Experimental and micromechanical study of size effects in the constrained deformation of metallic foams

Previous investigations have unveiled size effects in the strength of metallic foams under simple shear - the shear strength increases with diminishing specimen size, a phenomena similar to that shown by Fleck et al. (Acta Mat., 1994, Vol. 42, p. 475.) on the torsion tests of copper wires of various radii. In this study, experimental study of the constrained deformation of a foam layer sandwiched between two steel plates has been conducted. The sandwiched plates are subjected to combined shear and normal loading. It is found that measured yield loci of metallic foams in the normal and shear stress space corresponding to various foam layer thicknesses are self-similar in shape but their size increases as the foam layer thickness decreases. Moreover, the strains profiles across the foam layer thickness are parabolic instead of uniform; their values increase from the interfaces between the foam layer and the steel plates and reach their maximum in the middle of the foam layer, yielding boundary layers adjacent to the steel plates. In order to further explore the origin of observed size effects, micromechanics models have been developed, with the foam layer represented by regular and irregular honeycombs. Though the regular honeycomb model is seen to underestimate the size effects, the irregular honeycomb model faithfully captures the observed features of the constrained deformation of metallic foams.

Size effects in the constrained deformation of metallic foams

The constrained deformation of an aluminium alloy foam sandwiched between steel substrates has been investigated. The sandwich plates are subjected to through-thickness shear and normal loading, and it is found that the face sheets constrain the foam against plastic deformation and result in a size effect: the yield strength increases with diminishing thickness of foam layer. The strain distribution across the foam core has been measured by a visual strain mapping technique, and a boundary layer of reduced straining was observed adjacent to the face sheets. The deformation response of the aluminium foam layer was modelled by the elastic-plastic finite element analysis of regular and irregular two dimensional honeycombs, bonded to rigid face sheets; in the simulations, the rotation of the boundary nodes of the cell-wall beam elements was set to zero to simulate full constraint from the rigid face sheets. It is found that the regular honeycomb under-estimates the size effect whereas the irregular honeycomb provides a faithful representation of both the observed size effect and the observed strain profile through the foam layer. Additionally, a compressible version of the Fleck-Hutchinson strain gradient theory was used to predict the size effect; by identifying the cell edge length as the relevant microstructural length scale the strain gradient model is able to reproduce the observed strain profiles across the layer and the thickness dependence of strength. © 2002 Elsevier Science Ltd. All rights reserved.

Fine scale structures from deformation of aluminium containing small alumina particles

Microstructures and mechanical properties have been studied in aluminium containing a fine dispersion of alumina particles, deformed by cold-rolling to strains between 1.4 and 3.5. The microstructure was characterised by TEM. The deformation structures evolved very rapidly, forming a nanostructured material, with fine subgrains about 0.2 μm in diameter and a fraction of high-angle boundaries which was already high at a strain of 1.4, but continued to increase with rolling strain. The yield stress and ductility of the rolled materials were measured in tension, and properties were similar for all materials. Yield stress measurements were correlated with estimates made using microstructural models. The role of small particles in forming and stabilising the deformation structure is discussed. This nanostructured cold-deformed alloy has mechanical properties which are usefully enhanced at comparatively low cost. This gives it, and similar particle-strengthened alloys, good potential for commercial exploitation. © 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Shear localization and recrystallization in dynamic deformation of 8090 Al-Li alloy

The microstructural evolution in localized shear deformation was investigated in an 8090 Al-Li alloy by split Hopkinson pressure bar (strain rate of approximately 10(3) s(-1)) at ambient temperature and 77 K. The alloy was tested in the peak-, over-, under-, and natural-aged conditions, that provide a wide range of microstructural parameters and mechanical properties. Two types of localized shear bands were distinguished by optical microscopy: the deformed shear band and the white-etching shear band. They form at different stages of deformation during localization. There are critical strains for the occurrence of deformed and white-etching localized shear deformation, at the imposed strain rate. Observations by transmission electron microscopy reveal that the white-etching bands contain fine equiaxed grains; it is proposed that they are the result of recrystallization occurring during localization. The deformed-type bands are observed after testing at 77 K in all heat treatment conditions, but they are not as well defined as those developed at ambient temperature. Cracking often occurs along the localized shear at ambient temperature. The decrement in temperature is favorable for the nucleation, growth and coalescence of the microcracks along the shear bands, inducing fracture.

Theoretical investigation of epitaxial deformation and the hcp-bcc transition of alkali metals

The deformation of alkali metals K, Rb, and Cs under epitaxial deformation is studied via the ab initio pseudopotential plane wave method using the local-density approximation. Under loading from the stable fee phase, metastable stares along directions [001], [111], and [201] are identified. One metastable state, presented at direction [201], has a very low symmetry in contrast to the planes [001] and [201]. Our results show that the softening direction and sequences of growth is significantly affected by the existence of the metastable states and magnitude of the energy barrier. The resulting softening sequences from soft to hard are [201], [110], [001], and [111] under biaxial compression and [001], [111], [201], and [110] under biaxial tension. An orthorhombic deformation path is used to investigate the fact, that the structure of the alkali films K and Cs evolve from the quasihexagonal structure into the (110)-oriented bcc structure, observed by experiments.

Experimental Study of Surface Deformation and Flow Pattern on Buoyant-Thermocapillary Convection

Free surface deformation is one of the most important physical phenomena in fluids with free surface. In the present paper, convection and surface deformation caused by thermocapillary effect in a rectangular cavity were investigated. In ground experiments, the convection was also affected by gravity. The cavity has a horizontal cross section of 52mm×42mm and the thikkness of the liquid layer is 4mm. Temperature difference between two sides of the liquid layer was increased gradually, and the flow in liquid layer will develop from steady to unstable convection. An optical diagnostic system consisting of a revised Michelson interferometer with image processor was developed to study fluid surface deformation in convection, and the displacements of free surface oscillation were determined. PIV technique was adopted to observe the evolution of flow pattern, and the velocity fields were obtained quantitatively. The present experiments demonstrate that surface deformation is quite distinct in buoyant-thermocapillary convection. in order to understand the mechanism of buoyant-thermocapillary convection, not only the hydrothermal wave instability but also the surface wave instability should be discussed.

A New Deformation Theory with Strain Gradient Effects

A new phenomenological deformation theory with strain gradient effects is proposed. This theory, which belongs to nonlinear elasticity, fits within the framework of general couple stress theory and involves a single material length scale l. In the present theory three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom u(i). omega(i) has no direct dependence upon ui and is called the micro-rotation, i.e. the material rotation theta(i) plus the particle relative rotation. The strain energy density is assumed to only be a function of the strain tensor and the overall curvature tensor, which results in symmetric Cauchy stresses. Minimum potential principle is developed for the strain gradient deformation theory version. In the limit of vanishing 1, it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in details. Comparisons between the present theory and the theory proposed by Shizawa and Zbib (Shizawa, K., Zbib, H.M., 1999. A thermodynamical theory gradient elastoplasticity with dislocation density Censor: fundamentals. Int. J. Plast. 15, 899) are given. With the same hardening law as Fleck et al. (Fleck, N.A., Muller, G.H., Ashby, M.F., Hutchinson, JW., 1994 Strain gradient plasticity: theory and experiment. Acta Metall. Mater 42, 475), the new strain gradient deformation theory is used to investigate two typical examples, i.e. thin metallic wire torsion and ultra-thin metallic beam bend. The results are compared with those given by Fleck et al, 1994 and Stolken and Evans (Stolken, J.S., Evans, A.G., 1998. A microbend test method for measuring the plasticity length scale. Acta Mater. 46, 5109). In addition, it is explained for a unit cell that the overall curvature tensor produced by the overall rotation vector is the work conjugate of the overall couple stress tensor. (C) 2002 Elsevier Science Ltd. All rights reserved.

Some observations describing the electrochemical surface annealing of austenitic stainless steel

Cold-worked austenitic stainless steels have been subject to a pulsed electrochemical treatment in fairly concentrated aqueous solutions of sodium nitrite. The electrochemical reactions that occur transform the strain-induced martensite phase, originally formed by the cold work, back to the austenite phase. However, unlike the conventional thermal annealing process, electrochemically induced surface annealing also hardens the surface of the alloy. Because the process causes transformation of the surface martensite, we term it "electrochemical surface annealing", despite the fact that it results in an increase in surface hardness.

Deformation and Failure of Polymer Bonded Explosives under Diametric Compression Test

The tensile deformation and failure of polymer bonded explosives (PBXs), a particulate composite, is studied in this paper. Two HMX-based PBXs with different binder were selected for study. A diametric compression test, in which a disc-shaped specimen is loaded diametrically, was chosen to generate tensile failure in the materials. The quasi-static tensile properties and the tensile creep properties were studied by using conventional displacement transducers to measure the lateral strain along the horizontal diameter. The whole-field in-plane creep deformation was measured by using the technique of high resolution moire´ interferometry. Real time microscopic examination was conducted to monitor the process of deformation and failure of PBXs by using a scanning electron microscope equipped with a loading stage. A manifold method (MM) was used to simulate the deformation and failure of PBX samples under the diametric compression test, including the crack initiation, crack propagation and final cleavage fracture. The mechanisms of deformation and failure of PBXs under diametric compression were analyzed. The diametric compression test and the techniques developed in this research have proven to be applicable to the study of tensile properties of PBXs.

Size Effects in Micro-bending Deformation of MEMS Devices Based on the Discrete Dislocation Theory

In the present research, the discrete dislocation theory is used to analyze the size effect phenomena for the MEMS devices undergoing micro-bending load. A consistent result with the experimental one in literature is obtained. In order to check the effectiveness to use the discrete dislocation theory in predicting the size effect, both the basic version theory and the updated one are adopted simultaneously. The normalized stress-strain relations of the material are obtained for different plate thickness or for different obstacle density. The prediction results are compared with experimental results.

Stress reduction and bond stability during thermal annealing of tetrahedral amorphous carbon

A comprehensive study of the stress release and structural changes caused by postdeposition thermal annealing of tetrahedral amorphous carbon (ta-C) on Si has been carried out. Complete stress relief occurs at 600-700°C and is accompanied by minimal structural modifications, as indicated by electron energy loss spectroscopy, Raman spectroscopy, and optical gap measurements. Further annealing in vacuum converts sp3 sites to sp2 with a drastic change occurring after 1100°C. The field emitting behavior is substantially retained up to the complete stress relief, confirming that ta-C is a robust emitting material. © 1999 American Institute of Physics.

Influencia de diferentes dosis de productos inductores de la floración (Carburo de calcio y ethrell), en dos variedades de piña (Ananas comosus (L) Merril) sobre la calidad post-cosecha

El presente estudio se estableció entre el 25 y 26 de Octubre del año 2002, con el objetivo de conocer la influencia de los productos hormonales inductores de la floración de la piña sobre la calidad post-cosecha. En los Rios (Ticuantepe) con la variedad Cayena lisa y en Mirazul del Llano (Masatepe) con la variedad Monte lirio. El diseño experimental fue un bifactorial en bloques completos al azar (BCA). Factor A, productos: Carburo de calcio, Etrhell y la combinación de ambos. Factor B, dosis de 30 y 50 cc. El área de las parcelas experimentales para cada variedad fue de 223.2 m2 con una población estimada de 864 plantas. En la calidad interna para la variedad Cayena lisa, los mayores valores fueron 12.45 porciento grados brix y 4.15 pH obtenidos con el producto Carburo de calcio más Urea y con la dosis de 50 cc. En la variedad Monte lirio 6.79 porciento grados brix con Ethrell y con la dosis de 30 cc; el pH fue de 4.43 con Carburo de calcio más Urea, con la dosis de 50 cc. En la calidad externa los frutos con mayores valores se obtuvieron en la variedad Monte lirio, la altura obtenida fue de 18 .63 cm con Carburo de calcio más Urea y con la dosis de 50 cc, el diámetro fue de 13.29 cm obtenido con Ethrell y la dosis de 30 cc, el peso fue de 2,282.70 g. obtenido con Carburo de calcio más Urea y con la dosis de 50 cc; el peso de la corona más bajo fue de 107.65 g. obtenido con Carburo de calcio más Ethrell y la dosis de 30 cc. En la variedad Cayena lisa la mayor altura fue de 16.55 cm obtenida con Ethrell y la dosis de 30 cc; el diámetro fue de 11.16 cm obtenido con Carburo de calcio más Ethrell y la dosis de 50 cc; el peso fue de 1,397.00 g. obtenido con Ethrell y la dosis de 30 cc, el peso de la corona más bajo fue de 102.60 g. obtenido con Ethrell y la dosis de 50 cc. Económicamente el tratamiento de menor costo, con mayor beneficio neto y con mejores resultados en la calidad post-cosecha es el Carburo de calcio más Urea en dosis de 50 cc.

Shear deformation analysis on laser-induced reverse bulging and plugging

A new kind of failure mode is observed in circular brass foils in which their peripheries are fixed and their surfaces are subjected to a long pulsed laser over a central region. The failure is classified into three stages; they are referred to as thermal bulging, localized shear deformation and perforation by plugging. A distinct feature of the failure mode is that bulging and plugging occurred in the direction opposite to the incident laser beam. To study the failure mode, we investigate the non-linear response of heated, non-homogeneous circular plates. Based on the large deflection equations of Berger [J. Appl. Mech. 22 (3), 465-472 (1965)], Ohnabe and Mizuguchi [Int. J. Non-Linear Mech. 28 (4), 365-372 (1993)] and the parabolic shear deformation theory of Bhimaraddi and Stevens [J. Appl. Mech. 51 (1), 195-198 (1984)], we have derived new coupled governing equations of shear deformation and deflection. The new equations are solved, for the plate with a clamped edge, by the Galerkin and iterative methods. The numerical results for the shear deformation distribution are in good agreement with the experimental observation.

Post-earthquake behaviour of footings employing densification to mitigate liquefaction

In situ densification is a popular technique to protect shallow foundations from the effects of earthquake-induced liquefaction, current design being based on semiempirical rules. Poor understanding of the mechanisms governing the performance of soil-structure systems during and after earthquakes inhibits the use of narrow densified zones, which could contribute to optimise the use of densification if the increase in post-earthquake settlement is restrained. Therefore this paper investigates the long-term behaviour of a footing built on densified ground and surrounded by liquefiable ground, centrifuge experiments being used to identify the mechanisms occurring in the ground during and after a seismic simulation. The differential excess pore pressure generated in the ground during the shaking and the processes of vertical stress concentration and subsequent redistribution observed under the footing dominate the system behaviour. The results enlighten the complex mechanisms determining the post-earthquake settlement when densification is carried out to mitigate liquefaction effects. The improvement in performance resulting from widening the zone of densification is rationally explained which encourages the development of new design concepts that may enhance the future use of densification as a liquefaction resistance measure. © 2007 Thomas Telford Ltd.

Deformation behavior and microstructure effect in 2124Al/SiCp composite

Dynamic compression tests were performed by means of a Split Hopkinson Pressure Bar (SHPB). Test materials were 2124Al alloys reinforced with 17% volume fraction of 3, 13 and 37 μm SiC particles, respectively. Under strain rate ε = 2100 l/s, SiC particles have a strong effect on σ_0.2 of the composites and the σ_0.2 increases with different SiC particle size in the following order: 2124Al-alloy → 124Al/SiC_p (37 μm) → 2124Al/SiC_p (13 μm) → 2124Al/SiC_p (3 μm), and the strain hardening of the composites depends mainly on the strain hardening of matrix, 2124A1 alloy. The results of dimensional analysis present that the flow stress of these composites not only depends on the property of reinforcement and matrix but also relates to the microstructure scale, matrix grain size, reinforcement size, the distance between reinforcements and dislocations in matrix. The normalized flow stress here is a function of inverse power of the edge-edge particle spacing, dislocation density and matrix grain size. Close-up observation shows that, in the composite containing SiC particles (3 μm), localized deformation formed readily comparing with other materials under the same loading condition. Microscopic observations indicate that different plastic flow patterns occur within the matrix due to the presence of hard particles with different sizes.