An experimental investigation of dynamic crack propagation in a brittle material reinforced with a ductile layer

The fracture behavior of a dynamically loaded edge crack in a brittle-ductile layered material, as a function of applied loading rate, was experimentally investigated. Layered specimens were prepared by sandwiching a thin layer of ductile aluminum between two thick layers of brittle Homalite-100. The layers were bonded using Loctite Depend 330 adhesive, and a naturally sharp edge crack was introduced in one of the Homalite-100 layers. These single-edge notched specimens were loaded in dynamic three-point bending using a modified Hopkinson bar. The fracture process was imaged in real time using dynamic photoelasticity in conjunction with digital high-speed photography, and the applied load and load-point displacement histories were determined from the strain signals recorded at two locations on the Hopkinson bar. The results of this study indicated two distinct mechanisms of dynamic failure, depending on the applied loading rate. At lower loading rates, the starter crack arrested on reaching the aluminum layer and then caused delamination along the aluminum–Homalite interface. On the contrary, as the loading rate was increased, interfacial delamination was followed by crack re-initiation in the Homalite layer opposite to the initial starter crack. It was determined that the times required for crack initiation, delamination and crack re-initiation decreased as the loading rate was increased. However, it was also observed that the applied load values associated with each event increased with increasing loading rate. These observations indicate that both the dynamic failure process and plausibly the failure mode transition are affected by the rate-dependent properties of Homalite, aluminum and the interfacial bond. Finally, based on the measured peak loads and the observed failure mechanisms it was concluded that the incorporation of a thin ductile reinforcement layer can increase both the overall fracture toughness and strength of a nominally brittle material.     

不同应变率下两种岩石的压缩破碎特征试验研究

为了研究不同岩石在不同应变率下压缩时裂纹的产生规律及破坏模式,将石灰岩和红砂岩制成试件,研究其在不同应变率和受力模式下裂纹的形成模式。开展了两种岩石的准静态压缩和动态压缩试验,采用高速摄影机记录了裂纹的产生和破坏模式。对两种岩石试件的裂纹形态进行对比,基于岩石的物理性质、受力状态、能量演化分析,得到了在不同应变率下压缩时产生差异性的原因。结果表明:准静态压缩下岩石试件受压的破坏模式也会因应变率的不同而存在差异,并且破坏模式的差异对岩石试件的抗压强度将产生显著的影响;从能量演化的角度分析,入射能量的大小将会决定岩石试样动态抗压强度曲线是否出现起伏;动态压缩时,裂纹的周向扩展速度与岩石抗压强度呈正相关。     

两层星形网络的特征值谱及同步能力

多层网络是当今网络科学研究的一个前沿方向.本文深入研究了两层星形网络的特征值谱及其同步能力的问题.通过严格导出的两层星形网络特征值的解析表达式,分析了网络的同步能力与节点数、层间耦合强度和层内耦合强度的关系.当同步域无界时,网络的同步能力只与叶子节点之间的层间耦合强度和网络的层内耦合强度有关;当叶子节点之间的层间耦合强度比较弱时,同步能力仅依赖于叶子节点之间的层间耦合强度;而当层内耦合强度比较弱时,同步能力依赖于层内耦合强度;当同步域有界时,节点数、层间耦合强度和层内耦合强度对网络的同步能力都有影响.当叶子节点之间的层间耦合强度比较弱时,增大叶子节点之间的层间耦合强度会增强网络的同步能力,而节点数、中心节点之间的层间耦合强度和层内耦合强度的增大反而会减弱网络的同步能力;而当层内耦合强度比较弱时,增大层内耦合强度会增强网络的同步能力,而节点数、层间耦合强度的增大会减弱网络的同步能力.进一步,在层间和层内耦合强度都相同的基础上,讨论了如何改变耦合强度更有利于同步.最后,对两层BA无标度网络进行数值仿真,得到了与两层星形网络非常类似的结论.     

The caustic approach to Rayleigh-waves and their interaction with surface irregularities

During the past 25 years the method of caustics has matured to the stage where it offers a highly potential tool for qualitative as well as quantitative solutions of engineering problems in many fields. In conjunction with high-speed recording techniques such as high-speed cinematography, the method of caustics serves as a means for visualizing the highly complex interaction processes that occur when elastic stress waves interact with material inhomogeneities or discontinuities such as inclusions, surface or embedded cracks and contacting surfaces during impact.In this contribution, the method of caustics is applied to a number of dynamic problems all of which are associated with the propagation and interaction of Rayleigh-waves:

• the pseudo-caustic of a Rayleigh-wave;

• Rayleigh-wave generation during dynamic impact of two elastic bodies;

• Rayleigh-wave interaction with a shallow embedded crack;

• Rayleigh-wave interaction with various configurations of sets of surface cracks.

Sequences of high-speed cinematographic recordings of the evolution of a dynamic process provide the raw data for data and image analysis for the determination of stress intensity factors, contact forces, load-time traces or other quantities of physical interest.The paper also discusses some of the advantages and disadvantages of the method of caustics over other methods currently used in photomechanics such as dynamic photoelasticity. Data reduction and analysis aspects will also be highlighted.     

多层单向耦合星形网络的特征值谱及同步能力分析

随着复杂网络同步的进一步发展,对复杂网络的研究重点由单层网络转向更加接近实际网络的多层有向网络.本文分别严格推导出三层、多层的单向耦合星形网络的特征值谱,并分析了耦合强度、节点数、层数对网络同步能力的影响,重点分析了层数和层间中心节点之间的耦合强度对多层单向耦合星形网络同步能力的影响,得出了层数对多层网络同步能力的影响至关重要.当同步域无界时,网络的同步能力与耦合强度、层数有关,同步能力随其增大而增强;当同步域有界时,对于叶子节点向中心节点耦合的多层星形网络,当层内耦合强度较弱时,层内耦合强度的增大会使同步能力增强,而层间叶子节点之间的耦合强度、层数的增大反而会使同步能力减弱;当层间中心节点之间的耦合强度较弱时,层间中心节点之间的耦合强度、层数的增大会使同步能力增强,层内耦合强度、层间叶子节点之间的耦合强度的增大反而会使同步能力减弱.对于中心节点向叶子节点耦合的多层星形网络,层间叶子节点之间的耦合强度、层数的增大会使同步能力增强,层内耦合强度、节点数、层间中心节点之间的耦合强度的增大反而会使同步能力减弱.     

Crack motion in viscoelastic solids: The role of the flash temperature

We present a simple theory of crack propagation in viscoelastic solids. We calculate the energy per unit area, G(v), to propagate a crack, as a function of the crack tip velocity v. Our study includes the non-uniform temperature distribution (flash temperature) in the vicinity of the crack tip, which has a profound influence on G(v). At very low crack tip velocities, the heat produced at the crack tip can diffuse away, resulting in very small temperature increase: in this “low-speed” regime the flash temperature effect is unimportant. However, because of the low heat conductivity of rubber-like materials, already at moderate crack tip velocities a very large temperature increase (of order of 1000 K) can occur close to the crack tip. We show that this will drastically affect the viscoelastic energy dissipation close to the crack tip, resulting in a “hot-crack” propagation regime. The transition between the low-speed regime and the hot-crack regime is very abrupt, which may result in unstable crack motion, e.g. stick-slip motion or catastrophic failure, as observed in some experiments. In addition, the high crack tip temperature may result in significant thermal decomposition within the heated region, resulting in a liquid-like region in the vicinity of the crack tip. This may explain the change in surface morphology (from rough to smooth surfaces) which is observed as the crack tip velocity is increased above the instability threshold.     

Atomistic simulation of the self-diffusion in Fe (1 1 1) surface

The formation energies, the intra- and inter-layer self-diffusion activation energies of a single vacancy in Fe (1 1 1) surface have been investigated with the modified analytical embedded-atom method (MAEAM). The results show that the effect of the surface is down to the sixth layer for the formation and intra-layer migration of the vacancy. It is easier for a vacancy to form and to migrate in intra-layer in the first (especially), the second and the third layer. For inter-layer migration, a single vacancy in each of the first six layers is favorable to migrate to the upper layers. On the contrary, a single vacancy in the seventh, the eighth and the ninth layers is favorable to migrate to the lower layers.     

韧性材料的微裂纹扩展与分叉的晶体相场模拟

采用晶体相场方法研究韧性单晶材料在双轴拉伸条件下微裂纹扩展与分叉的演化过程,分析应变、温度、初始裂口形状等因素对裂纹扩展和分叉的影响.结果表明:对于简单的单向拉伸,应变需要达到一定的临界值,裂纹扩展才会启动.对于二组相互垂直的双轴拉伸作用,当应变达到临界值后,裂纹扩展过程中会发生分叉现象.温度越高,裂纹扩展越快且分叉越多.裂纹在扩展过程中,体系能量不断降低,当裂纹出现分叉时,体系能量降低得更快.在裂纹扩展过程中,有时是会在裂尖处前方出现微小的空洞,类似在裂纹尖端前方出现位错发射情况,这些微小的空洞逐渐扩大连成裂纹.本文所得结果与相关模拟结果和实验结果符合.     

Influence of Surface Transition Layers on Phase Transformation and Pyroelectric Properties of Ferroelectric Thin Film

Taking into account surface transition layers （STLs）, we study the phase transformation and pyroelectric properties of ferroelectric thin films by employing the transverse Ising model （TIM） in the framework of the mean field approximation. The distribution functions representing the intra-layer and inter-layer couplings between the two nearest neighbour pseudo-spins are introduced to characterize STLs. Compared with the results obtained by the traditional treatments for the thin films using only the single surface transition layer （SSL）, it is shown that the STL model reflects a more realistic and comprehensive situation of films. The effects of various parameters on the phase transformation properties have shown that STL can make the Curie temperature of the film higher or lower than that of the corresponding Sulk material, and the thickness of STL is a key factor influencing the film properties. For a film with definite thickness, there exists a critical STL thickness at which ferroelectricity will disappear when the intra-layer and inter-layer interactions are weak.     

CRACK IDENTIFICATION IN VIBRATING BEAMS USING THE ENERGY METHOD

An energy-based numerical model is developed to investigate the influence of cracks on structural dynamic characteristics during the vibration of a beam with open crack(s). Upon the determination of strain energy in the cracked beam, the equivalent bending stiffness over the beam length is computed. The cracked beam is then taken as a continuous system with varying moment of intertia, and equations of transverse vibration are obtained for a rectangular beam containing one or two cracks. Galerkin's method is applied to solve for the frequencies and vibration modes. To identify the crack, the frequency contours with respect to crack depth and location are defined and plotted. The intersection of contours from different modes could be used to identify the crack location and depth.     

Toughening Effect of Poly(ethene-co-1-butene)-graft-methyl Methacrylate and Acrylonitrile on Styrene-acrylonitrile Copolymer (SAN)

Poly(ethene-co-1-butene)-graft-methyl methacrylate-acrylonitrile (PEB-g-MAN), synthesized by suspension grafting copolymerization of methyl methacrylate and acrylonitrile onto PEB, was blended with styrene-acrylonitrile copolymer (SAN). The mechanical properties, phase structure, toughening mechanism, miscibility, and thermal stability of the SAN/PEB-g-MAN blends were studied using a pendulum impact tester, tension tester, scanning electron microscopy (SEM), transmission electron microscopy (TEM), dynamic mechanical analysis (DMA), and thermogravimetric analysis (TG). The results showed that PEB-g-MAN has an excellent toughening effect on SAN resin. The notched impact strength of the blends (containing 25 wt% PEB) was 63.3 kJ/m², which was nearly 60 times that of SAN resin. The brittle-ductile transition of SAN/PEB-g-MAN blends occurred when the weight percentage of PEB was between 17.5 and ～20 wt%. SAN and PEB-g-MAN were partially miscible. The toughening mechanism of the blends changed with the PEB content. When the PEB content was low, the toughening mechanism of the blends was branching and termination of cracks with slight cavitation. As the content of PEB increased, the toughing mechanism gradually changed from branching and termination of crack with slight cavitation to both branching and termination of crack and cavitation, to extensive cavitation, and finally to shear yielding accompanied by cavitation. The phase structure of the blends changed from a “sea-island’’ structure to a cocontinuous structure as the PEB content increased. ATG analysis showed that the thermal properties of the SAN resin in the blends were enhanced by adding the PEB-g-MAN.     

Feed-forward chains of recurrent attractor neural networks with finite dilution near saturation

A stationary state replica analysis for a dual neural network model that interpolates between a fully recurrent symmetric attractor network and a strictly feed-forward layered network, studied by Coolen and Viana, is extended in this work to account for finite dilution of the recurrent Hebbian interactions between binary Ising units within each layer. Gradual dilution is found to suppress part of the phase transitions that arise from the competition between recurrent and feed-forward operation modes of the network. Despite that, a long chain of layers still exhibits a relatively good performance under finite dilution for a balanced ratio between inter-layer and intra-layer interactions.     

Atomistic simulation of the vacancy in Ni (1 1 0) surface

Both the formation energies and the intra- and inter-layer diffuse activation energies of a vacancy in the first six atomic planes of Ni (1 1 0) surface have been investigated by means of molecular dynamics (MD) in conjunction with the semi-experiential many-body potential of the modified analytical embedded-atom method (MAEAM). The results show that the effect of the surface is only down to the fifth-layer. It is easer for a vacancy in the first or second layer to form and to migrate in intra-layer. For the inter-layer migration, a vacancy in the second or third layer is favorable to migrate to the upper layer, this is not the case for a vacancy in the fourth or fifth layer.     

Path prediction of kinked and branched cracks in plane situations

Using the asymptotic expansion of the stress field ahead a curved extension of a straight crack, some general results on the paths selected by kinked and branched cracks are derived. When dealing with the dynamic branching instability of a single propagation crack, the experimentally observed shape of the branches is recovered without introducing any adjustable parameter. It is shown that the length scale introduced by the curved extension of the branches is given by the geometrical length scale of the experiment. The theoretical results agree quantitatively with the experimental findings.     

A high-speed photographic study of fast cracks in shocked diamond

Six fracture surfaces have been observed extending at velocities between c_R (the Rayleigh wave velocity) and 1.3c_R in high-speed photographs of four diamond specimens. The diamonds were embedded in a transparent polymer and shocked in plate impact experiments. The measured velocities exceed limiting velocities proposed in theoretical and practical studies of single mode I cracks in diamond. The fracture surfaces probably extend by initiation and coalescence of multiple tensile fractures along a single cleavage plane. This mechanism is dependent on the suppression of cracks branching from the {111} growth plane in diamond and considers the population of flaws near a propagating crack tip.     

多层网络级联失效的预防和恢复策略概述

现实生活中,与国计民生密切相关的基础设施网络大多不是独立存在的,而是彼此之间相互联系或依赖的,于是用于研究这些系统的多层网络模型随之产生.多层网络中的节点在失效或者遭受攻击后会因"层内"和"层间"的相互作用而产生级联效应,从而使得失效能够在网络层内和层间反复传播并使得失效规模逐步放大.因此,多层网络比单个网络更加脆弱.多层网络级联失效产生的影响和损失往往是非常巨大的,所以对多层网络级联失效的预防和恢复的研究具有重大意义.就多层网络级联失效的预防而言,主要包含故障检测,保护重要节点,改变网络耦合机制和节点备份等策略.就多层网络发生级联失效后的恢复策略而言,主要包含共同边界节点恢复、空闲连边恢复、加边恢复、重要节点优先恢复、更改拓扑结构、局域攻击修复、自适应边修复等策略.     

Voice and Physical Appearance in Female-to-Male Transsexuals

The study aims to investigate if a similar interaction between physical appearance and voice could be found in female-to-male transsexuals as had been observed in male-to-female transsexuals. A panel of judges rated “maleness” of seven female-to-male transsexuals from video-recorded speech samples using three modes of presentation: auditory-only presentation, visual-only presentation, and audiovisual presentation. For the group of transsexuals as a whole, no significant differences were found between scores given in the auditory-only mode or the visual-only mode and those given in the audiovisual mode. Analysis of individual results, however, yielded significant differences in some individuals and there was some relation with hormone treatment. There was no significant correlation between the ratings of “maleness” in the auditory-only mode and fundamental frequency. Physical appearance in female-to-male transsexuals appears not to be a strong influencing factor in general, but may interact with gender recognition based on the voice in some individuals. The absence of a correlation between fundamental frequency and rating of maleness could mean that in female-to-male transsexuals, fundamental frequency is a relatively less important factor for gender expression or perhaps also that a higher voice in males is more accepted than a lower voice in females.     

Crack detection in single-crystalline silicon wafers using impact testing

This paper presents acoustic measurements obtained by mechanically exciting vibratory modes in single-crystalline silicon wafers with hairline periphery cracks of different type and location. The data presented shows a dependence of natural frequencies, peak amplitudes and damping levels of four audio vibration modes in the frequency range up to 1000 Hz on crack type and crack location. Data from defective wafers exhibit lower natural frequencies, higher damping levels, and lower peak amplitudes. The results suggest an impact test method may be useful for solar cell crack detection and quality control.     

Dynamic caustics and its applications

For the study of elastodynamic problems of propagating cracks it is necessary to evaluate the dynamic stress intensity factor K^d_I which depends on the form of expressions for the stress components existing at the running crack tip at any instant of the propagation of the crack and the corresponding dynamic mechanical and optical properties of the material of the specimen under identical loading conditions. In this paper the distortion of the form of the corresponding reflected caustic from the lateral faces of a dynamically loaded transparent and optically inert specimen containing a transverse crack running under constant velocity was studied on the basis of complex potential elasticity theory and the influence of this form on the value of the dynamic stress intensity factor was given. The method was applied to the study of a propagating Mode I crack in a PMMA specimen under various propagation velocities and the corresponding dynamic stress intensity factor K^d_I evaluated. Also, crack propagation behaviour of notched composites in dynamic loading modes are reviewed and evaluated. A relatively large data base using metal-epoxy particulates, rubber-toughened poly(methyl methacrylate), and Sandwich plates are given. In all cases, a combination of high-speed photography and the optical method of dynamic caustics has been used. Results on the dynamic crack propagation mode, fracture toughness and crack propagation velocities of several rubber-modified composite models are presented. The composite models studied include specimens with one and/or two ‘complex’ two-stage inclusions, i.e. PMMA round inclusions surrounded by concentric rubber rings, one and/or press-fifting inclusions without rubber interface, all under dynamic loading. In all cases both qualitative and quantitative results were obtained. Also, results on crack propagation mode, crack propagation velocity, stress intensity factors and on the influence of the sandwich phases on crack propagation mode are presented.     

无序性对脆性材料冲击破碎的影响

脆性材料受冲击荷载作用产生损伤开裂是一个连续介质离散化的过程.采用连续离散耦合方法模拟了一个脆性圆球以不同初始速度与刚性板的冲击,重点研究了无序性对脆性材料冲击破碎的影响,并对其内在机理进行了分析.本文不考虑材料细观结构的无序性,材料的无序仅体现在细观断裂参数的非均质性.数值实验同样揭示了脆性材料在冲击破坏中存在两种破坏模式,即低速时接触区域的局部损伤和高速时的整体碎裂.研究表明,材料无序性对临界冲击速度、破碎模式、碎片形态影响显著.随着无序度增加,材料的临界速度增大,损伤开裂由少量贯穿性裂纹主导转变为全域性的分叉裂纹.高无序度圆球冲击产生的碎片表面更粗糙,体型更为扁平细长.这与细观断裂的主导机制有关,无序度较高时剪切导致开裂的比重更大,碎片内部损伤裂纹面更多.