Creep rupture has two universality classes

¹ Department of Theoretical Physics, University of Debrecen P.O. Box 5, H-4010 Debrecen, Hungary
² Departamento de Física Teórica, Universidad de Zaragoza - Zaragoza 50009, Spain
³ Instituto de Biocomputación y Física de Sistemas Complejos, Universidad de Zaragoza Zaragoza 50009, Spain
⁴ Institute for Computational Physics, University of Stuttgart Pfaffenwaldring 27, 70569 Stuttgart, Germany

Received: 31 January 2003
Accepted: 23 May 2003

Abstract

Objects subject to a steady load will often resist it for a long time before weakening and suddenly failing. This process can be studied by fiber bundle models, in which fibers fail in a random fashion that depends both upon the integrity of their neighbors and the load to which they are subjected. In this letter, we introduce a new fiber bundle model that allows us to examine how the behavior of such a system depends upon the range over which each fiber interacts with its neighbors. Using analytical and numerical arguments, we show that for all systems there is a critical load below which the system reaches equilibrium, and above which it fails in finite time. We consider how the time to failure depends upon how much the applied load exceeds the critical load, and find two universality classes. For short-range interactions, failure is abrupt, and time to failure is independent of load. For long-range interactions, the time to failure depends upon the excess load as a power law. The transition between these two universality classes is sharp as a function of the range of interaction. In both universality classes, the distribution of times between breaking events obeys a power law as the system creeps towards failure.