Crackling noise in advanced gravitational wave detectors: A model of the steel cantilevers used in the test mass suspensions

The response of elastic materials to external changing conditions can proceed through small and discrete releases of stress, rather than a continuous and smooth deformation as described by the classical elasticity theory. In a macroscopic elastic body, the sum of all those small crackling events can create a detectable displacement noise (crackling noise). In this paper we consider the case of the steel cantilevers used in the seismic isolation systems of ground based gravitational wave detectors, to provide the vertical isolation needed to reach the detector target sensitivity. Those instruments are reaching unprecedented displacement sensitivity, at a level that might be limited by crackling noise in the aforementioned cantilevers. Understanding this source of noise is extremely important, especially considering its intrinsic nonlinear nature. Since a detailed microscopical model of crackling noise in polycrystalline steel is not available at the moment, we suggest a phenomenological microscopical model, and the focus of this paper is on how crackling noise scales with the size and geometry of the cantilevers. The goal of this paper is to provide a method to scale up future measurements of crackling noise from small test cantilevers to the large ones used in advanced gravitational wave detectors.