Damage evolution, localization and failure of solids subjected to impact loading

In order to reveal the underlying mesoscopic mechanism governing the experimentally observed failure in solids subjected to impact loading, this paper presents a model of statistical microdamage evolution to macroscopic failure, in particular to spallation. Based on statistical microdamage mechanics and experimental measurement of nucleation and growth of microcracks in an Al alloy subjected to plate impact loading, the evolution law of damage and the dynamical function of damage are obtained. Then, a lower bound to damage localization can be derived. It is found that the damage evolution beyond the threshold of damage localization is extremely fast. So, damage localization can serve as a precursor to failure. This is supported by experimental observations. On the other hand, the prediction of failure becomes more accurate, when the dynamic function of damage is fitted with longer experimental observations. We also looked at the failure in creep with the same idea. Still, damage localization is a nice precursor to failure in creep rupture.

Morphological Stability of Epitaxial Thin Elastic Films by Van Der Waals Force

The morphological stability of epitaxial thin elastic films on a substrate by van der Waals force is discussed. It is found that only van der Waals force with negative Hamaker constant (A < 0) tends to stabilize the film, and the lower bound for the Hamaker constant is also obtained for the stability of thin film. The critical value of the undulation wavelength is found to be a function of both film thickness and external stress. The charateristic time-scale for surface mass diffusion scales to the fourth power to the wavelength of the perturbation.

Measurement Of Fracture Toughness And Interfacial Shear Strength Of Hard And Brittle Cr Coating On Ductile Steel Substrate

The fracture toughness and interfacial adhesion properties of a coating on its substrate are considered to be crucial intrinsic parameters determining performance and reliability of coating-substrate system. In this work, the fracture toughness and interfacial shear strength of a hard and brittle Cr coating on a normal medium carbon steel substrate were investigated by means of a tensile test. The normal medium carbon steel substrate electroplated with a hard and brittle Cr coating was quasi-statically stretched to induce an array of parallel cracks in the coating. An optical microscope was used to observe the cracking of the coating and the interfacial decohesion between the coating and the substrate during the loading. It was found that the cracking of the coating initiated at critical strain, and then the number of the cracks of the coating per unit axial distance increased with the increase in the tensile strain. At another critical strain, the number of the cracks of the coating became saturated, i.e. the number of cracks per unit axial distance became a constant after this critical strain. Based on the experiment result, the fracture toughness of the brittle coating can be determined using a mechanical model. Interestingly, even when the whole specimen fractured completely under an extreme strain of the substrate, the interfacial decohesion or buckling of the coating on its substrate was completely absent. The test result is different from that appeared in the literature though the identical test method and the brittle coating/ductile metal substrate system are taken. It was found that this difference can be attributed to an important mechanism that the Cr coating on the steel substrate has a good adhesion, and the ultimate interfacial shear strength between the Cr coating and the steel substrate has exceeded the maximum shear flow strength level of the steel substrate. This result also indicates that the maximum shear flow strength level of the ductile steel substrate can be only taken as a lower bound estimate on the ultimate shear strength of the interface. This estimation of the ultimate interfacial shear strength is consistent with the theoretical analysis and prediction presented in the literature.

Regularity of strain distribution in short-fiber/whisker reinforced composites

Based on studies on the strain distribution in short-fiber/whisker reinforced metal matrix composites, a deformation characteristic parameter, lambda is defined as a ratio of root-mean-square strain of the reinforcers identically oriented to the macro-linear strain along the same direction. Quantitative relation between lambda and microstructure parameters of composites is obtained. By using lambda, the stiffness moduli of composites with arbitrary reinforcer orientation density function and under arbitrary loading condition are derived. The upper-bound and lower-bound of the present prediction are the same as those from the equal-strain theory and equal-stress theory, respectively. The present theory provides a physical explanation and theoretical base for the present commonly-used empirical formulae. Compared with the microscopic mechanical theories, the present theory is competent for stiffness modulus prediction of practical engineering composites in accuracy and simplicity.

Fracture criterion based on the higher-order asymptotic fields

A complete development for the higher-order asymptotic solutions of the crack tip fields and finite element calculations for mode I loading of hardening materials in plane strain are performed. The results show that in the higher-order asymptotic solution (to the twentieth order), only three coefficients are independent. These coefficients are determined by matching with the finite element solutions carried out in the present paper (our attention is focused on the first five terms of the higher-order asymptotic solution). We obtain an analytic characterization of crack tip fields, which conform very well to the finite element solutions over wide range. A modified two parameter criterion based on the asymptotic solution of five terms is presented. The upper bound and lower bound fracture toughness curves predicted by modified two parameter criterion are given. These two curves agree with most of the experimental data and fully capture the proper trend.

Some new bounds on eigenvalues of the Hadamard product and the Fan product of matrices

Let A and B be nonsingular M-matrices. A lower bound on the minimum eigenvalue q(B circle A(-1)) for the Hadamard product of A(-1) and B, and a lower bound on the minimum eigenvalue q(A star B) for the Fan product of A and B are given. In addition, an upper bound on the spectral radius rho(A circle B) of nonnegative matrices A and B is also obtained. These bounds improve several existing results in some cases and the estimating formulas are easier to calculate for they are only depending on the entries of matrices A and B. (C) 2009 Elsevier Inc. All rights reserved.

Linearization Method and Linear Complexity

We focus on the relationship between the linearization method and linear complexity and show that the linearization method is another effective technique for calculating linear complexity. We analyze its effectiveness by comparing with the logic circuit method. We compare the relevant conditions and necessary computational cost with those of the Berlekamp-Massey algorithm and the Games-Chan algorithm. The significant property of a linearization method is that it needs no output sequence from a pseudo-random number generator (PRNG) because it calculates linear complexity using the algebraic expression of its algorithm. When a PRNG has n [bit] stages (registers or internal states), the necessary computational cost is smaller than O(2n). On the other hand, the Berlekamp-Massey algorithm needs O(N2) where N ( 2n) denotes period. Since existing methods calculate using the output sequence, an initial value of PRNG influences a resultant value of linear complexity. Therefore, a linear complexity is generally given as an estimate value. On the other hand, a linearization method calculates from an algorithm of PRNG, it can determine the lower bound of linear complexity.

Stability shear stress and equilibrium cross-sectional geometry of sheltered tidal channels

This study relates tidal channel cross-sectional area (A) to peak spring discharge (Q) via a physical mechanism, namely the stability shear stress ( tau sub(S)) just necessary to maintain a zero gradient in net along-channel sediment transport. It is assumed that if bed shear stress ( tau ) is greater than tau sub(S), net erosion will occur, increasing A, and reducing tau similar to (Q/A) super(2) back toward tau sub(S). If tau < tau sub(S) there will be net deposition, reducing A and increasing tau toward tau sub(S). A survey of the literature allows estimates of Q and A at 242 sections in 26 separate sheltered tidal systems. Assuming a single value of tau sub(S) characterizes the entire length of a given tidal channel, it is predicted that along-channel geometry will follow the relation Ah sub(R) super(1) super(/) super(6) similar to Q. Along-channel regressions of the form Ah sub(R) super(1) super(/) super(6) similar to Q super( beta ) give a mean observed value for beta of 1.00 plus or minus 0.06, which is consistent with this concept. Results indicate that a lower bound on tau sub(S) (and an upper bound on A) for stable channels is provided by the critical shear stress ( tau sub(C)) just capable of initiating sediment motion. Observed tau sub(S) is found to vary among all systems as a function of spring tidal range (R sub(sp)) according to the relation tau sub(S) approximately 2.3 R sub(sp) super(0.79) tau sub(C). Observed deviations from uniform tau sub(S) along individual channels are associated with along-channel variation in the direction of maximum discharge (i.e., flood-versus ebb-dominance).

中国近海和西北太平洋温跃层时空变化分析、模拟及预报

温度跃层是反映海洋温度场的重要物理特性指标，对水下通讯、潜艇活动及渔业养殖、捕捞等有重要影响。本文利用中国科学院海洋研究所“中国海洋科学数据库”在中国近海及西北太平洋（110ºE-140ºE,10ºN-40ºN）的多年历史资料（1930-2002年，510143站次），基于一种改进的温跃层判定方法，分析了该海域温跃层特征量的时空分布状况。同时利用Princeton Ocean Model(POM)，对中国近海，特别是东南沿海的水文结构进行了模拟，研究了海洋水文环境对逆温跃层的影响。最后根据历史海温观测资料，利用EOF分解统计技术，提出了一种适于我国近海及毗邻海域，基于现场有限层实测海温数据，快速重构海洋水温垂直结构的统计预报方法，以达到对现场温跃层的快速估计。 历史资料分析结果表明，受太阳辐射和风应力的影响，20°N以北研究海域，温跃层季节变化明显，夏季温跃层最浅、最强，冬季相反，温跃层厚度的相位明显滞后于其他变量，其在春季最薄、秋季最厚。12月份到翌年3月份，渤、黄及东海西岸，呈无跃层结构，西北太平洋部分海域从1月到3月份，也基本无跃层结构。在黄海西和东岸以及台湾海峡附近的浅滩海域，由于风力搅拌和潮混合作用，温跃层出现概率常年较低。夏季，海水层化现象在近海陆架海域得到了加强，陆架海域温跃层强度季节性变化幅度(0.31°C/m)明显大于深水区(约0.05°C/m)，而前者温跃层深度和厚度的季节性变化幅度小于后者。20°N以南研究海域，温跃层季节变化不明显。逆温跃层主要出现在冬、春季节（10月-翌年5月）。受长江冲淡水和台湾暖流的影响，东南沿海区域逆温跃层持续时间最长，出现概率最大，而在山东半岛北及东沿岸、朝鲜半岛西及北岸，逆温跃层消长过程似乎和黄海暖流有关。多温跃层结构常年出现于北赤道流及对马暖流区。在黑潮入侵黄、东、南海的区域，多温跃层呈现明显不同的季节变化。在黄海中部，春季多温跃层发生概率高于夏季和秋季，在东海西部，多跃层主要出现在夏季，在南海北部，冬季和春季多温跃层发生概率大于夏季和秋季。这些变化可能主要受海表面温度变化和风力驱动的表层流的影响。 利用Princeton Ocean Model(POM)，对中国东南沿海逆温跃层结构进行了模拟，模拟结果显示，长江冲淡水的季节性变化以及夏季转向与实际结果符合较好，基本再现了渤、黄、东海海域主要的环流、温盐场以及逆温跃层的分布特征和季节变化。通过数值实验发现，若无长江、黄河淡水输入，则在整个研究海域基本无逆温跃层出现，因此陆源淡水可能是河口附近逆温跃层出现的基本因素之一。长江以及暖流（黑潮和台湾暖流）流量的增加，均可在不同程度上使逆温跃层出现概率及强度、深度和厚度增加，且暖流的影响更加明显。长江对东南沿海逆温跃层的出现，特别是秋季到冬季初期，有明显的影响，使长江口海域逆温跃层位置偏向东南。暖流对于中国东南沿海的逆温跃层结构，特别是初春时期，有较大影响，使长江口海域的逆温跃层位置向东北偏移。 通过对温跃层长期变化分析得出，黄海冷水团区域，夏季温跃层强度存在3.8年左右的年际变化及18.9年左右的年代际变化，此变化可能主要表现为对当年夏季和前冬东亚地区大气气温的热力响应。东海冷涡区域，夏季温跃层强度存在3.7年的年际变化，在El Nino年为正的强度异常，其可能主要受局地气旋式大气环流变异所影响。谱分析同时表明，该海域夏季温跃层强度还存在33.2年的年代际变化，上世纪70年代中期，温跃层强度由弱转强，而此变化可能与黑潮流量的年代际变化有关。 海洋水温垂直结构的统计预报结果显示，EOF分解的前四个主分量即能够解释原空间点温度距平总方差的95%以上，以海洋表层附近观测资料求解的特征系数推断温度垂直结构分布的结果最稳定。利用东海陆架区、南海深水区和台湾周边海域三个不同区域的实测CTD样本廓线资料，对重构模型的检验结果表明，重构与实测廓线的相关程度超过95%的置信水平。三个区重构与实测温度廓线值的平均误差分别为0.69℃，0.52℃，1.18℃，平均重构廓线误差小于平均气候偏差，统计模式可以很好的估算温度廓线垂直结构。东海陆架海区温度垂直重构廓线与CTD观测廓线获得的温跃层结果对比表明，重构温跃层上界、下界深度和强度的平均绝对误差分别为1.51m、1.36m和0.17℃/m，它们的平均相对误差分别为24.7%、8.9%和22.6%，虽然温跃层深度和强度的平均相对误差较大，但其绝对误差量值较小。而在南海海区，模型重构温跃层上界、下界和强度的平均绝对预报误差分别为4.1m、27.7m和0.007℃/m，它们的平均相对误差分别为16.1%、16.8%和9.5%，重构温跃层各特征值的平均相对误差都在20%以内。虽然南海区温跃层下界深度平均绝对预报误差较大，但相对于温跃层下界深度的空间尺度变化而言（平均温跃层下界深度为168m），平均相对误差仅为16.8%。因此说模型重构的温度廓线可以达到对我国陆架海域、深水区温跃层的较好估算。 基于对历史水文温度廓线观测资料的分析及自主温跃层统计预报模型，研制了实时可利用微机简单、快捷地进行温跃层估算及查询的可视化系统，这是迄今进行大范围海域温跃层统计与实时预报研究的较系统成果。

边坡工程的极限分析上限法

Theory of limit analysis include upper bound theorem and lower bound theorem. To deal with slope stability analysis by limit analysis is to approximate the real solution from upper limit and lower limit. The most used method of limit analysis is upper bound theorem, therefore it is often applied to slope engineering in many cases. Although upper bound approach of limit analysis can keep away from vague constitutive relation and complex stress analyses, it also can obtain rigorous result. Assuming the critical surface is circular slip surface, two kinematically admissible velocity fields for perpendicular slice method and radial slice method can be established according to the limit analysis of upper bound theorem. By means of virtual work rate equation and strength reduction method, the upper-bound solution of limit analysis for homogeneous soil slope can be obtained. A log-spiral rotational failure mechanism for homogeneous slope is discussed from two different conditions which represent the position of shear crack passing the toe and below the toe. In the dissertition, the author also establishes a rotational failure mechanics with combination of different logarithmic spiral arcs. Furthermore, the calculation formula of upper bound solution for inhomogeneous soil slope stability problem can be deduced based on the upper bound approach of rigid elements. Through calculating the external work rate caused by soil nail, anti-slide pile, geotechnological grid and retaining wall, the upper bound solution of safety factor of soil nail structure slope, slip resistance of anti-slide pile, critical height of reinforced soil slope and active earth pressure of retaining wall can be obtained by upper bound limit analysis method. Taking accumulated body slope as subject investigated, with study on the limit analysis method to calculate slope safety factor, the kinematically admissible velocity fields of perpendicular slice method for slope with broken slip surface is proposed. Through calculating not only the energy dissipation rate produced in the broken slip surfaces and the vertical velocity discontinuity, but also the work rate produced by self-weight and external load, the upper bound solution of slope with broken slip surface is deduced. As a case study, the slope stability of the Sanmashan landslide in the area of the Three Gorges reservoir is analyzed. Based on the theory of limit analysis, the upper bound solution for rock slope with planar failure surface is obtained. By means of virtual work-rate equation, energy dissipation caused by dislocation of thin-layer and terrane can be calculated; furthermore, the formulas of safety factor for upper bound approach of limit analysis can be deduced. In the end, a new computational model of stability analysis for anchored rock slope is presented after taking into consideration the supporting effect of rock-bolts, the action of seismic force and fissure water pressure. By using the model, not only the external woke-rate done by self-weight, seismic force, fissure water pressure and anchorage force but also the internal energy dissipation produced in the slip surface and structural planes can be totally calculated. According to the condition of virtual work rate equation in limit state, the formula of safety factor for upper bound limit analysis can be deduced.

基于精细结构描述及数值试验的断续节理岩体力学参数智能选取

Evaluating the mechanical properties of rock masses is the base of rock engineering design and construction. It has great influence on the safety and cost of rock project. The recognition is inevitable consequence of new engineering activities in rock, including high-rise building, super bridge, complex underground installations, hydraulic project and etc. During the constructions, lots of engineering accidents happened, which bring great damage to people. According to the investigation, many failures are due to choosing improper mechanical properties. ‘Can’t give the proper properties’ becomes one of big problems for theoretic analysis and numerical simulation. Selecting the properties reasonably and effectively is very significant for the planning, design and construction of rock engineering works. A multiple method based on site investigation, theoretic analysis, model test, numerical test and back analysis by artificial neural network is conducted to determine and optimize the mechanical properties for engineering design. The following outcomes are obtained: (1) Mapping of the rock mass structure Detailed geological investigation is the soul of the fine structure description. Based on statistical window，geological sketch and digital photography，a new method for rock mass fine structure in-situ mapping is developed. It has already been taken into practice and received good comments in Baihetan Hydropower Station. (2) Theoretic analysis of rock mass containing intermittent joints The shear strength mechanisms of joint and rock bridge are analyzed respectively. And the multiple modes of failure on different stress condition are summarized and supplied. Then, through introducing deformation compatibility equation in normal direction, the direct shear strength formulation and compression shear strength formulation for coplanar intermittent joints, as well as compression shear strength formulation for ladderlike intermittent joints are deducted respectively. In order to apply the deducted formulation conveniently in the real projects, a relationship between these formulations and Mohr-Coulomb hypothesis is built up. (3) Model test of rock mass containing intermittent joints Model tests are adopted to study the mechanical mechanism of joints to rock masses. The failure modes of rock mass containing intermittent joints are summarized from the model test. Six typical failure modes are found in the test, and brittle failures are the main failure mode. The evolvement processes of shear stress, shear displacement, normal stress and normal displacement are monitored by using rigid servo test machine. And the deformation and failure character during the loading process is analyzed. According to the model test, the failure modes quite depend on the joint distribution, connectivity and stress states. According to the contrastive analysis of complete stress strain curve, different failure developing stages are found in the intact rock, across jointed rock mass and intermittent jointed rock mass. There are four typical stages in the stress strain curve of intact rock, namely shear contraction stage, linear elastic stage, failure stage and residual strength stage. There are three typical stages in the across jointed rock mass, namely linear elastic stage, transition zone and sliding failure stage. Correspondingly, five typical stages are found in the intermittent jointed rock mass, namely linear elastic stage, sliding of joint, steady growth of post-crack, joint coalescence failure, and residual strength. According to strength analysis, the failure envelopes of intact rock and across jointed rock mass are the upper bound and lower bound separately. The strength of intermittent jointed rock mass can be evaluated by reducing the bandwidth of the failure envelope with geo-mechanics analysis. (4) Numerical test of rock mass Two sets of methods, i.e. the distinct element method (DEC) based on in-situ geology mapping and the realistic failure process analysis (RFPA) based on high-definition digital imaging, are developed and introduced. The operation process and analysis results are demonstrated detailedly from the research on parameters of rock mass based on numerical test in the Jinping First Stage Hydropower Station and Baihetan Hydropower Station. By comparison，the advantages and disadvantages are discussed. Then the applicable fields are figured out respectively. (5) Intelligent evaluation based on artificial neural network (ANN) The characters of both ANN and parameter evaluation of rock mass are discussed and summarized. According to the investigations, ANN has a bright application future in the field of parameter evaluation of rock mass. Intelligent evaluation of mechanical parameters in the Jinping First Stage Hydropower Station is taken as an example to demonstrate the analysis process. The problems in five aspects, i. e. sample selection, network design, initial value selection, learning rate and expected error, are discussed detailedly.

The role of cell-surface-bound phosphatases in species competition within natural phytoplankton assemblage: an in situ experiment

Despite it is widely acknowledged that the ability to hydrolyze dissolved organic matter using extracellular phosphatases is diverse in fresh water phytoplankton, the competition within single species related to presence and quantity of cell-surface-bound phosphatases has not been examined in natural conditions yet. Here, we studied phytoplankton species competition in a freshwater reservoir during an in situ experiment. A natural plankton community, with the exclusion of large zooplankton, was enclosed in permeable dialysis bags inside two large containers of different bioavailable phosphate concentrations. Phytoplankton species biomass and the abundance of bacteria were determined in purpose to compare the development of enclosed microbial communities. Total and cell-surface-bound phosphatase activities in the phytoplankton were investigated using the Fluorescently Labelled Enzyme Activity (FLEA) technique that allows for direct microscopic detection of phosphatase-positive cells and, with image cytometry, enables quantification of phosphatase hydrolytic capacity. Production of extracellular phosphatases was not completely inhibited or stopped in the phosphate-enriched environment, phytoplankton cells only showed the activity less often. Under the phosphate-nonenriched conditions, the production of phosphatases was enhanced, but active species did not proliferate amongst phytoplankton assemblage. Further, specific growth rates of the phosphatase-positive species in the non-enriched environment were lower than the same phosphatase-positive species in phosphate-enriched environment. Interestingly, the phosphatase-positive cells of Ankyra ancora increased their size in both treatments equally, although the population in phosphate-enriched environment grew much faster and the cell-specific phosphatase activity was lower. We hypothesize that brand new daughter cells had sufficient phosphorus reserves and therefore did not employ extracellular phosphatases until they matured and needed extra bioavailable phosphorus to support their metabolism before cell division. Based on presented in situ experiment, we propose that the ability to hydrolyze organic polymers and particles with cell-surface-hound phosphatases is advantageous for longer persistence of given population in a phosphate-scarce environment; although phosphatase-positive species cannot dominate the reservoir phytoplankton solely because of specific phosphorus-scavenging strategy.

Optical response of high-order band gap photonic crystal applying in-plane in one-dimensional integration

A new broadband filter, based on the high-order band gap in one-dimensional photonic crystal (PCs) of the form Si vertical bar air vertical bar Si vertical bar air vertical bar Si vertical bar air vertical bar Si vertical bar air vertical bar Si vertical bar air vertical bar Si, has been designed by the plane wave expansion method (PWEM) and transfer matrix method (TMM) and fabricated by lithography. The optical response of this filter to normal-incident and oblique-incident light proves that utilizing the high-order band gaps of PCs is an efficient method to lower the difficulties of fabricating PCs, increase the etching depth of semiconductor materials, and reduce the coupling loss at the interface between optical fibers and PC device. (c) 2007 Elsevier B.V. All rights reserved.

Band-gap bowing and p-type doping of (Zn, Mg, Be)O wide-gap semiconductor alloys: a first-principles study

Using a first-principles band-structure method and a special quasirandom structure (SQS) approach, we systematically calculate the band gap bowing parameters and p-type doping properties of (Zn, Mg, Be)O related random ternary and quaternary alloys. We show that the bowing parameters for ZnBeO and MgBeO alloys are large and dependent on composition. This is due to the size difference and chemical mismatch between Be and Zn(Mg) atoms. We also demonstrate that adding a small amount of Be into MgO reduces the band gap indicating that the bowing parameter is larger than the band-gap difference. We select an ideal N atom with lower p atomic energy level as dopant to perform p-type doping of ZnBeO and ZnMgBeO alloys. For N doped in ZnBeO alloy, we show that the acceptor transition energies become shallower as the number of the nearest neighbor Be atoms increases. This is thought to be because of the reduction of p-d repulsion. The N-O acceptor transition energies are deep in the ZnMgBeO quaternary alloy lattice-matched to GaN substrate due to the lower valence band maximum. These decrease slightly as there are more nearest neighbor Mg atoms surrounding the N dopant. The important natural valence band alignment between ZnO, MgO, BeO, ZnBeO, and ZnMgBeO quaternary alloy is also investigated.

Photoluminescence from ZnS1-xTex alloys under hydrostatic pressure

ZnS1-xTex (0.02less than or equal toxless than or equal to0.3) alloys are studied by photoluminescence under hydrostatic pressure at room temperature. Only a wide emission band is observed for each sample. Its peak energy is much lower than the corresponding band gap of alloys. These bands are ascribed to the radiative annihilation of excitons bound at Te-n(ngreater than or equal to2) isoelectronic centers. The pressure coefficients of the emission bands are smaller than those of alloy band gaps from 48% to 7%. The difference of the pressure coefficient of the emission band and the band gap increases when the binding energy of Te-n centers decreases. It seems contrary to our expectation and needs further analysis. The integrated intensities of emission bands decrease with increasing pressure due to the decreasing of the absorption coefficient associated with the Te-n centers under pressure. According to this model the Stokes shifts between the emission and absorption bands of the Te-n centers are calculated, which decrease with the increasing Te composition in alloys.