Influence of temperature and strain rate on the mechanical behavior of three amorphous polymers: Characterization and modeling of the compressive yield stress

Uniaxial compression stress–strain tests were carried out on three commercial amorphous polymers: polycarbonate (PC), polymethylmethacrylate (PMMA), and polyamideimide (PAI). The experiments were conducted under a wide range of temperatures (−40 °C to 180 °C) and strain rates (0.0001 s⁻¹ up to 5000 s⁻¹). A modified split-Hopkinson pressure bar was used for high strain rate tests. Temperature and strain rate greatly influence the mechanical response of the three polymers. In particular, the yield stress is found to increase with decreasing temperature and with increasing strain rate. The experimental data for the compressive yield stress were modeled for a wide range of strain rates and temperatures according to a new formulation of the cooperative model based on a strain rate/temperature superposition principle. The modeling results of the cooperative model provide evidence on the secondary transition by linking the yield behavior to the energy associated to the β mechanical loss peak. The effect of hydrostatic pressure is also addressed from a modeling perspective.     

Integral-based constitutive equation for rubber at high strain rates

High-speed experiments were conducted to characterize the deformation and failure of Styrene Butadiene Rubber at impact rates. Dynamic tensile stress–strain curves of uniaxial strip specimens and force–extension curves of thin sheets were obtained from a Charpy tensile impact apparatus. Results from the uniaxial tension tests indicated that although the rubber became stiffer with increasing strain rates, the stress–strain curves remained virtually the same above 280 s⁻¹. Above this critical strain rate, strength, fracture strain and toughness decreased with increasing strain rates. When strain rates were below 180 s⁻¹, the initial modulus, tensile strength and breaking extension increased as the strain rate increased. Between strain rates of 180 and 280 s⁻¹, the initial modulus and tensile strength increased with increasing strain rates but the extension at break decreased with increasing strain rates. A hyper-viscoelastic constitutive relation of integral form was used to describe the rate-dependent material behavior of the rubber. Two characteristic relaxation times, 5 ms and 0.25 ms, were needed to fit the proposed constitutive equation to the data. The proposed constitutive equation was implemented in ABAQUS Explicit via a user-defined subroutine and used to predict the dynamic response of the rubber sheets in the experiments. Numerical predictions for the transient deformation and failure of the rubber sheet were within 10% of experimental results.     

Spatiotemporal variations of PM2.5 and PM10 concentrations between 31 Chinese cities and their relationships with SO2, NO2, CO and O3

The variations of mass concentrations of PM_2.5, PM₁₀, SO₂, NO₂, CO, and O₃ in 31 Chinese provincial capital cities were analyzed based on data from 286 monitoring sites obtained between March 22, 2013 and March 31, 2014. By comparing the pollutant concentrations over this length of time, the characteristics of the monthly variations of mass concentrations of air pollutants were determined. We used the Pearson correlation coefficient to establish the relationship between PM_2.5, PM₁₀, and the gas pollutants. The results revealed significant differences in the concentration levels of air pollutants and in the variations between the different cities. The Pearson correlation coefficients between PMs and NO₂ and SO₂ were either high or moderate (PM_2.5 with NO₂: r = 0.256–0.688, mean r = 0.498; PM₁₀ with NO₂: r = 0.169–0.713, mean r = 0.493; PM_2.5 with SO₂: r = 0.232–0.693, mean r = 0.449; PM₁₀ with SO₂: r = 0.131–0.669, mean r = 0.403). The correlation between PMs and CO was diverse (PM_2.5: r = 0.156–0.721, mean r = 0.437; PM₁₀: r = 0.06–0.67, mean r = 0.380). The correlation between PMs and O₃ was either weak or uncorrelated (PM_2.5: r = −0.35 to 0.089, mean r = −0.164; PM₁₀: r = −0.279 to 0.078, mean r = −0.127), except in Haikou (PM_2.5: r = 0.500; PM₁₀: r = 0.509).     

The mechanisms governing the activation of dislocation sources in aluminum at different strain rates

This article examines the time to activate Frank–Read sources in response to macroscopic strain rates ranging from 10¹ s⁻¹ to 10¹⁰ s⁻¹ in aluminium under athermal conditions. We develop analytical models of the bowing of a pinned dislocation segment as well as numerical simulations of three dimensional dislocation dynamics. We find that the strain rate has a direct influence on both the activation time and the source strength of Frank–Read sources at strain rates up to 10⁶ s⁻¹, and the source strength increases in almost direct proportion to the strain rate. This contributes to the increase in the yield stress of materials at these strain rates. Above 10⁶ s⁻¹, the speed of the bowing segments reaches values that exceed the domain of validity of the linear viscous drag law, and the drag law is modified to account for inertial effects on the motion of the dislocation. As a result the activation times of Frank–Read sources reach a finite limit at strain rates greater than 10⁸ s⁻¹, suggesting that Frank–Read sources are unable to operate before homogeneous nucleation relaxes elastic stresses at the higher strain rates of shock loading. Elastodynamic calculations are carried out to compare the contributions of Frank–Read sources and homogeneous nucleation of dislocations to plastic relaxation. We find that at strain rates of 5×10⁷ s⁻¹ homogeneous nucleation becomes the dominant generation mechanism.     

Simple constitutive modelling of nonlinear viscoelasticity under general extension

We study the behaviour of a single integral constitutive equation, capable of providing analytic expressions for the viscoelastic stress in extensional flows of a variety of deformation histories and geometries, ranging from uniaxial to equibiaxial. It is based on the use of a stress damping function, with a power-law dependence on the elongation, λ: h(λ) = 1/λⁿ. The parameter n (0 ≤ n ≤ 2) signifies the nonlinear viscoelastic character of the material and, therefore, is an inverse measure of network connectivity strength of the underlying microstructure. This renders the constitutive approach applicable to incompressible polymers of a variable degree of branching, strain hardening and stress thinning behavior. Methods of connecting n with the macromolecular architecture and the alignment strength of the flow are also explored.     

Superiority of PANS compared to LES in predicting a rudimentary landing gear flow with affordable meshes

Results of simulations of the flow around a rudimentary landing gear are presented in the paper. A newly proposed improved Partially-Averaged Navier–Stokes (PANS) method using k − ε − ζ − f turbulence model is used for prediction of the flow. The results are compared with the experimental data but also with the results of two LES simulations performed using the PANS computational grids. PANS simulations predicted the flow in good agreement with the experimental data. LES predicted a non-physical creation of separation over the front wheels that does not exist in the PANS prediction and was not observed in the experimental oil film. PANS simulations showed low sensitivity to the grid refinement. They show clear advantage compared with the LES simulations when the computational grid is inadequate for resolution of the near-wall flow structures.     

Effects of multi-dopants (Zn and Ho) in stabilizing spinel structure for cathode materials in lithium rechargeable batteries—Novel chelated sol–gel synthesis

Multi-doped spinels, namely LiMn₂O₄ and LiZn_xHo_yMn_2−x−yO₄ (x = 0.10–0.18; y = 0.02–0.10), for use as cathode materials for lithium-ion rechargeable batteries were synthesized via sol–gel method, using lauric acid as the chelating agent, to obtain micron-sized particles. The physical properties of the synthesized samples were investigated using differential thermal analysis, Fourier-transform infrared spectroscopy, X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy, energy-dispersive X-ray analysis, and electrochemical methods. XRD showed that LiMn₂O₄ and LiZn_xHo_yMn_2−x−yO₄ have high degrees of crystallinity and good phase purities. The SEM images of LiMn₂O₄ showed an ice-cube morphology with particles of size 1 μm. Charge–discharge studies showed that undoped LiMn₂O₄ delivered the discharge capacity of 124 mA h/g with coulombic efficiency of 95% during the first cycle, whereas doped spinels delivered discharge capacities of 125, 120, and 127 mA h/g in the first cycle with coulombic efficiencies of 96%, 91%, and 91%, respectively.     

Multi-cycle deformation of semicrystalline polymers: Observations and constitutive modeling

Experimental data are reported on isotactic polypropylene in multi-cycle uniaxial tensile tests where a specimen is stretched up to some maximum strain and retracted down to the zero minimum stress, while maximum strains increase with number of cycles. Fading memory of deformation history is observed: when two samples are subjected to loading programs that differ along the first n − 1 cycles only, their stress–strain diagrams coincide starting from the nth cycle. Constitutive equations are developed in cyclic viscoelasticity and viscoplasticity of semicrystalline polymers, and adjustable parameters in the stress–strain relations are found by fitting the experimental data. Results of numerical simulation demonstrate that the model predicts the fading memory effect quantitatively. To confirm that the observed phenomenon is typical of semicrystalline polymers, experimental data are presented in tensile cyclic tests with large strains on low density polyethylene and compressive cyclic tests on poly(oxymethylene).     

Rheological–dynamical analogy: Prediction of damping parameters of hysteresis damper

This research aims to predict the damping parameters of hysteresis damper based on an analytical rheological–dynamical (RDA) visco-elasto-plastic solution of one-dimensional longitudinal continuous vibrations of a bar. A visco-elasto-plastic bar or damper is an energy dissipation device. An attempt is made to estimate quantitatively the influence of material physical parameters of materials on the damping ratio in both the linear visco-elastic analysis and the nonlinear visco-elasto-plastic analysis of damper subjected to external vibration forces. Two types of damping are considered: viscous damping in the case of linear analysis, defined as stiffness and/or mass proportional and, in the case of nonlinear analysis, hysteresis damping caused by inelastic deformations of damper. Owing to the visco-elastic nature of the materials of the damper and the frequency dependence of the viscous damping ratio ξ, it is useful to consider separately the situations arising when ξ is positive (the system is stable) and when it is negative. A negative damping ratio means that the complementary solution of the response would not die away (the system is unstable because of factor e^{ξ · ω · t}). In the case of nonlinear analysis, the force–displacement relation is nonlinear, so it is very difficult to predict the actual damping and stiffness coefficients, even if the force–displacement characteristic is simply perfect elasto-plastic. Using the RDA method, which takes into account the rate of release of visco-elasto-plastic energy of the dissipation devices; nonlinear behaviors are linearized, enabling to obtain the equivalent damping and stiffness coefficients and the effective period for the damper.     

Discrete element method simulations of Mars Exploration Rover wheel performance

Mars Exploration Rovers (MERs) experienced mobility problems during traverses. Three-dimensional discrete element method (DEM) simulations of MER wheel mobility tests for wheel slips of i = 0, 0.1, 0.3, 0.5, 0.7, 0.9, and 0.99 were done to examine high wheel slip mobility to improve the ARTEMIS MER traverse planning tool. Simulations of wheel drawbar pull and sinkage MIT data for i ⩽ 0.5 were used to determine DEM particle packing density (0.62) and contact friction (0.8) to represent the simulant used in mobility tests. The DEM simulations are in good agreement with MIT data for i = 0.5 and 0.7, with reasonable but less agreement at lower wheel slip. Three mobility stages include low slip (i < 0.3) controlled by soil strength, intermediate slip (i ∼ 0.3–0.6) controlled by residual soil strength, and high slip (i > 0.6) controlled by residual soil strength and wheel sinkage depth. Equilibrium sinkage occurred for i < 0.9, but continuously increased for i = 0.99. Improved DEM simulation accuracy of low-slip mobility can be achieved using polyhedral particles, rather than tri-sphere particles, to represent soil. The DEM simulations of MER wheel mobility can improve ARTEMIS accuracy.     

Emission of organic carbon,elemental carbon and water-soluble ions from crop straw burning under flaming and smoldering conditions

Emissions from major agricultural residues were measured using a self-designed combustion system. Emission factors (EFs) of organic carbon (OC), elemental carbon (EC), and water-soluble ions (WSIs) (K⁺, NH₄⁺, Na⁺, Mg²⁺, Ca²⁺, Cl⁻, NO₃⁻, SO₄^2–) in smoke from wheat and rice straw were measured under flaming and smoldering conditions. The OC₁/TC (total carbon) was highest (45.8% flaming, 57.7% smoldering) among carbon fractions. The mean EFs for OC (EF_OC) and EC (EF_EC) were 9.2 ± 3.9 and 2.2 ± 0.7 g/kg for wheat straw and 6.4 ± 1.9 and 1.1 ± 0.3 g/kg for rice straw under flaming conditions, while they were 40.8 ± 5.6 and 5.8 ± 1.0 g/kg and 37.6 ± 6.3 and 5.0 ± 1.4 g/kg under smoldering conditions, respectively. Higher EC ratios were observed in particulate matter (PM) mass under flaming conditions. The OC and EC for the two combustion patterns were significantly correlated (p < 0.01, R = 0.95 for wheat straw; p < 0.01, R = 0.97 for rice straw), and a higher positive correlation between OC₃ and EC was observed under both combustion conditions. WSIs emitted from flaming smoke were dominated by Cl⁻ and K⁺, which contributed 3.4% and 2.4% of the PM mass for rice straw and 2.2% and 1.0% for wheat straw, respectively. The EFs of Cl⁻ and K⁺ were 0.73 ± 0.16 and 0.51 ± 0.14 g/kg for wheat straw and 0.25 ± 0.15 and 0.12 ± 0.05 g/kg for rice straw under flaming conditions, while they were 0.42 ± 0.28 and 0.12 ± 0.06 g/kg and 0.30 ± 0.27 and 0.05 ± 0.03 g/kg under smoldering conditions, respectively. Na⁺, Mg²⁺, and NH₄⁺ were vital components in PM, comprising from 0.8% (smoldering) to 3.1% (flaming) of the mass. Strong correlations of Cl⁻ with K⁺, NH₄⁺, and Na⁺ ions were observed in rice straw and the calculated diagnostic ratios of OC/EC, K⁺/Na⁺ and Cl⁻/Na⁺ could be useful to distinguishing crop straw burning from other sources of atmospheric pollution.     

Revegetated herbaceous plant species on a compacted skid road

This study intended to determine the plant species on a skid road subjected to soil compaction due to timber skidding in a pure sessile oak (Quercus petrea L.) forest. Our previous studies show that ground based skidding destroyed the soil and ecosystem. The timber skidding limits recovery and growth of plant cover on skid roads. However, some herbaceous plant species show healthy habitat, and they can revegetate and survive after the extreme degradation in study area.The composition and cover-abundance scales of these plant species investigated in a 100 m × 3 m transect. Twelve plant species belongs to 10 plant family were determined. Compositae and Liliaceae were the most abundant families. Daphne pontica L., Smilax aspera L., Trachystemon orientalis (L.) G. Don, Carex distachya Desf. var. distachya Desf. have the highest cover-abundance scale among all of determined species on compacted skid road.     

Real-time measurements of PM2.5, PM10–2.5, and BC in an urban street canyon

A continuous dichotomous beta gauge monitor was used to characterize the hourly content of PM_2.5, PM_10–2.5, and Black Carbon (BC) over a 12-month period in an urban street canyon of Hong Kong. Hourly vehicle counts for nine vehicle classes and meteorological data were also recorded. The average weekly cycles of PM_2.5, PM_10–2.5, and BC suggested that all species are related to traffic, with high concentrations on workdays and low concentrations over the weekends. PM_2.5 exhibited two comparable concentrations at 10:00–11:00 (63.4 μg/m³) and 17:00–18:00 (65.0 μg/m³) local time (LT) during workdays, corresponding to the hours when the numbers of diesel-fueled and gasoline-fueled vehicles were at their maximum levels: 3179 and 2907 h⁻¹, respectively. BC is emitted mainly by diesel-fueled vehicles and this showed the highest concentration (31.2 μg/m³) during the midday period (10:00–11:00 LT) on workdays. A poor correlation was found between PM_2.5 concentration and wind speed (R = 0.51, P-value > 0.001). In contrast, the concentration of PM_10–2.5 was found to depend upon wind speed and it increased with obvious statistical significance as wind speed increased (R = 0.98, P-value < 0.0001).     

Experimental quantification of the plastic blunting process for stage II fatigue crack growth in one-phase metallic materials

The plastic blunting process during stage II fatigue crack growth was studied in pure polycrystalline Ni to investigate effects of strain localization and inelastic behavior on the kinematics of crack advance. Correlations were obtained between strain fields ahead of a fatigue crack, crack advance per cycle and crack growth kinetics. Strain fields were quantified using a combination of in situ loading experiments, scanning electron microscopy and digital image correlation for 8 < ΔK < 20 MPa m^1/2 and a fixed load ratio of 0.1. Results indicate that strain localized along a dominant deformation band, which was usually crystallographic and carried mostly pure shear for large loads and was of mixed character for lower loads. Instances of double deformation bands were observed, with bands acting either in a simultaneous or alternating fashion. It was found that the area integral of the opening strain for values larger than a given threshold, an “integrated” strain, had a power-law relationship with ΔK, with the exponent approximately equal to the Paris exponent (m). Therefore, the crack growth rate was proportional to the integrated strain. An analysis based on this correlation and the presence of dominant shear bands indicated that the integrated strain is related to the accumulated displacement in the band. This, in turn, is proportional to the product of the cyclic plastic zone radius and the average shear strain ahead of the tip, which represents a basic length scale for plastic blunting. Assumptions on the load dependence of these quantities, based on their observed spatial variation, allowed estimating $m=2\left(1+\frac{1}{1+n^{\prime }}\right)$, where n′ is the cyclic hardening exponent (0 < n′ < 1). This gives 3 < m < 4, which accounts for about 50% of the observed values of m between 1.5 and 6 for a wide variety of metallic materials.     

Mechanics of the rate-dependent elastic–plastic deformation of glassy polymers from low to high strain rates

A combined experimental and analytical investigation has been performed to understand the mechanical behavior of two amorphous polymers—polycarbonate and poly(methyl methacrylate)—at strain rates ranging from 10⁻⁴ to 10⁴ s⁻¹. This range in strain rates was achieved in uniaxial tension and compression tests using a dynamic mechanical analyzer (DMA), a servo-hydraulic testing machine, and an aluminum split-Hopkinson pressure bar. DMA tension tests were used to characterize the viscoelastic behavior of these materials, with focus on the rate-dependent shift of material transition temperatures. Uniaxial compression tests on the servo-hydraulic machine (10⁻⁴ to 1 s⁻¹) and the split-Hopkinson pressure bar (10³ to 10⁴ s⁻¹) were used to characterize the rate-dependent yield and post-yield behavior. Both materials were observed to exhibit increased rate sensitivity of yield under the same strain rate/temperature conditions as the β-transition of the viscoelastic behavior. A physically based constitutive model for large strain deformation of thermoplastics was then extended to encompass high-rate conditions. The model accounts for the contributions of different molecular motions which become operational and important in different frequency regimes. The new features enable the model to not only capture the transition in the yield behavior, but also accurately predict the post-yield, large strain behavior over a wide range of temperatures and strain rates.     

Thermo-mechanical response of nylon 101 under uniaxial and multi-axial loadings: Part I,Experimental results over wide ranges of temperatures and strain rates

A comprehensive study of the thermo-mechanical response of a thermoplastic polymer, nylon 101 is presented. Quasi-static and dynamic compression uniaxial and multi-axial experiments (stress states) were performed at a wide range of strain rates (10⁻⁵ to 5000 s⁻¹) and temperatures (−60 to 177 °C or −76 to 350 °F). The material is found to be non-linearly dependent on strain rate and temperature. The change in volume after plastic deformation is investigated and is found to be negligibly small. The relaxation and creep responses at room temperature are found to be dependent on strain rate and the stress–strain level at which these phenomena are initiated. Total deformation is decomposed into visco-elastic and visco-plastic components; these components have been determined at different levels of deformation. Results from non-proportional uniaxial to biaxial compression, and torsion experiments, are also reported for three different strain rates at room temperature. It is shown that nylon 101 has a response dependent on the hydrostatic pressure.     

Influence of temperature on a carbon–fibre epoxy composite subjected to static and fatigue loading under mode-I delamination

In this paper, interlaminar crack initiation and propagation under mode-I with static and fatigue loading of a composite material are experimentally assessed for different test temperatures. The material under study is made of a 3501-6 epoxy matrix reinforced with AS4 unidirectional carbon fibres, with a symmetric laminate configuration [0°]_16/S. In the experimental programme, DCB specimens were tested under static and fatigue loading. Based on the results obtained from static tests, fatigue tests were programmed to analyse the mode-I fatigue behaviour, so the necessary number of cycles was calculated for initiation and propagation of the crack at the different temperatures. G–N curves were determined under fatigue loading, N being the number of cycles at which delamination begins for a given energy release rate. G_ICmax–a, a–N and da/dN–a curves were also determined for different G_cr rates (90%, 85%, 75%, etc.) and different test temperatures: 90 °C, 50 °C, 20 °C, 0 °C, ?30 °C and ?60 °C.     

Periodic group crack problems in an infinite plate

This paper investigates periodic group crack problems in an infinite plate. The periodic group crack is composed of infinite groups with numbering from j = −∞, …, −2, −1, 0, 1, 2, …, to j = ∞, and the groups are placed periodically. The same loading condition and the same geometry are assumed for cracks in all groups. A singular integral equation is used to solve the problems. The singular integral equation is formulated on cracks of the 0th group (or the central group) with the collection of influences from the infinite groups. The influences of many neighboring groups to the central group are evaluated exactly. Meantime, the influences of many remote groups to the central group can be summed up into one term approximately. The stress intensity factors at crack tips can be evaluated from the solution of the singular integral equation. It is found from some sample problems that the obtained results are very accurate. Finally, several numerical examples are presented and interaction among the group cracks is addressed.     

Differences in tractor performance parameters between single-wheel 4WD and dual-wheel 2WD driving systems

Vertical wheel load and tire pressure are both easily managed parameters which play a significant role in tillage operations for limiting slip which involves energy loss. This aspect to a great extent affects the fuel consumption and the time required for soil tillage. The main focus of this experiment was to determine the effect on the wheels’ slip, the fuel consumption and the field performance of a tractor running in a single-wheel 4WD driving system and in a dual-wheel 2WD driving system, due to the variations in air pressure of the tires as well as in the ballast mass. With no additional mass, the lowest fuel consumption was reached by a tractor with the least air pressure in the tires and running in a dual-wheel 2WD driving system. It was determined that for a stubble cultivation with a medium-power (82.3 kW) tractor running in a dual-wheel 2WD driving system, the hourly fuel consumption was by 1.15 L h⁻¹ (or 7.3%), the fuel consumption per hectare by 0.35 L ha⁻¹ (or 7.9%) and the field performance by 0.05 ha h⁻¹ (or 1.25%) lower compared to a single-wheel 4WD driving system, when driving wheels’ slip for both modes was the same, i.e., at 8–12%.     

Irreversible thermodynamics of triple junctions during the intergranular void motion under the electromigration forces

A rigorous reformulation of internal entropy production and the rate of entropy flow is developed for multi-component systems consisting of heterophases, interfaces and/or surfaces. The result is a well-posed moving boundary value problem describing the dynamics of curved interfaces and surfaces associated with voids and/or cracks that are intersected by grain boundaries. Extensive computer simulations are performed for void configuration evolution during intergranular motion. In particular we simulate evolution resulting from the action of capillary and electromigration forces in thin film metallic interconnects having a “bamboo” structure, characterized by grain boundaries aligned perpendicular to the free surface of the metallic film interconnects. Analysis of experimental data utilizing previously derived mean time to failure formulas gives consistent values for interface diffusion coefficients and enthalpies of voids. 3.0 × 10⁻⁶ exp(−0.62 eV/kT) m² s⁻¹ is the value obtained for voids that form in the interior of the aluminum interconnects without surface contamination. 6.5 × 10⁻⁶ exp(−0.84 eV/kT) m² s⁻¹ is obtained for those voids that nucleate either at triple junctions or at the grain boundary-technical surface intersections, where the chemical impurities may act as trap centers for hopping vacancies.