Failure process of a bundle of plastic fibers

Abstract

We present an extension of fiber bundle models considering that failed fibers still carry a fraction 0 < or = alpha < or = 1 of their failure load. The value of alpha interpolates between the perfectly brittle failure (alpha = 0) and perfectly plastic behavior (alpha = 1) of fibers. We show that the finite load bearing capacity of broken fibers has a substantial effect on the failure process of the bundle. In the case of global load sharing it is found that for alpha --> 1 the macroscopic response of the bundle becomes perfectly plastic with a yield stress equal to the average fiber strength. On the microlevel, the size distribution of avalanches has a crossover from a power law of exponent approximately 2.5 to a faster exponential decay. For localized load sharing, computer simulations revealed a sharp transition at a well-defined value alpha(c) from a phase where macroscopic failure occurs due to localization as a consequence of local stress enhancements, to another one where the disordered fiber strength dominates the damage process. Analyzing the microstructure of damage, the transition proved to be analogous to percolation. At the critical point alpha(c), the spanning cluster of damage is found to be compact with a fractal boundary. The distribution of bursts of fiber breakings shows a power-law behavior with a universal exponent approximately 1.5 equal to the mean-field exponent of fiber bundles of critical strength distributions. The model can be relevant to understand the shear failure of glued interfaces where failed regions can still transmit load by remaining in contact.

Brittle-to-ductile transition in a fiber bundle with strong heterogeneity

“…This widely different strength of the components combined with appropriate coupling results in an improved damage tolerance which has a high relevance for applications [20,21]. It has been shown that in heterogeneous materials, varying the local mechanical response and of the amount of disorder of the components one * ferenc.kun@science.unideb.hu can achieve a transition from brittle to quasibrittle or even to ductile failure [22][23][24][25].…”

Time-dependent mechanical behavior of human amnion: Macroscopic and microscopic characterization

“…Stress-relaxation and cyclic experiments on human amnion showed a stresslevel-dependent response and, surprisingly, lower dissipation at higher strain levels, which could indicate an intrinsic coupling of strain-and time-dependency [15,16]. Stress-relaxation in soft biological tissues arises from microstructural mechanisms, such as relaxation of single collagen fibrils [33,34], global rearrangement of collagen microstructure [34,35,36], progressive failures of crosslinks [37,38,39], liquid phase rearrangement or dehydration [40,41], and may depend on the stress level reached [42]. The specific mechanisms determining the mechanical time-dependence of amnion have not yet been identified.…”

Universality class of fiber bundles with strong heterogeneities

“…To capture the effect of disorder, recently several stochastic fracture models have been proposed such as the fiber bundle model (FBM) and lattice models of fuses or springs [1][2][3][4][5][6][7]. Based on these models, analytic calculations and computer simulations revealed that macroscopic fracture of disordered materials shows interesting analogies with phase transitions and critical phenomena having several universal features independent of specific material details [1,[4][5][6][8][9][10]. It has been found that under a slowly increasing external load macroscopic failure is preceded by a bursting activity due to the cascading nature of local breakings [3,4].…”