Stress-strain behavior of a polyurea and a polyurethane from low to high strain rates

The large deformation stress-strain behavior of thermoplastic-elastomeric polyurethanes and elastomeric-thermoset polyureas is strongly dependent on strain rate. Their mechanical behavior at very high strain rates is of particular interest due to their role as a protective coating on structures to enhance structural survivability during high rate loading events. Here we report on the uniaxial compression stress-strain behavior of a representative polyurea and a representative polyurethane over a wide range in strain rates, from 0.001 s⁻¹ to 10,000 s⁻¹, successively marching through each order of magnitude in strain rate using equipment relevant for testing at each particular rate. These results are further analyzed in association with recently reported compressive data on the same materials by Yi et al. [Polymer 2006;47(1):319-29] and intermediate rate tensile data on the same polyurea by Roland et al. [Polymer 2007;48(2):574-8]. The polyurea tested is seen to undergo transition from a rubbery-regime behavior at low rates to a leathery-regime behavior at the highest rates, consistent with the earlier compression study as well as the recent tension study; the polyurethane tested is observed to undergo transition from a rubbery-regime behavior at the low rates to a glassy behavior at the highest rates. The uniaxial compression data for the polyurea are found to be fully consistent with the recently reported uniaxial tension data over the range of rates studied, demonstrating the consistency and complementary aspects of testing at high rates in both compression and tension.     

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.     

Creep behavior of TiCxN1−x-CoTi cermets synthesized by mechanically induced self-sustaining reaction

The plastic flow of TiC_xN_1−x-CoTi cermets has been investigated by uniaxial compression tests carried out in argon atmosphere at temperatures between 1100 and 1200 °C. Two different cermets, with 5 wt.% W or WC content as sintering additives, have been explored to assess the influence of the sintering additives on creep. The microstructural observations of deformed samples and the mechanical results indicate that the hard phase (ceramic grains) controls the plastic deformation. The stress exponent changes from 1 to 2 with increasing strain rate, suggesting a transition in the deformation mechanism from diffusional creep to grain boundary sliding; both with similar activation energy values of about 400 kJ/mol. This value of activation energy agrees with C diffusion in the carbonitride grains as the strain rate controlling mechanism.     

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.     

Evolution of the structure and mechanical behaviour of a carbon foam at very high temperatures

Mechanical behaviour of a low density carbon/carbon composite at very high temperature is studied in relation with its microstructure. This composite is a syntactic foam made of carbon microbeads with a binder and voids. The resulting geometrical density is 0.3 g cm⁻³. Compressive tests from room temperature up to 3100 °C with a very high heating rate (180 °C s⁻¹) have been conducted. Intermediate temperature tests have also been performed and show an obvious modification of mechanical behaviour from around 2000 °C. This result is related to a sudden modification of structure and texture of the carbonaceous matter during the high temperature mechanical test. A strong plastic deformation occurs when the mechanical experiment is performed at 3100 °C whereas the material elastically deforms at room temperature.     

Plastic deformation of polyethylene crystals as a function of crystal thickness and compression rate

Plastic deformation of polyethylene (PE) samples with crystals of various thickness was studied during uniaxial compression with initial compressive strain rates of 5.5×10⁻⁵, 1.1×10⁻³ and 5.5×10⁻³ s⁻¹. Samples with a broad range of crystals thickness, from usual 20 up to 170 nm, were obtained by crystallization under high pressure. The samples underwent recoverable compression below the compression ratio of 1.05-1.07. Following yield, plastic flow sets in above a compression ratio of 1.12. At a compression rate of 5.5×10⁻⁵ s⁻¹ the yield stress increases with the increase of crystal thickness up to 40 nm. For crystals thicker than 40 nm the yield stress levels off and remains constant. This experimental dependence was compared with the model developed on the basis of classical crystal plasticity and the monolithic nucleation of screw dislocations from polymer crystals. In that model contrary to the experimental evidence, the yield stress does not saturate with increase of crystal thickness. The activation volumes determined from strain rate jump experiments and from stress relaxation for crystals thicker than 40 nm are nearly constant at a level of 8.1 nm³. This activation length agrees very well with 40 nm for crystal thickness above which the yield stress levels off. It is proposed, as shown in a companion communication, that for PE crystals thicker than 40 nm two other modes of dislocation emission in the form of half loops of edge and screw dislocations begin to govern the strain rate, which no longer depend on lamella thickness.     

The properties of poly(tetrafluoroethylene) (PTFE) in tension

Samples of DuPont 7A and 7C Teflon (PTFE, poly(tetrafluoroethylene)) were tested in tension at strain-rates between 2×10⁻⁴ and 0.1 s⁻¹ and temperatures between −50 and 150 °C. Additionally, using a Hopkinson bar, a temperature series was undertaken in tension between −50 and 23 °C at a strain rate of 800 s⁻¹. To investigate the small-strain response, strain gauges were used to measure axial and transverse strain allowing the Poisson ratio to be calculated. The effect of crystallinity was investigated using 7C material thermally processed to produce more amorphous material. As expected, the tensile mechanical properties of PTFE are significantly affected by strain-rate and temperature, but only to a limited extent by crystallinity. The Poisson ratio at small strains was found to differ in tension (≈0.36) and compression (≈0.46). Failure behavior and microstructure were correlated to temperature induced phase transitions.     

Experimental characterisation and constitutive modelling of RTM-6 resin under impact loading

The response to mechanical loading of the thermosetting resin system RTM-6 has been investigated experimentally as a function of strain rate and a constitutive model has been applied to describe the observed and quantified material behaviour. In order to determine strain rate effects and to draw conclusions about the hydrostatic stress dependency of the material, specimens were tested in compression and tension at strain rates from 10⁻³ to 10⁴ s⁻¹. A Standard screw-driven tensile machine was used for quasi-static testing, with an ‘in house’ hydraulic rig and Hopkinson bars for medium and high strain rates, respectively. At all rates appropriate photography and optical metrology have been used for direct strain measurement, observation of failure and validation of experimental procedures. In order to enable the experimental characterisation of this brittle material at very high rates in tension, a novel pulse shaping technique has been applied. With the help of this device, strain rates of up to 3800 s⁻¹ have been achieved while maintaining homogeneous deformation state until specimen fracture in the gauge section of the tensile specimens. The yield stress and initial modulus increased with increasing strain rate for both compression and tension, while the strain to failure decreased with strain rate in tension. An existing constitutive model, the Goldberg model has been extended in order to take into account the nonlinear strain rate dependence of the elastic modulus. The model has been validated against 3-point impact bending tests of prismatic RTM-6 beams.     

Superplasticity of a multiphase fine-grained Mo-Si-B alloy

Mo-9Si-8B-3Hf alloy consisting of a Mo solid solution and intermetallic phases Mo₃Si and Mo₅SiB₂ was fabricated by hot pressing sintering to yield a fine microstructure with all three phases being in the size range of micrometer. The tensile properties of this alloy were evaluated in vacuum at elevated temperatures. This alloy displayed extensive plasticity or superplasticity at temperatures ranging from 1400 °C to 1560 °C with strain rate of 3 × 10^− 4 s^− 1. The tensile elongation of 410% was measured at 1560 °C. Grain boundary sliding was the main mechanism of plastic deformation for this alloy.     

Measurement of through-plane effective thermal conductivity and contact resistance in PEM fuel cell diffusion media

An experimental study was performed to determine the through-plane thermal conductivity of various gas diffusion layer materials and thermal contact resistance between the gas diffusion layer (GDL) materials and an electrolytic iron surface as a function of compression load and PTFE content at 70 °C. The effective thermal conductivity of commercially available SpectraCarb untreated GDL was found to vary from 0.26 to 0.7 W/(m °C) as the compression load was increased from 0.7 to 13.8 bar. The contact resistance was reduced from 2.4×10⁻⁴ m²°C/W at 0.7 bar to 0.6×10⁻⁴ m²°C/W at 13.8 bar. The PTFE coating seemed to enhance the effective thermal conductivity at low compression loads and degrade effective thermal conductivity at higher compression loads. The presence of microporous layer and PTFE on SolviCore diffusion material reduced the effective thermal conductivity and increased thermal contact resistance as compared with the pure carbon fibers. The effective thermal conductivity was measured to be 0.25 W/(m °C) and 0.52 W/(m °C) at 70 °C, respectively at 0.7 and 13.8 bar for 30%-coated SolviCore GDL with microporous layer. The corresponding thermal contact resistance reduced from 3.6×10⁻⁴ m²°C/W at 0.7 bar to 0.9×10⁻⁴ m²°C/W at 13.8 bar. All GDL materials studied showed non-linear deformation under compression loads. The thermal properties characterized should be useful to help modelers accurately predict the temperature distribution in a fuel cell.     

The properties of poly(tetrafluoroethylene) (PTFE) in compression

Samples of DuPont 7A and 7C Teflon (PTFE, poly(tetrafluoroethylene)) were tested in compression at strain-rates between 10⁻⁴ and 1 s⁻¹ and temperatures between −198 and 200 °C. Additionally, using a Split-Hopkinson pressure bar, a temperature compression series was undertaken between −100 and 150 °C at a strain rate of 3200 s⁻¹. To investigate the small-strain response, strain gauges were used to measure axial and transverse strain allowing the Poisson ratio to be quantified. As expected, the mechanical properties were found to be strongly affected by strain-rate and temperature. Moduli were found by several methods and the trend, with respect to temperature, lends weight to the suggestion that the glass-transition temperature of PTFE is ≈−100 °C. The physical properties of the sintered PTFE were measured and the crystallinities measured by several techniques.     

The large strain compression,tension, and simple shear of polycarbonate

Polymeric materials subjected to large strains undergo an evolution in molecular orientation. The developing orientation and corresponding strengthening are highly dependent on the state of strain. In this paper, we examine and compare the very different stress-strain results of polycarbonate produced from four types of mechanical testing: uniaxial compression, plane strain compression, uniaxial tension, and simple shear. These tests produce different states of orientation within the material and, in the case of simple shear, the principle axes of orientation rotate during the deformation. The ability of the recent constitutive model of Arruda and Boyce (1992) to predict the to predict the observed behavior is evaluated. The model has been incoporated into a finite element code in order to properly simulate the material behavior during the inhomogenous deformations of tension (cold drawing) and simple shear. The material properties of the model are obtained from the uniaxial compression test and the model is then found to be truly predictive of the other states of deformation demonstrating its fully three dimensional capability. The disadvantages of the tensile and simple shear tests for obtaining the data needed to accurately quantify the large strain material behavior of polymers are shown and discussed.     

Influence of sample thickness on fracture behaviour of a polyketone and a polyketone-rubber blend

The influence of sample thickness on the fracture behaviour of an aliphatic polyketone and a blend of this polymer and 10 wt% core-shell rubber was studied. The sample thickness was varied from 0.1 to 8 mm. The skin morphology was studied by SEM. The fracture behaviour was studied on single edge notch specimen at a high strain rate (30 s⁻¹) in the temperature range of −40 to 120 °C. The fracture stress, fracture strain and fracture energies were determined. The temperature development in the notch area was followed with an Infra Red camera. The cavitation of the rubber particles was studied on tensile bars with a laser setup.With decreasing specimen thickness the fracture energies increased strongly and the brittle-ductile transition shifted to lower temperatures this both for the aliphatic polyketone and the polyketone-rubber blend. The deformation in these materials in accompanied with a strong temperature increase in the deformation zone. The addition of rubber particles decreases the sensitivity towards the thickness. However, in very thin samples the cavitation of the rubber particles is more difficult and the rubber toughening effect decreases. The strong thickness effects on the fracture toughness indicate for both the homo polymer and the blend indicate that data from a standard test with 4 mm thick samples are not representative for thin walled applications.     

The effects of thermomechanical history and strain rate on antiplasticization of PVC

Antiplasticization is mechanically characterized by an increase in the polymer stiffness and/or yield strength upon the incorporation of a small amount of a low-molecular weight diluent. It is attributed to hindrance of the local β-relaxation motions of the polymer. Here, we have studied the effects of thermal treatment, plastic deformation, and strain rate on the antiplasticization of the yield stress of a 95 wt% poly(vinyl chloride)/5 wt% dioctyl phthalate (PVC/5 wt% DOP) compound. Two thermal treatments were applied to the materials - cooling to room temperature from above T_g by a quench or by a slow oven-cool anneal. When compressed at low to moderate strain rates, antiplasticization was observed in the annealed (physically aged) PVC/5 wt% DOP but not in the quenched (unaged) PVC/5 wt% DOP. Load-unload-reload compression cycles revealed that antiplasticization can be erased by plastic strain; the anomalously high yield stress of PVC/5 wt% DOP observed in the first load cycle softens to a value lower than that of the neat PVC in subsequent cycles. The results indicate that disordered, high free volume microstructural states, obtained either from thermal quenching or from plastic straining, liberate the beta motions of the PVC molecule which, in turn, erase antiplasticization of the yield stress. Earlier work on the rate-dependence of yield has demonstrated that beta motions must be stress-activated in order to yield neat PVC when deformed at high strain rates (>100/s). Hence, we have characterized the rate-dependence of the antiplasticization of the yield stress by testing the annealed materials in uniaxial compression over a wide range of strain rates (10⁻⁴/s-3000/s). Antiplasticization was observed in PVC/5 wt% DOP in the low strain rate regime where beta motions are free in neat PVC but hindered in PVC/5 wt% DOP; however, the antiplasticization (elevation of yield stress) gradually diminished with increasing strain rate.     

Strain recovery of post-yield compressed semicrystalline poly(butylene terephthalate)

Cubic specimens of a semicrystalline poly(butylene terephthalate) (PBT) have been compressed up to post-yield deformation levels with a fast (3.0 × 10⁻² s⁻¹) and a slow (1.5 × 10⁻⁴ s⁻¹) strain rate at three different temperatures (25 °C, 45 °C, and 100 °C, i.e. below, close and above the glass transition temperature of the material, T_g, respectively). Differently from literature results reported for amorphous polymers, semicrystalline PBT shows that, after a post-yield deformation, recovery occurs also at temperatures higher than T_g, and that an irreversible deformation, ?_irr, is set in the material. The irreversible strain component has been evaluated as the residual deformation after a thermal treatment of 1 h at 180 °C.After unloading, isothermal strain recovery has been monitored for time periods of 1 h at various temperatures. From the obtained data, strain recovery master curves have been constructed by a time-temperature superposition scheme. The features of the recovery process for the various deformation conditions have been analysed. In particular, it appears that specimens deformed below T_g show a lower irreversible component, whereas, when deformed above T_g, they display a higher irreversible deformation and a slower recovery process. Moreover, the effect of deformation rate appears particularly marked for samples deformed above T_g.     

High strain rate mechanical behavior of polyurea

Stress-strain measurements are reported for an elastomeric polyurea in uniaxial tension over a range of strain rates from 0.06 to 573 s⁻¹. The experiments were carried out on a new drop weight test instrument, which provides mechanical data at strain rates up to 1000 s⁻¹, filling the gap between conventional low speed instruments and split Hopkinson bar tests. The tensile data obtained herein are compared with recent high strain rate compression data on the same material [Yi et al. Polymer 2006;47:319-29]. Advantages of the present measurements include a more uniform strain rate and the ability to ensure homogeneous strain.     

Ageing of marine coating in natural and artificial seawater under mechanical stresses

In order to study the effect of a visco-elastic stress (tension and compression mode) onto the performances of a thick marine organic coating, free films and coated panels were immersed in natural seawater and in NaCl 3 wt.% solution at room temperature (20 °C), fixed temperature (45 °C) or under cyclic temperatures. Free films were analysed using uniaxial elongation and Dynamic Mechanical Analysis (DMA) and the degradation of coated samples was investigated using Electrochemical Impedance Spectroscopy (EIS).     

Microstructure transformation and stress-strain behavior of isotactic polypropylene under large plastic deformation

The macroscopic stress-strain behavior of monoclinic polypropylene samples was investigated at 70°C under uniaxial tension and simple shear by means of a special videometric testing system that gives access to the constitutive equation of plastic behavior at constant strain rate up to large deformation. At several levels of plastic strain, the microstructural evolution of the material was characterized by means of X-ray scattering, densitometry and viscoelastic analysis. It appears that the strain hardening is high in tension, whereas it is nearly zero in shear. This behavior is associated with the development of a fiber texture in tension, which differs drastically from the planar crystalline texture developed in shear. Furthermore, it is shown that structural damage takes place as the plastic deformation proceeds in tension, while only little damage is recorded in shear. A viscoplastic model has been developed that specifically tales into account the various slip systems activated in the polypropylene crystallites and the elastic interactions of the lamellae through a self-consistent scheme. Simulations based on this model reproduce correctly the contrasting strain-hardening in tension and in shear and the different crystalline textures induced for these two loading paths.     

Microstructural design and high temperature tensile deformation behaviour of 8 mol% yttria stabilized cubic zirconia (8YCSZ) with SiO2 additions

In the present study, the microstructural evolution and high temperature deformation behaviours of 8 mol% Y₂O₃ stabilized cubic zirconia (8YCSZ) containing up to 10 wt% SiO₂ is investigated. The experimental results show that the SiO₂ doped specimens sintered at 1400 °C contain only the cubic crystalline phase and SiO₂ has the very limited solubility of 0.3 wt% in cubic zirconia. This suggests that only small part of the SiO₂ dissolves in the cubic zirconia and the rest of SiO₂ segregates at grain boundaries and multiple junctions as amorphous (glassy) phase. This glassy phase prevents the grain growth by minimizing grain boundary energy and mobility, which results from solute segregation at the grain boundary and its drag. The deformation of the undoped 8YCSZ is characterized by large strain hardening with limited elongation. This is mainly due to severe grain growth during high temperature deformation. The addition of the SiO₂ results in a decrease in strain hardening and enhanced tensile elongation. These effects have been further improved with the increase of the SiO₂ addition reaching the elongation to failure of 152% for 10 wt% SiO₂ doped specimen in tension at a temperature of 1400 °C and strain rate of 1.3 × 10⁻⁴ s⁻¹. The decreased strain hardening and increased ductility in the SiO₂ doped specimens are due to the segregation of amorphous glassy phase to the grain boundaries, thus hindering grain growth and facilitating grain boundary sliding, which is the primary mechanism of deformation in fine grained materials at high temperatures.     

Mobility evolution during tri-axial deformation of a glassy polymer

In this study, the evolution of mobility with deformation in a glassy polymer is compared in cases of dilatationally dominated longitudinal and deviatorically dominated uniaxial deformation. The mobility is evaluated via stress relaxation experiments performed at various points along the stress–strain curve, including pre-yield, yield, and post-yield regions. At T_g−5 °C the mobility decreases with deformation in uniaxial extension, but increases with deformation in tri-axial extension. The τ_eff relaxation time calculated for longitudinal deformation exhibits a dramatically different dependence on the excess volume than the relaxation time obtained in structural relaxation experiments. Finally, the criterion for cavitational failure is proposed based on the thermodynamic stability considerations.