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.

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.

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.

Evolution of Localized Damage Zone in Heterogeneous Media

Evolution of localized damage zone is a key to catastrophic rupture in heterogeneous materials. In the present article, the evolutions of strain fields of rock specimens are investigated experimentally. The observed evolution of fluctuations and autocorrelations of strain fields under uniaxial compression demonstrates that the localization of deformation always appears ahead of catastrophic rupture. In particular, the localization evolves pronouncedly with increasing deformation in the rock experiments. By means of the definition of the zone with high strain rate and likely damage localization, it is found that the size of the localized zone decreases from the sample size at peak load to an eventual value. Actually, the deformation field beyond peak load is bound to suffer bifurcation, namely an elastic unloading part and a continuing but localized damage part will co-exist in series in a specimen. To describe this continuous bifurcation and localization process observed in experiments, a model on continuum mechanics is developed. The model can explain why the decreasing width of localized zone can lead stable deformation to unstable, but it still has not provided the complete equations governing the evolution of the localized zone.

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.

A rigorous analytical method for doubly periodic cylindrical inclusions under longitudinal shear and its application

An infinite elastic solid containing a doubly periodic parallelogrammic array of cylindrical inclusions under longitudinal shear is studied. A rigorous and effective analytical method for exact solution is developed by using Eshelby's equivalent inclusion concept integrated with the new results from the doubly quasi-periodic Riemann boundary value problems. Numerical results show the dependence of the stress concentrations in such heterogeneous materials on the periodic microstructure parameters. The overall longitudinal shear modulus of composites with periodic distributed fibers is also studied. Several problems of practical importance, such as those of doubly periodic holes or rigid inclusions, singly periodic inclusions and single inclusion, are solved or resolved as special cases. The present method can provide benchmark results for other numerical and approximate methods. (C) 2003 Elsevier Ltd. All rights reserved.

非均质材料损伤破坏的数值模拟软件开发及强韧化机理研究

本文针对平面链网模型与空间链网模型，发展了模拟非均质材料的数值软件，旨在分析材料的损伤破坏特征，寻找材料细观结构同宏观力学行为之间的相互联系，探讨材料强韧化机理以及评估材料的力学性能。采用可视化技术设计的具有交互式功能的图象用户界面，能根据具体材料对象构造特定材料模型来分析其力学行为与服役能力。初步结果表明，无论是材料弹性阶段的性质还是损伤演化阶段材料中裂纹的萌生、扩展、汇集和材料的最终失效等现象都与已有的理论结果及试验结果符合得很好。另外，本文还对材料的强韧化机理作了探索。

Dynamic damage and failure in viscoplastic materials

In this paper, a dynamic damage model in ductile solids under the application of a dynamic mean tensile stress is developed. The proposed model considers void nucleation and growth as parts of the damage process under intense dynamic loading (strain rates epsilon greater than or equal to 10(3) s(-1)). The evolution equation of the ductile void has the closed form, in which work-hardening behavior, rate-dependent contribution and inertial effects are taken into account. Meanwhile, a plate impact test is performed for simulating the dynamic fracture process in LY12 aluminum alloy. The damage model is incorporated in a hydrodynamic computer code, to simulate the first few stress reverberations in the target as it spalls and postimpact porosity in the specimen. Fair agreement between computed and experimental results is obtained. Numerical analysis shows that the influence of inertial resistance on the initial void growth in the case of high loading rate can not be neglected. It is also indicated that the dynamic growth of voids is highly sensitive to the strain rates.

Catastrophic rupture of heterogeneous brittle materials under impact loading

The catastrophic failure of heterogeneous brittle materials under impact loading is not fully understood. To describe the catastrophic failure behavior of heterogeneous brittle materials under impact loading, an elasto-statistical-brittle (ESB) model is proposed in this paper. The ESB model characterizes the disordered inhomogeneity of material at mesoscopic scale with the statistical description of the shear strength of mesoscopic units. If the applied shear stress reaches the strength, the mesoscopic unit fails, which causes degradation in the shear modulus of the material. With a simplified ESB model, the failure wave in brittle material under uni-axial compression is analyzed. It is shown that the failure wave is a wave of strain or particle velocity resulted from the catastrophic fracture in an elastically stressed brittle media when the impact velocity reaches a critical value. In addition, the failure wave causes an increase in the rear surface velocity, which agrees well with experimental observations. The critical condition to generate failure wave and the speed of failure wave are also obtained.

Heterogeneous enantioselective epoxidation catalyzed by Mn(salen) complexes grafted onto mesoporous materials by phenoxy group

Three chiral Mn(salen) complexes were immobilized into different mesoporous material via phenoxy group by a simplified method and they show high activity and enantioselectivity for asymmetric epoxidation of various substituted unfunctional olefins. The heterogeneous Mn(salen) catalysts show comparable ee values for asymmetric epoxidation of styrene and 6-cyano-2,2-dimethylchromene and much higher ee values for epoxidation of a-methylstyrene (heterogeneous 79.7% ee versus homogeneous 26.4% ee) and cis-beta-methylstyrene (heterogeneous 94.9% ee versus homogeneous 25.3% ee for cis-epoxide) than the homogeneous catalysts. These heterogeneous catalysts also remarkably alter the cis/trans ratio of epoxides for asymmetric epoxidation of cis-beta-methylstyrene (heterogeneous 21 versus homogeneous 0.38). The axial tether group does not make a big effect on ee values and the increase in ee value and change in cis/trans ratio are mainly attributed to the axial immobilization mode and the support effect of heterogeneous catalysts. The catalysts keep constant ee values for the recycle tests of eight times for asymmetric epoxidation of a-methylstyrene. And several possibilities were proposed to elucidate the difference in ee values of heterogeneous catalysts from homogeneous catalysts. (c) 2005 Elsevier B.V. All rights reserved.

Influence of inertial and thermal effects on the dynamic growth of voids in porous ductile materials

The influence of inertial, thermal and rate - sensitive effects on the void growth at high strain rate in a thermal - viscoplastic solid is investigated by means of a theoretical model presented in the present paper. Numerical analysis of the model suggests that inertial, thermal and rate - sensitive effects are three major factors which greatly influence the behavior of void growth in the high strain rate case. Comparison of the mathematical model proposed in the present work and Johnson's model shows that if the temperature - dependence is considered, material viscosity eta can take the experimentally measured values.

The Geo-DSCM System and Its Application to the Deformation Measurement of Rock Materials

Digital Speckle Correlation Method (DSCM) is a useful tool for whole field deformation measurement, and has been applied to analyze the deformation field of rock materials in recent years. In this paper, a Geo-DSCM system is designed and used to analyse the more complicated problems of rock mechanics, such as damage evolution and failure procedure. A weighted correlation equation is proposed to improve the accuracy of displacement measurement on a heterogeneous deformation field. In addition, a data acquisition system is described that can synchronize with the test machine and can capture speckle image at various speeds during experiment. For verification of the Geo-DSCM system, the failure procedure of a borehole rock structure is inspected and the evolution of the deformation localization is analysed. It is shown that the deformation localization generally initializes at the vulnerable area of the rock structure but may develop in a very complicated way.

Photoluminescence from heterogeneous SiGe/Si nanostructures prepared via a two-step approach strategy

A two-step approach of preparation for SiGe/Si heterogeneous nanostructures, which combined with ultra-high vacuum chemical deposition and electrochemical anodization techniques, is demonstrated. Uniformly distributed nanostructures with a quite uniform distribution of size and morphology are obtained. A strong room-temperature photoluminescence from the nanostructures was observed with a narrow full-width at half-maximum of around 110 meV. The possible origins of the two main peaks at around 1.6 and 1.8 eV have been discussed in detail. The two-step approach is proved to be a promising method to fabricate new Si-based optoelectronic materials. (C) 2009 Elsevier B.V. All rights reserved.

Chiral synthesis on catalysts immobilized in microporous and mesoporous materials

This paper reviews the recent progress made in the asymmetric synthesis on chiral catalysts in porous materials and discusses the effects of surface and pores on enantio-selectivity (confinement effect). This paper also summarizes various approaches of immobilization of the chiral catalysts onto surfaces and into pores of solid inorganic supports such as microporous and mesoporous materials. The most important reactions surveyed for the chiral synthesis in porous materials include epoxidation. hydrogenation, hydroformylation, Aldol and Diels-Alder reactions, etc. The confinement effect originated from the surfaces and the pores turns out to be a general phenomenon. which may make the enantioselectivity increase (positive effect) or decrease (negative effect). The confinement effect becomes more pronounced particularly when the bonding between the catalyst and the surface is more rigid and the pore size is tuned to a suitable range. It is proposed that the confinement in chiral synthesis is essentially a consequence of subtle change in transition states induced by weak-interaction in pores or on surfaces. It is also anticipated that the enantioselectivity could be improved by tuning the confinement effect based on the molecular designing of the pore/surface and the immobilized catalysts according to the requirements of chiral reactions.

Effect of annealing on the viscoelastic and viscoplastic responses of low-density polyethylene

Two series of tensile tests with constant crosshead speeds (ranging from 5 to 200 mm/min) and tensile relaxation tests (at strains from 0.03 to 0.09) were performed on low-density polyethylene in the subyield region of deformations at room temperature. Mechanical tests were carried out on nonannealed specimens and on samples annealed for 24 h at the temperatures T = 50, 60, 70, 80, and 100 degreesC. Constitutive equations were derived for the time-dependent response of semicrystalline polymers at isothermal deformations with small strains. A polymer is treated as an equivalent heterogeneous network of chains bridged by temporary junctions (entanglements, physical crosslinks, and lamellar blocks). The network is thought of as an ensemble of mesoregions linked with each other. The viscoelastic behavior of a polymer is modeled as a thermally induced rearrangement of strands (separation of active strands from temporary junctions and merging of dangling strands with the network). The viscoplastic response reflects sliding of junctions in the network with respect to their reference positions driven by macrostrains. Stress-strain relations involve five material constants that were found by fitting the observations.