Universality behind Basquin’s Law of Fatigue

Abstract

Basquin's law of fatigue states that the lifetime of the system has a power-law dependence on the external load amplitude, tf approximately sigma 0- alpha, where the exponent alpha has a strong material dependence. We show that in spite of the broad scatter of the exponent alpha, the fatigue fracture of heterogeneous materials exhibits universal features. We propose a generic scaling form for the macroscopic deformation and show that at the fatigue limit the system undergoes a continuous phase transition. On the microlevel, the fatigue fracture proceeds in bursts characterized by universal power-law distributions. We demonstrate that the system dependent details are contained in Basquin's exponent for time to failure, and once this is taken into account, remaining features of failure are universal.

Disorder-induced brittle–to–quasi-brittle transition in fiber bundles

“…One of the most important modeling approaches to the fracture of heterogeneous materials is the fiber bundle model (FBM) [2][3][4][5][6][7][8][9]. In the framework of the model the sample is discretized in terms of a parallel bundle of fibers.…”

A Model for Rolling Bearing Life with Surface and Subsurface Survival—Tribological Effects

“…This indicates that a common Weibull slope can be used in Eq. [29]. This equation can be used to back-calculate the surface damage parameter R s D u e I s /[Kln(1/0.9)] corresponding to 90% reliability of a bearing populations that are endurance tested.…”

“…Others exponents and constants used in Eqs. [29] and [25] can be taken from Ioannides, et al (12), leading to the results of Table 4.…”

“…Equation [29] represents a new general semi-analytical form for bearing life calculation, based only on the modifying factor a u with no surface damage components. It introduces an additional new surface damage function (or integral) I s to account for only the surface effects in bearing life, calculated from Eq.…”

Signal frequency distribution and natural-time analyses from acoustic emission monitoring of an arched structure in the Castle of Racconigi

“…Thus, acoustic emission (AE) monitoring during loading experiments gives insight into the evolution of microcrack networks in laboratory experiments and is possibly a tool for understanding the occurrence of fractures at larger scales (Mogi, 1962). Over the last decades, this approach has provided the opportunity to develop universal scaling laws reflecting the scale invariance and the self-similarity of fracture processes from the laboratory to the fault scale in time, space and magnitude domains (Turcotte, 1997;Bonnet et al 2001;Bak et al, 2002;Tosi et al, 2004;Corral, 2006;Davidsen et al, 2007;Kun et al, 2008). These studies should hopefully contribute to solving the main problems of earthquake prediction and the remaining life assessment of structural elements.…”