Local Load-sharing Rule Research Articles

Modeling of crack diffusion in composite materials

Our aim is to investigate the crack diffusion created at single region of composite materials by using the fiber bundle model. So, we have applied an external single crack in one fiber of the composite material, and we then continue to increase this load at a very slow rate until the considered fiber breaks and its load is redistributed to its neighboring intact ones. This breaking and redistribution dynamics repeat itself and this process ensures an advancing interfacial fracture and the area of the damaged region increases with time until a final crack of material. Our calculations are done in the context of the local load-sharing rule. The results show that the damaged region area increases with time by following the Lifshitz-Slyozof law with an exponent growth x=2. This permits us to deduce the behavior of the crack diffusion with the applied load. The corresponding results of the life time materials exhibit an exponential decreasing with the applied load and a linear decreasing with temperature.

Failure process in heterogeneous materials with randomly oriented fibers

Our aim in this study is to investigate the failure process in heterogeneous materials with randomly oriented fibers. In our proposed system, the fiber bundle model assumes that all the fibers are randomly oriented in all directions relative to the vertical one. Our calculations are performed in the framework of the local load-sharing rule, which states that the applied load of a broken fiber is redistributed only to its neighboring ones. The results show that this system presents a greater resistance than the classical one where the fibers are arranged parallel to the applied load. We found that the density of the broken fibers exhibited a power law and was linearly correlated with the applied load and temperature. However, the results show that the failure process of the considered system is characterized by an avalanche phenomenon with two different regimes. We also studied the crossover behavior of lifetime of the materials versus both applied load and temperature. We compared these results with those obtained from the classical model.

Crack diffusion in failure process of composite materials

ABSTRACTWe study the crack diffusion in composite materials subject to a local load-sharing fiber bundle model in two dimensions under an external load applied at a single point. By the use of the local load-sharing rule, the redistributed load remains localized along the boundary of the broken patch. We investigated the correlation function of the broken fibers. The results show that this magnitude decreases exponentially with time and it's characterized by a characteristic time which is inversely proportional to the diffusion coefficient of the localized crack. The results exhibit also that the crack correlation function in the failure process in composite materials decreases with both of applied load and temperature. We calculate then the diffusion coefficient of the localized crack. We have found that this diffusion coefficient increases by power law with the applied load and thermal noise.

Characterization of the failure process in composite materials by the Fiber Bundle Model

Our aim in this paper is to investigate the time distribution of the monomer intact fiber of a bundle model of fibers subject to a constant external load. Breaking process is created by thermally induced stress fluctuations followed by load redistribution with the local load-sharing rule (LLS) which subsequently leads to an avalanche of breakings. The results showed that the maximum number of the intact fiber monomer (MNIFM) was observed at time t1 proportional to the materials failure time tf independently of the temperature value (t1≈13tf). So, this parameter can characterize clearly the avalanche phenomenon observed in the failure process of the composite materials. Moreover, we have found that MNIFM presents a Gaussian variation with the applied load and exhibits a power law with the size of the system. The MNIFM temperature dependence was also investigated in this study.

Failure kinetic and scaling behavior of the composite materials: Fiber Bundle Model with the local load-sharing rule (LLS)

We investigate the spatial distribution of mechanical stresses of composite materials densely packed with thin glass fibers and yield so low transparency that the conventional method of photoelasticity testing fails to provide good quality birefringence fringes. The failure kinetic and the scaling behavior of theses materials are also studied. The calculations are done within the framework of the fiber bundle model with the local load-sharing rule (LLS) in which the load of the failing fiber is shared between only the nearest neighbor elements. We have found that the failure properties of these materials are characterized by the avalanche phenomena with two different timescales and the number of broken fibers presents a Boltzmann distribution. The failure time tf presents a power law with the applied force and the system size. The results show also that the failure kinetic of the composite materials is self-similar. The creep rupture is also investigated. The results show that these materials are characterized by a two creep regimes characterized by the Andrade’s law with a two different exponents, and separated by a cross over time tm more consisting with the experiment results.

Breaking Progress Simulation and Strength Prediction of Woven Fabric under Uni-axial Tensile Loading

The chain-of-bundles model and a Monte Carlo method were used to simulate the breaking progress of plain weave woven fabrics under uni-axial tensile load and to predict the tensile strength of the fabrics. The variations of the bending outline at the cross-over point between warp and weft and the additional strains of the crossing yarns by crimp interchange have been considered in order to analyze yarn interaction and to determine the critical length. Two approaches, shear-lag analysis (SLA) and the local load-sharing (LLS) rule, were used to calculate the stress concentration factors, which determine the load redistribution scheme once a yarn breaks. Then the Monte Carlo simulation was conducted to simulate the failure progress of woven fabrics. The simulation strength distributions of fabric samples can be fitted with two-parameter Weibull distribution. By comparison with the test data, it was found that the shape parameter of simulated strength by LLS rule was larger and the value of scale parameter smaller than that by SLA. The predicted strength by LLS was smaller than the test data, whereas that by SLA showed better agreement with the test data. It is likely that the SLA approach is more suitable for predicting the strength of woven fabrics under uni-axial tensile load.

Approximate upper and lower bounds for the strength of unidirectional composites

This paper addresses the problem of determining the probabilistic strength of unidirectional composites. We first calculated the stress-concentration factors (SCFs) around broken fibers in a three-dimensional, hexagonal-array model. Two approaches were tried to calculate the SCFs. One is a shear-lag analysis originated by Hedgepeth and Van Dyke and the other is close to a local load-sharing rule (LLS). These two sets of SCFs provide the upper and lower bounds of the strength. With these SCFs, we next carried out a Monte Carlo simulation to evaluate the strength of unidirectional composites in which a chain-of-bundles probability model and a Weibull distribution were used. Parametric studies were first conducted and a comparison with experiments and other existing theories was next done. Our `approximate' upper bound was lower than Rosen's prediction and lower bound, higher than Zweben's value. The value from the simulation was also close to the experimental results.

A Monte Carlo simulation of the stress-rupture of seven-fiber microcomposites

A direct-simulation Monte Carlo method (DSMC) has been applied to a chain-of-bundles model in order to simulate ifetime experiments with seven-fiber microcomposites. Strength and lifetime of the fibers in the composite are assumed to follow two-parameter Weibull distributions. Matrix creep effects are included in the model. Loads carried by broken fibers before breaking are distributed among the adjacent surviving ones, according to a local load-sharing rule. The lifetime values given by the simulation program are in good agreement with experimental data obtained by various investigators for graphite microcomposites. A parametric study is performed for graphite SFT microcomposites, where single fiber and matrix properties are varied. The relationships obtained from this study agree very well with the predictions of earlier, theoretical probability models.

Lower-tail approximations for the probability of failure of three-dimensional fibrous composites with hexagonal geometry

The chain-of-bundles model for the strength of unidirectional fibrous materials is extended to cover 3D situations wherein the parallel filaments are arranged laterally in a hexagonal array. Within each bundle, the strengths of the fibres vary statistically and share load according to a local load-sharing rule, a rule which describes how the loads of failed fibres are redistributed on to nearby surviving fibres. We consider two idealized versions of this rule, one geometrically motivated and the other more mechanically motivated. We extend earlier asymptotic techniques for the 2D planar problem to the present 3D case, and obtain various approximations for the probability distribution for material strength. The Weibull distribution again emerges as central to the results, but the calculation of its shape and scale parameters is greatly complicated by the large number of new failure configurations that may arise in the hexagonal array of fibres. Earlier 2D results connecting the Weibull shape parameter to the critical failure sequence size do not in general hold in 3D settings. The general character of the results, however, is the same as in the 2D setting, with 3D materials being stronger because of the reduced severity of the fibre overloads in the hexagonal array. Also, the two local load-sharing rules though quite different in character yield surprisingly similar numerical results.