Energy bursts in fiber bundle models of composite materials

Finite-size effects on return interval distributions for weakest-link-scaling systems

The Weibull distribution is a commonly used model for the strength of brittle materials and earthquake return intervals. Deviations from Weibull scaling, however, have been observed in earthquake return intervals and the fracture strength of quasibrittle materials. We investigate weakest-link scaling in finite-size systems and deviations of empirical return interval distributions from the Weibull distribution function. Our analysis employs the ansatz that the survival probability function of a system with complex interactions among its units can be expressed as the product of the survival probability functions for an ensemble of representative volume elements (RVEs). We show that if the system comprises a finite number of RVEs, it obeys the κ-Weibull distribution. The upper tail of the κ-Weibull distribution declines as a power law in contrast with Weibull scaling. The hazard rate function of the κ-Weibull distribution decreases linearly after a waiting time τ(c) ∝ n(1/m), where m is the Weibull modulus and n is the system size in terms of representative volume elements. We conduct statistical analysis of experimental data and simulations which show that the κ Weibull provides competitive fits to the return interval distributions of seismic data and of avalanches in a fiber bundle model. In conclusion, using theoretical and statistical analysis of real and simulated data, we demonstrate that the κ-Weibull distribution is a useful model for extreme-event return intervals in finite-size systems.

Relaxation creep rupture of heterogeneous material under constant strain

We focus on a system consisting of an elastic part and a damageable part in series, to study the relaxation creep rupture of a heterogeneous system subjected to a uniaxial constant strain applied instantaneously. The viscoelastic behavior of the damageable part is modeled by a fiber bundle model consisting of Kelvin-Voigt elements and global load sharing is assumed for the redistribution of load following fiber breaking in the damageable part. Analytical and numerical calculations show that the global relaxation creep rupture appears if the elastic energy stored in the elastic part exceeded the fracture energy of the damageable part. The lifetime of the system strongly depends on the values of the applied external strain and the initial stiffness ratio k between the elastic part and the damageable part. We show that a higher stiffness ratio implies a more brittle system. Prior to complete failure, relaxation creep rupture exhibits a sequence of three stages, similar to creep rupture under constant stress, and the nominal force rate presents a power law singularity with a power index -1/2 near the global rupture time.

Prediction of the collapse point of overloaded materials by monitoring energy emissions

A bundle of many fibers with stochastically distributed breaking thresholds is considered as a model of composite materials. The fibers are assumed to share the load equally and to obey Hookean elasticity up to the breaking point. The bundle is slightly overloaded which leads to complete failure. We study the properties of emission bursts in which an amount of energy E is released. The analysis shows that the size of the energy bursts has a minimum when the system is halfway from the collapse point.

Hierarchical simulations for the design of supertough nanofibers inspired by spider silk

Biological materials such as spider silk display hierarchical structures, from nano to macro, effectively linking nanoscale constituents to larger-scale functional material properties. Here, we develop a model that is capable of determining the strength and toughness of elastic-plastic composites from the properties, percentages, and arrangement of its constituents, and of estimating the corresponding dissipated energy during damage progression, in crack-opening control. Specifically, we adopt a fiber bundle model approach with a hierarchical multiscale self-similar procedure which enables to span various orders of magnitude in size and to explicitly take into account the hierarchical topology of natural materials. Hierarchical architectures and self-consistent energy dissipation mechanisms (including plasticity), both omitted in common fiber bundle models, are fully considered in our model. By considering one of the toughest known materials today as an example application, a synthetic fiber composed of single-walled carbon nanotubes and polyvinyl alcohol gel, we compute strength and specific energy absorption values that are consistent with those experimentally observed. Our calculations are capable of predicting these values solely based on the properties of the constituent materials and knowledge of the structural multiscale topology. Due to the crack-opening control nature of the simulations, it is also possible to derive a critical minimal percentage of plastic component needed to avoid catastrophic behavior of the material. These results suggest that the model is capable of helping in the design of new supertough materials.

Random fiber bundle with many discontinuities in the threshold distribution

We study the breakdown of a random fiber bundle model (RFBM) with n discontinuities in the threshold distribution using the global load sharing scheme. In other words, n+1 different classes of fibers identified on the basis of their threshold strengths are mixed such that the strengths of the fibers in the ith class are uniformly distributed between the values sigma2i-2 and sigma2i-1, where 1< or =i< or =n+1 . Moreover, there is a gap in the threshold distribution between ith and (i+1)-th class. We show that although the critical stress depends on the parameter values of the system, the critical exponents are identical to that obtained in the recursive dynamics of a RFBM with a uniform distribution and global load sharing. The avalanche size distribution, on the other hand, shows a nonuniversal, non-power-law behavior for smaller values of avalanche sizes which becomes prominent only when a critical distribution is approached. We establish that the behavior of the avalanche size distribution for an arbitrary n is qualitatively similar to a RFBM with a single discontinuity in the threshold distribution (n=1) , especially when the density and the range of threshold values of fibers belonging to strongest (n+1)-th class is kept identical in all the cases.