Impact damage of laminated composite with energy dissipation: Part II — Damage evolution

Having developed the methodology for analyzing the failure of a ceramic/rubber/steel composite laminate impacted by a tungsten rod in Part I, Part II of the work is concerned with the progressive damage process where material continuity would be interrupted at different locations and time intervals. Depending on the time rate dependent threshold values of the surface and volume energy density, the degree and extent of damage by fragmentation, mass loss, etc. are determined by finite element calculations for time steps of 0.15, 5.0, 7.5, 10, 20, 21 and 21.5 μs. Stresses and strains possess an oscillatory character in time; they alternate in sign as the impact waves bounce back and forth in the three-layered dissimilar materials.Local strain rates of approximately 10⁵, 10³ and 10⁴ s⁻¹ are formed in the ceramic, rubber and steel layer respectively at locations underneath the tungsten rod after 16 μs of impact. A more wide range of strain ratio would have prevailed for a homogeneous layer of the same thickness. The tungsten rod is now badly fragmented while cracking near the surface of the ceramic is also predicted. Local temperature and dissipation energy density rise rapidly as time approached 20 μs. The maximum surface and volume.energy density in the ceramic near the impact region reached 260 MPa · m and 6.39 MPa, respectively. Complete disintegration of the tungsten rods occurred at 21.5 μs. At this time, the ceramic layer is perforated and the rubber layer is partially cracked. The back-up steel plate, however, remained in tack. These predictions agree qualitatively with past observations.     

The First Turbulence and First Fossil Turbulence

A model is proposed connecting turbulence, fossil turbulence and the big-bang origin of the universe. While details are incomplete, the model is consistent with our knowledge of these processes and is supported by observations. Turbulence arises in a hot big-bang quantum gravitational dynamics scenario at Planck scales. Chaotic, eddy-like motions produce an exothermic Planck particle cascade from 10^?35 m at 10³² K to 10⁸ larger, 10⁴ cooler, quark-gluon scales. A Planck-Kerr instability gives high Reynolds number (Re ～ 10⁶) turbulent combustion, space-time-energy-entropy and turbulent mixing. Batchelor-Obukhov-Corrsin turbulent-temperature fluctuations are preserved as the first fossil turbulence by inflation stretching the patterns beyond the horizon ct of causal connection faster than light speed c in time t～ 10^?33 sec. Fossil big-bang temperature turbulence reenters the horizon and imprints nucleosynthesis of H-He densities that seed fragmentation by gravity at 10¹² s in the low Reynolds number plasma before its transition to gas at t～ 10¹³ s and T～ 3000 K. Multiscaling coefficients of the cosmic microwave background (CMB) temperature anisotropies closely match those for high Reynolds number turbulence, Bershadskii, A. and Sreenivasan, K.R., Phys. Lett. A 299 (2002) 149-152; Bershadskii, A. and Sreenivasan, K.R., Phys. Lett. A 319 (2003) 21-23. CMB spectra support the interpretation that big-bang turbulence fossils triggered fragmentation of the viscous plasma at supercluster to galaxy mass scales from 10⁴⁶ to 10⁴² kg, Gibson, C.H., Appl. Mech. Rev. 49 (5) (1996) 299-315; Gibson, C.H., J. Fluids Eng. 122 (2000) 830-835; Gibson, C.H., Combust. Sci. Technol. (2004, to be published).     

An analog experiment of magma fragmentation: behavior of rapidly decompressed starch sirup

Paper reports a result of analog experiments regarding the simulation of magma fragmentation. We filled a starch sirup foam, as an analog material, in a 117–240 mm long and a 50 mm diameter high pressure chamber and exposed it to a rapid decompression. The foam was prepared by mixing starch sirups of dynamic viscosities ranging from 5 to 10¹² Pa· s at temperatures ranging from 293 to 343 K with nitrogen at 2.5 MPa gauge pressure. In ejecting high-pressure foams into a low-pressure chamber, diagnostics of foam’s fragmentation process were pressure measurment and high-speed video recording. Prior to decompression experiments, we examined visco-elastic properties of foam specimens by using a rheometer. The foam deformation under decompression was found to be axial–symmetrical, and strongly coupled with bubble growth and coalescence. These effects contributed even more efficiently to fragmentation processes than previous laboratory experiments using other analog materials. Fragment shapes varied widely depending on the temperature and water concentration of starch sirup foams, which proved that fragmentation process was governed by not only ductile deformation but also brittle failure, and determined by the degree of visco-elasticities of starch sirup foams.      

The fragmentation of cementitious composites in a jaw breaker

The paper reports about the fragmentation of cementitious composites in a laboratory jaw breaker. Two types of cement paste and six different concrete materials were investigated. Specific fragmentation energy and size distributions of the generated fragments were estimated. A microscopic inspection of the debris was also performed. Specific energy has values between 5 and 10 J/g. It is highest for a concrete with high porosity and lowest for a mortar. It is also found that the specific fragmentation energy depends on the amount of coarse aggregates in the material. Based on these findings, the specific fragmentation energy is linked to a brittleness parameter of the concrete materials derived from non-linear fracture mechanics. A detailed SEM-study showed features of non-linear fracture, namely crack branching, aggregate bridging, and pore–crack interaction. It was further found that a Rosin–Rammler–Sperling distribution best describes the size distribution of the generated fragments, except the mortar. An approximate estimation of the strain rate during the fragmentation was performed, and a value of s⁻¹ was calculated for concrete.     

Sound radiation by a system of vortices

The radiation of sound in a slightly compressible medium by elementary vortex formations is considered-two vortex filaments with identical intensities which radiate cylindrical waves, and two vortex rings with identical intensities which radiate spherical waves. It is shown that in the first case the sound intensity is proportional to M⁴, where T_ij=₀u_iu_j is the Mach number (N is the vortex intensity, 2h is the distance between vortices, and c is the speed of sound). In the second case, in a coordinate system fixed with the vortex rings, the sound intensity is proportional to M⁵, which is in agreement with the results of Lighthill [1, 2].In conclusion I wish to thank A. M. Obukhov for posing the problem and his discussion of the results.     

Grain orientation fragmentation in hot-deformed aluminium: Experiment and simulation

Grain orientation fragmentation is studied in a set of 176 individual grains of an aluminium polycrystal deformed in plane strain compression at 400 °C to a strain of $\epsilon =1.2$. Experimental observations were made by EBSD at successive strains of 0, 0.42, 0.77 and 1.2 on the internal surface of a split sample. Statistics of the in-grain orientation spreads were computed based on approximately 3000 orientation measurements per grain. A high-resolution finite element simulation (about 1000 elements per grain) was carried out on a polycrystal whose grains were assigned the initial experimental crystal orientations. The experimental and simulation results were compared in terms of the fractions of grains that exhibit fragmentation and the lattice orientations of the fragmenting grains. The numbers of fragmented grains increase with strain, reaching values of 10% in the experiment (2-D characterization) and 20% in the simulation (3-D characterization) at $\epsilon =1.2$. For both experiment and simulation, fragmentation is more likely in grains whose lattice is symmetrically oriented with respect to the loading axes. Under plane strain compression, the orientations of the fragmented grains coincide with regions of orientation space in which the reorientation velocity field in the plane perpendicular to the reorientation velocity direction is unstable.     

Set up of an experimental apparatus for the study of fragmentation of solid fuels upon severe heating

An experimental apparatus has been developed in order to perform tests of primary fragmentation of solid fuels under severe heating conditions. The device is a modified heated strip reactor, capable to reach 2000 °C in less than 0.2 s. Particles are laid on the strip and pyrolysed under inert or moderately oxidizing conditions. The char particles and their fragments, generated upon pyrolysis, can be recovered and analysed to assess the fragmentation propensity of the fuel.Some preliminary experiments have been carried out on two biomass samples in order to assess the time-temperature history of particles in the experimental apparatus. In particular biomass particles of approximately 2–3 mm have been used. The temperature of the heated strip reactor in such preliminary tests was varied between 1000 and 1600 °C, while the strip nominal heating rate was kept at 10⁴ °C/s and the holding time was set at the value of 10 s. A near infrared fast camera (38,000 frames/s) has been used to measure the temperature of the heated strip and of the particles during the tests. A heat up model was developed and validated against experimental results. The model was then used to estimate the temperature gradients across particles of biomass and of coal as well.Results show that the strip of the reactor reaches the set temperature in less than 0.2 s. When particles are laid on the strip, their bottom surface, which is in physical contact with the strip, immediately reaches the set temperature value. For 1 mm coal particles the upper surface can be considered at the same temperature as well. Under the most severe conditions tested (strip temperature of 1600 °C , biomass particles of 2 mm thickness) the temperature difference between the bottom and the upper face is 200 °C after 3 s and drops to 100 °C after 10 s. On the whole the experimental apparatus simulates uniform heating of the particles with reasonable approximation. In the next future the apparatus will be further upgraded to operate at pressures up to 20 bars.     

PMMA膨胀环动态拉伸碎裂实验研究

在强动载作用下, 脆性材料的碎裂问题是一个重要的研究课题, 而脆性材料在冲击拉伸载荷下的力学行为的实验研究相对较匮乏. 提出了一种动态拉伸断(碎)裂的液压膨胀环实验技术, 可用于准脆性/脆性材料的动态拉伸. 利用该技术对有机玻璃(PMMA)圆环试件进行了不同膨胀速度下的动态碎裂实验研究. 从回收碎片的断口形貌和碎片内部残余裂纹观察可知试件的破碎由环向拉伸应力造成, 碎片断口处发出的稀疏波会将周围的拉伸应力卸载, 从而抑制其他裂纹的进一步发展. 利用超高速相机记录了试件的膨胀碎裂过程, 利用DISAR激光速度干涉仪获得了试件外表面粒子的径向膨胀速度历史, 通过试件上的应变片获得了试件的应变历史和断裂应变. 实验结果表明: 在拉伸应变率150\mathrm{~}500s^{-1}范围, 材料的动态断裂应变低于准静态加载下的断裂应变, 体现出“动脆”现象; 随着加载应变率的提高, PMMA 材料的碎片尺寸减小; 无量纲化的PMMA圆环的平均碎片尺寸介于韧性碎裂模型和脆性碎裂模型的预测数值之间, 反映出材料的准脆性特性.      

Vortex rings in radially confined domains

The dynamics of vortex rings generated within confined domains are relevant to important hydrodynamic processes such as flow past heart valves or severe arterial constrictions. However, despite their importance, these flows have not received much attention to date. This study examines the development and evolution of radially confined vortex rings. Time-resolved digital particle image velocimetry was used to investigate two levels of radial confinement and a range of vortex ring strengths. We found that for severely confined vortex rings, the formation time and peak circulation values were unaffected for L/D ₀?<?4 cases and slightly affected for larger L/D ₀ cases. After pinch-off, circulation decay was observed with an approximately constant normalized circulation decay rate. We found that with increasing circulation strength, the nondimensional time delay between the pinch-off and the onset of circulation decay reduced due to an increased vortex ring diameter within the confinement domain and a reduction in the necessary time for the surface induced and core vorticity regions to interact. This study uncovers the dynamics of radially confined vortex rings and show that the nondimensional rate of circulation decay is dependent on the vortex ring confinement ratio (ratio of the vortex ring orifice diameter to the diameter of the outer cylinder), and the time delay between the vortex pinch-off and the onset of circulation is dependent on the vortex ring circulation strength.     

New method for testing composites at very high strain rates

A method was developed for testing and characterizing composite materials at strain rates in the 100 to 500 s^?1 regime. The method utilizes a thin ring specimen, 10.16 cm (4 in.) in diameter, 2.54 cm (1 in.) wide and 6–8 plies thick. This specimen is loaded by an internal pressure pulse applied explosively through a liquid. Pressure is measured by means of a calibrated steel ring instrumented with strain gages. Strains in the composite specimen are measured with strain gages. Strains in the calibration and specimen rings are recorded with a digital processing oscilloscope. The equation of motion is solved numerically and the data processed by the mini-computer attached to the oscilloscope. Results are obtained, and plotted by an X-Y plotter in the form of a dynamic stress-strain curve. Unidirectional 0-deg, 90-deg and 10-deg off-axis graphite/epoxy rings were tested at strain rates up to 690 s^?1. Times to failure ranged between 30 and 60 μs. The 0-deg properties which are governed by the fibers do not vary much from the static ones with only small increases in modulus. The 90-deg properties show much higher than static modulus and strength. The dynamic in-plane shear properties, obtained from the 10-deg off-axis specimens, are noticeably higher than static ones. In all cases the dynamic ultimate strains do not vary much from the static values.     

Sub-nanomol per second flow measurement near atmospheric pressure

 We present a measurement technique designed to accurately measure small flow rates near atmospheric pressure, and demonstrate the ability to measure flows on the order of 10^-10 mol/sec. The technique is based upon a modification of a constant-volume mass accumulation scheme where the flow rate is measured by monitoring the change in pressure of a known volume of gas. We identify two phenomena, thermally-induced fluctuations and thermodynamically-induced fluctuations, which will affect the resolution and dynamic range of the instrumentation and discuss how the problems associated with them can be mitigated. We estimate the resolution to be approximately 2.0×10^-13 mol/s, and the maximum measurable flow rate to be to the order 2×10^-9 mol/s. Received: 16 July 1996/Accepted: 2 June 1997     

BPNN用于含氮、硫杂环润滑油添加剂抗磨性能的定量构效关系研究

采用反向传播神经网络法(Back Propagation Neural Network,简称:BPNN)对31种含氮、硫的2-烷基黄原酸酯类润滑油添加剂的抗磨性能进行了摩擦学定量构效关系(Quantitative Structure Tribo-ability Relationship,简称:QSTR)的研究,得到了具有良好的稳定性和预测能力的BPNN-QSTR模型(R~2=0.998 4,R~2(LOO)=0.695 9,q~2=0.879 1).参考输入层的12种2D和3D结构描述符的敏感度,对影响抗磨性能的分子结构进行了相应的探讨.结果表明:分子中的N和S杂原子对其抗磨损性能有显著的影响;同时,分子长度、所含双键S原子和芳香环数量以及分子支化程度等都是影响抗磨性能的主要因素.     

Crown incident radiant heat flux measurements in an industrial,regenerative, gas-fired,flat-glass furnace

Crown incident radiant heat flux measurements performed during both firing and non-firing cycles are reported, for the first time, in the combustion space of a regenerative, side-port, 455 metric ton/day, gas-fired, flat-glass furnace. Measurements were acquired through six crown access holes along the furnace axial centerline. Video and visual observations of the glass surface were also made through access ports in the furnace. A three-dimensional numerical model of the turbulent mixing, reaction, and heat transfer processes is also used to predict radiant heat flux to the crown. The measured crown incident radiant heat flux profile during firing cycles rises from 425 kW/m² close to the batch feeder to a peak of 710 kW/m² near the center of the combustion space, followed by a drop to approximately 575 kW/m² near the furnace working end. Numerical model results are in relatively good agreement with measured results. During non-firing reversal cycles, measured flux levels at the crown rise from 320 kW/m² near the batch feeder, to a maximum of 565 kW/m² closest to the spring zone. Increases in crown incident radiant heat flux due to combustion are quantified, with nominal increases of 105 kW/m² in regions closest to the batch feeder and approximately 155 kW/m² in the center of the combustion space. Lower increases from combustion (85 and 12 kW/m²) are exhibited in locations closest to the furnace working end. During the 20–25 s non-firing reversal period, the incident heat flux to the crown typically decreased between 20 and 50 kW/m² at each measured location. Variation of heat flux to the crown during 15-min firing cycles is typically 3–6% of the total incident heat flux, with a maximum typically occurring one-third of the way into the cycle (5–6 min) and declining during the remaining two-thirds of the period.     

Modeling of ductile fragmentation that includes void interactions

The failure and fragmentation of ductile materials through the nucleation, growth, and coalescence of voids is important to the understanding of key structural materials. In this model of development effort, ductile fragmentation of an elastic–viscoplastic material is studied through a computational approach which couples these key stages of ductile failure with nucleation site distributions and wave propagation, and predicts fragment spacing within a uniaxial strain approximation. This powerful tool is used to investigate the mechanical and thermal response of OFHC copper at a strain rate of 10⁵. Once the response of the material is understood, the fragmentation of this test material is considered. The average fragment size as well as the fragment size distribution is formulated.     

Potassium sodium tartrate-assisted hydrothermal synthesis of BaLuF5:Yb3+/Er3+ nanocrystals

Highly-dispersed BaLuF₅:Yb³⁺/Er³⁺ nanocrystals were prepared by a facile potassium sodium tartrate-assisted hydrothermal method. The average particle size was approximately 20–25 nm. The formation mechanism is discussed. Potassium sodium tartrate led to form a complex with an approximately three-dimensional network structure, which insured largely concurrent nucleation. As a result, we acquired uniform nanoparticles. The hydrothermal temperature, holding time, and pH value were important factors affecting the formation of the BaLuF₅:Yb³⁺/Er³⁺ nanocrystals. We investigated their influence on the formation and realized the optimal reaction parameters. Remarkably, potassium sodium tartrate also contributed to the biocompatibility and potential biomedical applications of BaLuF₅:Yb³⁺/Er³⁺ nanocrystals by decomposing into small organic groups attached to the nanoparticles.     

Predicting soil fragmentation during tillage operation using fuzzy logic approach

One of the main characteristics of the soil structure, which affects the plant growth and its yield, is its aggregates size. Correct tillage operations leads to prevention from soil degradation and help to maintain and improve its physical, chemical, and biological characteristics. In this paper, a model based on fuzzy logic approach was used to describe the soil fragmentation for seedbed preparation in the composition of primary and secondary tillage implements of subsoiler, moldboard plow and disk harrow as conventional tillage composition in the region. Field experiments were carried out at educational and research farms of faculty of agriculture, University of Mohaghegh Ardabili. In this paper, an intelligent model, based on Mamdani approach fuzzy modeling principles, was developed to predict soil fragmentation during tillage operation. The model inputs included soil moisture content, tractor forward speed and soil sampling depth. The fuzzy model consisted of 50 rules, in which three parameters of root mean square error (RMSE), relative error (ɛ), and coefficient of determination (R²) were used to evaluate the fuzzy model. These parameters were calculated 0.167%, 3.95%, and 0.988%, respectively. According to the results of this research, the fuzzy model can be introduced as one of the methods for predicting soil fragmentation during the tillage operation with high accuracy.     

Acoustic Sounding of Vortex Rings in a Continuously Stratified Fluid

The experimental simulation of solitary vortex rings in a stratified fluid performed using high-frequency echo-sounding and optical visualization methods shows that on the range from turbulent to laminar regimes the vortex is a volume inhomogeneity with a sound scattering cross-section m _vU ⁵, where U is the translational velocity. The absolute value of m _v is determined by the microscale component of the vortex microstructure, which is commensurable with the sounding sonic wave length.     

Computer extended series for a thermally driven gas centrifuge

Linearized, multidimensional, thermally driven flow in a gas centrifuge can be approximately described in regions away from the ends by Onsager's homogeneous pancake equation.¹ Upon reformulation of the general problem, we find a new, simple and rigorous closed form, analytical solution by assuming a special separable solution and replacing the usual Ekman end cap boundary conditions with idealized impermeable, free slip boundary conditions. Then the flow may be described by an ordinary differential equation with solutions in terms of simple, classical functions. By identifying a small parameter, say ?, defining the semi-long bowl approximation, and assuming a power series expansion in ?, a sequence of asymptotic approximations to the master potential is obtained. Not surprisingly, the leading order term involves the well known ‘long bowl’ solution. Using the so-called ‘solving’ property of the 1-D pancake Green's function,² we determine the next higher order solution. This recursive process is carried out on the computer to find all the terms up to O(?⁴). Consequently, the solution of some complex rotating, viscous, heat conducting flow problems that normally require large mainframe computers can be better understood.     

Effect of droplet size on the rheological properties of highly-concentrated w/o emulsions

Rheological properties of highly concentrated emulsions of the water-in-oil type were studied. Water phase (concentration approximately 91%) consists of a supersaturated aqueous solution of nitrate salts; water comprises less than 20% by mass. The average size of droplets, D, in the emulsions was varied. It was found that the emulsions are non-Newtonian liquids and flow curves measured in a sweep regime of shearing have clear low-shear-rate Newtonian domain. The complete flow curves are fitted by the Cross equation. The elastic modulus is practically constant in a very wide frequency range. Hence the viscoelastic relaxation processes might be expected at times >>100 s and in the short-term side of the curve at approximately 0.01 s. The elastic modulus (measured in oscillating testing and in elastic recovery as well) is proportional to D^-2 while the Newtonian viscosity is proportional to D^–1.The time effects were observed: it was found that the emulsions behave as rheopectic materials because prolonged shearing results in an increase of viscosity in the low shear rate domain of several orders of magnitude.Presented in part at the First Annual European Rheological Conference, Guimarães, Portugal, 11–13 September 2003     

Features of the turbulent wall pressure field on a long towed cylinder

Turbulent wall pressure fluctuation correlation functions were measured in water on a towed cylindrical model of length 129.8 m and diameter 3.8 cm for steady speeds ranging from 6.2 to 15.5 m/s. The drag on the model was measured with a strut-mounted load cell to provide estimates of the momentum thickness and friction velocity that are used for scaling the correlation functions. Very high momentum thickness Reynolds numbers Re_θ were achieved, and varied from 4.8 × 10⁵ to 1.1 × 10⁶. The ratio of boundary layer thickness to cylinder radius was approximately 24, which is an order of magnitude greater than previous laboratory investigations. The ratio of momentum thickness to viscous length scale is significantly greater than for flat plate cases at comparable Re_θ. A similarity scaling is shown to be more effective than outer or inner boundary layer scalings for collapsing the correlation functions. Comparisons with the early streamwise and transverse correlation measurements of Willmarth and Yang are favorable, and show consistent trends of a more rapid loss of correlated energy for cylindrical turbulent boundary layers than for flat plate cases. Convection velocities are also presented and shown to collapse well with separation scaled on outer variables. A simple model that relates the peak of the correlation function to the average coherence levels is shown to be valid for spatial separations less than the approximate momentum thickness.