spannungsdichte

Spannungsdichte, translated as stress intensity, is a fundamental concept in fracture mechanics. It quantifies the severity of stress in the vicinity of a crack tip in a solid material. Unlike nominal stress, which is calculated by dividing the applied load by the original cross-sectional area, spannungsdichte specifically accounts for the geometric singularity that occurs at the sharp point of a crack. As a crack propagates through a material, the stress field ahead of it becomes infinitely large in a theoretical elastic model. Spannungsdichte provides a more realistic measure of this stress concentration, as it remains finite and is a function of the applied load, crack length, and the geometry of the component.

The most common form of spannungsdichte is the Mode I spannungsdichte, denoted as K_I. This mode represents opening or tensile loading, where the crack surfaces are pulled apart. A critical value of spannungsdichte, known as the fracture toughness (K_Ic), exists for each material. When the applied spannungsdichte reaches or exceeds the fracture toughness, catastrophic crack growth and failure of the component will occur. This concept is crucial for assessing the structural integrity of materials and designing components that can safely withstand expected loads and environmental conditions, particularly in applications where fatigue or brittle fracture is a concern.