The Wöhler curve is a graphical representation used in materials science to illustrate the relationship between cyclic stress and the number of cycles to failure in a material. Named after the German chemist Friedrich Wöhler, this curve helps engineers understand how materials behave under repeated loading, which is crucial for designing components that experience fatigue. Typically, the Wöhler curve shows that as the applied stress increases, the number of cycles a material can endure before failure decreases. This relationship is vital for predicting the lifespan of materials in applications such as bridges, aircraft, and machinery, where fatigue failure can lead to catastrophic results.