Full-field characterization of mechanical behavior of polyurethane foams

The foam material of interest in this investigation is a rigid closed-cell polyurethane foam PMDI with a nominal density of 20 pcf (320 kg/m³). Three separate types of compression experiments were conducted on foam specimens. The heterogeneous deformation of foam specimens and strain concentration at the foam–steel interface were obtained using the 3-dimensional digital image correlation (3D-DIC) technique. These experiments demonstrated that the 3D-DIC technique is able to obtain accurate and full-field large deformation of foam specimens, including strain concentrations. The experiments also showed the effects of loading configurations on deformation and strain concentration in foam specimens. These DIC results provided experimental data to validate the previously developed viscoplastic foam model (VFM). In the first experiment, cubic foam specimens were compressed uniaxially up to 60%. The full-field surface displacement and strain distributions obtained using the 3D-DIC technique provided detailed information about the inhomogeneous deformation over the area of interest during compression. In the second experiment, compression tests were conducted for cubic foam specimens with a steel cylinder inclusion, which imitate the deformation of foam components in a package under crush conditions. The strain concentration at the interface between the steel cylinder and the foam specimen was studied in detail. In the third experiment, the foam specimens were loaded by a steel cylinder passing through the center of the specimens rather than from its end surface, which created a loading condition of the foam components similar to a package that has been dropped. To study the effects of confinement, the strain concentration and displacement distribution over the defined sections were compared for cases with and without a confinement fixture.     

High-velocity deformation properties of polyurethane foams

This paper presents the results of dynamic uniaxial-stress tests performed on polymer-foam material. A water-blown ester polyurethane foam designated as rigid and a castor-oil-base polyurethane foam designated as semirigid were tested in tension and compression at rates of loading from 10^?3 in./in./sec to 10³ in./in./sec at room temperature. A gas-operated medium-strain-rate machine was used for rates of loading from 10^?3 to about 10² in./in./sec. Tests at higher rates were performed on a split Hopkinson-bar device. Highspeed photographic techniques were used to study dynamic fracture.     

Modeling morphology evolution and mechanical behavior during thermo-mechanical processing of semi-crystalline polymers

A new model is proposed that combines statistical mechanics and thermodynamic aspects to characterize orientation development, nucleation and growth of crystallites, and chain entanglement slippage with interdependent relationships necessary to accurately correlate and in some cases predict the morphology and mechanical behavior of semi-crystalline polymers during various thermo-mechanical processes in the rubbery state, close to the glass transition temperature. Internal state variables (ISVs) that directly represent the underlying microstructure state are used to characterize polymer morphology and the resulting properties throughout deformation. The model uses fundamental thermodynamic coefficients for polyethylene terephthalate (PET) and is correlated to experimental data at various strain rates and temperatures just above the glass transition temperature. Experimental data are used that measure the stress, amorphous orientation, and crystallinity during uniaxial deformation of PET. The model is found to correlate well to these experimental data.     

Analytical models for the mechanical behavior of closed and open-cell Al foams

Two 3D analytical models are proposed for the determination of mechanical properties of Al closed and open-cell foams under compression load. The first model, referring to closed cell foams, is symmetrical, considering ellipsoid cells equally arranged in a rectangular plate, whereas the second one, related to open-cell foams, consists of a simple unit parallelepiped cell.The closed cell model produces much higher values of the plateau stress than comparable experimental results, mainly due to the associated conditions of symmetry, contrary to the open-cell model which yields values close to experimental and theoretical results of other investigators. Additionally, in the latter case, a unit cubic cell is also considered for comparison reasons. Both models are solved by the finite element method using a commercial program. The open-cell model is simple, time sparing and easy to use. Finally, a fracture analysis of the model is conducted based on the energy density concept and results are given for distortion and dilatational effects.     

Three-dimensional modeling of the mechanical property of linearly elastic open cell foams

Three-dimensional Voronoi models are developed to investigate the mechanical behavior of linearly elastic open cell foams. Dependence of the Young’s modulus, Poisson’s ratio and bulk modulus of the foams on the relative density is evaluated through finite element analysis. Obtained results show that in the low density regime the Young’s modulus and bulk modulus of random Voronoi foams can be well represented by those of Kelvin foams, and are sensitive to the geometric imperfections inherent in the microstructure of foams. In contrast, the compressive plateau stress of the foams is less sensitive to the imperfections. Failure surface of the foams subject to multi-axial compression is determined and is found to comply with the maximum compressive principal stress criterion, consistent with available experimental observations on polymer foams. Numerical results also show that elastic buckling of cell edges at microscopic level is the dominant mechanism responsible for the compressive failure of elastic open cell foams.     

Effect of structural and mechanical characteristics of the composite material on the deformation of a reflector antenna

This is a study of the effect of structural and mechanical characteristics of a composite material on the stress–strain state of a reflector antenna shaped as a composite thin shell of revolution subjected to gravity, wind, and temperature loads. The boundaryvalue problem for the system of partial differential equations governing the behavior of this structure is reduced to a sequence of boundaryvalue problems for inhomogeneous systems of ordinary differential equations with variable coefficients. The resulting stiff systems of equations are solved by Godunov's method of discrete orthogonalization.     

Simultaneous measurement of viscoelastic changes and cell opening during processing of flexible polyurethane foam

A parallel-plate rheomete was constructed and used to study the development of dynamic shear modulus and cell opening under forced adiabatic conditions for a series of flexible slabstock polyurethane foams. Typical industrial formulations were used. The plates were heated to follow the adiabatic temperature profile of a real foam bun during foaming. The rheometer overcomes difficulties encountered in other methods such as heat loss and bubble damage caused by the probe.A four-stage modulus development profile was observed: initial bubble growth, bubble network, polymer stiffening and final curing. Chemical structure development was also studied under forced adiabatic conditions, using Fourier transform infrared spectroscopy. Polymer stiffening coincided with bidentate (hydrogen-bonded) urea formation.The normal force exerted by the expanding foam on the plates was found to be a function of the rate of foam expansion and the foam modulus. A sudden drop in the normal force typically coincides with the visually observed blow-off in the reacting foam bun, thus the normal force profile is a new and accurate indicator of cell opening. The normal force profile clearly shows that cell opening occurs just after the onset of polymer stiffening, thus illustrating the role of polymer rheology in the cell opening mechanism.Dedicated to the memory of Professor Tasos C. PapanastasiouPortions presented at the SPI Polyurethanes Technical/Marketing Conference, October 9–12, 1994, Boston, massachusetts, USA (Best paper award) and at the XIIth International Congress on Rheology, August 18–23, 1996, Québec City, Québec, Canada.     

Impact of mixing procedure on phase morphology and fracture mechanical properties of carbon black-filled NR/SBR blends

Based on a viscoelastic model, the filler distribution and the amount of interphase of carbon black-filled blends of natural rubber (NR) with styrene-butadiene rubber (SBR) are evaluated. Hereby, the total dissipated energy \(G''\) during dynamical straining is decomposed into the contributions of the different polymer phases and the interphase. For the NR/SBR blends, we find a higher filling of the SBR phase and the interphase and a lower filling of the NR phase. The filler distribution itself depends not only on the affinity of the polymer to the filler but also on the mixing procedure. This is investigated by studying NR/SBR blends prepared by two different mixing procedures. In the standard mixing procedure, the polymers are mixed first, and then, the filler is added. In the batch mixing procedure, the filler is previously mixed in the NR only and then blended with SBR. Batch mixing is resulting in an increase in the filling of the interphase due to filler transfer from NR to SBR. The results for the filler distribution are compared to fatigue crack propagation rates under pulsed excitation. The crack propagation is accelerated when substituting NR with SBR. The batched samples show higher crack propagation rates at higher tearing energies due to a worse dispersion of the carbon black and/or higher filler loading of the interphase.     

Assessment of material uncertainties in solid foams based on local homogenization procedures

The present study is concerned with a numerical prediction and assessment of uncertainties in the macroscopic material properties of solid foams. The material properties are determined by means of a homogenization analysis considering a large scale representative volume element. The microstructure for the representative volume element is determined randomly using a Voronoï tesselation in Laguerre geometry with prescribed cell size distribution. For assessment of the scatter in the effective material response, the homogenization scheme is applied to subsets of the large scale representative volume element. By this means, an interrelation between the local microstructural characteristics and the local mesoscopic material response is established. In a first approach, the individual cells of the foam microstructure are employed as testing volume elements. As an alternative, a moving window technique is applied. The sets of homogenization results obtained by both approaches are evaluated by stochastic methods. For the local effective properties, a distinct scatter is observed. The results in both cases reveal that the local porosity is the most important influence parameter. For the microstructures investigated, only weak local correlations of the effective stiffnesses with a rapid spatial decay of the correlation is observed.     

The kinetic nature of material deformation and fracture

Some physical mechanisms of deformation and fracture of solids are considered on the basis of state-transition kinetics. The effect of stress state on the energy barriers of state transition is studied for the process of deformation and fracture. Evolution equations are derived with and without consideration of the damage effect on the evolution of deformation and fracture. Some relations between various theories of deformation and fracture are found.     

Analysis and simulation for tensile behavior of anisotropic open-cell elastic foams

Based on the elongated Kelvin obtained to investigate the tensile behavior Kelvin model＇s periodicity and symmetry in model, a simplified periodic structural cell is of anisotropic open-cell elastic foams due to the whole space. The half-strut element and elastic deflection theory are used to analyze the tensile response as done in the previous studies. This study produces theoretical expressions for the tensile stress-strain curve in the rise and transverse directions. In addition, the theoretical results are examined with finite element simulation using an existing formula. The results indicate that the theoretical analysis agrees with the finite element simulation when the strain is not too high, and the present model is better. At the same time, the anisotropy ratio has a significant effect on the mechanical properties of foams. As the anisotropy ratio increases, the tensile stress is improved in the rising direction but drops in the transverse direction under the same strain.     

The effect of large deformation and material nonlinearity on gel indentation

A gel, an aggregate of polymers with solvents, has dual attributes of solid and liquid as solvent migrates in and out of the polymer network. Indentation has recently been used to characterize the mechanical properties of gels. This paper evaluates the effects of large deformation and material nonlinearity on gel indentation through theoretical modeling and finite element analysis. It is found that large deformation significantly affects the interpretation of the experimental observations and the classical relation between indentation force and depth has limitations for large deformation. The material nonlinearity does not play a very important role on indentation experiment so that the poroelasticity is a good approximation. Based on these observations, this paper proposes an alternative approach to measure the mechanical properties of gels, namely, uniaxial compression experiment.     

Influence of thermal aging on tensile and creep behavior of thermoplastic polyurethane

Changes in mechanical and physical properties of polyurethane thermoplastic during aging at 70 °C and 90 °C were investigated. The loss weight response was analyzed by gravimetric measurements under these temperatures. Changes in appearance and morphology of TPU after thermal aging were revealed by optical microscopy. The prolongation of the thermal exposure time, up to 270 days, leads to a progressive increase in tensile strength. In fact, elastic modulus and stress at 200% of strain were increased with thermal exposure time. These results can be explained by the increase of thermal stability due to the increase of material rigidity and the decrease in chain mobility. The evolution of the mechanical properties from tensile tests seems to be well correlated to the creep behavior. Finally, Scanning Electron Microscopy (SEM) revealed the modification of TPU morphology fracture surface after thermal aging.     

The effects of relative density of metal foams on the stresses and deformation of beam under bending

The exact analytic solution of the pure bending beam of metallic foams is given. The effects of relative density of the material on stresses and deformation are revealed with the Triantafillou and Gibson constitutive law (TG model) taken as the analysis basis. Several examples for individual foams are discussed, showing the importance of compressibility of the cellular materials. One of the objects of this study is to generalize Hill’s solution for incompressible plasticity to the case of compressible plasticity, and a kinematics parameter is brought into the analysis so that the velocity field can be determined. The English text was polished by Yunming Chen.     

Microstructural size effects on mechanical properties of high purity nickel

The aim of this article is to provide experimental results in order to understand the microstructural size effects which occur with a decrease in the thickness of polycrystalline nickel samples from 3.2 mm to 12.5 μm. The influence of the thickness, grain size and ratio thickness to grain size on the mechanical properties and strain hardening were investigated by mechanical tests and TEM observations. The results show the presence of three different domains of mechanical behaviour: polycrystalline, multicrystalline and quasi-single crystalline depending on the thickness and on the number of grains across the thickness. The transition between the three domains is due to the occurrence of surface effects involving a decrease in the long-range internal backstress revealed by the TEM observations.     

Mechanical behavior of sandwich composite beams made of foams and functionally graded materials

We investigate sandwich composite beams using a direct approach which models slender bodies as deformable curves endowed with a certain microstructure. We derive general formulas for the effective stiffness coefficients of composite elastic beams made of several non-homogeneous materials. A special attention is given to sandwich beams with foam core, which are made of functionally graded or piecewise homogeneous materials. In the case of small deformations, the theoretical predictions are compared with experimental measurements for the three-point bending of sandwich beams, showing a very good agreement. For functionally graded sandwich columns we obtain the analytical solutions of bending, torsion and extension problems and compare them with numerical results computed by the finite element method.