Three-dimensional large-strain tensile deformation of neat and calcium carbonate-filled high-density polyethylene

The large-strain tensile deformation of high-density polyethylene and high-density polyethylene filled with two volume fractions (f) of calcium carbonate particles is studied via an optical method. Digital image correlation is used to determine the local displacement gradients and full-field displacements during uniaxial tension tests on specimens of rectangular cross-section. A novel technique measures simultaneously, with a single camera, the deformation in all three dimensions. Full-field strain contours, macroscopic true stress-true strain behavior, and local volumetric strains are reduced from the raw test data. The true stress-true strain data shows an increase in modulus, but a decrease in yield stress and subsequent strain hardening, with increasing f. These results are strong evidence of particle debonding and are corroborated by an increase in volumetric strain with increasing f.     

Material modeling and solid phase forming of polycarbonate sheet

The Maxwell-Voigt type mechanical model proposed by Haward and Thackray was further modified to describe the strain rate dependent stress-strain behavior of polycarbonate under the uniaxial loading condition. Major modifications included effects associated with different hardening components of inelastic resistance and the related temperature dependent material behavior. The modified analytical model was shown to describe some of the important features of the stress-strain behavior of polycarbonate specimens tested over the range of strain rates and temperatures. Using the stress-strain relationship as input data; several finite element analyses were made to predict the behavior of polycarbonate sheets under a simple solid phase cup forming process. The computed strain distributions agreed reasonably with the measured values obtained from the gridded polycarbonate sheet that was formed at an elevated temperature. Some of the key assumptions that were used in the analysis are discussed.     

Application of an interpenetrating network model to the necking in the microcrystalline region in four annealed isotactic polypropylene films subjected to uniaxial stretching at room temperature

The microscopic infrared dichroism, mesoscale deformation and macroscopic stress measurements are made on the microcrystalline region in four annealed isotactic polypropylene (iPP) thin films subjected to uniaxial stretching at room temperature. Results reveal that volume dilatation might occur during stretching and the necking causes the anisotropic shrinkage in the thickness and the width directions. The average orientation function f_av and the true stress as a function of local draw ratio in the samples showing volume dilatation can be respectively overlapped onto those of the sample undergoing constant volume deformation. The pseudo-affine deformation is applicable for molecular orientation at f_av<0.50 and the true stress-strain relationship on the mesoscale can be well described in the same region by the interpenetrating network model previously proposed for necking in the quenched iPP film. This model becomes invalid for deformations above f_av=0.50 due to that plastic deformations in the crystalline phase, depending on the annealing time, start to play a major role.     

Strain hardening equation and the prediction of tensile strength of rolled polymers

A number of thermoplastic polymers were tested in tension to investigate their strain hardening behavior. A strain hardening equation has been proposed in terms of the true stress, true strain and two constants σ_o and m. The three material constants, viz. σ_o m and the true fracture strain, are shown to be adequate to describe completely the material's nonlinear viscoelastic or the so-called “plastic” behavior. The true stress-strain data for the polymers rolled to varying amounts of cold-work fits the strain hardening plot of the unrolled material. The same strain hardening equation, therefore, applies to rolled materials as well. The procedure for predicting the tensile strength of rolled materials is given.     

Rate dependent finite deformation stress-strain behavior of an ethylene methacrylic acid copolymer and an ethylene methacrylic acid butyl acrylate copolymer

The large strain deformation behaviors of an ethylene methacrylic acid (EMAA) copolymer and an ethylene methacrylic acid butyl acrylate (EMAABA) copolymer are evaluated and compared in compression over nearly eight orders of magnitude in strain rate, from 10⁻⁴ to almost 10⁴/s. Transition regimes are quantified using dynamic mechanical analysis. The stress-strain behavior of these copolymers exhibits a relatively stiff initial behavior followed by a rollover to a more compliant response. The low strain modulus, the rollover stress and the large deformation stress-strain behavior are strongly dependent on strain rate. The proximity of the material glass transition to the room temperature test conditions results in a substantial change in the nature of the rate sensitivity of the stress-strain behavior as one moves over the range of strain rates. The mechanical behavior of the EMAA is contrasted to that of a corresponding EMAABA terpolymer and to its sodium-neutralized counterpart (EMAABA_Na). The nature of the rate sensitivity of the room temperature stress-strain behavior of EMAA transitions from a behavior near the glassy end of the leathery regime at low rates to a near glassy behavior at high rates. The butyl acrylate content in the EMAABA lowers the glass transition temperature and leads to a more compliant mechanical behavior (reduced initial stiffness, reduced rollover stress, reduced post-rollover stress level) at room temperature. The EMAABA behavior transitions from a rubbery-like behavior at the lowest rates to a leathery-like behavior at the highest rates. Upon sodium neutralization, the overall stiffness and flow stress levels are enhanced likely due to the presence of the ionic aggregates; the glass transition of EMAABA_Na is broadened in comparison to the EMAABA, giving a rate dependent room temperature behavior that transitions through the leathery regime with increasing strain rate. A constitutive model that separately accounts for the distinct deformation resistances of the crystalline domains and the amorphous domains is able to capture the changes in rate dependent deformation behavior of the EMAA copolymers studied herein. The crystalline domains provide resistance to flow across a wide window in rate and temperature whereas the amorphous domains provide increasing resistance as the strain rate is increased and the material effectively transitions through the glass transition regime, providing a mechanism for changing rate sensitivity.     

Bubble breakage phenomena,phase holdups and mass transfer in three-phase fluidized beds with floating bubble breakers

The individual phase holdups and mass transfer characteristics in three-phase fluidized beds with different floating bubble breakers have been determined in a 2.0 m high Plexiglas column of inner diameter 0.142 m. The bubble breaking phenomena by the breakers have been studied via a photographic method in a two-dimensional Plexiglas column. The volumetric mass transfer coefficient k_La in three-phase fluidized beds with hexagonal-shaped breakers is up to 40% greater than that in beds without floating bubble breakers. The bed porosity ε_L + ε_g, gas-phase holdup ε_g, and volumetric mass transfer coefficient k_La increase with an increase in the volume ratio of floating bubble breakers to solid particles, V_f/V_s, up to around 0.15, and thereafter decrease with V_f/V_s in three-phase fluidized beds with floating bubble breakers. Also, k_La increases with increasing breaker density, projected area and contact angle between the floating bubble breakers and the water. The volumetric mass transfer coefficients in terms of the Sherwood number in three-phase fluidized beds with the various floating bubble breakers have been correlated with the volume ratio of floating bubble breakers to solid particles, the particle Reynolds number based on the local isotropic turbulence theory and the modified Weber number.     

Effects of soft-segment prepolymer functionality on structure-property relations in RIM copolyurethanes

Segmented copolyurethanes comprising 40-60% by weight of polyurethane hard segments (HS) and polyether soft-segment (SS) with different functionalities (SS-f_n), have been formed by reaction injection moulding (RIM). The HS were formed from 4,4′ diphenylmethane diisocyanate (MDI) reacted with ethane diol (ED). The three SS-prepolymers used were all hydroxyl-functionalised poly(oxypropylene-b-oxyethylene)s with different nominal functionalities (f_n) of 2, 3 and 4 but with a constant molar mass per functional group of ∼2000 g mol⁻¹. RIM materials were characterised using differential scanning calorimetry, dynamic mechanical thermal analysis, tensile stress-strain and single-edge notch fracture studies. Predictions using a statistical model of the RIM-copolymerisation showed that increasing SS-f_n lead to more rapid development of copolymer molar mass with isocyanate conversion. Experimentally, the RIM-PU exhibited a wide range of mechanical behaviour resulting from differences in molecular and morphological structures. Increasing SS-f_n produced materials with improved mould release behaviour and fracture resistance. However, increasing SS-f_n also reduced the degree of phase separation developed in the copolyurethanes, resulting in increased modulus-temperature dependence and poorer tensile properties.     

Finite strain behavior of poly(ethylene terephthalate) (PET) and poly(ethylene terephthalate)-glycol (PETG)

Uniaxial and plane strain compression experiments are conducted on amorphous poly(ethylene terephthalate) (PET) and poly(ethylene terephthalate)-glycol (PETG) over a wide range of temperatures (25-110 °C) and strain rates (.005-1.0 s⁻¹). The stress-strain behavior of each material is presented and the results for the two materials are found to be remarkably similar over the investigated range of rates, temperatures, and strain levels. Below the glass transition temperature (θ_g=80 °C), the materials exhibit a distinct yield stress, followed by strain softening then moderate strain hardening at moderate strain levels and dramatic strain hardening at large strains. Above the glass transition temperature, the stress-strain curves exhibit the classic trends of a rubbery material during loading, albeit with a strong temperature and time dependence. Instead of a distinct yield stress, the curve transitions gradually, or rolls over, to flow. As in the sub-θ_g range, this is followed by moderate strain hardening and stiffening, and subsequent dramatic hardening. The exhibition of dramatic hardening in PETG, a copolymer of PET which does not undergo strain-induced crystallization, indicates that crystallization may not be the source of the dramatic hardening and stiffening in PET and, instead molecular orientation is the primary hardening and stiffening mechanism in both PET and PETG. Indeed, it is only in cases of deformation which result in highly uniaxial network orientation that the stress-strain behavior of PET differs significantly from that of PETG, suggesting the influence of a meso-ordered structure or crystallization in these instances. During unloading, PETG exhibits extensive elastic recovery, whereas PET exhibits relatively little recovery, suggesting that crystallization occurs (or continues to develop) after active loading ceases and unloading has commenced, locking in much of the deformation in PET.     

Dynamic mechanical properties of polyurethane elastomers using a nonmetallic Hopkinson bar

A modified split Hopkinson-bar apparatus, in which the striker and input/output bars are made of polycarbonate instead of metal, was used to study three typical examples of a high-density flexible polyurethane elastomer (PORON) in sheet form. This variation of the device reduces a mismatch in impedance between the input/output bars and the specimen, thus allowing the stress in the specimen to reach a uniform state before significant engineering strain is induced. Dynamic compressive stress-strain curves were obtained from the measured incident, transmitted, and reflected waves. This article presents the behavior of these foams as a function of strain rate; for PORON 4701-05-20125-1637 under strain rates of 2.67 × 10⁻³ s⁻¹ to 4500 s⁻¹, the stress-strain response can be described by a function comprising a rate-dependent modulus and a strain-dependent factor, while for PORON 4701-01-30125-1604 and 4701-12-30062-1604, only loading at high strain rates yields similar characteristics. Empirical equations were derived to characterize these mechanical properties; in addition, characteristics relating to energy-absorption capability as well as deformation under approximately constant stress were also studied. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 619–631, 1997     

High strain rate compressive response of the Cf/SiC composite

Carbon fiber reinforced ceramic owns the properties of lightweight, high fracture toughness, excellent shock resistance, and thus overcomes ceramic's brittleness. The researches on the advanced structure of astronautics, marine have exclusively evaluated the quasi-static mechanical response of carbon fiber reinforced ceramics, while few investigations are available in the open literature regarding elastodynamics. This paper reports the dynamic compressive responses of a carbon fiber reinforced silicon carbide (C_f/SiC) composite (CFCMC) tested by the material test system 801 machine (MTS) and the split Hopkinson pressure bar (SHPB). These tests were to determine the rate dependent compression response and high strain rate failure mechanism of the C_f/SiC composite in in-plane and out-plane directions. The in-plane compressive strain rates are from 0.001 to 2200?s^?1, and that of the out-plane direction are from 0.001 to 2400?s^?1. The compressive stress-strain curves show the C_f/SiC composite has a property of strain rate sensitivity in both directions while under high strain rate loadings. Its compressive stiffness, compressive stress, and corresponding strain are also strain rate sensitive. The compressive damage morphologies after high strain rate impacting show different failure modes for each loading direction. This study provides knowledge about elastodynamics of fiber-reinforced ceramics and extends their design criterion with a reliable evaluation while applying in the scenario of loading high strain rate.     

Large deformation rate-dependent stress-strain behavior of polyurea and polyurethanes

The thermoplastic elastomer polyurethane and the elastomeric thermoset polyurea are finding new applications in increasing the survivability of structures under impact loading, including those encountered in blast and ballistic events. However, the mechanical behavior of polyurea and polyurethane materials under these high rate conditions is relatively unknown. Here, the rate-dependent stress-strain behavior of one polyurea and three representative polyurethane materials is studied by dynamic mechanical analysis, quasi-static compression testing and split Hopkinson pressure bar (SHPB) testing. The polyurethane chemistries were chosen to probe the influence of the hard segment content on the mechanical behavior, where the volume fraction and the amorphous vs. crystalline structure of the hard segment domains were varied. The large strain stress-strain behavior of polyurea and polyurethane shows strong hysteresis, cyclic softening, and strong rate-dependence. The polyurethane with a non-crystalline well-dispersed hard segment morphology did not exhibit cyclic softening. The materials are observed to transition from a rubbery-like behavior under low strain rate (∼10⁻³-10⁰ s⁻¹) loading conditions to either a leathery or glassy-like behavior under high strain rate (∼10⁻³ s⁻¹) loading conditions.     

Rheology and colloidal structure of silver nanoparticles dispersed in diethylene glycol

Rheological behavior of agglomerated silver nanoparticles (~ 40 nm) suspended in diethylene glycol over a wide range of volumetric solids concentrations (? = 0.11–4.38%) was studied. The nanoparticle suspensions generally exhibited a yield pseudoplastic behavior. Bingham plastic, Herschel–Bulkley and Casson models were used to evaluate the shear stress-shear rate dependency. Analyzing the effect of silver concentrations on the yield stress and viscosity of the suspensions followed an exponential form, revealing an increase in the degree of interparticle interactions with increasing solid concentrations. Fractal dimension (D_f) was estimated from the suspension yield stress and ? dependence, and was determined as D_f = 1.51–1.62 for the flocculated nanoparticle suspensions. This suggested that the suspension structure was probably dominated by the diffusion-limited cluster–cluster aggregation (DLCA) due mostly to the strong attractions involved in the interparticle potentials. Maximum solids concentration of the suspensions was determined to be ?_m = 11%.     

Non-linear, rate-dependent strain-hardening behavior of polymer glasses

This study is concerned with the finite, large strain deformation behavior of polymeric glasses. True stress-strain curves in uniaxial compression obtained for five different polymeric glasses: polycarbonate, polystyrene, poly(2,6-dimethyl-1,4-phenylene oxide), and linear and cross-linked poly(methylmethacrylate), revealed a strain-hardening response during plastic deformation that is strain-rate dependent and deviates from neo-Hookean behavior. An empirical modification of the so-called compressible Leonov model by a strain dependent activation volume is suggested, which describes the strain-rate dependent large strain behavior of these glassy polymers in good agreement with experimental data.     

Abnormal Curie temperature behavior and enhanced strain property by controlling substitution site of Ce ions in BaTiO3 ceramics

Dopants have a great effect on the phase transition behavior and the properties of the ferroelectrics. Here we report an abnormal Curie temperature (T_c) behavior and enhanced strain property by controlling the doping site of Ce ions in the BaTiO₃ ceramics. The Ce doped A-site and B-site BaTiO₃ ceramics (BT-xCe-A and BT-xCe-B, x=2, 4, 6, 8 mol%) were prepared by a conventional solid state reaction method through a different sintering temperature. The Raman test and the XPS results give evidence that Ce is successfully incorporated into Ba-site as Ce³⁺ in the BT-xCe-A samples, and into Ti-site as Ce⁴⁺ in the BT-xCe-B samples. Different doping sites have distinct phase transition behavior. Compared with the BT-xCe-A ceramics, the BT-xCe-B ceramics show higher T_c, and the T_c show abnormal increasing behavior with the increase of the Ce content. In the Ce doped BaTiO₃ system, this phenomenon has not been reported before. The origin of the higher T_c and its increasing behavior is discussed from the viewpoint of the larger local strain field generated by the Ce⁴⁺ ions entering into B-site. Besides, the BT-xCe-B ceramics show a stronger diffuse phase transition behavior. The reason is considered that the Ce substituting B-site leads to a multiphase coexistence, which induces more frustration states for the polarization according to the random defect field theory. Due to such distinct phase transition behavior, the BT-xCe-B ceramics show the enhanced maximum polarization (P_max) and enhanced strain properties compared with the BT-xCe-A ceramics. This work may provide a promising way to design high performance materials by controlling the substituting site of the dopant in other lead-free systems.     

Cyclic viscoplasticity of solid polymers: The effects of strain rate and amplitude of deformation

Observations are reported on polypropylene random copolymer in uniaxial cyclic tensile tests with various strain rates (ranging from 1.7 × 10⁻⁴ to 8.3 × 10⁻³ s⁻¹). Each cycle of deformation involves tension up to the maximal strain ε_max (from 0.05 to 0.20) and retraction down to the zero stress. The study focuses on deformation programs with 10-50 cycles in each test. A constitutive model is derived for the viscoplastic behavior of a solid polymer at three-dimensional cyclic deformations with small strains. Material constants in the stress-strain relations are found by fitting the experimental data. Good agreement is demonstrated between the observations and the results of numerical simulation.     

The effect of strain rate on the stress–strain curve of oriented polymers. I. Presentation of experimental results

The stress-strain curves of viscose, nylon 6.6, poly(ethylene terephthalate), polyacrylonitrile, and polypropylene have been determined at a large number of different strain rates between 10^?4 and 330 sec.^?1. The shape of these stress-strain curves and its change with strain rate is shown to depend upon whether the material is tested above or below its glass temperature. The stress-strain curves of materials tested below their glass temperature consists of an initial straight portion followed by a yield point at a few per cent strain. The breaking strain is only slightly affected by strain rate, and the energy to rupture increases with increasing rate. For materials tested above their glass temperature the initial portion of the stress-strain curves in nonlinear, and the yield strain is much higher than for the other materials. There is a small range of strain rate, in which the breaking strain falls sharply to the yield strain with increasing rate, and the energy to rupture also decreases. Outside this range the energy to rupture increases with increasing rate.     

Thermal conductivity and thermal expansivity of in situ composites of a liquid crystalline polymer and polycarbonate

The thermal conductivity and thermal expansivity of extruded blends of a liquid crystalline polymer (LCP) and polycarbonate (PC) with volume fraction (V_f) of LCP between 0.09 and 0.8 have been measured as functions of draw ratios λ ranging from 1.3 to 15. At V_f < 0.3, the LCP domains are dispersed in a PC matrix and the aspect ratio of the domains increases with increasing λ. At V_f > 0.55, phase inversion has occurred and the LCP becomes the continuous phase. The axial thermal conductivity K_∥ increases while the axial expansivity α_∥ decreases sharply with increasing λ, as a result of the higher aspect ratio of the LCP fibrils and the improved molecular orientation within the fibrils. Since the transverse thermal conductivity and expansivity are little affected by drawing, the blends exhibit strong anisotropy in the thermal conduction and expansion behavior at high λ. At V_f < 0.3, the behavior of K_∥ is reasonably modeled by the Halpin-Tsai equation for short fiber composites. At high draw ratio (λ = 15), all the blends behave like unidirectional continuous fiber composites, so K_∥ and α_∥ follow the rule of mixtures and the Schapery equation, respectively.     

A predictive model for the mechanical behavior of particulate composites. Part II: Comparison of model predictions to literature data

The energy balance model presented in Part I is applied here to data taken from the literature. Care was taken to choose well-characterized systems to give a true test of the model's predictive character, rather than its ability to curve-fit the data. The effects of concentration, particle size, strain rate, and temperature on the stress-strain and dilatation curves are examined. Good agreement is seen for each of these variables. This predictive approach will allow the design of particulate composites with given mechanical behavior, and analysis of material behavior in various geometries and conditions.