Densification Regime Research Articles

Predictions of the Elastic–Plastic Compressive Response of Functionally Graded Polymeric Composite Lattices Manufactured by Three-Dimensional Printing

Abstract We use three-dimensional printing to manufacture lattices with uniform and graded relative density, made from a composite parent material comprising a nylon matrix reinforced by short carbon fibers. The elastic–plastic compressive response of these solids is measured up to their densification regime. Data from experiments on the lattices with uniform relative density are used to deduce the dependence of their elastic–plastic homogenized constitutive response on their relative density, in the range 0.2–0.8. These data are used to calibrate finite element (FE) simulations of the compressive response of functionally graded lattices (FGLs), which are found in good agreement with the corresponding measurements, capturing the salient features of the measured stress versus strain responses. This exercise is repeated for two lattice topologies (body-centered cubic and Schwarz-P). The phenomenological constitutive models produced in this study can be used in topology optimization to maximize the performance of 3D-printed FGLs components in terms of stiffness, strength, or energy absorption.

The Symmpact: A Direct-Impact Hopkinson Bar Setup Suitable for Investigating Dynamic Equilibrium in Low-Impedance Materials

BackgroundMeasuring the dynamic behavior of low-impedance materials such as foams is challenging. Their low acoustic impedance means that sensitive force measurement is required. The porous structure of foams also gives rise to dynamic compaction waves, which can result in unusual behavior, in particular if the foam material is so thick, that dynamic force equilibrium is not reached.ObjectiveThis work investigates comparatively large polyurethane foam specimens with densities in the range of 80 – 240 kg/m3 to deliberately achieve a state away from force equilibrium during high-rate compaction. The aim is to understand how an increase in strain rate leads to a reduction in strength for such materials.MethodsA specialized direct-impact Hopkinson bar is employed. It uses polycarbonate bars to achieve the required long pulse duration of 2.6 ms to compress the large specimens into the densification regime. In contrast to existing setups, both striker and output bar are instrumented with strain gauges to monitor force equilibrium. The absence of an input bar allows monitoring force equilibrium more accurately. Special attention is paid to the calibration of strain gauges, taking non-linear effects, wave dispersion and attenuation into account. Digital Image Correlation is employed to analyze elastic and plastic compaction waves by means of Lagrange diagrams.ResultsDepending on density, the specimens show saturation of dynamic strength increase at high rates of strain approx 500 /s, or even negative strain rate sensitivity in case of the lowest density. The occurrence of apparent negative strain rate sensitivity is accompanied by a localized structural collapse front, moving at a low velocity of approx 10 m/s through the material. This apparent strain rate sensitivity is a structural effect which is related to the thickness of the specimen.ConclusionsThe primary aim of material characterization using Hopkinson bars is to achieve a state of force equilibrium. For this reason, very thin specimens are usually employed. However, data gathered in this way is not representative for thick foam layers. Here, an increase of strain rate can lead to a decrease of strength if homogeneous deformation is replaced by a dynamic compaction wave. This behavior can occur at strain rates encountered under conditions such as automotive crash.

A semi-analytical model for laser induced densification in fused silica at elevated temperatures

A semi-analytical model for deterministic surface smoothing of fused silica below the evaporation temperature threshold is presented. Using this model, a method for calculating deterministic track depths for laser polishing fused silica is derived and validated with experiments. Model predictions were in good agreement with experiment across varying laser preheating temperature and power. With the semi-analytical method presented here, deterministic laser smoothing can be achieved in the densification regime to close the process loop of laser polishing.

Correlation Modeling between Morphology and Compression Behavior of Closed-Cell Al Foams Based on X-ray Computed Tomography Observations

In the last decades, great attention has been focused on the characterization of cellular foams, because of their morphological peculiarities that allow for obtaining effective combinations of structural properties. A predictive analytical model for the compressive behavior of closed-cell Al foams, based on the correlation between the morphology of the cellular structure and its mechanical response, was developed. The cells’ morphology of cylindrical specimens was investigated at different steps of compression by X-ray computed tomography, in order to detect the collapse evolution. The structure, typically inhomogeneous at local level, was represented by developing a global virtual model consisting of homogeneous cells ordered in space, that was fitted on the experimentally detected structure at each deformation step. As a result, the main parameters characterizing the two-dimensional cells morphology (equivalent diameter, circularity), processed by the model, allowed to simulate the whole compression stress–strain curve by enveloping those obtained for each step. The model, fitted on the previous foam, was validated by comparing the simulated stress–strain curve and the corresponding experimental one, detected for similar foams obtained by different powder compositions. The effectiveness in terms of an accurate prediction of the compression response up to the final densification regime has been confirmed.

Kinetics of densification/phase transformation and transport properties of Mg-Sn cubic/trigonal composites

The Mg-Sn materials are interesting because of useful semiconducting properties and particularly because of their earth abundant, environmentally friendly constituent elements. The cubic Mg2Sn phase appears in the equilibrium phase diagram and has been extensively studied, while the transport properties of the trigonal phase—that does not appear in the phase diagram—have not been reported. We produced dense composites composed of cubic (stable) and trigonal (metastable) phases using a combination of high energy ball milling and current activated pressure assisted densification (CAPAD). We present a kinetic study of the densification and cubic to trigonal phase transformation. In addition, we present transport property measurements of cubic/trigonal composites. We determine densification rates and observe distinct densification regimes, attributed to the cubic-to-tetragonal phase transformation as well as porosity removal. Transport property measurements reveal that altering the amount of metastable phase in the composites changes both the electrical and thermal properties. The electrical conductivity significantly increases with increasing trigonal phase fraction. The thermal conductivities are similar for all compositions, which is likely due to the nanocrystalline character of the composites.

Continuum modeling of crushing of low density foams

Under compression deformation in low-density foams localizes into narrow bands of crushed cells. Crushing spreads at nearly constant stress with crushed and relatively undeformed material coexisting. The material returns to homogeneous deformation with increasing stress when the crushing has spread over the whole specimen. This paper presents a first attempt at representing the inhomogeneous behavior exhibited by open-cell aluminum alloy foams with relative density of 8%. A plasticity model is presented with a compressible yield function calibrated to a set of multiaxial foam crushing tests coupled with a non-associated flow rule. An essential component of the modeling effort is the introduction of a softening branch to the material stress-strain response. A cubical finite element model with an irregular mesh of solid elements is used to simulate a set of numerical crushing tests on micromechanically accurate foam models performed in a true triaxial apparatus in Yang and Kyriakides (2019). Small geometric imperfections are used to trigger localized deformation in the form of planar bands of high strain normal to the loading directions of compression. The bands broaden with the stresses tracing plateaus that mimic the random foam test results. The predicted mean stress–change in volume responses perform equally well up to a volume reduction of about 50%. At higher compressions, the stresses exhibit the gradual increase characteristic of foams in the densification regime. These parts of the stress–displacement trajectories, and mean stress–change in volume responses under-predict to some degree those recorded in the random foams. The material hardening in the densification regime appears to be deformation-dependent causing this difference.

Highly-doped Nd:YAG ceramics fabricated by conventional and high pressure SPS

Abstract Spark plasma sintering (SPS) is an effective process for the fabrication of highly transparent oxide ceramics for photonic applications. In the present study, Nd-doped yttrium aluminum garnet (Nd:YAG) ceramics with various dopant concentrations (0.5–5 at.%) were fabricated at 1300–1400 °C using conventional SPS (60 MPa) and high pressure (300 MPa) conditions. The appearance, X-ray diffraction pattern, densification regime, microstructure, mechanical and optical properties were compared; the dependency on Nd concentration and sintering pressure is discussed. The pressure applied during the sintering process seemed to have only a minor effect on the luminescent properties, while the mechanical properties were superior for the samples sintered under high pressure conditions. The known concentration quenching phenomenon was observed and an equation for estimation of the Nd concentration, based on phosphorescence lifetime, is suggested.

Phase transformation as the mechanism of mechanical deformation of vertically aligned carbon nanotube arrays: Insights from mesoscopic modeling

Vertically aligned carbon nanotube (VACNT) arrays or “forests” behave mechanically as foams when compressed, exhibiting a characteristic nonlinear stress – strain response. However, the fiber structure of VACNT forests is unlike that of cellular foams, and the microscopic mechanisms of the deformation are quite different. While numerous studies have addressed the mechanical response of VACNT forests undergoing uniaxial compression, the underlying deformation mechanisms are not yet fully established. In this paper, we report the results of large-scale mesoscopic simulations of the uniaxial compression of a VACNT forest composed of 2-μm-long carbon nanotubes (CNTs) as well as three structurally distinct forests composed of 0.6-μm-long CNTs. The simulations reveal that the compressive deformation proceeds as a phase transformation from an original low-density phase composed of vertically aligned CNT bundles to a densified phase with horizontal alignment of CNTs. The two phases are separated by a well-defined interfacial layer, which advances during the compressive deformation through localized bending and folding of nanotubes. For the 2-μm-tall forest, the folding involves correlated displacements of multiple CNT bundles, hinting on the origin of the collective buckling behavior observed in experiments. The characteristic three-stage stress-strain dependence (an initial "elastic" peak followed by an extended plateau region and a sharp rise of stress in the densification regime), commonly observed in experimental probing of the mechanical properties of VACNT forests, is reproduced in all of the simulations, suggesting that the heterogeneous propagation of densification front may be the general mechanism of the mechanical deformation of VACNT forests.

High strain rate out‐of‐plane compression of birch plywood from ambient to cryogenic temperatures

AbstractAn extensive series of compression tests with birch plywood specimens is conducted in the out‐of‐plane direction. Various experimental conditions are tested with different temperatures and strain rates. To this end, a specially designed Split Hopkinson pressure bar protocol is defined, and the specimen dimensions are validated from quasi‐static EN789 standards experiments. Temperatures are ranging from ambient down to −170°C, while strain rates are increased from 0.004/s up to 700/s. The analysis of the experimental results focuses on the hardening behaviour and the following densification regime at large strains. Evolution with temperature and strain rate of the four coefficients of the stress versus strain curve interpolation is discussed, and models are proposed.

Crumpled paper sheets: Low-cost biobased cellular materials for structural applications

Several low-density crumpled paper-based materials were fabricated by varying both the volume fraction and the geometry and mechanical properties of paper sheets. Their 3D architecture was investigated using X-ray microtomography. Microstructure descriptors such as the pore size distribution, the mean curvature distribution and the volume fraction of ordered domains were finely analyzed. Their mechanical properties were also assessed using uniaxial compression tests. Our results showed that crumpled materials exhibited a particular porous microstructure with a reproducible mechanical behavior between foams and entangled fibrous materials. Their compressive behavior was characterized by successive elastic, strain-hardening and densification regimes. The effects of the geometry, microstructure and mechanical properties of the sheets on the process-induced microstructures and mechanical performances were discussed. In particular, a simple micromechanical approach was used to estimate analytically and from the 3D images the role of ridges and ordered domains on the mechanical properties of crumpled papers. The evolution of their Young's moduli and yield stresses were studied as a function of their relative densities and compared with experimental data available in the literature for other cellular materials, showing that crumpled papers are promising renewable alternatives to standard polymer foams for several engineering applications, due to the proper combination of mechanical properties, porosity, cost, and easy fabrication.

Cellulose nanofibril foams: Links between ice-templating conditions, microstructures and mechanical properties

This study aimed at investigating how ice templating conditions affected the shrinkage, the microstructure, and the mechanical properties of cellulose nanofibril (NFC) foams. Enzymatic and TEMPO-oxidized NFC foams were fabricated using two solidification techniques, i.e., quenching NFC suspensions in temperature-controlled baths, and mechanical stirring of NFC suspensions during solidification followed by quenching, prior to freeze-drying. Foams prepared by direct quenching using stabilized TEMPO-oxidized NFC suspensions exhibited higher specific mechanical properties and more regular anisotropic cells with unimodal size than enzymatic NFC foams. In addition, NFC concentration and NFC morphology severely affected the foam shrinkage and the geometry of foam cells. Controlling the solidification had also a drastic effect on the foam microstructure, e.g. foams prepared by mechanical stirring and quenching exhibited bimodal cell size and enhanced mechanical properties. The compressive behavior of foams showed successive elastic, strain-hardening and densification regimes with auxetic effects and strain localization. Both the elastic modulus and the yield stress were power-law functions of the foam relative density whose exponents reached unusual high values for enzymatic NFC foams, potentially because of their chaotic microstructures. The evolution of a typical TEMPO-oxidized NFC foam was studied under compression using X-ray microtomography, unveiling deformation mechanisms at the cell scale.

Strain rate effects on the compressive response of wood and energy absorption capabilities – Part A: Experimental investigations

Strain rate effect on wood material is of major interest when dealing with applications dedicated to energy absorption or wood machining. To understand and evaluate the strain rate influence on the wood responses, three experimental apparatus are used in order to cover a large range of strain rates, between 0.001 and 600s-1, and to allow observing densification regime for strains until 70%. The influence of strain rate on mechanical properties, in particular, initial crushing stress, plateau stress and specific absorbed energies is investigated in the three orthotropic directions for two wood species (spruce and beech) really different in terms of relative density and microstructure. It is noticed that wood properties are strain rate sensitive and this sensitivity depends on the loading direction.

Hardening under compression in Au foams

We report the results of compressive tests for a model bi-continuous nanoporous gold structure using atomistic simulations focusing on the densification regime and the plasticity mechanisms taking place. The stress – strain response follows a logarithmic evolution proportional to the inverse of strain and we provide a simple scaling law for this behavior. Hardening is correlated to the dislocation density and an exponential dependence is revealed. The plasticity mechanisms were inspected revealing the presence of Hirth and Frank partials contributing to the hardening of the sample. Lomer–Cottrel locks, perfect dislocations, and twinning were also found.

The Politics of Post‐Suburban Densification in Canada and France

AbstractThis debate specifically focuses on densification as a particular dimension of (post‐) suburbanization. In the introduction, we discuss densification, along with ‘compactness' and ‘intensification', conceptual terms that have become buzzwords within urban planning. Objectives associated with these tend to be presented in the literature within a normative framework, structured by a critique of the negative effects attributed to sprawl. The perspective here is different. It is not normative but critical, and articulated around the analysis of political and social issues, related to the transformation of wider metropolitan space. Three main themes are developed: (1) the politics of densification (the environmental arguments favouring densification are highly plastic, and are thus often used to defend projects or initiatives which are actually determined by other agendas); (2) why morphology matters (a similar number of houses or square metres can be established in many different ways, and those different ways have political and social meaning); (3) the diversity of suburban densification regimes (it is not only the landscapes of the suburbs that are diverse, but also the local bodies governing them—between the small residential municipalities of the Paris periurbs and the large inner suburbs of Toronto lies a broad spectrum).

Analysis of the compressive response of Nano Fibrillar Cellulose foams

Nano Fibrillar Cellulose (NFC) is fast emerging as a biomaterial with promising applications, one of which is cellular foam. The inner structure of the foam can take various shapes and hierarchical micro-structures depending on the manufacturing parameters. The compressive response of foams developed from these materials is currently a primary criterion for the material development. In this work, we focus on the connection between the non-linear part of the response and the inner structure of the material. We study the effect of internal contact and its contribution to gradual stiffening in the energy absorbing region and accelerated stiffening in the densification region of the large strain compressive response. We use the finite element method in this study and discuss the applicability and efficiency of different modelling techniques by considering well defined geometries and available experimental data. The relative contribution of internal contact is singled out and mapped onto the overall compressive response of the material. The effect of initial non-straightness of the cell walls is studied through superposing differing percentages of the buckling modes on the initial geometry. The initial non-straightness is seen to have a significant effect for only strains up to 1%. The secant modulus measured at slightly higher strains of 4%, demonstrates lesser effect from the non-straightness of cell walls. The simulations capture the compressive response well into the densification regime and there is an order of magnitude agreement in between simulations and experiments. We observed that internal contact is crucial for capturing the trend of compressive response.

Density-driven structural transformations inB2O3glass

The method of in situ high-pressure neutron diffraction is used to investigate the structure of ${\mathrm{B}}_{2}{\mathrm{O}}_{3}$ glass on compression in the range from ambient to 17.5(5) GPa. The experimental results are supplemented by molecular dynamics simulations made using a newly developed aspherical ion model. The results tie together those obtained from other experimental techniques to reveal three densification regimes. In the first, ${\mathrm{BO}}_{3}$ triangles are the predominant structural motifs as the pressure is increased from ambient to 6.3(5) GPa, but there is an alteration to the intermediate range order which is associated with the dissolution of boroxol rings. In the second, ${\mathrm{BO}}_{4}$ motifs replace ${\mathrm{BO}}_{3}$ triangles at pressures beyond 6.3 GPa and the dissolution of boroxol rings continues until it is completed at 11--14 GPa. In the third, the B-O coordination number continues to increase with pressure to give a predominantly tetrahedral glass, a process that is completed at a pressure in excess of 22.5 GPa. On recovery of the glass to ambient from a pressure of 8.2 GPa, triangular ${\mathrm{BO}}_{3}$ motifs are recovered but, relative to the uncompressed material, there is a change to the intermediate range order. The comparison between experiment and simulation shows that the aspherical ion model is able to provide results of unprecedented accuracy at pressures up to at least 10 GPa.

Experimental investigation and discrete simulation of fragmentation in expanded breakfast cereals

The fragmentation behaviour of brittle airy cereal product is studied both numerically and experimentally. A cereal food item is subjected to severe compression up to the densification stage. Experimental evidence of typical airy food behaviour is pointed out including elasticity, cell collapse and densification regimes. In order to better explain the observed behaviour, especially the resulting fragmentation, a numerical approach is proposed based on the discrete element method. Predicted results show good agreement with experimental mechanical responses. In particular, the maximum force values for fragmentation and the size of resulting fragments are in good accordance with experiments. Our numerical results show that the observed fragment size distribution is the consequence of a small number of rupture events of cell walls. This result highlights the role of the airy structure associated with a particular tendency to form a bimodal size distribution of fragments.

Mechanical behavior of porous magnesium/alumina composites with high strength and low density

Porous alumina-reinforced magnesium composites were synthesized through a powder metallurgical method and characterized using optical microscope, scanning electron microscope, and compression testing. The microstructural study exhibited that the average pore sizes increased with the increase of porosity and were about 25μm, 70μm, and 100μm for the samples with 10%, 28%, and 38% porosities respectively. The mechanical characterization indicated that (i) the stress–strain curves were composed of three regimes: an initial regime that deformed elastically along an approximately linear line, a long and intermediate regime, and a densification regime with a steep increase of stress; (ii) the synthesized porous magnesium composites possessed lower density and higher yield strength than those of cast dense magnesium; (iii) the average yield strength and Young's modulus were anisotropic for the porous magnesium composites synthesized in this work.

Effect of the Q‐switch parameters on the sintering behavior of laser micro sintering Cu‐based metal powder using Q‐switched Nd‐YAG laser

PurposeThe purpose of this paper is to investigate the effect of the Q‐switching parameters on the sintering behavior of laser micro sintering Cu‐based metal powder, using Q‐switched 1064 nm Nd‐YAG laser.Design/methodology/approachAn experimental study has been performed. Metal powder mixture with Cu and Cu‐P alloy powders has been utilized. Q‐switching duration of 15 μs∼25 μs, rate of 25 kHz∼45 kHz have been used.FindingsThe results show that as the Q‐switching rate and duration increases, the peak laser power decreases and the densification enhances. However, an optimal peak laser power exists and if the peak laser power is too low, the density of the sample is also low. The densification regime of laser micro‐sintering is not only caused by the liquid phase filling the pores, but is also caused by the Cu powder migrating and by coalescence, e.g. including initial stage and intermediate stage of the traditional furnace liquid phase sintering. However, the degree of these stages depends on the peak power and input laser energy.Originality/valueThe effect of the Q‐switching parameters on sintering behavior of laser micro sintering Cu‐based metal powder using Q‐switched 1064 nm Nd‐YAG laser has been obtained. It is found that the densification behavior is Q‐switching parameters dependent, although the average laser power is same. The densification regime of laser micro‐sintering includes initial stage and intermediate stage of the traditional furnace liquid phase sintering, but the degree is Q‐switching parameters dependent.

Non-Debye normalization of the glass vibrational density of states in mildly densifiedsilicate glasses

The evolution of the boson peak with densification at medium densification rates (up to2.3%) in silicate glasses was followed through heat capacity measurements and lowfrequency Raman scattering. It is shown that the decrease of the boson peakinduced by densification does not conform to that expected from a continuousmedium; rather it follows a two step behaviour. The comparison of the heat capacitydata with the Raman data shows that the light-vibration coupling coefficientis almost unaffected in this densification regime. These results are discussed inrelation to the inhomogeneity of the glass elastic network at the nanometre scale.