Weibull modulus for diverse strength due to sample-specificity

By sample specificity it is meant that specimens with the same nominal material parameters and tested under the same environmental conditions may exhibit different behavior with diversified strength. Such an effect has been widely observed in the testing of material failure and is usually attributed to the heterogeneity of material at the mesoscopic level. The degree with which mesoscopic heterogeneity affects macroscopic failure is still not clear. Recently, the problem has been examined by making use of statistical ensemble evolution of dynamical system and the mesoscopic stress re-distribution model (SRD). Sample specificity was observed for non-global mean stress field models, such as the duster mean field model, stress concentration at tip of microdamage, etc. Certain heterogeneity of microdamage could be sensitive to particular SRD leading to domino type of coalescence. Such an effect could start from the microdamage heterogeneity and then be magnified to other scale levels. This trans-scale sensitivity is the origin of sample specificity. The sample specificity leads to a failure probability Phi (N) with a transitional region 0 < (N) < 1, so that globally stable and catastrophic modes could co-exist. It is found that the scatter in strength can fit the Weibull distribution very well. Hence, the Weibull modulus is indicative of sample specificity. Numerical results obtained from the SRD for different non-global mean stress fields show that Weibull modulus increases with increasing sample span and influence region of microdamage.

Fracture statistics of brittle materials: Weibull or normal distribution

The fit of fracture strength data of brittle materials (Si3N4, SiC, and ZnO) to the Weibull and normal distributions is compared in terms of the Akaike information criterion. For Si3N4, the Weibull distribution fits the data better than the normal distribution, but for ZnO the result is just the opposite. In the case of SiC, the difference is not large enough to make a clear distinction between the two distributions. There is not sufficient evidence to show that the Weibull distribution is always preferred to other distributions, and the uncritical use of the Weibull distribution for strength data is questioned.

Influence of threshold stress on the estimation of the Weibull statistics

The influence of threshold stress on the estimation of the Weibull statistics is discussed in terms of the Akaike information criterion. Numerical simulations show that, if sample data are limited in number and threshold stress is not too large, the two-parameter Weibull distribution is still a preferred choice. For example, the fit of strength data of glass and ceramics to the two- and three-parameter Weibull distributions is compared.

Effects of Microstructural Heterogeneity on the Spallation Behavior of Materials

It is of utmost importance to understand the spallation behaviour of heterogeneous materials. In this paper, a driven nonlinear threshold model with stress fluctuation is presented to study the effects of microstructural heterogeneity on continuum damage evolution. The spallation behavior of heterogeneity material is analyzed with this model. The heterogeniety of mesoscopic units is characterized in terms of Weibull modulus m of strength distibution and stress fluctuation parameter k. At high stress, the maximum damage increases with m; while at low stress, the maximum damage decreases. In addition, for low stress, severe stress fluctuation causes higher damage; while for high stress, causes lower damage.

固体的统计细观力学--连接多个耦合的时空尺度

从固体力学所面临的新的挑战--多物理、多尺度耦合及其现状的描述开始,以层裂过程为例,说明了这些多尺度非平衡问题的基本困难在于,在固体中不同尺度上有不同的微结构层次及不同的演化物理和速率.接下来,概述了一些针对这一困难的独特的思路及其成果.第3部分强调了一些统计平均方法的范式,以及处理包含多个时间和空间尺度的问题的新思路,特别是非平衡损伤演化导致宏观失效的问题.在第4部分,简要评述了一些连接多个空间和时间尺度的细观力学框架,如位错理论,物理细观力学,Weibull理论,随机理论等,并且阐述了其中蕴含的跨尺度

Catastrophic Rupture Induced Damage Coalescence in Heterogeneous Brittle Media

In heterogeneous brittle media, the evolution of damage is strongly influenced by the multiscale coupling effect. To better understand this effect, we perform a detailed investigation of the damage evolution, with particular attention focused on the catastrophe transition. We use an adaptive multiscale finite-element model (MFEM) to simulate the damage evolution and the catastrophic failure of heterogeneous brittle media. Both plane stress and plane strain cases are investigated for a heterogeneous medium whose initial shear strength follows the Weibull distribution. Damage is induced through the application of the Coulomb failure criterion to each element, and the element mesh is refined where the failure criterion is met. We found that as damage accumulates, there is a stronger and stronger nonlinear increase in stress and the stress redistribution distance. The coupling of the dynamic stress redistribution and the heterogeneity at different scales result in an inverse cascade of damage cluster size, which represents rapid coalescence of damage at the catastrophe transition.

A Nonlinear Threshold Model Applied to Spallation Analysis

Spallation in heterogeneous media is a complex, dynamic process. Generally speaking, the spallation process is relevant to multiple scales and the diversity and coupling of physics at different scales present two fundamental difficulties for spallation modeling and simulation. More importantly, these difficulties can be greatly enhanced by the disordered heterogeneity on multi-scales. In this paper, a driven nonlinear threshold model for damage evolution in heterogeneous materials is presented and a trans-scale formulation of damage evolution is obtained. The damage evolution in spallation is analyzed with the formulation. Scaling of the formulation reveals that some dimensionless numbers govern the whole process of deformation and damage evolution. The effects of heterogeneity in terms of Weibull modulus on damage evolution in spallation process are also investigated.

Directly synthesized strong, highly conducting, transparent single-walled carbon nanotube films

We report the direct synthesis of strong, highly conducting, and transparent single-walled carbon nanotube (SWNT) films. Systematically, tests reveal that the directly synthesized films have superior electrical and mechanical properties compared with the films made from a solution-based filtration process: the electrical conductivity is over 2000 S/cm and the strength can reach 360 MPa. These values are both enhanced by more than 1 order. We attribute these intriguing properties to the good and long interbundle connections. Moreover, by the help of an extrapolated Weibull theory, we verify the feasibility of reducing the interbundle slip by utilizing the long-range intertube friction and estimate the ultimate strength of macroscale SWNTs without binding agent.

Miner累积损伤理论的试验验证和统计分析

本文通过对LY12-CZ铝合金板材光滑试件和中心孔试件的常幅加载和变幅加载疲劳试验,对Miner累积损伤理论进行了试验验证,并对累积周比的分散性作了统计分析,发现累积周比的分散性服从Weibull分布,因此本文提出以最小累积周比值或以与一定存活率相应的累积周比值进行安全寿命估计的观点。

加卸载响应比与损伤变量关系研究

首先介绍加卸载响应比的2个基本参量,并从损伤力学的基本理论出发,引入损伤变量,结合加卸载响应比方法的思想,推导用损伤和应变定义的加卸载响应比,并以Weibull分布作为随机分布函数,建立且分析损伤变量与加卸载响应比之间的联系,并进一步考察Weibull指数对两者关系的影响.然后利用岩石破坏声发射实验的数据,用声发射数密度描述岩石试件的损伤演化过程,并由此根据损伤和应变定义的加卸载响应比,结合实验过程中的损伤和应变,计算花岗岩试件的加卸载响应比曲线,并与用Benioff应变作响应量计算的加卸载响应比曲线进行比较,发现两者具有相当程度的一致性,两者的加卸载响应比值都经历了出现异常→升高到最大值→急剧回落→岩石试件破裂或失稳,这一规律与实际地震震例中加卸载响应比的演化趋势是一致的,同时也说明在实际地震预测中用Benioff应变作为响应量来计算加卸载响应比是合理的.最后介绍意大利那不勒斯大学完成的二层楼房的加卸载实验,且对实验结果进行分析.建立的加卸载响应比与损伤变量的关系,不仅为加卸载响应比用来定量研究脆性介质的损伤程度提供更为坚实的基础,而且也可能为评估大型建筑的损伤和预测工程事故开辟新道路.

一种岩石概率型本构及其应用

在岩石材料非均匀特性的基础上,建立了弹塑性概率材料本构.认为材料单元的切线模量与破坏强度都是服从二参数Weibull分布的随机量,通过用户材料子程序将该本构导入到LS-DYNA3D中,推导了程序流程,分析了导入过程中的关键技术.算例验证表明,应用该本构模拟得出的现象与实验观测完全一致,这是确定性本构无法实现的.

Effects of Microstructural Heterogeneity on The Spallation Behavior of Materials

It is of utmost importance to understand the spallation behaviour of heterogeneous materials. In this paper, a driven nonlinear threshold model with stress fluctuation is presented to study the effects of microstructural heterogeneity on continuum damage evolution. The spallation behavior of heterogeneity material is analyzed with this model. The heterogeniety of mesoscopic units is characterized in terms of Weibull modulus m of strength distibution and stress fluctuation parameter k. At high stress, the maximum damage increases with m; while at low stress, the maximum damage decreases. In addition, for low stress, severe stress fluctuation causes higher damage; while for high stress, causes lower damage.

Catastrophic Rupture Induced Damage Coalescence in Heterogeneous Brittle Media

In heterogeneous brittle media, the evolution of damage is strongly influenced by the multiscale coupling effect. To better understand this effect, we perform a detailed investigation of the damage evolution, with particular attention focused on the catastrophe transition. We use an adaptive multiscale finite-element model (MFEM) to simulate the damage evolution and the catastrophic failure of heterogeneous brittle media. Both plane stress and plane strain cases are investigated for a heterogeneous medium whose initial shear strength follows the Weibull distribution. Damage is induced through the application of the Coulomb failure criterion to each element, and the element mesh is refined where the failure criterion is met. We found that as damage accumulates, there is a stronger and stronger nonlinear increase in stress and the stress redistribution distance. The coupling of the dynamic stress redistribution and the heterogeneity at different scales result in an inverse cascade of damage cluster size, which represents rapid coalescence of damage at the catastrophe transition.