Influence of strain softening on the fracture of plain concrete beams

Fracture behaviour of notched and un-notched plain concrete slender beams subjected to three-point or four-point bending is analyzed through a one-dimensional model, also called Softening Beam Model. Fundamental equations of equilibrium are used to develop the model. The influence of structural size in altering the fracture mode from brittle fracture to plastic collapse is explained through the stress distribution across the uncracked ligament obtained by varying the strain softening modulus. It is found that at the onset of fracture instability, stress at the crack tip is equal to zero. The maximum load and fracture load are found to be different and a unique value for the fracture load is obtained. It is shown that the length of the fracture process zone depends on the value of the strain softening modulus. Theoretical limits for fracture process zone length are also calculated. Several nonlinear fracture parameters, such as, crack tip opening displacement, crack mouth opening displacement and fracture energy are computed for a wide variety of beam specimens reported in the literature and are found to compare very well with experimental and theoretical results. It is demonstrated that by following a simple procedure, both pre-peak and post-peak portions of load versus crack mouth opening displacement curve can be obtained quite accurately. Further, a simple procedure to calculate the maximum load is also developed. The predicted values of maximum load are found to agree well with the experimental values. The Softening Beam Model (SBM), proposed in this investigation is very simple and is based on rational considerations. It can completely describe the fracture process from the beginning of formation of the fracture process zone till the onset of fracture instability.A l'aide d'un modèle unidimensionnel dit ldquoSoftening Beam Modelrdquo (SBM), on analyse le comportement à rupture de poutres élancées pleines entaillées ou non, soumises en flexion en trois ou quatre points. Des équations fondamentales d'équilibre sont utilisées pour développer le modèle. On explique l'influence de la taille du composant sur l'altération du mode de rupture en rupture fragile et en effondrement plastique par la distribution par la distribution des contraintes sur le ligament non fissuré lorsque varie le module d'adoucissement. On trouve que la contrainte à l'extrémité de la fissure est nulle est nulle au début de l'instabilité de la rupture. La charge maximum et la charge à la rupture sont trouvées différentes, et on obtient une valeur unique de la charge à la rupture. On montre que la longueur de la zone concernée par le processus de rupture d'pend de la valeur du module d'adoucissement. On calcule également les limites théoriques de longueur de cette zone. Divers paramètres de rupture non linéaire sont calculés pour une large gamme d'éprouvettes en poutres reprises dans la littérature; on trouve qu'il existe une bonne concordance avec les résultats expérimentaux et théoriques. On démontre qu'en suivant une procédure simple on peut obtenir avec une bonne précision la courbe reliant les portions avant et après le pic de sollicitation en fonction du COD de la fissure. En outre, on développe une procédure simple pour calculer la charge maximum. Les valeurs prédites sont en bon accord avec les valeurs expérimentales. Le modèle SBM proposé est très simple et est basé sur des considérations rationnelles. Il est susceptible de décrire complètement le processus de rupture depuis le début de la formation de la zone intéressée jusqu'à l'amorçage de la rupture instable.

Chemical toughening of epoxies. II. Mechanical, thermal, and microscopic studies of epoxies toughened with hydroxyl-terminated poly(butadiene-co-acrylonitrile)

Diglycidyl ether–bisphenol-A-based epoxies toughened with various levels (0–12%) of chemically reacted liquid rubber, hydroxyl-terminated poly(butadiene-co-acrylonitrile) (HTBN) were studied for some of the mechanical and thermal properties. Although the ultimate tensile strength showed a continuous decrease with increasing rubber content, the toughness as measured by the area under the stress-vs.-strain curve and flexural strength reach a maximum around an optimum rubber concentration of 3% before decreasing. Tensile modulus was found to increase for concentrations below 6%. The glass transition temperature Tg as measured by DTA showed no variation for the toughened formulations. The TGA showed no variations in the pattern of decomposition. The weight losses for the toughened epoxies at elevated temperatures compare well with that of the neat epoxy. Scanning electron microscopy revealed the presence of a dual phase morphology with the spherical rubber particles precipitating out in the cured resin with diameter varying between 0.33 and 6.3 μm. In contrast, a physically blended rubber–epoxy showed much less effect towards toughening with the precipitated rubber particles of much bigger diameter (0.6–21.3 μm).

Effect of Substrate and Annealing Temperatures on Mechanical Properties of Ti-rich NiTi Films

The effect of substrate and annealing temperatures on mechanical properties of Ti-rich NiTi films deposited on Si (100) substrates by DC magnetron sputtering was studied by nanoindentation. NiTi films were deposited at two substrate temperatures viz. 300 and 400 degrees C. NiTi films deposited at 300 degrees C were annealed for 4 h at four different temperatures, i.e. 300, 400, 500 and 600 degrees C whereas films deposited at 400 degrees C were annealed for 4 h at three different temperatures, i.e. 400, 500 and 600 degrees C. The elastic modulus and hardness of the films were found to be the same in the as-deposited as well as annealed conditions for both substrate temperatures. For a given substrate temperature, the hardness and elastic modulus were found to remain unchanged as long as the films were amorphous. However, both elastic modulus and hardness showed an increase with increasing annealing temperature as the films become crystalline. The results were explained on the basis of the change in microstructure of the film with change in annealing temperature.

Electron-beam weld microstructures and properties of aluminium-lithium alloy 8090

Lithium-containing aluminium alloys are of considerable current interest in the aerospace and aircraft industries because lithium additions to aluminium improve the modulus and decrease the density compared to conventional aluminium alloys. Few commercial aluminium-lithium alloys have emerged for use in the aerospace industry. One such candidate is 8090, a precipitation-hardenable Al-Li-Cu-Mg alloy. The influence of electron-beam welding on the microstructure and mechanical properties of alloy 8090 material has been evaluated through microscopical observations and mechanical tests. Microscopic observations of the electronbeam welds revealed an absence of microporosity and hot cracking, but revealed presence of microporosity in the transverse section of the weld. Mechanical tests revealed the electronbeam weld to have lower strength, elongation and joint efficiency. A change in microscopic fracture mode was observed for the welded material when compared to the unwelded counterpart. An attempt is made to rationalize the behaviour in terms of competing mechanistic effects involving the grain structure of the material, the role of matrix deformation characteristics, grain-boundary chemistry and grain-boundary failure.

Parametric instability of stochastic columns

Columns which have stochastically distributed Young's modulus and mass density and are subjected to deterministic periodic axial loadings are considered. The general case of a column supported on a Winkler elastic foundation of random stiffness and also on discrete elastic supports which are also random is considered. Material property fluctuations are modeled as independent one-dimensional univariate homogeneous real random fields in space. In addition to autocorrelation functions or their equivalent power spectral density functions, the input random fields are characterized by scale of fluctuations or variance functions for their second order properties. The foundation stiffness coefficient and the stiffnesses of discrete elastic supports are treated to constitute independent random variables. The system equations of boundary frequencies are obtained using Bolotin's method for deterministic systems. Stochastic FEM is used to obtain the discrete system with random as well as periodic coefficients. Statistical properties of boundary frequencies are derived in terms of input parameter statistics. A complete covariance structure is obtained. The equations developed are illustrated using a numerical example employing a practical correlation structure.

Influence of Substrate Temperature and Deposition Rate on Structural and Mechanical Properties of Shape Memory NiTi Films

NiTi thin films deposited by DC magnetron sputtering of an alloy (Ni/Ti:45/55) target at different deposition rates and substrate temperatures were analyzed for their structure and mechanical properties. The crystalline structure, phase-transformation and mechanical response were characterized by X-ray diffraction (XRD), Differential Scanning Calorimetry (DSC) and Nano-indentation techniques, respectively. The films were deposited on silicon substrates maintained at temperatures in the range 300 to 500 degrees C and post-annealed at 600 degrees C for four hours to ensure film crystallinity. Films deposited at 300 degrees C and annealed for 600 degrees C have exhibited crystalline behavior with Austenite phase as the prominent phase. Deposition onto substrates held at higher deposition temperatures (400 and 500 degrees C) resulted in the co-existence of Austenite phase along with Martensite phase. The increase in deposition rates corresponding to increase in cathode current from 250 to 350 mA has also resulted in the appearance of Martensite phase as well as improvement in crystallinity. XRD analysis revealed that the crystalline film structure is strongly influenced by process parameters such as substrate temperature and deposition rate. DSC results indicate that the film deposited at 300 degrees C had its crystallization temperature at 445 degrees C in the first thermal cycle, which is further confirmed by stress temperature response. In the second thermal cycle the Austenite and Martensite transitions were observed at 75 and 60 degrees C respectively. However, the films deposited at 500 degrees C had the Austenite and Martensite transitions at 73 and 58 degrees C, respectively. Elastic modulus and hardness values increased from 93 to 145 GPa and 7.2 to 12.6 GPa, respectively, with increase in deposition rates. These results are explained on the basis of change in film composition and crystallization. (C) 2010 Published by Elsevier Ltd

Measurement of complex optical flow with use of an augmented generalized gradient scheme

We present a method for measuring the local velocities and first-order variations in velocities in a timevarying image. The scheme is an extension of the generalized gradient model that encompasses the local variation of velocity within a local patch of the image. Motion within a patch is analyzed in parallel by 42 different spatiotemporal filters derived from 6 linearly independent spatiotemporal kernels. No constraints are imposed on the image structure, and there is no need for smoothness constraints on the velocity field. The aperture problem does not arise so long as there is some two-dimensional structure in the patch being analyzed. Among the advantages of the scheme is that there is no requirement to calculate second or higher derivatives of the image function. This makes the scheme robust in the presence of noise. The spatiotemporal kernels are of simple form, involving Gaussian functions, and are biologically plausible receptive fields. The validity of the scheme is demonstrated by application to both synthetic and real video images sequences and by direct comparison with another recently published scheme Biol. Cybern. 63, 185 (1990)] for the measurement of complex optical flow.

Measurement of complex optical flow with use of an augmented generalized gradient scheme

We present a method for measuring the local velocities and first-order variations in velocities in a time-varying image. The scheme is an extension of the generalized gradient model that encompasses the local variation of velocity within a local patch of the image. Motion within a patch is analyzed in parallel by 42 different spatiotemporal filters derived from 6 linearly independent spatiotemporal kernels. No constraints are imposed on the image structure, and there is no need for smoothness constraints on the velocity field. The aperture problem does not arise so long as there is some two-dimensional structure in the patch being analyzed. Among the advantages of the scheme is that there is no requirement to calculate second or higher derivatives of the image function. This makes the scheme robust in the presence of noise. The spatiotemporal kernels are of simple form, involving Gaussian functions, and are biologically plausible receptive fields. The validity of the scheme is demonstrated by application to both synthetic and real video images sequences and by direct comparison with another recently published scheme [Biol. Cybern. 63, 185 (1990)] for the measurement of complex optical flow.

Substrate-dependent structure, microstructure, composition and properties of nanostructured TiN films

Titanium nitride films of a thickness of similar to 1.5 mu m were deposited on amorphous and crystalline substrates by DC reactive magnetron sputtering at ambient temperature with 100% nitrogen in the sputter gas. The growth of nanostructured, i.e. crystalline nano-grain sized, films at ambient temperature is demonstrated. The microstructure of the films grown on crystalline substrates reveals a larger grain size/crystallite size than that of the films deposited on amorphous substrates. Specular reflectance measurements on films deposited on different substrates indicate that the position of the Ti-N 2s band at 2.33 eV is substrate-dependent, indicating substrate-mediated stoichiometry. This clearly demonstrates that not only structure and microstructure, but also chemical composition of the films is substrate-influenced. The films deposited on amorphous substrates display lower hardness and modulus values than the films deposited on crystalline substrates, with the highest value of hardness being 19 GPa on a lanthanum aluminate substrate. (C) 2011 Elsevier Ltd. All rights reserved.

Electrical transport properties of 0.5Li(2)O-0.5M(2)O-2B(2)O(3) (M = Li, Na and K) glasses

Transparent glasses in the system 0.5Li(2)O-0.5M(2)O-2B(2)O(3) (M = Li, Na and K) were fabricated via the conventional melt quenching technique. The amorphous and glassy nature of the samples was confirmed via the X-ray powder diffraction and the differential scanning calorimetry, respectively. The frequency and temperature dependent characteristics of the dielectric relaxation and the electrical conductivity were investigated in the 100 Hz-10 MHz frequency range. The imaginary part of the electric modulus spectra was modeled using an approximate solution of Kohrausch-Williams-Watts relation. The stretching exponent, (3, was found to be temperature independent for 0.5Li(2)O-0.5Na(2)O-2B(2)O(3) (LNBO) glasses. The activation energy associated with DC conduction was found to be higher (1.25 eV) for 0.5Li(2)O-0.5K(2)O-2B(2)O(3) (LKBO) glasses than that of the other glass systems under study. This is attributed to the mixed cation effect. (C) 2011 Elsevier By. All rights reserved.

Structural Behavior of Story-High Cement-Stabilized Rammed-Earth Walls under Compression

A rammed-earth wall is a monolithic construction made by compacting processed soil in progressive layers in a rigid formwork. There is a growing interest in using this low-embodied-carbon building material in buildings. The paper investigates the strength and structural behavior of story-high cement-stabilized rammed-earth (CSRE) walls, reviews literature on the strength of CSRE, and discusses results of the compressive strength of CSRE prisms, wallettes, and story-high walls. The strength of the story-high wall was compared with the strength of wallettes and prisms. There is a nearly 30% reduction in strength as the height-to-thickness ratio increases from about 5 to 20. The ultimate compressive strength of CSRE walls predicted using the tangent modulus theory is in close agreement with the experimental values. The shear failures noticed in the story-high walls resemble the shear failures of short-height prism and wallette specimens. The paper ends with a discussion of structural design and characteristic compressive strength of CSRE walls. DOI: 10.1061/(ASCE)MT.1943-5533.0000155. (C) 2011 American Society of Civil Engineers.

High-pressure synchrotron X-ray diffraction study of the pyrochlores: Ho2Ti2O7, Y2Ti2O7 and Tb2Ti2O7

Synchrotron-based X-ray diffraction was used to study the phase diagrams and determine the compressibilities of the pyrochlore rare-earth titanates Ho2Ti2O7, Y2Ti2O7 and Tb2Ti2O7 to 50GPa. The bulk moduli of the cubic phase of these materials were calculated to be 213 +/- 2, 204 +/- 3 and 199 +/- 1GPa, respectively. The onset of a structural phase change from cubic to monoclinic was observed near 37, 42 and 39GPa, respectively. The bulk modulus for the high pressure monoclinic phase of Y2Ti2O7 has been determined to be 185 +/- 3GPa.

Effect of thermal annealing on the dielectric properties of KTiOPO4 single crystals

Dielectric properties of potassium titanyl phosphate have been investigated as a function of thickness and frequency, as well as annealing treatment under various atmospheres. The low frequency dielectric constant of KTP crystals is shown to depend upon the sample thickness, and this feature is attributed to the existence of surface layers. The frequency-dependent dielectric response of KTP exhibits a non-Debye type relaxation, with a distribution of relaxation times. The dielectric behavior of KTP samples annealed in various atmospheres shows that the low frequency dielectric constant is influenced by the contribution from the space charge layers. Prolonged annealing of the samples leads to a surface degradation, resulting in the formation of a surface layer of lower dielectric constant. This surface degradation is least when annealed in the presence of dry oxygen. From the analysis of the dielectric data using complex electric modulus, alpha(m) has been evaluated for the virgin and annealed samples. (C) 1996 American Institute of Physics.

Verifying scalings for bending rigidity of bilayer membranes using mesoscale models

The bending rigidity kappa of bilayer membranes was studied with coarse grained soft repulsive potentials using dissipative particle dynamics (DPD) simulations. Using a modified Andersen barostat to maintain the bilayers in a tensionless state, the bending rigidity was obtained from a Fourier analysis of the height fluctuations. From simulations carried out over a wide range of membrane thickness, the continuum scaling relation kappa proportional to d(2) was captured for both the L-alpha and L-beta phases. For membranes with 4 to 6 tail beads, the bending rigidity in the L-beta phase was found to be 10-15 times higher than that observed for the L-alpha phase. From the quadratic scalings obtained, a six fold increase in the area stretch modulus, k(A) was observed across the transition. The magnitude of increase in both kappa and k(A) from the L-alpha to the L-beta phase is consistent with current experimental observations in lipid bilayers and to our knowledge provides for the first time a direct evaluation of the mechanical properties in the L-beta phase.

Nonlinear static and dynamic damped response of a composite rectangular plate resting on a two-parameter elastic foundation

Nonlinear static and dynamic response analyses of a clamped. rectangular composite plate resting on a two-parameter elastic foundation have been studied using von Karman's relations. Incorporating the material damping, the governing coupled, nonlinear partial differential equations are obtained for the plate under step pressure pulse load excitation. These equations have been solved by a one-term solution and by applying Galerkin's technique to the deflection equation. This yields an ordinary nonlinear differential equation in time. The nonlinear static solution is obtained by neglecting the time-dependent variables. Thc nonlinear dynamic damped response is obtained by applying the ultraspherical polynomial approximation (UPA) technique. The influences of foundation modulus, shear modulus, orthotropy, etc. upon the nonlinear static and dynamic responses have been presented.