Statistical and stochastic description of microvoid evolution observed in dynamic failure of ductile materials

A brief review is presented of statistical approaches on microdamage evolution. An experimental study of statistical microdamage evolution in two ductile materials under dynamic loading is carried out. The observation indicates that there are large differences in size and distribution of microvoids between these two materials. With this phenomenon in mind, kinetic equations governing the nucleation and growth of microvoids in nonlinear rate-dependent materials are combined with the balance law of void number to establish statistical differential equations that describe the evolution of microvoids' number density. The theoretical solution provides a reasonable explanation of the experimentally observed phenomenon. The effects of stochastic fluctuation which is influenced by the inhomogeneous microscopic structure of materials are subsequently examined (i.e. stochastic growth model). Based on the stochastic differential equation, a Fokker-Planck equation which governs the evolution of the transition probability is derived. The analytical solution for the transition probability is then obtained and the effects of stochastic fluctuation is discussed. The statistical and stochastic analyses may provide effective approaches to reveal the physics of damage evolution and dynamic failure process in ductile materials.

Direct Numerical Simulation Of Hypersonic Boundary-Layer Transition Over A Blunt Cone

Direct numerical simulation of transition How over a blunt cone with a freestream Mach number of 6, Reynolds number of 10,000 based on the nose radius, and a 1-deg angle of attack is performed by using a seventh-order weighted essentially nonoscillatory scheme for the convection terms of the Navier-Stokes equations, together with an eighth-order central finite difference scheme for the viscous terms. The wall blow-and-suction perturbations, including random perturbation and multifrequency perturbation, are used to trigger the transition. The maximum amplitude of the wall-normal velocity disturbance is set to 1% of the freestream velocity. The obtained transition locations on the cone surface agree well with each other far both cases. Transition onset is located at about 500 times the nose radius in the leeward section and 750 times the nose radius in the windward section. The frequency spectrum of velocity and pressure fluctuations at different streamwise locations are analyzed and compared with the linear stability theory. The second-mode disturbance wave is deemed to be the dominating disturbance because the growth rate of the second mode is much higher than the first mode. The reason why transition in the leeward section occurs earlier than that in the windward section is analyzed. It is not because of higher local growth rate of disturbance waves in the leeward section, but because the growth start location of the dominating second-mode wave in the leeward section is much earlier than that in the windward section.

On the mechanism of void growth and the effect of straining mode in ductile materials

Finite element analysis is employed to investigate void growth embedded in elastic-plastic matrix material. Axisymmetric and plane stress conditions are considered. The simulation of void growth in a unit cell model is carried out over a wide range of triaxial tensile stressing or large plastic straining for various strain hardening materials to study the mechanism of void growth in ductile materials. Triaxial tension and large plastic strain encircling around the void are found to be of most importance for driving void growth. The straining mode of incremental loading which favors the necessary strain concentration around void for its growth can be characterized by the vanishing condition of a parameter called "the third invariant of generalized strain rate". Under this condition, it accentuates the internal strain concentration and the strain energy stored/dissipated within the material layer surrounding the void. Experimental results are cited to justify the effect of this loading parameter. (C) 2000 Elsevier Science Ltd. All rights reserved.

Features of the supercritical transition in the wake of a circular cylinder

The features of the wake behind a uniform circular cylinder at Re = 200, which is just beyond the critical Reynolds number of 3-D transition, are investigated in detail by direct numerical simulations by solving 3-D incompressible Navier-Stokes equations using mixed spectral-spectral-element method. The high-order splitting algorithm based on the mixed stiffly stable scheme is employed in the time discretization. Due to the nonlinear evolution of the secondary instability of the wake, the spanwise modes with different wavelengths emerge. The spanwise characteristic length determines the transition features and global properties of the wake. The existence of the spanwise phase difference of the primary vortices shedding is confirmed by Fourier analysis of the time series of the spanwise vorticity and attributed. to the dominant spanwise mode. The spatial energy distributions of various modes and the velocity profiles in the near wake are obtained. The numerical results indicate that the near wake is in 3-D quasi-periodic laminar state with transitional behaviors at this supercritical Reynolds number.

Numerical exploration of new features on three-dimensional transition of a cylinder wake

The three-dimensional transition of the wake flow behind a circular cylinder is studied in detail by direct numerical simulations using 3D incompressible N-S equations for Reynolds number ranging from 200 to 300. New features and vortex dynamics of the 3D transition of the wake are found and investigated. At Re = 200, the flow pattern is characterized by mode A instability. However, the spanwise characteristic length of the cylinder determines the transition features. Particularly for the specific spanwise characteristic length linear stable mode may dominate the wake in place of mode A and determine the spanwise phase difference of the primary vortices shedding. At Re = 250 and 300 it is found that the streamwise vortices evolve into a new type of mode - "dual vortex pair mode" downstream. The streamwise vortex structures switch among mode A, mode B and dual vortex pair mode from near wake to downstream wake. At Re = 250, an independent low frequency f(m) in addition to the vortex shedding frequency f(s) is identified. Frequency coupling between f(m) and f(s) occurs. These result in the irregularity of the temporal signals and become a key feature in the transition of the wake. Based on the formation analysis of the streamwise vorticity in the vicinity of cylinder, it is suggested that mode A is caused by the emergence of the spanwise velocity due to three dimensionality of the incoming flow past the cylinder. Energy distribution on various wave numbers and the frequency variation in the wake are also described.

Sample-specific behavior in failure models of disordered medial

The concept ''sample-specific'' is suggested to describe the behavior of disordered media close to macroscopic failure. it is pointed out that the transition from universal scaling to sample-specific behavior may be a common phenomenon in failure models of disordered media. The dynamical evolution plays an important role in the transition.

Strain-energy density ratio criterion for failure of composite-materials

n the authors' previous paper, the Strain Energy Density Ratio (SEDR) criterion was proposed. As an example of applications, it was used to predict cracking direction of mixed-mode fracture in a random short fibre laminated composite.

Prediction of mixed-mode cracking direction in random, short-fibre composite-materials

The prediction of cracking direction in composite materials is of significance to the design of composite structures. This paper presents several methods for predicting the cracking direction in the double grooved tension-shear specimen which gives mixed-mode cracking. Five different criteria are used in this analysis: two of them have been used by other investigators and the others are proposed by the present authors. The strain energy density criterion proposed by G.C. Sih is modified to take account of the influence of the anisotropy of the strength on the direction of crack. The two failure criteria of Tsai-Hill and Norris are extended to predict the crack orientation. The stress distributions in the near-notch zone are calculated by using the 8-node quadrilateral isoparametric finite element method. The predictions of all the criteria except one are in good agreement with the experimental measurement. In addition, on the basis of the FEM results, the size of the zone in which the singular term is dominant is estimated.

Direct numerical simulation of hypersonic boundary layer transition over a blunt cone with a small angle of attack

The direct numerical simulation of boundary layer transition over a 5° half-cone-angle blunt cone is performed. The free-stream Mach number is 6 and the angle of attack is 1°. Random wall blow-and-suction perturbations are used to trigger the transition. Different from the authors’ previous work [Li et al., AIAA J. 46, 2899(2008)], the whole boundary layer flow over the cone is simulated (while in the author’s previous work, only two 45° regions around the leeward and the windward sections are simulated). The transition location on the cone surface is determined through the rapid increase in skin fraction coefficient (Cf). The transition line on the cone surface shows a nonmonotonic curve and the transition is delayed in the range of 0° ≤ θ ≤ 30° (θ = 0° is the leeward section). The mechanism of the delayed transition is studied by using joint frequency spectrum analysis and linear stability theory (LST). It is shown that the growth rates of unstable waves of the second mode are suppressed in the range of 20° ≤ θ ≤ 30°, which leads to the delayed transition location. Very low frequency waves VLFWs� are found in the time series recorded just before the transition location, and the periodic times of VLFWs are about one order larger than those of ordinary Mack second mode waves. Band-pass filter is used to analyze the low frequency waves, and they are deemed as the effect of large scale nonlinear perturbations triggered by LST waves when they are strong enough.The direct numerical simulation of boundary layer transition over a 5° half-cone-angle blunt cone is performed. The free-stream Mach number is 6 and the angle of attack is 1°. Random wall blow-and-suction perturbations are used to trigger the transition. Different from the authors’ previous work [ Li et al., AIAA J. 46, 2899 (2008) ], the whole boundary layer flow over the cone is simulated (while in the author’s previous work, only two 45° regions around the leeward and the windward sections are simulated). The transition location on the cone surface is determined through the rapid increase in skin fraction coefficient (Cf). The transition line on the cone surface shows a nonmonotonic curve and the transition is delayed in the range of 20° ≤ θ ≤ 30° (θ = 0° is the leeward section). The mechanism of the delayed transition is studied by using joint frequency spectrum analysis and linear stability theory (LST). It is shown that the growth rates of unstable waves of the second mode are suppressed in the range of 20° ≤ θ ≤ 30°, which leads to the delayed transition location. Very low frequency waves (VLFWs) are found in the time series recorded just before the transition location, and the periodic times of VLFWs are about one order larger than those of ordinary Mack second mode waves. Band-pass filter is used to analyze the low frequency waves, and they are deemed as the effect of large scale nonlinear perturbations triggered by LST waves when they are strong enough.

Physical investigations of small particles : (I) aerosol particle charging and flux enhancement and (II) whispering gallery mode sensing

Part I

Particles are a key feature of planetary atmospheres. On Earth they represent the greatest source of uncertainty in the global energy budget. This uncertainty can be addressed by making more measurement, by improving the theoretical analysis of measurements, and by better modeling basic particle nucleation and initial particle growth within an atmosphere. This work will focus on the latter two methods of improvement.

Uncertainty in measurements is largely due to particle charging. Accurate descriptions of particle charging are challenging because one deals with particles in a gas as opposed to a vacuum, so different length scales come into play. Previous studies have considered the effects of transition between the continuum and kinetic regime and the effects of two and three body interactions within the kinetic regime. These studies, however, use questionable assumptions about the charging process which resulted in skewed observations, and bias in the proposed dynamics of aerosol particles. These assumptions affect both the ions and particles in the system. Ions are assumed to be point monopoles that have a single characteristic speed rather than follow a distribution. Particles are assumed to be perfect conductors that have up to five elementary charges on them. The effects of three body interaction, ion-molecule-particle, are also overestimated. By revising this theory so that the basic physical attributes of both ions and particles and their interactions are better represented, we are able to make more accurate predictions of particle charging in both the kinetic and continuum regimes.

The same revised theory that was used above to model ion charging can also be applied to the flux of neutral vapor phase molecules to a particle or initial cluster. Using these results we can model the vapor flux to a neutral or charged particle due to diffusion and electromagnetic interactions. In many classical theories currently applied to these models, the finite size of the molecule and the electromagnetic interaction between the molecule and particle, especially for the neutral particle case, are completely ignored, or, as is often the case for a permanent dipole vapor species, strongly underestimated. Comparing our model to these classical models we determine an “enhancement factor” to characterize how important the addition of these physical parameters and processes is to the understanding of particle nucleation and growth.

Part II

Whispering gallery mode (WGM) optical biosensors are capable of extraordinarily sensitive specific and non-specific detection of species suspended in a gas or fluid. Recent experimental results suggest that these devices may attain single-molecule sensitivity to protein solutions in the form of stepwise shifts in their resonance wavelength, \lambda_{R}, but present sensor models predict much smaller steps than were reported. This study examines the physical interaction between a WGM sensor and a molecule adsorbed to its surface, exploring assumptions made in previous efforts to model WGM sensor behavior, and describing computational schemes that model the experiments for which single protein sensitivity was reported. The resulting model is used to simulate sensor performance, within constraints imposed by the limited material property data. On this basis, we conclude that nonlinear optical effects would be needed to attain the reported sensitivity, and that, in the experiments for which extreme sensitivity was reported, a bound protein experiences optical energy fluxes too high for such effects to be ignored.

Boundary-layer transition on a slender cone in hypervelocity flow with real gas effects

The laminar to turbulent transition process in boundary layer flows in thermochemical nonequilibrium at high enthalpy is measured and characterized. Experiments are performed in the T5 Hypervelocity Reflected Shock Tunnel at Caltech, using a 1 m length 5-degree half angle axisymmetric cone instrumented with 80 fast-response annular thermocouples, complemented by boundary layer stability computations using the STABL software suite. A new mixing tank is added to the shock tube fill apparatus for premixed freestream gas experiments, and a new cleaning procedure results in more consistent transition measurements. Transition location is nondimensionalized using a scaling with the boundary layer thickness, which is correlated with the acoustic properties of the boundary layer, and compared with parabolized stability equation (PSE) analysis. In these nondimensionalized terms, transition delay with increasing CO₂ concentration is observed: tests in 100% and 50% CO₂, by mass, transition up to 25% and 15% later, respectively, than air experiments. These results are consistent with previous work indicating that CO₂ molecules at elevated temperatures absorb acoustic instabilities in the MHz range, which is the expected frequency of the Mack second-mode instability at these conditions, and also consistent with predictions from PSE analysis. A strong unit Reynolds number effect is observed, which is believed to arise from tunnel noise. N_Tr for air from 5.4 to 13.2 is computed, substantially higher than previously reported for noisy facilities. Time- and spatially-resolved heat transfer traces are used to track the propagation of turbulent spots, and convection rates at 90%, 76%, and 63% of the boundary layer edge velocity, respectively, are observed for the leading edge, centroid, and trailing edge of the spots. A model constructed with these spot propagation parameters is used to infer spot generation rates from measured transition onset to completion distance. Finally, a novel method to control transition location with boundary layer gas injection is investigated. An appropriate porous-metal injector section for the cone is designed and fabricated, and the efficacy of injected CO₂ for delaying transition is gauged at various mass flow rates, and compared with both no injection and chemically inert argon injection cases. While CO₂ injection seems to delay transition, and argon injection seems to promote it, the experimental results are inconclusive and matching computations do not predict a reduction in N factor from any CO₂ injection condition computed.

Effect of superstructure stiffness on liquefaction-induced failure Mechanisms

Soil liquefaction following strong earthquakes causes extensive damage to civil engineering structures. Foundations of buildings, bridges etc can suffer excessive rotation/settlement due to liquefaction. Many of the recent earthquakes bear testimony for such damage. In this article a hypothesis that "Superstructure stiffness can determine the type of liquefaction-induced failure mechanism suffered by the foundations" is proposed. As a rider to this hypothesis, it will be argued that liquefaction will cause failure of a foundation system in a mode of failure that offers least resistance. Evidence will be offered in terms of field observations during the 921 Ji-Ji earthquake in 1999 in Taiwan and Bhuj earthquake of 2001 in India. Dynamic centrifuge test data and finite element analyses results are presented to illustrate the traditional failure mechanisms. Copyright © 2010, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.

A fast detailed-chemistry modelling approach for simulating the SI-HCCI transition

An established Stochastic Reactor Model (SRM) is used to simulate the transition from Spark Ignition (SI) to Homogeneous Charge Compression Ignition (HCCI) combustion mode in a four cylinder in-line four-stroke naturally aspirated direct injection SI engine with cam profile switching. The SRM is coupled with GT-Power, a one-dimensional engine simulation tool used for modelling engine breathing during the open valve portion of the engine cycle, enabling multi-cycle simulations. The mode change is achieved by switching the cam profiles and phasing, resulting in a Negative Valve Overlap (NVO), opening the throttle, advancing the spark timing and reducing the fuel mass as well as using a pilot injection. A proven technique for tabulating the model is used to create look-up tables in both SI and HCCI modes. In HCCI mode several tables are required, including tables for the first NVO, transient valve timing NVO, transient valve timing HCCI and steady valve timing HCCI and NVO. This results in the ability to simulate the transition with detailed chemistry in very short computation times. The tables are then used to optimise the transition with the goal of reducing NO x emissions and fluctuations in IMEP. Copyright © 2010 SAE International.

A detailed chemistry simulation of the SI-HCCI transition

A Stochastic Reactor Model (SRM) has been used to simulate the transition from Spark Ignition (SI) mode to Homogeneous Charge Compression Ignition (HCCI) mode in a four cylinder in-line four-stroke naturally aspirated direct injection SI engine with cam profile switching. The SRM is coupled with GT-Power, a one-dimensional engine simulation tool used for modelling engine breathing during the open valve portion of the engine cycle, enabling multi-cycle simulations. The model is initially calibrated in both modes using steady state data from SI and HCCI operation. The mode change is achieved by switching the cam profiles and phasing, resulting in a Negative Valve Overlap (NVO), opening the throttle, advancing the spark timing and reducing the fuel mass as well as utilising a pilot injection. Experimental data is presented along with the simulation results. The model is used to investigate key control parameters and their effects on parameters that are difficult to measure experimentally. The effect of the spark in the first HCCI cycles is found to have a major impact on the stability of the transition. Copyright © 2010 SAE International.

Modeling mode i fracture of bitumen films

The fracture behavior of thin films of bitumen in double cantilever beam (DCB) specimens was investigated over a wide range of temperature and loading rate conditions using finite-element analysis. The model includes a phenomenological model for the mechanical behavior of bitumen, implemented into a special-purpose finite-element user material subroutine, combined with a cohesive zone model (CZM) for simulating the fracture process. The finite-element model is validated against experimental results from laboratory tests of DCB specimens by comparing measured and predicted load-line deflection histories and fracture energy release rates. Computer simulation results agreed well with experimental data of DCB joints containing bitumen films in terms of peak stress, fracture toughness, and stress-strain history response. The predicted "normalized toughness," G=2h, was found to increase in a power-law manner with effective temperaturecompensated strain rate in the ductile region as previously observed experimentally. In the brittle regime, G=2h is virtually constant. The model successfully captured the ductile and brittle failure behavior of bitumen films in opening mode (tension) for stable crack growth conditions. © 2013 American Society of Civil Engineers.