hand, they are used as a mostly uncontrollable argument in the interpretation of unexpected failure. On the other hand, they are utilized as a valuable and cheap tool in improving the strength of components.It is well established the principally no material states of practical importance exist which are free of residual stresses. Consequently, the evaluation and assessment of residual stresses in technical parts is of great importance. In this respect, special interest is focussed on such residual stress states which improve the materials behaviour under particular loading conditions.This paper deals with the fundamental aspects of the assessment of statically and cyclically loaded components bearing 1st kind residual stresses. First, some basic principles of the theory of elasticity and the theory of equivalent stresses are outlined. Then, well‐accepted definitions of residual stresses are presented. Afterwards, characteristics of the mechanical resistance of materials are described, which can be determined from simple loading tests. Subsequently, the principles of elementary failure considerations are treated followed by a discussion of the influence of residual stresses on the behaviour of statically loaded components. Typical examples are dealt with. Finally, some basic facts concerning the fatigue behaviour of metallic materials are described, and the consequences of residual stresses on cyclically loaded components are discussed. Presenting characteristic examples, the progress is documented which has recently been achieved in the understanding of the effects of residual stresses on the fatigue behaviour of differently treated mate