Fracture and yielding behaviors of polystyrene/ethylene‐propylene rubber blends: Effects of interfacial agents

The aim of this work is to investigate the effects of two triblock copolymers, used as coupling agents, on fracture and yielding behaviors of a blend of 80 volume % of polystyrene (PS) and 20 volume %of ethylene‐propylene rubber (EPR), over a large range of loading rates and temperatures. For this purpose, blends containing different concentrations of two triiblock copolymers were studied at various test conditions. The focus was put on the time‐temperature dependence of fracture performance of the blends. Addition of triblock copolymer makes the PS/EPR blend more ductile. The time‐temperature dependence of the brittle‐ductile transition in fracture performance of the blend is controlled by an energy activation process. The interfacial agent lowers the temperature at brittle‐ductile transition and reduces the energy barrier controlling the fracture process. This effect, however, is much more pronounced for the lower molecular weight interfacial agent. The correlation between temperature, loading rate and yield stress of the blends seems to be controlled by a molecular relaxation process according to the Ree‐Eyring theory. This model, based on the assumption of two relaxation processes (α and β) acting in parallel, allows prediction of yield stress at various loading rates and temperatures. Addition of the interfacial agents results in a reduction of the activation energy and an increase in the activation volume V* for both the α and β processes. Furthermore, the similarity of the value of the activation energy ΔH_β in the β yielding process and the energy barrier ΔH controlling the brittle‐ductile transition in fracture seems to suggest that a similar secondary relaxation mechanism controls the yielding and the fracture behavior of the blend.     

The modulus and yield stress of glassy poly(methyl methacrylate) at strain rates up to 103 inch/inch/second

Specimens of poly(methyl methacrylate) (PMMA) were compressed at nominally constant strain rates ranging from 10^?5 to 10³ in./in./sec. at 0, 22, 50, and 115°C. A plot of stress at a small fixed strain (2%) and constant temperature versus logarithm of strain rate is sigmoidal in shape and, furthermore, time-temperature superposition could be used to construct a master curve of stress versus temperature-compensated strain rate. It is suggested that the sigmoidal curve is a manifestation of the β transition in PMMA, and this is supported by the measured value of activation energy and the strain rate value at the point of inflection on the curve. By contrast, yield stress varies linearly with log \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm \varepsilon }\limits^{\rm.} $\end{document}. Time-temperature superposition could not be applied. Rationalizing on the basis of the high stress form of the Eyring equation, yielding is by a yet unspecified molecular mechanism in which activation volume has the order of magnitude of a monomer unit but increases with increasing temperature.     

Viscoplastic deformation of an epoxy resin at elevated temperatures

The tensile behavior under monotonic loading and stress‐relaxation testing of an epoxy resin has been studied. Experimental data at various strain rates and three temperatures from ambient up to just below T_g were performed, to study the transition from the brittle behavior to a ductile and therefore viscoplastic one. Dynamic mechanical analysis was applied to study the glass transition region of the material. Furthermore, a three‐dimensional viscoplastic model was used to simulate the experimental results. This model incorporates all features of yield, strain softening, strain hardening, and rate/temperature dependence. The multiplicative decomposition of the deformation tensor into an elastic and viscoplastic part has also been applied, following the element arrangement in the mechanical model. A stress‐dependent viscosity was controlling the stress–strain material behavior, involving model parameters, calculated from the Eyring plots. A new equation for the evolution of the activation volume with deformation was proposed, based on a probability density function. The model capability was further verified by applying the same set of parameters to predict with a good accuracy the stress‐relaxation data as well. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 2027–2033, 2006     

The effect of temperature on compressive fatigue of polystyrene

Compressive fatigue experiments have been designed to compare this long term mechanical life property with shorter term stress-strain behavior. Fatigue lifetime curves can be represented by three distinct regions. The fatigue failure curves shift to shorter lifetimes and lower stresses as temperature is increased. The results are discussed in terms of the Zhurkov model of static fatigue failure. Using a Coulomb-Navier yield criterion modified rate expression, it is clear that activation energy and activation volume are functions of temperature. A change in temperature dependence of activation energy and endurance limiting stress occurs near the β transition suggesting that this molecular process is related to the fatigue process. The nearly identical dependence of fatigue and stress-strain activation energies and activation volumes with temperature suggest that both deformation processes may be controlled by a similar mechanism, i.e., localized plastic deformation. Utilizing these concepts, a simple model of fatigue allows correlation of the endurance limiting stress and the number of stress cycles at the endurance limiting stress with measures of resistance to plastic flow as determined from stress-strain data for this polystyrene. These data are used to project the longest and shortest mechanical fatigue lifetimes for these deformation conditions.     

Ductile and brittle behavior of amorphous polymers. Relationship with activation energy for glass transition and mechanical fracture

An equation correlating the activation energy for the glass transition with T_R, a characteristic reference temperature, the fractional free volume, and the rate of change of the fractional free volume was developed. The resultant activation energies for about 30 polymers are given and favorably compare with the literature. The relationship between the activation energy and the bond-rupture energy indicates whether a polymer will fail in a ductile or brittle fashion. More accurate results are shown to be dependent on the stress, the stress concentration, molecular orientation, frequency of load application, and temperature. Equations correlating all these with the activation energies are given. These results are in agreement with the molecular domain model. Experimental observations from the literature seem to corroborate the suggestion that the molecular domain model holds in the amorphous solid, too.     

The effect of temperature on the delayed yield and failure of “plasticized” epoxy resin

Epoxy-Versamid specimens were loaded in tension up to failure at different constant strain-rates and temperatures. Results revealed three modes of behavior prevailing at different temperature-strain-rate regions and associated with brittle, ductile and rubbery failure modes. The ductile region was found to be confined within a narrow band on the temperature-strain-rate plane, and is characterized by a yield plateau in the stress-strain curve and by linear dependence of yield stress on log strain rate and temperature. Yield strain seems to be almost unaffected by strain-rate, but decreases slightly with temperature rise. Analysis indicated that experimental data within the ductile region are consistent with Eyring's formulation for non-Newtonian viscoplastic flows. It leads to the evaluation of the “apparent activation energy” and activation volume for the two epoxy systems tested. Comparison with previous work indicates that the above parameters as well as yield stress and elastic modulus tend to increase with the decrease of the Versamid content in the resin.     

The effect of time and temperature on the mechanical behavior of a “plasticized” epoxy resin under different loading modes

Epoxy–Versamid specimens were loaded in tension, compression, and flexure at different strain rates and temperatures to determine mode of failure, yield stress and strain, and tangent and relaxation moduli. Stress-strain curves were used to define brittle, ductile, ductile-rubbery, and rubbery modes of behavior which prevailed in different temperature-strain rate regions. The time-temperature superposition principle was applied to yield stress, initial tangent moduli, and relaxation moduli data for all three types of loading. The transition regions, tangent and relaxation moduli, and shift factors were the same in tension, compression, and flexure. Thus the most convenient mode of loading can be used to determine the general time-temperature dependence. The ratio of compressive-to-tensile yield stress was almost constant over the entire ductile region. Flexural yielding data were used to predict yield stress in tension and compression, and stress relaxation master curves were shown to be related to elastic modulus vs. strain rate curves. The yielding phenomenon was interpreted using Eyring's theory of non-Newtonian viscoplastic flow. The apparent activation energy and activation volume were larger for tension than compression. A theory is offered to explain why yielding can occur in a cross-linked system.     

The effect of time and temperature on the mechanical behavior of epoxy composites

A crosslinked epoxy resin consisting of a 60/40 weight ratio of Epon 815 and Versamid 140 and composites of this material with glass beads, unidirectional glass fibers and air (foams) were tested in tension, compression and flexure to determine the effect of time and temperature on the elastic properties, yield properties and modes of failure. Unidirectional continuous fiber-filled samples were tested at different fiber orientation angles with respect to the stress axis. Strain rates ranged from 10^?4 to 10 in./in.-min and the temperature from ?1 to 107°C. Isotherms of tangent modulus versus strain rate were shifted to form master modulus curves. The moduli of the filled composites and the foams were predictable over the entire strain rate range. It was concluded that the time-temperature shift factors for tangent moduli and the time-temperature shift factors for stress relaxation were identical and were independent of the type and concentration of filler as well as the mode of loading. The material was found to change from a brittle-to-ductile-to-rubbery failure mode with the transition temperatures being a function of strain rate, filler content, filler type and fiber orientation angle, indicating that the transition is perhaps dependent on the state of stress. In the ductile region, an approximately linear relationship between yield stress and log strain is evident in all cases. The isotherms of yield stress versus log strain rate were shifted to form a practically linear master plot that can be used to predict the yield stress of the composites at any temperature and strain rate in the ductile region. The time-temperature shift factors for yielding were found to be independent of the type, concentration and orientation of filler and the mode of loading. Thus, the composite shift factors seem to be a property of the matrix and not dependent on the state of stress. The compressive-to-tensile yield stress ratio was practically invariant with strain rate for the unfilled matrix, while fillers and voids raised this ratio and caused it to increase with a decrease in strain rate. The yield strain of the composites is less than the unfilled matrix and is a function of fiber orientation and strain rate.     

Precrack hysteresis energy in determining its ductile–brittle transition. III. Effect of temperature

A temperature variable has been used to correlate the precrack hysteresis energy and the corresponding ductility in terms of ductile–brittle transition behavior for polycarbonate. When the precrack plastic zone exceeds a critical value, crack extension thereafter will be effectively contained within the domain of the plastic zone and result in ductile fracture. Whether a specimen will fail in a ductile mode or a brittle mode is actually already being decided before the onset of crack initiation. The precrack elastic storage energy, total input energy minus hysteresis energy, is the major driving force to strain the crack tip for crack initiation. A higher testing temperature with lower yield stress converts a greater fraction of the input energy into the precrack hysteresis energy and relieves the storage strain energy available for crack initiation. A polycarbonate-toughening mechanism of incrasing temperature is very similar to the presence of rubber by reducing yield stress and increasing the precrack plasticity. © 1994 John Wiley & Sons, Inc.     

Dynamical Flow Properties of Single Crystals of Sapphire, I

The tensile deformation of sapphire was studied as a function of the temperature and of the strain rate. The ranges of the two variables were approximately 1200° to 1700°C and 10⁻³ to 10⁻¹in. per in. per minute. The work showed the existence of a relatively sharp temperature transition between completely brittle fracture and massive plastic flow, the specific transition temperature being sensitively related to the strain rate. For the limits of the rate range used, the transition temperature increased from approximately 1270° to 1520°c. In going through a range of only a few degrees of temperature near the transition, it was possible to obtain either no plastic flow on the low-temperature side or a relatively large amount of the order of a 100% extension on the high-temperature side. The stress-strain relation for plastic flow was found to be characterized by a pronounced yield-point drop; i.e., the stress required to initiate macroscopic flow was approximately double that required for subsequent flow. The magnitudes of both the upper and lower yield stresses were temperature sensitive and both decreased approximately exponentially with increasing temperature for a given strain rate. An inverse dependency of a similar kind was found for the effect of strain rate under conditions of isothermal testing. On the other hand, the fracture stress before yielding was found to be essentially independent of both temperature and strain rate, lying in a scatter band of approximately 16,000 to 20,000 psi. As the testing temperature at a given strain rate was lowered, the plastic yield stress therefore rose sharply. The transition temperature between ductile and brittle behavior was interpreted to correspond to the temperature at which the upper yield stress equaled the fracture stress. Since the lower yield stress was only half the upper yield stress, extensive flow then became possible whenever the transition temperature for yielding was exceeded.     

Phenoxy/Hytrel blends. II. Dynamic and tensile properties of unreacted miscible blends

The dynamic and tensile properties of Brabender mixed, compression‐molded miscible, and unreacted polyhydroxy ether of bisphenol A (Ph)/Hytrel blends were studied. Blending mainly produced a decrease in the specific volume, and in the strength of the β transition of Ph. The β transition strength decrease was attributed to both specific interactions and specific volume decrease. The measured modulus of elasticity, yield stress, and ductility of the blends were discussed as a result of the combined effect of the β transition strength decrease, crystallinity, and free volume content changes, and the position of the T_gs of the blends with respect to the testing temperature. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 72: 85–93, 1999     

Effect of aging on the compressive yielding of PAN-based carbon fiber/polycarbonate composites

The compressive yield behavior and the effect of aging in boiling water on the mechanical properties of polycarbonate composites reinforced with PAN-based carbon fibers were studied at different filler contents and over a range of strain rates. The Young's modulus, yield stress, and yield strain are reported as a function of aging time. Other mechanical parameters such as the activation energy and volume of the yielding process were determined through the Eyring theory. The increase of both Young's modulus and yield stress with aging in boiling water is explained by structural changes. The mechanical properties of the composite were correlated with the morphology and its glass transition temperature.     

Relationship between viscoelastic transition and yield behavior of phenolphthalein poly(ether ketone)

The viscoelastic behavior of phenolphthalein poly(ether ketone) (PEK-C) and its relationship to yielding was studied. The following phenomena were observed: (1) The relaxation behavior at strain near yield closely approximated that at low strain but near the T_g; (2) the temperature and strain rate dependence of yield stress could be modeled by the one-process Eyring theory and the value of the activation volume was the same as that of the glass transition; and (3) according to the Zhurkov–Bueche equation, the α transition was related to the yield behavior. All these results indicated that the glass transition was the main factor that controlled the yield behavior. © 1996 John Wiley & Sons, Inc.     

Effects of strain rate and comonomer on the brittle–ductile transition of polymers

The effect of rate on the brittle–ductile transition of polymers can be given by an Arrhenius-type equation with activation energy between those of α and β transitions and given by where E_b is the activation energy for brittle-ductile transition, E_α is that for α transition, E_β is that for β transition, T_g is the glass transition temperature, T_b is the brittle–ductile transition temperature at 0.1 min.^?1, T_α is the α transition temperature at 1 cps, and T_β is the β transition temperature at 1 cps. The plots of T_b versus the weight fraction (w) of comonomer are sigmoidal, with an inflection point at w = 0.5.     

Molecular dynamics simulations of deformation mechanisms of amorphous polyethylene

Molecular dynamics simulations were used to study deformation mechanisms during uniaxial tensile deformation of an amorphous polyethylene polymer. The stress-strain behavior comprised elastic, yield, strain softening and strain hardening regions that were qualitatively in agreement with previous simulations and experimental results. The chain lengths, number of chains, strain rate and temperature dependence of the stress-strain behavior was investigated. The energy contributions from the united atom potential were calculated as a function of strain to help elucidate the inherent deformation mechanisms within the elastic, yield, and strain hardening regions. The results of examining the partitioning of energy show that the elastic and yield regions were mainly dominated by interchain non-bonded interactions whereas strain hardening regions were mainly dominated by intra-chain dihedral motion of polyethylene. Additional results show how internal mechanisms associated with bond length, bond angle, dihedral distributions, change of free volume and chain entanglements evolve with increasing deformation.     

Fracture and impact properties of polycarbonates and MBS elastomer-modified polycarbonates

Mechanical properties of polycarbonates (PCs) and elastomer-modified polycarbonates with various molecular weights (MW) are investigated. Higher MW PCs show slightly lower density, yield stress, and modulus. The ductile–brittle transition temperature (DBTT) of the notched impact strength decreases with the increase of PC MW and with the increase of elastomer content. The elastomer-modified PC has higher impact strength than does the unmodified counterpart if the failure is in the brittle mode, but has lower impact strength if the failure is in the ductile mode. The critical strain energy release rate (G_c) measured at ?30°C decreases with the decrease of PC MW. The extrapolated zero fracture energy was found at M_n = 6800 or MFR = 135. The G_c of the elastomer-modified PC (MFR = 15, 5% elastomer) is about twice that of thee unmodified one. The presence of elastomer in the PC matrix promotes the plane–strain localized shear yielding to greater extents and thus increases the impact strength and G_c in a typically brittle fracture. Two separate modes, localized and mass shear yielding, work simultaneously in the elastomer-toughening mechanism. The plane–strain localized shear yielding dominates the toughening mechanism at lower temperatures and brittle failure, while the plane–stress mass shear yielding dominates at higher temperatures and ductile failure. For the elastomer-modified PC (10% elastomer), the estimated extension ratio of the yielding zone of the fractured surface is 2 for the ductile failure and 5 for the brittle crack. A criterion for shifting from brittle to ductile failure based on precrack critical plastic-zone volume is proposed.     

Studies of poly(2,6-dimethyl-1,4-phenylene oxide) blends: 2. Poly(4-methylstyrene)

Blends of poly(2,6-dimethyl-1,4-phenylene oxide) (PMMPO) and poly(4-methylstyrene) (P4MS) were found to be compatible from a variety of experimental methods including calorimetric, density, and mechanical property measurements. Blend property behavior was similar to that widely reported for PMMPO/polystyrene (PS) blends. For each blend composition studied, a single glass transition temperature (T_g) was detected by differential scanning calorimetry. The compositional dependence of blend T_g was equally well represented by the empirical inverse rule of mixtures or by the Couchman thermodynamic expression. Density measurements of molded films suggested a mild excess volume of mixing that was slightly smaller than that observed for blends of PMMPO and PS. As in the case for PMMPO/PS, densification in the solid state may be associated with the observed mechanical property behavior of the PMMPO/P4MS blends. Initial modulus at each blend composition was larger than would be predicted by a simple weighted average of component polymer values. Tensile deformation changed from a ductile to a brittle mode of failure with increasing P4MS composition. The yield stress for ductile compositions and ultimate stress of brittle samples were both higher than found for the corresponding unblended polymers and higher than would be predicted from a simple additive relationship of weighted component properties. Blend impact strength determined by small strain rate tensile tests rapidly decreased to low levels with increasing P4MS composition. This drop in impact strength became more composition sensitive at higher loading rates during multiaxial deformation in an instrumented dart impact tester.     

Mechanical and Fracture Behaviour Evaluation of Commercial Acrylic Bone Cements

The deformation and fracture behaviour of some commercial acrylic bone cements have been investigated. Cements were characterized by gel permeation chromatography, dynamic mechanical analysis and scanning electron microscopy. The influence of liquid to powder ratio, curing temperature, strain rate and non-reacted monomer was analysed for one radiolucent cement. Results showed that the β transition activation process influences both deformation and fracture behaviour. Fracture surface stress whiteness revealed the presence of crazes as the main plastic deformation mechanism. Non-reacted monomer acted as a plasticizer leading to materials with lower yield strength, σ_y, that induces crack tip blunting and improves toughness. It appears that the presence of radiopacifier fillers also improves fracture toughness by promoting interactions between the crack and the second phase dispersion. © 1997 SCI.     

Solid‐state structure and properties of hyperbranched polyols

Structure–property relationships were studied in a series of hyperbranched polyesters based on dimethoxypropionic acid with ethoxylated pentaerythritol as the core. In DSC thermograms, all the polyols exhibit a prominent glass transition and a small melting endotherm. It is possible to model the glass transition temperature of hyperbranched polymers by adapting a method used to calculate the glass transition temperature of dendritic polymers. Because the glass transition occurs near ambient temperature, small changes in the glass transition temperature with generation number have a large effect on the mechanical properties. Polyols that are above the glass transition temperature are ductile. Polyols that are below the glass transition temperature are brittle. When deposited from a dilute solution, the polyols form monolayer aggregates of spherical molecules. The aggregates are stabilized by hydrogen bonding of terminal repeat units. The observation of a yield stress indicates that the intermolecular associations provide a level of resistance to deformation. However, because the globular structure does not permit the usual processes of orientation and strain hardening, the neck gradually thins until it fractures at an engineering strain above 100%. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 1207–1217, 2000     

Tensile yield in poly(4-methyl pentene-1)

Uniaxial tension tests to the yield point were performed on a crystalline polymer, poly(4-methyl pentene-1) (PMP) as a function of temperature from 21° to 200°C at a strain rate of 2 min^?1. After testing, the specimens showed considerable stress whitening as a result of microvoid formation. Yield energy was found to be a linear function of temperature extrapolating to zero at the melting point (240°C). Thus, the behavior of this crystalline polymer is similar to that of glassy polymers, but with the melting temperature, rather than the glass transition temperature, as the reference point. The ratio of thermal to mechanical energy input to produce yielding is an order of magnitude smaller for PMP than it is for glassy polymers. The ratio of yield stress to Young's modulus is about 0.02, which is typical for polymers. Yield stress is a linear function of log strain rate, which implies that yielding can be described as a segmental flow rate process in which the applied stress biases the activation energy. The activation volume is on the order of 20 monomer unit volumes and increases as the temperature increases. The activation energy is 19 kcal/mol.