The "Method of Tensile Triangles" was introduced as a design tool that mimics the rules of nature for the shape optimization of a design scheme with respect to increased fatigue life and reduced weight. It was inspired by the shape of buttress roots in trees. Like them it bridges a corner-like notch with tensile loaded triangles. The notch shape may be scaled up and down according to the individual design space limitations of the technical structure.Failure often starts at the cracks tips and slot ends in technical components, because these domains are highly loaded due to stress concentrations. Conventional rounding or drilling away of these crack tips can only lower the stresses. By means of the "Method of Tensile Triangles", stress concentrations can be minimized and the endings redesigned and compressed.In this paper the "Method of Tensile Triangles" will be explained and it will be shown, by results of Finite Element analyses, how the destructive effect of crack tips and slot ends in technical components can be eliminated.

A B S T R A C T Recently, the 'method of tensile triangles' has been introduced for optimizing the shape of notches by adding material at overloaded regions but also to remove unloaded material from an oversized design proposal.In this work, we apply the method to demonstrate that the unloaded region in the vicinity of a crack has the shape of spindle-shaped hole, which looks like two dunce caps mirrored at the crack line. Also, these shapes can be predicted by the 'method of tensile triangles' without any FEM-effort. Furthermore, we show a new way to stop cracks by deviating the crack tip into a shape-optimized pattern leading to a compressive stress that closes the crack tip. This procedure is now used in chemical engineering.

Trees attach thicker tree rings at overloaded places. This principle is mimicked here in order to delay crack initiation and propagation. Bulges are attached beside notches to reduce stress concentrations. The bulges have to be shape optimized so as to not cause notch stresses themselves. Brittle coating can act as a warner near notches. The crack stoppers are described by FEM and the result is verified by comparative fatigue testing of prototypes leading to up to 21 times longer fatigue life.