Extracting material response from simple mechanical tests on hardening-softening-hardening viscoplastic solids

Compliant foams are usually characterized by a wide range of desirable mechanical properties. These properties include viscoelasticity at different temperatures, energy absorption, recoverability under cyclic loading, impact resistance, and thermal, electrical, acoustic and radiation-resistance. Some foams contain nano-sized features and are used in small-scale devices. This implies that the characteristic dimensions of foams span multiple length scales, rendering modeling their mechanical properties difficult. Continuum mechanics-based models capture some salient experimental features like the linear elastic regime, followed by non-linear plateau stress regime. However, they lack mesostructural physical details. This makes them incapable of accurately predicting local peaks in stress and strain distributions, which significantly affect the deformation paths. Atomistic methods are capable of capturing the physical origins of deformation at smaller scales, but suffer from impractical computational intensity. Capturing deformation at the so-called meso-scale, which is capable of describing the phenomenon at a continuum level, but with some physical insights, requires developing new theoretical approaches.

A fundamental question that motivates the modeling of foams is ‘how to extract the intrinsic material response from simple mechanical test data, such as stress vs. strain response?’ A 3D model was developed to simulate the mechanical response of foam-type materials. The novelty of this model includes unique features such as the hardening-softening-hardening material response, strain rate-dependence, and plastically compressible solids with plastic non-normality. Suggestive links from atomistic simulations of foams were borrowed to formulate a physically informed hardening material input function. Motivated by a model that qualitatively captured the response of foam-type vertically aligned carbon nanotube (VACNT) pillars under uniaxial compression [2011,“Analysis of Uniaxial Compression of Vertically Aligned Carbon Nanotubes,” J. Mech.Phys. Solids, 59, pp. 2227–2237, Erratum 60, 1753–1756 (2012)], the property space exploration was advanced to three types of simple mechanical tests: 1) uniaxial compression, 2) uniaxial tension, and 3) nanoindentation with a conical and a flat-punch tip. The simulations attempt to explain some of the salient features in experimental data, like
1) The initial linear elastic response.
2) One or more nonlinear instabilities, yielding, and hardening.

The model-inherent relationships between the material properties and the overall stress-strain behavior were validated against the available experimental data. The material properties include the gradient in stiffness along the height, plastic and elastic compressibility, and hardening. Each of these tests was evaluated in terms of their efficiency in extracting material properties. The uniaxial simulation results proved to be a combination of structural and material influences. Out of all deformation paths, flat-punch indentation proved to be superior since it is the most sensitive in capturing the material properties.

Velocity resolved - scalar modeled simulations of high Schmidt number turbulent transport

The objective of this thesis is to develop a framework to conduct velocity resolved - scalar modeled (VR-SM) simulations, which will enable accurate simulations at higher Reynolds and Schmidt (Sc) numbers than are currently feasible. The framework established will serve as a first step to enable future simulation studies for practical applications. To achieve this goal, in-depth analyses of the physical, numerical, and modeling aspects related to Sc>>1 are presented, specifically when modeling in the viscous-convective subrange. Transport characteristics are scrutinized by examining scalar-velocity Fourier mode interactions in Direct Numerical Simulation (DNS) datasets and suggest that scalar modes in the viscous-convective subrange do not directly affect large-scale transport for high Sc. Further observations confirm that discretization errors inherent in numerical schemes can be sufficiently large to wipe out any meaningful contribution from subfilter models. This provides strong incentive to develop more effective numerical schemes to support high Sc simulations. To lower numerical dissipation while maintaining physically and mathematically appropriate scalar bounds during the convection step, a novel method of enforcing bounds is formulated, specifically for use with cubic Hermite polynomials. Boundedness of the scalar being transported is effected by applying derivative limiting techniques, and physically plausible single sub-cell extrema are allowed to exist to help minimize numerical dissipation. The proposed bounding algorithm results in significant performance gain in DNS of turbulent mixing layers and of homogeneous isotropic turbulence. Next, the combined physical/mathematical behavior of the subfilter scalar-flux vector is analyzed in homogeneous isotropic turbulence, by examining vector orientation in the strain-rate eigenframe. The results indicate no discernible dependence on the modeled scalar field, and lead to the identification of the tensor-diffusivity model as a good representation of the subfilter flux. Velocity resolved - scalar modeled simulations of homogeneous isotropic turbulence are conducted to confirm the behavior theorized in these a priori analyses, and suggest that the tensor-diffusivity model is ideal for use in the viscous-convective subrange. Simulations of a turbulent mixing layer are also discussed, with the partial objective of analyzing Schmidt number dependence of a variety of scalar statistics. Large-scale statistics are confirmed to be relatively independent of the Schmidt number for Sc>>1, which is explained by the dominance of subfilter dissipation over resolved molecular dissipation in the simulations. Overall, the VR-SM framework presented is quite effective in predicting large-scale transport characteristics of high Schmidt number scalars, however, it is determined that prediction of subfilter quantities would entail additional modeling intended specifically for this purpose. The VR-SM simulations presented in this thesis provide us with the opportunity to overlap with experimental studies, while at the same time creating an assortment of baseline datasets for future validation of LES models, thereby satisfying the objectives outlined for this work.

Small scale turbulence in high Karlovitz number premixed flames

The purpose of this thesis is to characterize the behavior of the smallest turbulent scales in high Karlovitz number (Ka) premixed flames. These scales are particularly important in the two-way coupling between turbulence and chemistry and better understanding of these scales will support future modeling efforts using large eddy simulations (LES). The smallest turbulent scales are studied by considering the vorticity vector, ω, and its transport equation.

Due to the complexity of turbulent combustion introduced by the wide range of length and time scales, the two-dimensional vortex-flame interaction is first studied as a simplified test case. Numerical and analytical techniques are used to discern the dominate transport terms and their effects on vorticity based on the initial size and strength of the vortex. This description of the effects of the flame on a vortex provides a foundation for investigating vorticity in turbulent combustion.

Subsequently, enstrophy, ω² = ω • ω, and its transport equation are investigated in premixed turbulent combustion. For this purpose, a series of direct numerical simulations (DNS) of premixed n-heptane/air flames are performed, the conditions of which span a wide range of unburnt Karlovitz numbers and turbulent Reynolds numbers. Theoretical scaling analysis along with the DNS results support that, at high Karlovitz number, enstrophy transport is controlled by the viscous dissipation and vortex stretching/production terms. As a result, vorticity scales throughout the flame with the inverse of the Kolmogorov time scale, τ_η, just as in homogeneous isotropic turbulence. As τ_η is only a function of the viscosity and dissipation rate, this supports the validity of Kolmogorov’s first similarity hypothesis for sufficiently high Ka numbers (Ka ≳ 100). These conclusions are in contrast to low Karlovitz number behavior, where dilatation and baroclinic torque have a significant impact on vorticity within the flame. Results are unaffected by the transport model, chemical model, turbulent Reynolds number, and lastly the physical configuration.

Next, the isotropy of vorticity is assessed. It is found that given a sufficiently large value of the Karlovitz number (Ka ≳ 100) the vorticity is isotropic. At lower Karlovitz numbers, anisotropy develops due to the effects of the flame on the vortex stretching/production term. In this case, the local dynamics of vorticity in the strain-rate tensor, S, eigenframe are altered by the flame. At sufficiently high Karlovitz numbers, the dynamics of vorticity in this eigenframe resemble that of homogeneous isotropic turbulence.

Combined, the results of this thesis support that both the magnitude and orientation of vorticity resemble the behavior of homogeneous isotropic turbulence, given a sufficiently high Karlovitz number (Ka ≳ 100). This supports the validity of Kolmogorov’s first similarity hypothesis and the hypothesis of local isotropy under these condition. However, dramatically different behavior is found at lower Karlovitz numbers. These conclusions provides/suggests directions for modeling high Karlovitz number premixed flames using LES. With more accurate models, the design of aircraft combustors and other combustion based devices may better mitigate the detrimental effects of combustion, from reducing CO₂ and soot production to increasing engine efficiency.

DIFFERENTIAL GEOMETRICAL METHODS IN THE STUDY OF OPTICAL-TRANSMISSION (SCALAR THEORY) .2. TIME-DEPENDENT TRANSMISSION THEORY

By generalization of the methods presented in Part I of the study [J. Opt. Soc. Am. A 12, 600 (1994)] to the four-dimensional (4D) Riemannian manifold case, the time-dependent behavior of light transmitting in a medium is investigated theoretically by the geodesic equation and curvature in a 4D manifold. In addition, the field equation is restudied, and the 4D conserved current of the optical fluid and its conservation equation are derived and applied to deduce the time-dependent general refractive index. On this basis the forces acting on the fluid are dynamically analyzed and the self-consistency analysis is given.

Yielding of engineering polymers at strain rates of up to 500 s-1

A method is described for measuring the mechanical properties of polymers in compression at strain rates in the range approximately 300-500 s-1. A gravity-driven pendulum is used to load a specimen on the end of an instrumented Hopkinson output bar and the results are processed by a microcomputer. Stress-strain curves up to high strains are presented for polycarbonate, polyethersulphone and high density polyethylene over a range of temperatures. The value of yield stress, for all three polymers, was found to vary linearly with log (strain rate) at strain rates up to 500 s-1. © 1985.

The behaviour of laminar stratified methane/air flames in counterflow

Flames propagating through a mixture with a gradient of equivalence ratio have been previously demonstrated to travel faster or slower than their equivalent premixed flames. The present study aims to numerically investigate the response of strained laminar methane-air flames to such gradients. The flames are simulated in a counterflow configuration where a premixed reactant stream at equivalence ratio φR opposes a hot equilibrium stream at equivalence ratio φP. Premixed and stratified flames are compared with respect to the equivalence ratio φ* and the corresponding gradient ∇φ* at the point of peak heat release rate, for three strain rates, a=50, 300 and 500s-1 and a range of φ*. The effect of different stratification levels is also investigated by varying the ratio of φP to φR, Θ. Results indicate that, as long as flames stabilize within the diffusion layer and Θ>1, increased heat release rate Q is seen throughout the progress variable space in comparison to the premixed state. In contrast, an attenuation of heat release rate is seen for Θ<1. The enhancement (or attenuation) of heat release varies monotonically with Θ. The effect of stratification on flame behavior becomes more pronounced as the strain rate increases. The present study reveals the mechanisms for the propagation of quasi-steady stratified flames under lean and rich conditions: stratified flames are primarily dominated by the diffusion of heat under lean conditions, and diffusion of H2 under rich conditions. Thanks to species and thermal support, stratified flames continue to burn beyond the premixed lean and rich flammability limits. Further investigation on the unsteady response of flames to the fluctuating equivalence ratio implies that the steady results represent the unsteady response well, as long as φ* and ∇φ* are similar in both steady and unsteady cases. © 2013 The Combustion Institute.

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.

Measuring the compressive viscoelastic mechanical properties of human cervical tissue using indentation.

The human cervix is an important mechanical barrier in pregnancy which must withstand the compressive and tensile forces generated from the growing fetus. Premature cervical shortening resulting from premature cervical remodeling and alterations of cervical material properties are known to increase a woman׳s risk of preterm birth (PTB). To understand the mechanical role of the cervix during pregnancy and to potentially develop indentation techniques for in vivo diagnostics to identify women who are at risk for premature cervical remodeling and thus preterm birth, we developed a spherical indentation technique to measure the time-dependent material properties of human cervical tissue taken from patients undergoing hysterectomy. In this study we present an inverse finite element analysis (IFEA) that optimizes material parameters of a viscoelastic material model to fit the stress-relaxation response of excised tissue slices to spherical indentation. Here we detail our IFEA methodology, report compressive viscoelastic material parameters for cervical tissue slices from nonpregnant (NP) and pregnant (PG) hysterectomy patients, and report slice-by-slice data for whole cervical tissue specimens. The material parameters reported here for human cervical tissue can be used to model the compressive time-dependent behavior of the tissue within a small strain regime of 25%.

Generalized phenomenological model for the viscoelasticity of idealized asphalts

A generalized theory for the viscoelastic behavior of idealized bituminous mixtures (asphalts) is presented. The mathematical model incorporates strain rate and temperature dependency as well as nonmonotonic loading and unloading with shape recovery. The stiffening effect of the aggregate is included. The model is of phenomenological nature. It can be calibrated using a relatively limited set of experimental parameters, obtainable by uniaxial tests. It is shown that the mathematical model can be represented as a special nonlinear form of the Burgers model. This facilitates the derivation of numerical algorithms for solving the constitutive equations. A numerical scheme is implemented in a user material subroutine (UMAT) in the finite-element analysis (FEA) code ABAQUS. Simulation results are compared with uniaxial and indentation tests on an idealized asphalt mix. © 2014 American Society of Civil Engineers.

Strength correlations of cement-mixed soils using data mapping

Development of comparisons and correlations between the unconfined compressive strength (UCS) and the undrained triaxial compressive strength, qu, is essential for generalising performance and optimising the design of cement-stabilised soils. This paper introduces current work in collecting and collating data from a number of research projects involving both laboratory strength tests performed on identical cement-stabilised soil samples. The research project on cement-stabilised Singapore marine clays at the National University of Singapore has been used as an example to explain the work on comparing and correlating results from both tests by normalising data and constructing contour plots. The effect of variables on strength comparison and correlations was evaluated. The variation in strength correlations was found to be dependent on a number of factors including: soil properties, cement content, curing time and stress, total water/cement ratio, confining stress and strain rate. The results showed that at ~ 100 kPa confining stress, UCS and qu, had similar magnitudes. Correlations between strengths and other design variables are discussed and presented.

Hydrogen behavior in GaN epilayers grown by NH3-MBE

Hydrogen behavior in unintentionally doped GaN epilayers on sapphire substrates grown by NH3-MBE is investigated. Firstly, we find by using nuclear reaction analysis (NRA) that with increasing hydrogen concentration the background electron concentration increases, which suggests that there exists a hydrogen-related donor in undoped GaN, Secondly, Fourier transform infrared (FTIR) absorption and X-ray photoelectron spectroscopy (XPS) reveal Further that hydrogen atom is bound to nitrogen atom in GaN with a local vibrational mode at about 3211 cm(-1) Hence, it is presumed that the hydrogen-related complex Ga. . .H-N is a hydrogen-related donor candidate partly responsible for high n-type background commonly observed in GaN films. Finally, Raman spectroscopy results of the epilayers show that ill addition to the expected compressive biaxial strain, in some cases GaN films suffer from serious tensile biaxial strain. This anomalous behavior has been well interpreted in terms of interstitial hydrogen lattice dilation. (C) 2001 Elsevier Science B.V. All rights reserved.

Hydrogen behavior in GaN epilayers grown by NH3-MBE

Hydrogen behavior in unintentionally doped GaN epilayers on sapphire substrates grown by NH3-MBE is investigated. Firstly, we find by using nuclear reaction analysis (NRA) that with increasing hydrogen concentration the background electron concentration increases, which suggests that there exists a hydrogen-related donor in undoped GaN, Secondly, Fourier transform infrared (FTIR) absorption and X-ray photoelectron spectroscopy (XPS) reveal Further that hydrogen atom is bound to nitrogen atom in GaN with a local vibrational mode at about 3211 cm(-1) Hence, it is presumed that the hydrogen-related complex Ga. . .H-N is a hydrogen-related donor candidate partly responsible for high n-type background commonly observed in GaN films. Finally, Raman spectroscopy results of the epilayers show that ill addition to the expected compressive biaxial strain, in some cases GaN films suffer from serious tensile biaxial strain. This anomalous behavior has been well interpreted in terms of interstitial hydrogen lattice dilation. (C) 2001 Elsevier Science B.V. All rights reserved.

Shear transformation zone volume determining ductile–brittle transition of bulk metallic glasses

Three-point bending experiments were performed on as-cast and annealed samples of Zr52.5Cu17.9Ni14.6Al10Ti5 (Vit105) bulk metallic glasses over a wide range of temperatures varying from room temperature (293 K) to liquid nitrogen temperature (77 K). The results demonstrated that the free volume decrease due to annealing and/or cryogenic temperature can reduce the propensity for the formation of multiple shear bands and hence deteriorate plastic deformation ability. We clearly observed a sharp ductile-to-brittle transition (DBT), across which microscopic fracture feature transfers from micro-scale vein patterns to nano-scale periodic corrugations. Macroscopically, the corresponding fracture mode changes from ductile shear fracture to brittle tensile fracture. The shear transformation zone volume, taking into account free volume, temperature and strain rate, is proposed to quantitatively characterize the DBT behavior in fracture of metallic glasses.

Brittle-ductile transition of polypropylene/ethyllene-propylene-diene monomer blends induced by size, temperature, and time

To study the brittle-ductile transition (BDT) of polypropylene (PP)/ethylene-propylene-diene monomer (EPDM) blends induced by size, temperature, and time, the toughness of the PP/EPDM blends was investigated over wide ranges of EPDM content, temperature, and strain rate. The toughness of the blends was determined from the tensile fracture energy of the side-edge notched samples. The concept of interparticle distance (ID) was introduced into this study to probe the size effect on the BDT of PP/EPDM blends, whereas the effect of time corresponded to that of strain rate. The BDT induced by size, temperature, and time was observed in the fracture energy versus ID, temperature, and strain rate. The critical BDT temperatures for various EPDM contents at different initial strain rates were obtained from these transitions. The critical interparticle distance (IDc) increased nonlinearly with increasing temperature, and when the initial strain rate was lower, the IDc was larger. Moreover, the variation of the reciprocal of the initial strain rate with the reciprocal of temperature followed different straight lines for various EPDM contents. These straight lines were with the same slope.

Mechanical and thermal properties of high-density polyethylene toughened with glass beads

Glass beads were used to improve the mechanical and thermal properties of high-density polyethylene (HDPE). HDPE/glass-bead blends were prepared in a Brabender-like apparatus, and this was followed by press molding. Static tensile measurements showed that the modulus of the HDPE/glass-bead blends increased considerably with increasing glass-bead content, whereas the yield stress remained roughly unchanged at first and then decreased slowly with increasing glass-bead content. Izod impact tests at room temperature revealed that the impact strength changed very slowly with increasing glass-bead content up to a critical value; thereafter, it increased sharply with increasing glass-bead content. That is, the lzod impact strength of the blends underwent a sharp transition with increasing glass-bead content. It was calculated that the critical interparticle distance for the HDPE/glass-bead blends at room temperature (25degreesC) was 2.5 mum. Scanning electron microscopy observations indicated that the high impact strength of the HDPE/glass-bead blends resulted from the deformation of the HDPE matrix. Dynamic mechanical analyses and thermogravimetric measurements implied that the heat resistance and heat stability of the blends tended to increase considerably with increasing glass-bead content.