Creep rupture due to thermally induced cracking
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Creep rupture due to thermally induced cracking Naoki Yoshioka1, Ferenc Kun2 , and Nobuyasu Ito3 1
Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwake-cho, 6068502 Kyoto, Japan. 2 Department of Theoretical Physics, University of Debrecen, H-4010 Debrecen, P.O.Box: 5, Hungary. 3 Department of Applied Physics, Graduate School of Engineering, The University of Tokyo, 7-31, Hongo, Bunkyo-ku, 113-8656 Tokyo, Japan.
ABSTRACT We study sub-critical fracture driven by thermally activated crack nucleation in the framework of a fiber bundle model. Based on analytic calculations and computer simulations we show that in the presence of stress inhomogeneities, thermally activated cracking results in an anomalous size effect, i.e. the average lifetime of the system decreases as a power law of the system size, where the exponent depends on the external load and on the temperature. We propose a modified form of the Arrhenius law which provides a comprehensive description of the load, temperature, and size dependence of the lifetime of the system. On the micro-level, thermal fluctuations trigger bursts of breaking events which form a stochastic time series as the system evolves towards failure. Numerical and analytical calculations revealed that both the size of bursts and the waiting times between consecutive events have power law distributions, however, the exponents depend on the load and temperature. Analyzing the structural entropy and the location of consecutive bursts we show that in the presence of stress concentration the acceleration of the rupture process close to failure is the consequence of damage localization. INTRODUCTION 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 [1-7]. 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. On the macroscopic scale the rupture process is characterized by the strain-time diagram and by the lifetime of the system, which both have a complex dependence on the external load and on the temperature. In spite of the smooth macroscopic evolution, on the micro-scale, thermally activated breakdown proceeds in bursts which may be exploited to gain information about the approach of the system to failure. In th
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