Abstract
A phase diagram for a one-dimensional fiber bundle model is constructed with a continuous variation in two parameters guiding the dynamics of the model: strength of disorder and range of stress relaxation. When the range of stress relaxation is very low, the stress concentration plays a prominent role and the failure process is nucleating where a single crack propagates from a particular nucleus with a very high spatial correlation unless the disorder strength is high. On the other hand, a high range of stress relaxation represents the mean-field limit of the model where the failure events are random in space. At an intermediate disorder strength and stress release range, when these two parameters compete, the failure process shows avalanches and precursor activities. As the size of the bundle is increased, it favors a nucleating failure. In the thermodynamic limit, we only observe a nucleating failure unless either the disorder strength is extremely high or the stress release range is high enough so that the model is in the mean-field limit. A complex phase diagram on the plane of disorder strength, stress release range, and system size is presented showing different failure modes - 1) nucleation 2) avalanche, and 3) percolation, depending on the spatial correlation observed during the failure process.
Highlights
We study the spatial correlation during failure process of a fiber bundle model (FBM) [40, 41]
A high thermal fluctuation as well leads to a failure process, random in space, with the same universality class of a site percolation [47]
In Local Load Sharing Fiber Bundle Model: Variation in β, we explore the local load sharing limit of the model which can be achieved by setting a very high c
Summary
It is nearly a century since Alan Arnold Griffith developed his energy criterion for the fracture propagation of cracks in near-continuous solids [1, 2]. On the other hand, predicts the load distribution around an Inglis crack [36, 37] to be 1/r2-type where r is the distance from the crack tip This form for relaxation of local stress can be affected by many parameters like correlation among defects [38] and effect of the limited size of the sample [39]. A high thermal fluctuation as well leads to a failure process, random in space, with the same universality class of a site percolation [47] When we combine both the effects of stress release range and disorder strength, the model produces rich relaxation dynamics with different modes of failure − abrupt, non abrupt, nucleating, and random in space [48]. Such a study is carried out in the present article and can offer a nice insight into the fracture pattern
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