Simulation Study on the Avalanche Process of Continuous Damage Fiber Bundle Model with Strong Disorder

An extension of the continuous damage fiber bundle model with local load sharing describing the gradual degradation of strong disorder materials is numerically studied in detail. In order to capture the strong disorder of the component material, the total number of the degradation steps of a single fiber is supposed to be a Poisson distributed random number. Numerical calculations show that the model provides various types of constitutive behaviors and microscopic bursting activity which depend on the residual stiffness and the mean number of the degradation steps of fibers. Furthermore, simulations reveal that the critical stress and the step number of load increasing before complete rupture have a power law relation against the mean number of the degradation steps of fibers for small value of the degradation steps.     

Universality class of the fiber bundle model on complex networks

We investigate the failure characteristics of complex networks within the framework of the fiber bundle model subject to the local load sharing rule in which the load of the broken fiber is transferred only to its neighbor fibers. Although the load sharing is strictly local, it is found that the critical behavior belongs to the universality class of global load sharing where the load is transferred equally to all fibers in the system. From the numerical simulations and the analytical approach applied to the microscopic behavior, it is revealed that the emergence of a single dominant hub cluster of broken fibers causes the global load sharing effect in the failure process.     

Influence of disorder on the rupture process of fibrous materials

Based on computational modelling the influence of disorder on the rupture process of fibrous materials have been evaluated. This has been done by simulating a bundle of parallel fibers under a constant uniaxial force. The disorder process was introduced by randomly assigning a strength threshold to each fiber of the bundle according to the Weibull distribution. The results indicate that the rupture process is extremely sensitive to the disorder level. In particular, we demonstrated that the load necessary to break a fiber bundle with large disorder is smaller than that necessary to break a fiber bundle with small disorder.     

Damage in fiber bundle models

We introduce a continuous damage fiber bundle model and compare its behavior with that of dry fiber bundles. Several interesting constitutive behaviors, such as plasticity, are found in this model depending on the value of the damage parameter and on the form of the disorder distribution. We compare the constitutive behavior of global load transfer models, obtained analytically, with local load transfer models numerical simulations. The evolution of the damage is studied analyzing the cluster statistics for dry and continous damage fiber bundles. Finally, it is shown that quenched random thresholds enhance damage localization. Received 27 March 2000     

Fiber Bundle Model Under Heterogeneous Loading

The present work deals with the behavior of fiber bundle model under heterogeneous loading condition. The model is explored both in the mean-field limit as well as with local stress concentration. In the mean field limit, the failure abruptness decreases with increasing order k of heterogeneous loading. In this limit, a brittle to quasi-brittle transition is observed at a particular strength of disorder which changes with k. On the other hand, the model is hardly affected by such heterogeneity in the limit where local stress concentration plays a crucial role. The continuous limit of the heterogeneous loading is also studied and discussed in this paper. Some of the important results related to fiber bundle model are reviewed and their responses to our new scheme of heterogeneous loading are studied in details. Our findings are universal with respect to the nature of the threshold distribution adopted to assign strength to an individual fiber.     

Interphase characterization in polymer composites - monitoring of interphasial behavior in dependence on the mode of loading

Single fiber model composites consisting of epoxy resin matrix and differently sized glass fibers were investigated using pull-out tests, scanning electron microscopy (SEM), scanning force microscopy (SFM) and single fiber dynamic load test (SFDL). The inhomogeneous stress distribution along the embedded fiber length could be visualized by monitoring. SEM images showed either cohesive fracture or adhesive failure on pulled-out fibers with different sizings. The crack initiation and propagation were detected randomly and multiply distributed as the inhomogeneous interphase itself and depending strongly on the fiber-matrix model combination. The meniscus region acts as a material inhomogeneity and its appearence depends on the surface free energies of fiber and matrix and on the curing conditions of the resin. SFM in force modulation mode has visualized different interphase thicknesses and gradients of local stiffness. The SFDL test has been shown as a worthful tool for the comprehensive determination of fiber-matrix interaction.     

Fracture and second-order phase transitions

Using the global fiber bundle model as a tractable scheme of progressive fracture in heterogeneous materials, we define the branching ratio in avalanches as a suitable order parameter to clarify the order of the phase transition occurring at the collapse of the system. The model is analyzed using a probabilistic approach suited to smooth fluctuations. The branching ratio shows a behavior analogous to the magnetization in known magnetic systems with second-order phase transitions. We obtain a universal critical exponent beta approximately = 0.5 independent of the probability distribution used to assign the strengths of individual fibers.     

Scaling and Universality in the Burst Processes of Fiber Bundles

The burst process in a load-carrying bundle of fibers is considered. For the homogeneous model of fiber bundles, the numerical simulation shows that large bursts near complete failure exhibit universal scaling behavior. A simple inhomogeneous model of fiher failure is also proposed. The numerical results indicate that both homogeneous and inhcmogeneous models belong to the same universality class.     

Scaling behaviour in the fracture of fibrous materials

We study the existence of distinct failure regimes in a model for fracture in fibrous materials. We simulate a bundle of parallel fibers under uniaxial static load and observe two different failure regimes: a catastrophic and a slowly shredding. In the catastrophic regime the initial deformation produces a crack which percolates through the bundle. In the slowly shredding regime the initial deformations will produce small cracks which gradually weaken the bundle. The boundary between the catastrophic and the shredding regimes is studied by means of percolation theory and of finite-size scaling theory. In this boundary, the percolation density scales with the system size L, which implies the existence of a second-order phase transition with the same critical exponents as those of usual percolation. Received 24 June 1999     

高浓度纤维增强材料介电特性计算方法

针对复合材料的微观结构非均匀和各向异性特点带来的数值方法计算慢、内存消耗大的问题,利用均匀化方法计算纤维增强复合材料的等效电磁参数.采用了纤维低体积添加比至高体积添加比的迭代方法,同时提出了一个描述材料微观结构的修正的特征长度,将现有的均匀化方法推广至非准静态(微波频段)条件下高纤维浓度情况.提出的修正的均匀化模型可直接用于反射系数、屏蔽效能等计算,其屏蔽效能与实际微观结构复合材料的数值仿真结果进行了对比,验证了提出的等效电磁参数计算公式的有效性和频率适用范围.     

Simultaneous Failures of the Nonuniform-Stressed Fiber Bundle

The burst process in a load-carrying bundle of the identical fibers, in which each fiber is initially stressed randomly, js considered. The distribution function of the simultaneous burst sizes is obtained analy tically. It is shown that this model belongs to the same class of universality as the model discussed by Hemmer and Hansen (1991).     

Intrinsic transmission bandwidths of graded-index plastic optical fibers

We theoretically demonstrate that microscopic heterogeneous properties can enhance the transmission bandwidths of graded-index plastic optical fibers (POFs) for short-haul communication networks. The heterogeneities of the POF cores are quantitatively correlated with mode couplings by modifying the coupled power equation with consideration of the spatial correlation characteristics of the heterogeneities. Using the modified theory, we clarify that the larger fluctuation size and/or amplitude results in higher bandwidth because of greater forward scattering and/or higher scattering efficiency, respectively. This suggests that the multimode fiber bandwidths can depend on the macroscopically observed index profiles as well as on the microscopic material properties.     

A Numerical Investigation on the Influence of Steel Fiber Shape and Interface Strength in Reinforced Concrete

Not all steel fiber reinforced concrete composites are equally effective in enhancing structural performance. Their mechanical behaviour strongly depends upon the reinforcement morphology as well as the properties of the interface lying between steel reinforcement and concrete matrix. Using bone-shaped short (BSS) steel fibers, instead of conventional straight short (CSS) steel fibers, to reinforce concrete has demonstrated their potential in improving toughness, ductility and energy absorbing capacity under impact significantly and simultaneously. Accomplishing a strong steel–concrete interface leads to a slight increase in composite strength but simultaneously to a significant decrease in its toughness. Due to the sensitivity of steel reinforced concrete performance on these complex geometric and material parameters, the development of a numerical tool capable of simulating accurately the composite mechanical behaviour and thus leading to optimized design solutions is desirable. The physical problem of the present work involves a typical concrete composite uniformly reinforced with steel fibers subjected to tensional loading. A micromechanical non-linear finite element formulation is utilized in order to predict the load transfer characteristics and the failure process. A linear material behaviour is assumed for the steel component; a non-linear multi-crack material response is used to describe concrete while a mix-mode bilinear behaviour is utilized for the interface providing separation of primary material phases. Numerical results are presented in terms of the global design parameters. The influence of the fiber end shape, the interface strength and the fiber volume fraction on the composite strength and toughness is addressed and consequently optimized design preferences arise.     

基于单光纤对模型的光纤束调制函数的建模与仿真

基于单光纤对光强调制特性的函数表达式,建立了双束型光纤束的调制函数,并引入一个虚拟轴间距参量,建立了随机型光纤束的光强调制函数.同时又在视内圈光纤束为单根粗光纤的情况下,建立了同轴I型和同轴型光纤束的光调制函数.在随机型和同轴型光纤束模型的基础上建立了双圈型(DC)和同轴随机型(C-R)光纤束的光调制系数.最后对上述光纤束的调制特性函数进行了计算机仿真实验.     

环圈光纤的失效预测

以光纤的机械可靠性为主线综述了光纤材料中固有裂纹的生长和传播所导致的光纤断裂机制.在该断裂力学的基础上推导了传统通信光纤在平直应用中的寿命预测模型.继而分析了处于弯曲构型中的传感环圈光纤表面的应力分布,然后在与传统理论相同的基本断裂机理下,类比于通信光纤可靠性模型的推导,据此应力分析给出了评估这种环圈光纤的机械可靠性的一般模型.进而从工程应用的角度简化了所推导出的一般模型,使之能够快速简单地给出环圈光纤失效概率的保守评估.在此简化模型的基础上,数值计算了目前常见的几种传感环圈中的光纤在服役期间的累积失效概率;其结果同时也显示了该环圈光纤的失效概率对光纤参量、环圈参量以及工艺参量的依赖关系.根据这一依赖关系,不仅可以快速评估在各种服役应力条件下具有不同寿命要求的光纤环圈的失效概率,同时也能对这些环圈的设计提供参考.     

光纤耦合LD输出光场特性研究

根据光纤传输的模式理论,分析了单芯光纤输出端面的光场分布.利用单模光纤测量了纤端光场的强度分布,拟合了光纤输出端面光强分布的近似表达式.根据此数值计算和实验测量了多芯光纤输出端面的强度分布,结果基本吻合.表明光纤出射端面的光强分布应是介于高斯分布和几何分布之间的一种准高斯分布.     

Bulk strain energy density in randomly reinforced polymer composites with antifriction dispersed additives

Bulk strain energy density was numerically simulated for epoxy-phenol-based composites randomly reinforced with short polyimide fibers, with antifriction dispersed polytetrafluoroethylene (PTFE) additives. A mathematical model was constructed using the notion of a stress concentration operator (fourth-rank tensor) that relates volume averaged, or external, stresses within a heterogeneous material with their local values within an individual heterogeneity. The simulation was based on a generalized singular approximation of random field theory used to solve a stochastic differential equation of equilibrium of an elastic medium. This approximation yields an explicit expression for stress concentration in a composite material. The explicit expression allows one to analyze the distribution of bulk strain energy density depending on the composition, structure, volume and mass fraction of heterogeneities, and on the type and value of applied load. We studied how the considered energy characteristic depends on the type of external mechanical loading and concentration of isotropic components in the model composites. It is shown that with the increasing concentration of polyimide fibers at a fixed concentration of PTFE inclusions, the bulk strain energy density values of all components decrease and approach each other independently of the type of external loading. The form of these dependences is nonlinear. A change in the mass fraction of dispersed PTFE inclusions in the model composites exerts little effect on local energy values of all components under any of the considered applied external loads.     

Mechanical properties of flat braided composite with flexible interphase

Textile composites have been used extensively as industrial materials because of the excellent mechanical properties resulting from the continuously oriented fiber bundle. In a study of the mechanical properties, it is important to consider the fiber/matrix interface property as for other composite materials. In a recent study, the fiber/matrix interface is regarded as an interphase that has its own material constants and thickness; consequently, the mechanical properties of a composite can be controlled by specifically designing the interphase. In this study, we applied this concept to braided composites with flexible resin as interphase for the purpose of designing the interphase. In a static tensile test, though there were no improvements in Noncut specimens (normal braided composites), but a Cut specimen (each side of the Noncut specimen was cut) with flexible interphase was improved in fracture load and displacement. The observation of the specimen edge was carried out and it was confirmed that the progress of debonding at the fiber bundle intersection was interrupted by a flexible interphase, and a matrix crack did not occur in the Cut specimen with flexible interphase. In a fiber bundle pull-out test, it was confirmed that debonding progressed not into the fiber/resin interface but into the flexible interphase in the specimen with flexible interphase, and the interfacial property at the fiber bundle intersection was improved.     

Cracks in random brittle solids:

Statistical models are essential to get a better understanding of the role of disorder in brittle disordered solids. Fiber bundle models play a special role as a paradigm, with a very good balance of simplicity and non-trivial effects. We introduce here a variant of the fiber bundle model where the load is transferred among the fibers through a very compliant membrane. This Soft Membrane fiber bundle mode reduces to the classical Local Load Sharing fiber bundle model in 1D. Highlighting the continuum limit of the model allows to compute an equivalent toughness for the fiber bundle and hence discuss nucleation of a critical defect. The computation of the toughness allows for drawing a simple connection with crack front propagation (depinning) models.     

Relation between rotational and translational dynamic heterogeneities in water

We use molecular dynamics simulations to probe the rotational dynamics of the extended simple point charge model of water for a range of temperatures down to 200 K, 6 K above the mode coupling temperature. We find that rotational dynamics is spatially heterogeneous; i.e., there are clusters of molecules that rotate significantly more than the average for a given time interval, and we study the size and the temporal behavior of these clusters. We find that the position of a rotational heterogeneity is strongly correlated with the position of a translational heterogeneity, and that the fraction of molecules belonging to both kinds of heterogeneities increases with decreasing temperature. We further find that although the two types of heterogeneities are not identical, they are related to the same physical picture.