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Abstract
We study the effect of the competition between disorder and stress enhancement in fracture processes using the local load sharing fiber bundle model, a model that hovers on the border between analytical tractability and numerical accessibility. We implement a disorder distribution with one adjustable parameter. The model undergoes a localization transition as a function of this parameter. We identify an order parameter for this transition and find that the system is in the localized phase over a finite range of values of the parameter bounded by a transition to the non-localized phase on both sides. The transition is first order at the lower transition and second order at the upper transition. The critical exponents characterizing the second order transition are close to those characterizing the percolation transition. We determine the spatiotemporal correlation function in the localized phase. It is characterized by two power laws as in invasion percolation. We find exponents that are consistent with the values found in that problem.
Highlights
It has been known for a long time that heterogeneities make materials more resilient against failure under load by offsetting the point at which a microfracture becomes unstable [1]
IV, we study the spatiotemporal correlation function first introduced by Furuberg et al [24] in connection with invasion percolation
We have here studied the effect of the competition between disorder and stress enhancement using the local load sharing fiber bundle model
Summary
It has been known for a long time that heterogeneities make materials more resilient against failure under load by offsetting the point at which a microfracture becomes unstable [1]. As the failure process proceeds, these high-stress spots will start dominating As it was argued by Roux and Hansen [14] disorder makes local failures repulsive whereas the stress field makes them attractive. In the failure process, the disorder tends to dominate, resulting in local failures appearing distributed throughout the material. It should be noted that Stormo et al [23] studied the interplay between disorder and stress enhancement in the soft clamp model which is a more complex version of the fiber bundle model than the version we study here Their conclusions differ from those we present here; this is due to a very different way of analyzing the fracture process.
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