The fracture of a climbing rope: a phenomenological approach

Abstract

For the fracture process of a climbing rope, two mechanisms are responsible: plastic deformation and local damage of the contact zone between the rope and the anchor. These mechanisms are described by two analytical models represented by nonlinear difference equations. The plastic deformation equation can be linked to a catastrophe-theoretical model. From the equation describing local damage accumulation, the Palmgren–Miner rule can be derived. The used energy-based approach allows the combination of these models and thus the calculation of the number of falls to failure as a function of the ratio of fall energy/energy storage capacity. The behavior of climbing ropes tested by subsequent UIAA falls can be quantitatively explained by these models.