Prof. Dr Uwe Zerbst, Bundesanstalt für Materialforschung und -prüfung (BAM), Berlin, Germany. The acronym IBESS stands for “Integrale Bruchmechanische Ermittlung der Schwingfestigkeit von Schweißverbindungen“ which, translated from German, means „Integral fracture mechanics determination of the fatigue strength of welds”. The method introduced in this study is the outcome of a German research cluster in which eight partners were involved. A list of them is found at the end of this study. The IBESS method is characterized by a number of partially novel aspects and elements of fracture mechanics applied to the evaluation of fatigue strength of welds.