Instrumented Macroindentation Techniques for Polymers and Composites – Mechanical Properties,Fracture Toughness and Time-Dependent Behaviour as a Function of the Temperature

An innovative cooling and heating device has been successfully applied to an instrumented macrohardness testing machine in close collaboration with the company Zwick/Roell. The prototype allows the local time-dependent analysis of mechanical properties such as Martens hardness and indentation modulus, as well as fracture toughness and creep and relaxation behaviour at temperatures ranging from −100 °C to +100 °C. On the basis of load–indentation depth, load–time or indentation depth–time diagrams, the indentation behaviour as a function of test speed and/or temperature (which has rarely been done for polymers in the macro-range of loading) depending on matrix and materials composition (amorphous/semicrystalline thermoplastics, epoxy resins, micro- and nanocomposites) has been analysed. Martens-hardness, indentation modulus on the one hand and creep compliance and relaxation modulus on the other have been found to be strongly temperature dependent. Adequate methods of indentation fracture mechanics have been enhanced for polymers and applied to determine the fracture toughness of very different polymer-based materials.     

A model for non-linear creep in polypropylene

Measurements of the creep behaviour of a polypropylene polymer under uniaxial tension have been modelled using a stretched exponential function with four parameters. Non-linear behaviour arises because one of the parameters, related to a mean retardation time for the relaxation process responsible for creep, is dependent on stress. Creep curves measured under a uniaxial tensile stress and a uniaxial compressive stress of the same magnitude are different. The differences can be described by relating the retardation time parameter to an effective stress that is determined by the magnitude of both the shear component of the stress and the hydrostatic component. This analysis has then been generalised to enable expressions to be formulated for creep behaviour under an arbitrary multiaxial stress state. This requires an assumption that either the Poisson's ratio or the bulk modulus is independent of time. The validity of this assumption has been evaluated through comparisons of predictions of creep under a pure shear stress with measurements, which show that a time-independent Poisson's ratio is the better approximation. Although not the main theme of the paper, examples are given illustrating the dependence of model parameters on the structure of the crystalline and amorphous regions of the polymer. This is particularly relevant to the application of the model to the analysis of the creep behaviour of welded polypropylene where properties will, in general, be influenced by the heat treatment.     

A Universal Reduced Rupture Creep Approach for Prediction of Long Term Failure Behavior of Aged Glass Polymers from the Short Term Test of Rupture Creep Compliance by the Unified Master Curved Extrapolation

The prediction of long term failure behaviors and lifetime of aged glass polymers from the short term tests of reduced rupture creep compliance (or strain) is one of difficult problems in polymer science and engineering. A new “universal reduced rupture creep approach” with exact theoretical analysis and computations is proposed in this work. Failure by creep for polymeric material is an important problem to be addressed in the engineering. A universal equation on reduced extensional failure creep compliance for PMMA has been derived. It is successful in relating the reduced extensional failure creep compliance with aging time, temperature, levels of stress, the average growth dimensional number and the parameter in K-W-W function. Based on the universal equation, a method for the prediction of failure behavior, failure strain criterion, failure time of PMMA has been developed which is named as a universal “reduced rupture creep approach”. The results show that the predicted failure strain and failure time of PMMA at di?erent aging times for different levels of stress are all in agreement with those obtained directly from experiments, and the proposed method is reliable and practical. The dependences of reduced extensional failure creep compliance on the conditions of aging time, failure creep stress, the structure of fluidized-domain constituent chains are discussed. The shifting factor, exponent for time-stress superposition at differentlevels of stress and the shifting factor, exponent for time-time aging superposition at different aging time are theoretically defined respectively.     

Anomalous aging in two-phase systems: Creep and stress relaxation differences in rubber-toughened epoxies

From time–aging time superposition principles, similar to time–temperature superposition, one would expect similar shifting or superposition behaviors for both creep and stress relaxation responses. In particular, for isotropic homogeneous systems, in the linear viscoelastic regime, consideration of superposition in rheology by Markowitz¹ or the discussion by Ferry² from the Kramers–Kronig relation would seem to demand that creep and stress relaxation shift in the same way. Here we report on results from creep and stress relaxation measurements in two-phase, rubber-toughened epoxies that exhibit Boltzman additivity of creep or relaxation behaviors and follow the time–aging time superposition behavior in creep, but not in stress relaxation. While the lack of superposition in stress relaxation is, perhaps, not surprising, the finding that the creep responses at different aging times superimpose while the stress relaxation responses do not, presents an anomalous behavior that has not been previously reported. In addition, our findings show that the stress relaxation responses show short time “softening” upon aging. Possible reasons for the anomalous behaviors are briefly considered. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1167–1174, 1997     

Thermal conductivity behaviour of polymers around glass transition and crystalline melting temperatures

The thermal conductivity of five semi-crystalline and four amorphous polymers was determined within a wide range of temperature, starting at room temperature and going up to temperatures above the polymer melting point (Tm) for semi-crystalline polymers or above the glass transition temperature (Tg) for amorphous polymers. Two transient techniques were employed in the experimental investigation: the hot wire technique for the group of amorphous polymers, and the laser flash technique for the semicrystalline polymers. As expected, the experimental results show that Tg exerts a measureable influence on the thermal conductivity of amorphous polymers. In the case of semi-crystalline polymers, a singular behaviour of the thermal conductivity is observed within the Tm range. In order to explain the anomalous behaviour, the influence of these transition temperatures on the thermal conductivity behaviour with temperature has been analysed in terms of a phonon conduction process and temperature variations of specific heat and modulus of elasticity of the analyzed polymers.     

Linear viscoelasticity of side chain liquid crystal polymer

Small amplitude oscillatory shear has been used to study thermotropic liquid-crystalline polymers that have mesogenic groups pendant to flexible backbones. The polymers studied form nematic and smectic glasses, enabling viscoelastic response to be studied over a wide range of frequencies using time-temperature superposition. In contrast to main chain liquid-crystalline polymers, the nematic side chain polymers exhibit linear viscoelastic response over a wide range of strain amplitudes that is independent of thermal and shear histories. Viscoelastic response is very sensitive to smectic-nematic and smectic-isotropic transitions, but insensitive to the nematic-isotropic transition, as time-temperature superposition applies across this transition. We compare viscoelastic data with diffusion data by calculating the time τ that it takes a polymer to diffuse a distance equal to its coil size R (τ=R₂/D). At frequencies lower than 1/τ side chain polymers in their nematic show the terminal response characteristic of viscoelastic liquids. In their smectic, they are still strongly viscoelastic at frequencies lower than 1/τ and approach the terminal response of a viscoelastic solid at the lowest frequencies. Implications of such behaviour are discussed.     

Molecular Dynamics of PGA Bioabsorbable Polymer During Isothermal Cold Crystallization

An investigation was carried out on the molecular dynamics of poly(glycolide) (PGA) in its completely amorphous state and during isothermal cold crystallization. Experimental results were generated over a wide range of frequency and temperature by broad-band dielectric spectroscopy (DRS). The variation of the average relaxation time (defined as τ= ½πf_max where f_max is the frequency at maximum loss for the main α relaxation) has been studied during cold crystallization and the temperature dependence of this average relaxation time for completely amorphous and crystallized samples has been analyzed. This behaviour has been modelled by Havriliak-Negami and Vogel-Fulcher equations. The sensitiveness of the segmental dynamics to the degree of crystallinity has been analyzed, taking into account the relaxing segments and the amorphous layers between lamellae. Supporting evidence about the thermal behaviour of the polymers has been obtained with DSC. Complementarily, the evolution of the morphologies obtained during crystallization processes has been followed by optical microscopy.     

Time–temperature-dependent behavior of a substituted poly(paraphenylene): Tensile,creep, and dynamic mechanical properties in the glassy state

The linear viscoelastic behavior of a poly(paraphenylene) with a benzoyl substituent has been examined using tensile, dynamic mechanical, and creep experiments. This amorphous polymer was shown to have a tensile modulus of 1–1.5 Msi, nearly twice that of most common engineering thermoplastics. The relaxation behavior, which is similar to that of common thermoplastics, can be described by the WLF equation. Outstanding creep resistance was observed at low temperatures, with rubbery-like behavior being exhibited as the temperature approached T_g. Physical aging was shown to interact with long-term creep, rendering time–temperature superposition invalid for predicting the long-term properties. The effect of physical aging on the creep behavior was characterized by the shift rate μ. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 70: 2971–2979, 1998     

Physical aging of an amorphous polyimide: Enthalpy relaxation and mechanical property changes

The physical aging behavior of an isotropic amorphous polyimide possessing a glass transition temperature of approximately 239°C was investigated for aging temperatures ranging from 174 to 224°C. Enthalpy recovery was evaluated as a function of aging time following sub‐T_g annealing in order to assess enthalpy relaxation rates, and time‐aging time superposition was employed in order to quantify mechanical aging rates from creep compliance measurements. With the exception of aging rates obtained for aging temperatures close to T_g, the enthalpy relaxation rates exhibited a significant decline with decreasing aging temperature while the creep compliance aging rates remained relatively unchanged with respect to aging temperature. Evidence suggests distinctly different relaxation time responses for enthalpy relaxation and mechanical creep changes during aging. The frequency dependence of dynamic mechanical response was probed as a function of time during isothermal aging, and failure of time‐aging time superposition was evident from the resulting data. Compared to the creep compliance testing, the dynamic mechanical analysis probed the shorter time portion of the relaxation response which involved the additional contribution of a secondary relaxation, thus leading to failure of superposition. Room temperature stress‐strain behavior was also monitored after aging at 204°C, with the result that no discernible embrittlement due to physical aging was detected despite aging‐induced increases in yield stress and modulus. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1931–1946, 1999     

Relating creep and creep rupture in PMMA using a reduced variable approach

Creep and creep rupture of PMMA at high stresses have been characterized and found to be relatable by use of reduced variables. It is shown that when the creep compliances can be correlated by a superposition principle for which the vertical shift is the ratio of the applied stress to a reference stress and when strain at failure is a constant, a commonly used failure criterion (that the product of the strain rate at failure and the time to failure is constant) becomes valid. The reduced variables approach is found to apply to two greatly different thermal histories. Consistent with the concept of physical aging, the response of a quenched sample is simply shifted along the log time axis to shorter times relative to the response of the aged sample.     

The influence of short-chain branching on the creep behavior of oriented polyethylene,and its effect on the efficiency of crosslinking by electron irradiation

Studies have been made of the creep behavior of oriented (15:1) polyethylenes containing 0.4 and 1.3 butyl branches per 1000 C atoms. Increasing the branch concentration reduces significantly the creep strain and the equilibrium strain rate. The data have been fitted to an established model comprising two thermally activated processes in parallel, relating to the amorphous network at low stress, and the crystal phase at high stress. Analysis based on this model indicates the similarity between branching, entanglements, and crosslinks on the creep response. The creep behavior of electron-beam-irradiated materials shows that increasing the branch concentration makes the polyethylene more susceptible to mainchain scission, indicated by increased creep flow rates at higher stress, consistent with previous rubber elasticity studies. Irradiation in an acetylene atmosphere with low (< 1 Mrad) doses is shown to reduce the creep rates at all accessible stresses, and this attributed to an increase in crosslinking compared with scission. © 1994 John Wiley & Sons, Inc.     

Study of the thermomechanical behavior of UHMWPE yarns under different loading paths

UHMWPE viscoelastic fibers show great interest as reinforcement within composites and especially when used in SRPs (Self-Reinforced Polymers). They provide ductility, lightness and recyclability, benefits that glass or carbon fibers cannot provide. It is, therefore, necessary to increase knowledge about the behavior of UHMWPE fibers. Before the thermomechanical characterization of these yarns, an experimental protocol is proposed, validated and it supplements the existing standard. Monotonous, load-unload and creep tensile tests were carried out on Doyentrontex® yarns. Temperature and strain rate dependencies were observed. A time-temperature superposition is used to reconstruct the evolutions of modulus at 0.5%, maximum strength, and strain at break at 23 °C over a wide range of strain rates. The behavior of the yarns studied appears to be complex. Indeed, at low temperatures, a hyperelastic type of behavior, combined with plasticity, predominates whereas a more elasto-viscoplastic one emerges at 100 °C. From creep tests, a time-temperature-stress level superposition leads to the reconstruction of the yarns creep behavior over a long period at the reference temperature 23 °C and the reference stress level, which is 40% of the stress at break in tensile tests at any given test temperature.     

Effects of temperature and stress on creep properties of ethylene tetrafluoroethylene (ETFE) foils for transparent buildings

Creep properties of ethylene tetrafluoroethylene (ETFE) foils are indispensable for evaluating serviceability limit state, especially under high temperature and high stress. This paper concerned temperature and stress effects on creep properties of ETFE foils with experimental and theoretical studies. Experimental results showed that dimensionless stress effect on creep properties could be higher than that of temperature effect. A unified equation incorporating temperature, stress and time based on experimental results was determined and could be utilized to calculate the stress limits and long-term creep strains. The stress limits in response to creep strain of 10% were less than 5 MPa, 4 MPa and 3 MPa for temperature ranges of 40–50 °C, 50–60 °C and 70–80 °C, respectively. The long-term creep strain of ETFE foils under 40 °C was 5.96% concerning 50-year working time.Master curves of ETFE foils were evaluated considering time-temperature superposition (TTSP) and time-stress superposition (TSSP). Long-term creep strains with these master curves were identified and compared with experimental creep strains. It is found that TTSP could be a little underestimation of creep strains while TSSP could overestimate creep strains to some extent. Moreover, the maximum creep strain difference was only 0.48%, which justified the feasibility and suitability of using the unified equation to predict creep strains of ETFE foils.     

Confirmation of universality of time–humidity superposition principle for various water‐absorbable polymers through dynamic viscoelastic measurements under controlled conditions of relative humidity and temperature

Dynamic viscoelastic measurements were made for storage (E′) and loss (E″) tensile moduli of water‐absorbable polymers such as nylon‐6, nylon‐66, poly(vinyl alcohol), ethylene–vinyl alcohol copolymers, and regenerated cellulose under the control of stepwise scanned relative humidity at constant temperature by changes in the strain frequency over a wide range. Smooth master curves of log(E′) and log(E″) plotted against log(frequency) were successfully obtained for all samples. The evaluated shift factors changed with the relative humidity and could be interpreted well on the basis of a concept of free volume in the amorphous region. The free volume was affected sensitively, depending on the heat‐treatment condition and the types of polymers used. For nylon‐66 film, the dynamic viscoelastic measurements were made at different humidities and temperatures, from which one smooth master curve was obtained. This experimental result is important in realizing the similar effect of relative humidity and temperature on the expansion of free volume of the amorphous phase: the shift factor change induced by the relative humidity change of about 30% was equivalent to the shift factor change induced by the temperature change of about 30 °C. That is, the time–humidity superposition principle and the time–temperature superposition principle were applicable as equivalent contributors to the mechanical property of water‐absorbable polymers. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1638–1650, 2001     

Compliance and viscosity of magnetic tape layers

Viscoelastic characteristics of polymer materials used in a fourth-generation archival magnetic tape are discussed. Results from creep experiments are presented, as well as transformed results from dynamic mechanical analysis (DMA). Time-temperature superposition and frequency-temperature superposition are used to predict properties beyond time and frequency ranges used for experiments. The role of constituent polymers in determining fundamental compliance and viscous characteristics of the magnetic tape layers is described. Comparisons are made between creep-compliance and dynamic-compliance. Viscosity parameters from Kelvin-Voigt curve fits of creep data are also compared with complex viscosity from DMA.     

Rheo-optical studies of polyurethane block polymers

Stress and birefringence relaxation have been measured for two polyurethane block polymers at several temperatures to 140°C. Superposition of the stress curves is possible, but the existence of multiple relaxation mechanisms makes such a process of questionable validity. Simple superposition of the birefringence relaxation was not possible. The time and temperature dependence of the stress-optical coefficient implies different mechanisms for mechanical and optical relaxation process. Analysis of the birefringence data requires consideration of nonorientational sources of birefringence.     

The effect of specific nucleation on tensile mechanical behaviour of isotactic polypropylene

Commercial-grade isotactic polypropylene was modified with a specific β-nucleation agent NJ-Star (N,N^′-dicyclohexylnaphthalene-2,6-dicarboxamide) in concentrations 0.03, 0.10 wt.% and with a specific α-nucleating agent Millad 3988 (1,2:3,4-bis-O-(3,4-dimethylbenzylidene)sorbitol) in a concentration of 1.0 wt.%. Specimens for mechanical studies were prepared by injection moulding. Two types of tensile mechanical testing were performed at room temperature: (1) stress-strain test encompassing the plastic behaviour well behind the yield point and (2) tensile creep in the region of non-linear viscoelasticity. The results derived from the stress-strain traces show a distinct decrease in Young's modulus and yield stress for samples containing the crystalline β-phase as compared with non-nucleated and α-nucleated samples. This decrease was more pronounced with samples containing the lower β-nucleant concentrations (0.03 wt.%). Higher compliance of specimens containing the β-phase was also manifested in their creep behaviour. However, the creep rate of the specimen with the higher nucleant content (0.10 wt.%) did not rise with time so that its creep curve intersected the creep curves of non-nucleated and α-nucleated samples. Thus, at creep times longer than 1000 min, the sample with 0.1 wt.% of the β-nucleant showed a lower compliance than non-nucleated polypropylene and at 10 000 min reached the compliance of the α-nucleated sample. The different softening effect of the β-phase in the high-strain and low-strain regions has been ascribed to a specific structure of the amorphous interlayer induced by the presence of the β-crystallites.