University of Debrecen

Department of Theoretical Physics

H-4010 Debrecen, P.O.Box 5, Hungary


Phone: +36 52 417266 ext. 1388


Fax: +36 52 346758

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Ferenc Kun is professor at the Department of Theoretical Physics (UD). He received his PhD in 1997 and became doctor of the Hungarian Academy of Sciences (DSc) in 2010. As a PhD Student he studied at the Ecole Superieur de la Physique et Chimie Industrielle in Paris, and later on he was postdoc at the Institute of Computational Physics of the University of Stuttgart. His major research field is the physics of complex systems and the statistical physics of fracture and fragmentation phenomena.

Creep rupture due to thermally induced cracking

Sub-critical rupture, occurring under a constant load below the fracture strength of materials, is of fundamental importance in a wide range of physical, biological, and geological systems. Depending on the type of materials, creep rupture can have a wide variety of microscopic origins from the existence of frictional interfaces through the visco-elasticity of the constituents, to thermally activated aging processes. Recent experimental and theoretical investigations revealed the high importance of thermally activated micro-crack nucleation in creep phenomena with consequences reaching even to geological scales. Under creep loading failure often occurs as a sudden unexpected event following a short acceleration period which addresses safety problems for e.g. components of engineering constructions. Additionally, creep rupture underlies natural catastrophes such as landslides, stone and snow avalanches and it is also involved in the emergence of earthquakes.

Based on a fiber bundle model we showed that stress inhomogeneities play a crucial role in the process of thermally activated sub-critical rupture giving rise to a broad spectrum of novel behaviors. Stress concentrations, arising in the vicinity of failed regions of the material, make the system more sensitive to thermal fluctuations. As a consequence, an astonishing size effect emerges where the average time-to-failure of the model system decreases as a power law of the system size. The size scaling exponent depends both on the temperature and on the external load. We proposed a modified form of the Arrhenius law of lifetime which provides a comprehensive description of thermally activated breakdown phenomena [1,2,3].

Figure: (a) Average waiting time for ELS and LLS as function of the fraction of broken fibers . (b) Comparison of the curves of average waiting time and entropy as a function of. For LLS the entropy starts to decrease when the acceleration sets on. (c,d,e,f) Snapshots of an evolving system, where fibers are colored according to their load. Deep blue represents zero load hence indicating cracks in the system.

On the micro-level, thermally driven breakdown proceeds in bursts of breakings which are separated by waiting times. The size distribution of bursts and the distribution of waiting times between consecutive events proved to have power law functional forms followed by an exponential cutoff. The power law exponents have a complex dependence on the load and temperature of the system [1,3]. To characterize the overall time evolution of the system, we analyzed the average waiting time between bursts as a function of the fraction of broken fibers. Calculations showed that the thermally induced creep process has two phases: at low loads and high temperatures the process slows down after the load is set, which is then followed by an accelerating period. However, when the load is high enough the system continuously accelerates towards failure. We demonstrated that in the case of localized load sharing, the stress concentration around cracks leads to spatial correlation of breaking events and to an enhanced breaking probability which in turn is responsible for the early acceleration [1,2,3].

In order to quantify the effect of spatial correlation on the time evolution of the creep rupture process, we evaluated the structural entropy of avalanches and their consecutive positioning. As a very important outcome, our calculations revealed that the decreasing extension and the spatial localization of avalanches to a bounded region of the specimen are responsible for the acceleration towards macroscopic failure. Final failure is driven by a single growing crack which becomes unstable as the avalanches localize to its perimeter [3].

1. N. Yoshioka, F. Kun, and N. Ito, Physical Review Letters 101, 145502 (2008).
2. N. Yoshioka, F. Kun, and N. Ito, Physical Review E 82 055102(R) (2010).
3. N. Yoshioka, F. Kun, and N. Ito, Europhysics Letters 97, 26006 (2012).