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.     

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.     

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.     

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.     

A visco-elastoplastic constitutive model for large deformation response of polycarbonate over a wide range of strain rates and temperatures

The principal purpose in this paper is to present a combined experimental and analytical study to understand the mechanical behavior of polycarbonate (PC) under a wide range of temperatures (−40 °C to 100 °C) and strain rates (0.001 up to 5000 s⁻¹). Firstly, the experiments were conducted to obtain stress-strain response from low to high rates and temperatures. Then a robust physically consistent rate and temperature-dependent constitutive model is proposed to characterize large deformation mechanical behavior of PC. According to viscoelastic theory, a nonlinear-viscoelastic model is employed to understand the elastic response. Yielding behavior is described via cooperative model. As respect to post-yield regime, it is described by the conflict and interaction between softening and hardening behavior based on the integral-form softening and kinematic hardening model. The proposed constitutive model is successfully validated by the excellent agreement between model prediction and experiment results.     

The influence of temperature and strain rate on the constitutive and damage responses of polychlorotrifluoroethylene (PCTFE, Kel-F 81)

Polychlorotrifluoroethylene (PCTFE), also known as Kel-F 81, is a semi-crystalline fluoropolymer. Although it has been employed in a wide range of cryogenic components, valve seats, seals, and microelectronics packaging, its mechanical behavior has received limited coverage in the literature. In this work, we present the tensile and compressive constitutive response of PCTFE for a range of temperatures (−85 to 150 °C) and strain rates (1 × 10⁻⁴-2.9 × 10³ s⁻¹). Both large-strain experiments based on flow stress and small-strain dynamic mechanical analysis (DMA) using the elastic modulus exhibit a strong increase in the glass transition temperature, T_g, with increasing strain rate. The quasistatic fracture behavior of PCTFE is presented using J-integral fracture experiments. Finally, a discussion of the implication of the constitutive and damage responses of PCTFE on impact failure modes observed in Taylor impact experiments is presented.     

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.     

Constitutive modeling of polycarbonate during high strain rate deformation

A constitutive model is presented for large strain deformation of polycarbonate (PC) at high strain rates (above 10² s^?1). The proposed model considers the primary process (α) and the two secondary rate‐activated processes (β and γ). It is shown that the secondary transitions in the material affect the yield and post yield behavior of the material at high strain rates. The constitutive model has been implemented numerically into a commercial finite element code through a user material subroutine. The experimental results, obtained using a split Hopkinson pressure bar, are supported by dynamic mechanical thermal analysis (DMTA) and DSR (Decompose/Shift/Reconstruct) method. These are employed to gain understanding of the material transitions, and to further the linkages between material viscoelastic, yield, and stress–strain behavior. Comparison of model predictions with experimental data demonstrates the ability of model to capture the characteristic features of stress–strain curve of the material such as initial linear elasticity, global yield, strain softening, and strain hardening at very high strain rates (up to 10,000 s^?1). POLYM. ENG. SCI. 2013. © 2012 Society of Plastics Engineers     

Tensile mechanical properties and constitutive model for HTPB propellant at low temperature and high strain rate

To investigate the mechanical properties and fracture mechanisms of hydroxyl‐terminated polybutadiene (HTPB) propellant at low temperature and high strain rate, uniaxial tensile tests were conducted over the range of temperatures 233 to 298 K and strain rates 0.4 to 14.14 s^?1 using an INSTRON testing machine, and scanning electron microscope (SEM) was employed to observe the tensile fracture surfaces. The experimental results indicate that the deformation properties of HTPB propellant are remarkably influenced by temperature and strain rate. The characteristics of stress–strain curves at low temperatures are different from that at room temperature, and the effects of temperature and strain rate on the mechanical properties are closely related to the changes of properties and the fracture mechanisms of HTPB propellant. The dominating fracture mechanism depends much on the temperature and changes from the dewetting and matrix tearing at room temperature to the particle brittle fracture at low temperature, and the effect of strain rate only alters the mechanism in a quantitative manner. Finally, a nonlinear viscoelastic constitutive model incorporating the damage evolution and the effects of temperature and strain rate was developed to describe the stress responses of this propellant under the test conditions. During this process, the Schapery‐type constitutive theories were applied and one damage variable was considered to establish the damage evolution function. The overlap between experimental results and predicted results are generally good, which confirms that the developed constitutive model is valid, however, further researches should be done due to some drawbacks in describing the deformation behaviors at very large strain. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42104.     

Stress - Optical behavior of Poly(m-xylylenediamine adipamide) (Nylon MXD6): Influence of molecular weight

The effect of molecular weight and rubbery state uniaxial stretching conditions on the mechano-optical behavior of Poly(m-xylylenediamine adipamide) (Nylon MXD6) films was investigated using a real time spectral birefringence stretching machine. The stress optical behavior exhibits a multi stage behavior that depends on process conditions as well as molecular weight. At low stretching temperatures and high rates the stress optical behavior was found to start with an initial glassy photo elastic behavior. Decreasing stretching rate or increasing processing temperature was found to eliminate this glassy photoelastic regime leading to the observation of a linear initial stress optical behavior past a temperature of 95 °C (T_ll). The stress optical constant (SOC) was about the same for both M.W. materials stretched at temperatures past T_ll, at 2.7 GPa⁻¹ for HPA6 and 2.61 GPa⁻¹ for LPA6. Following this initial regime, the behavior is controlled by the competition between orientation and relaxation during deformation. If the chain orientation relaxation is not suppressed by increasing the stretching rate and/or the molecular weight or by decreasing temperature, the material strain crystallizes.     

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.     

A novel sliding plate rheometer for molten plastics

A novel sliding plate rheometer has been developed that is suitable for use with molten plastics, concentrated polymer solutions, raw elastomers, and other viscoelastic or thixotropic materials. It can generate steady shear rates from 0.05 to 500 s^?1 and can also be used to measure linear viscoelastic properties. In addition, it can be used to measure a broad spectrum of nonlinear viscoelastic properties such as the nonlinear relaxation modulus and the shear stress growth coefficient. In order to measure these nonlinear properties it is necessary to generate large, uniform, transient deformations Involving high strain rates. Rotational and capillary melt rheometers are not capable of generating this type of deformation, and until now it was not convenient to use sliding plate rheometers for this type of application. However, the recent development of a reliable and robust shear stress transducer makes it very convenient to use the sliding plate geometry to carry out all of these tests. The new rheometer is described, and examples of the types of data it can generate are shown.     

Molecular response of a glassy polymer to active deformation

The behavior of a glassy polyethylene-like polymer undergoing active compressive deformation was investigated via molecular dynamics simulation. Several important features can be identified within the stress-strain response of the system. Namely, the system deforms elastically, yields, softens, and then at large strains exhibits strain hardening. Simulations reveal that the actively deforming polymer exhibits several distinct characteristics at the molecular scale. Active deformation is found to significantly increase the transition rate between different dihedral angle states as well as promote the propagation of dihedral angle flips along the chain. When deformation is stopped, the transition rates decrease and propagation of these transitions along the chain is once again hindered. Below the glass transition temperature, transitions are heterogeneously distributed within the system. However, a local density-transition rate correlation study shows that this transitional heterogeneity is not attributable to heterogeneity in the local density. Instead, the high local transition rates must be caused by stresses propagated along the chain backbone as indicated by changes in neighbor correlations with stress. The yield stress is determined as a function of strain rate between strain rates of 10⁸ s⁻¹ and 5×10¹⁰ s⁻¹. The activation volume within the context of the Eyring model is calculated to be 0.21 nm³ for this system.     

Plastic deformation and damage of polyoxymethylene in the large strain range at elevated temperatures

The deformation behaviour of polyoxymethylene has been studied in plane strain compression at temperatures from 120 °C up to 165 °C and in uniaxial tension and simple shear at 160 °C for strain rates from 10⁻⁴ to 1 s⁻¹. In uniaxial tension the stress-strain behaviour was determined by a novel video-controlled testing system. The measurements showed that there was a very significant evolution of volumetric strain, indicating that damage mechanisms play a key role in the plastic deformation behaviour.All tests showed similar deformation stages with a short region of visco-elastic behaviour followed by a rounded yield point. The von Mises equivalent yield stress for these tests showed a linear relationship with logarithmic strain rate, suggestive of an Eyring type thermally activated process. After yielding, all stress-strain curves showed a long plastic deformation regime, which in shear occurred at constant stress. In plane strain compression there was also only a very small increase in stress, in contrast to uniaxial tension where very significant strain hardening was observed at high strains, which is attributed to the onset of structural changes.     

The response of a glassy polymer in a loading/unloading deformation: The stress memory experiment

A ‘stress memory’ experiment was designed to expose the nonlinear viscoelastic relaxation processes in a glassy epoxy polymer. The stress memory experiment consists of (i) constant strain rate uniaxial loading to a pre-yield, yield or post-yield condition, (ii) unloading at the same strain rate to zero stress, (iii) holding the strain constant and (iv) monitoring the subsequent stress memory response, where the stress first increases to a maximum and then relaxes to an equilibrium value for that strain. This is an analog to the classic volume memory experiment by Kovacs (Fortschr Hochpolym Forsch, 3, 394, 1964). The stress memory response showed a strong dependence on the loading/unloading strain rate which cannot be predicted by linear viscoelasticity and also provides a significant challenge to a current nonlinear constitutive models. A recently developed Stochastic Constitutive Model (J Rheol, 57(3), 949, 2013) qualitatively predicts the effect of strain rate on the stress memory response.     

有限变形下的橡胶材料非线性高弹-粘弹性本构模型

本文基于唯象学原理提出了一种适用于橡胶材料在有限应变条件下的非线性高弹-粘弹性本构模型,该模型将应力拆分为两部分：第一部分基于Yeoh模型计算得到的高弹性应力;第二部分由Boltzmann叠加原理计算得到的带有率依赖性的粘弹性应力。该本构模型中应变依赖性的高弹性应力通过修正Zener模型中的非线性弹簧表示,时间及应变依赖性的粘弹性应力通过修正Zener模型中的非线性Maxwell模型表示。利用提出的高弹-粘弹性本构模型模拟不同应变条件下的拉伸、回复、应力松弛及多步松弛在内的复杂加载过程,并与实验值对比,结果表现出良好的吻合性,说明该本构模型的合理、可靠。     

A rate‐type nonlinear viscoelastic–viscoplastic cyclic constitutive model for polymers: Theory and application

A thermodynamically consistent rate‐type viscoelastic–viscoplastic constitutive model is developed in the framework of isothermal and small deformation to describe the nonlinear and time‐dependent deformation behaviors of polymers, e.g., ratchetting, creep, and stress relaxation. The model is proposed on the base of a one‐dimensional rheological model with several springs and dashpot elements. The strain is divided into viscoelastic and viscoplastic parts, and the stress is also decomposed into two components. Each stress component is further divided into elastic and viscoelastic sub‐components. The viscoelasticity is described by introducing pseudo potentials, and the ratchetting is considered by the viscoplastic flow which is derived by the codirectionality hypotheses. The capability of the proposed model to describe the nonlinear and time‐dependent deformation of polymers is then verified by comparing the simulations with the corresponding experimental results of polycarbonate (PC) polymer. It is shown that the nonlinear and time‐dependent stress–strain responses of the PC can be reasonably predicted by the proposed model. POLYM. ENG. SCI., 56:1375–1381, 2016. © 2016 Society of Plastics Engineers     

Quantitative relation between the relaxation time and the strain rate for polymeric solids under quasi‐static conditions

Relaxation time is an essential physical quantity reflecting the hysteresis of the microstructure of materials. To associate the relaxation time with the strain rate, the stress–strain curves of six types of polymers at low strain rate were normalized, and a nondimensional generalized Maxwell model incorporating strain‐rate‐dependent relaxation times was obtained by the internal variable theory of irreversible thermodynamics. The results indicate that the constitutive equation may capture well the normalized stress–strain behaviors that are not related to the strain rate. The ratio of the initial modulus to the secant modulus at the maximum stress was also found to not rely on the strain rate anymore. Furthermore, strain‐rate independence occurred only when the relaxation time was proportional to the time interval for stress from zero to the maximum stress. The relaxation time varied in a power law with the strain rate. The explicit relation is helpful for providing a concise and promising solution for predicting the quasi‐static mechanical response of viscoelastic solids. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 44114.     

Termination rate coefficients for acrylamide in the aqueous phase at low conversion

The kinetics of acrylamide (AAm) free radical polymerization at low conversion of monomer to polymer in the aqueous phase was investigated at 50 °C using γ-radiolysis relaxation, which is sensitive to radical-loss processes. The values of the termination rate coefficients for AAm ranged from 8×10⁶ to 3×10⁷ M⁻¹ s⁻¹ as the weight fraction of polymer ranged from 0.002 to 0.0035, which is significantly lower than the low-conversion values for monomers such as styrene (2×10⁸ M⁻¹ s⁻¹) and methyl methacrylate (4×10⁷ M⁻¹ s⁻¹) in organic media. These can be quantitatively explained by applying a chain-length-dependent model of free-radical polymerization kinetics [Russell GT, Gilbert RG, Napper DH. Macromolecules 1992;25:2459. [19]] in which termination kinetics are expressed in terms of a diffusion-controlled encounter of radicals which ultimately yields an expression for the chain-length-averaged termination rate coefficient, 〈k_t〉. The lower 〈k_t〉 for AAm arises due to a combination of the high k_p value, promoting rapid formation of slower terminating long chains, and the slow diffusion of short propagating chains, relative to other common monomers. The chain transfer to monomer constant for AAm in water at 50 °C, C_M, was estimated using the chain-length-distribution method with correction for band-broadening [Castro JV, van Berkel KY, Russell GT, Gilbert RG. Aust J Chem 2005;58:178. [21]] and found to be 1.2×10⁻⁴ (±10%). The diffusion characteristics for AAm were adapted from those obtained for a similar aqueous system (hydroxyethyl methacrylate) together with a 0.5 exponent for the power law dependence on penetrant degree of polymerization at zero weight fraction polymer. This provides an adequate fit to the 〈k_t〉 data. This is the first application of the chain-length-dependent model to describe experimental termination rate coefficients for an aqueous system at low conversion to polymer. The result that the experimental termination rate coefficients can be reproduced with an a priori model with physically reasonable parameters supports the physical assumptions underlying that model.     

Effect of pressure and temperature on viscosity of a borosilicate glass

During industrial glass production processes, the actual distribution of stress components in the glass during scribing remains, to date, poorly quantified, and thus continues to be challenging to model numerically. In this work, we experimentally quantified the effect of pressure and temperature on the viscosity of SCHOTT N‐BK7^® glass, by performing in situ deformation experiments at temperatures between 550 and 595°C and confining pressures between 100 and 300 MPa. Experiments were performed at constant displacement rates to produce almost constant strain rates between 9.70 × 10^?6 and 4.98 × 10^?5 s^?1. The resulting net axial stresses range from 81 to 802 MPa, and the finite strains range from 1.4% to 8.9%. The mechanical results show that the SCHOTT N‐BK7^® glass is viscoelastic near the glass transition temperature at 300 MPa of confining pressure. To elucidate the data, we incorporated both 1‐element and 2‐element generalized Maxwell viscoelastic models in an inversion approach, for which we provide MATLAB scrips. Results show that the 2‐element Maxwell model fits the experimental data well. The stress decreases with increasing temperature at 300 MPa and the temperature dependence yields a similar activation energy (601 ± 10 kJ mol^?1 or ?H/R = 7.2 × 10⁴ K) to a previously reported value at 1‐atm (615 kJ mol^?1 or ?H/R = 7.4 × 10⁴ K). The SCHOTT N‐BK7^® glass shows a limited linear increase in viscosity with increasing pressure of ~0.1 log₁₀ (Pa·s)/100 MPa, which is in agreement with the most recent 2‐internal‐parameter relaxation model (based on experiments).