Precrack hysteresis energy of elastomer-modified polycarbonates in determining its ductile–brittle transition

For ductile fracture, the precrack plastic zone has to exceed a critical value, and precrack hysteresis energy has been employed to characterize the plastic zone. The presence of elastomer in polycarbonate is able to enhance precrack hysteresis and, therefore, toughens the polycarbonate matrix. Higher precrack hysteresis means that a greater fraction of the input energy converts into plasticity and leaves less storage energy available to strain the crack tip for crack Initiation. If the precrack plastic zone is above the critical value before onset of initiation, the crack growth developed thereafter will be effectively contained within the domain of the plastic zone and results in mass shear, yielding ductile fracture. In this paper, the elastomer toughening is classified as promotion of ductile failure through mass shear yielding and the localized energy dissipation processes. The localized energy dissipations are further divided into the activities occurring on and underneath the fracture surface. A different approach in interpreting the elastomer-toughening mechanism is discussed in detail. © 1993 John Wiley & Sons, Inc.     

Precrack hysteresis energy in determining polycarbonate ductile–brittle transition. IV. Effect of strain rate

Effect of deformation rate on the ductile–brittle transition behavior for polycarbonate (PC) with different molar mass, notch radius, and rubber content has been investigated. PC with higher molar mass, notch radius, or rubber-modification possesses a higher critical strain rate when the ductile–brittle transition occurs. Whether a notched specimen will fail in a ductile mode or a brittle mode is already decided before the onset of the crack initiation. If size of the precrack plastic zone exceeds a critical level prior to onset of crack initiation, the crack extension developed later will propagate within the plastic zone and result in a ductile mode fracture. The precrack elastic storage energy, the input energy subtracting the hysteresis energy, is the main driving force to strain the crack tip for crack initiation. The precrack hysteresis energy (directly related to the precrack plasticity) increases with the decrease of the applied strain rate. Therefore, the strain rate is also closely related to the size of the precrack plastic zone. If the strain rate is lower than the critical strain rate, the specimen is able to grow a precrack plastic zone exceeding the critical plastic zone and results in a ductile mode fracture. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65: 655–665, 1997     

Effect of polycarbonate molecular weight on precrack hysteresis energy in determining its ductile-brittle transition

The distinctive ductile-brittle transition behavior of pseudoductile polymeric materials such as polycarbonate (PC) has been discovered to be closely related to the precrack hysteresis loss energy. The higher molecular weight (MW) PC with higher ductility also results in higher precrack hysteresis energy and therefore greater precrack plastic volume under condition of constant loads. If the precrack plastic volume exceeds a critical value, crack initiation thereafter will propagate within the domain of the plastic zone and results in ductile fracture. The deformation displacement is closely related to the precrack plastic volume, and the critical displacement actually determines the critical plastic volume. The higher molecular weight polycarbonate with higher entanglement density is able to withstand earlier crack initiation more effectively. Toughening plastics, such as rubber modification, is simply the result of delaying or retarding the crack initiation and allows the precrack plastic zone to grow over its critical value. A model of crack criterion based on precrack plastic zone is proposed to interpret the ductile-brittle transition phenomenon.     

A model for service life of polyethylene pipe exhibiting ductile–brittle transition in failure mode

This article proposes a model for predicting failure time of stressed polyethylene pipe materials that exhibit a failure mode transition from brittle to ductile as stress is increased. The model is based on data obtained using the constant tensile load (CTL) test and takes into account stress-versus-failure-time behavior in both brittle and ductile regimes, as well as in the transition regime. The model permits quantification of the ductile–brittle transition behavior not only from the standpoint of the location of the transition but also its breadth. It is illustrated that knowledge of these two separate parameters opens new avenues for understanding the molecular basis of the transition process. This research was conducted under the sponsorship of the Gas Research Institute.     

Time–temperature dependent brittle fracture of viscoelastic solids

The Griffith formulation is used to study fracture behavior of poly(methyl methacrylate) (PMMA) as a function of strain rate and temperature over the range 4.4 × 10^?5 ≤ ε ≤ 4.4 × 10^?2 in./in./sec and 25°C ≤ T ≤ T_g, T_g being the glass transition temperature. It is found that the transition from brittle to ductile failure occurs abruptly at a temperature T_f which is dependent on strain rate and is approximately the same as the glass transition temperature of the material. The Griffith brittle fracture criterion is found to apply below T_f for all strain rates. The brittle fracture behavior is shown to obey the time–temperature equivalence principle in the same way as the material's other viscoelastic properties, having the same shift function.     

Structure–property relationships for styrene crosslinked polyesters. II. Glass transition temperature

The glass transition temperature of 10 styrene-free polyester prepolymers and the corresponding networks crosslinked by about 40% by weight of styrene were determined by DSC (and by DMA in the case of networks). The glass transition temperature T_gL of an hypothetical copolymer containing all the difunctional units of the network was then calculated. It is an increasing function of the molar weight of the prepolymer and of the phthalate/maleate molar ratio. From IR and NMR measurements, it was established that the structural irregularities other than polyester chain ends, especially unreacted double bonds, can be neglected to a first approximation. A constituent repeat unit (CRU) defined on the basis of these results allows the calculation of the crosslink density n. Then, various theories of the effect of n on T_g are compared. It appears that neither the Fox and Loshaek nor the Di Marzio approach gives good results. The crosslinking constants are lower than those found for aliphatic skeleton polyesters or epoxies. In the series under study, they display a tendency to decrease with the aromatic content. Some possible reasons of this peculiar behavior are discussed.     

Characterization of styrene–methyl methacrylate–n-butyl acrylate terpolymers. II. Effects of sequence distribution on glass transition temperature

The effects of sequence distribution on the glass transition temperature (T_g) of the title terpolymers prepared by radical polymerization were studied. T_g was examined by thermomechanical analysis. The average diad concentrations, as estimation of sequence distributions were calculated from monomer reactivity ratios. A modified Gibbs–Dimarzio equation for binary copolymers was extended to terpolymers to explain the relation between observed T_g and average diad concentrations. The observed T_g showed good agreement with the calculated values determined by the extended equation.     

Effect of annealing at temperature around glass transition temperature on molecular orientation and shrinkage of ethylene–vinyl alcohol copolymers

The effect of annealing on the molecular arrangement of ethylene–vinyl alcohol copolymers (EVA) was studied by optical methods. Drawn samples were annealed at temperatures near the glass transition temperature T_g in two cases; the first case allowed thermal shrinkage and the second case did not. For annealing below T_g, the hydroxyl groups were rearranged only to the stable position. Thermal shrinkage occurred by annealing at temperatures between T_g and T_g + 20–30 K. In the case of annealing at temperatures above T_g + 30 K, thermal shrinkage and crystallization occurred. The crystallization by annealing made the drawn sample difficult to shrink.     

Effect of dissipation of mechanical energy on hysteresis combustion

Combustion, Explosion, and Shock Waves -     

Effect of temperature on fracture toughness of PC/ABS based on J-integral and hysteresis energy methods

The critical fracture toughness J_1c of the polycarbonate (PC)/acrylonitrile–butadiene–sty-rene (ABS) blend at different temperatures was obtained from ASTM E813-81, E813–87, and the recently developed hysteresis energy methods, respectively. The J_1c value increases with increase of the test temperature ranging from −60 to 70°C. the hysteresis energy method and the ASTM E813–81 method result in comparable J_1c values, while the ASTM E813–87 results in about 80–110% higher values. the critical initiation displacements determined from the plots of hysteresis energy and the true crack growth length vs. crosshead displacement are very close. This indicates that the critical initiation displacement determined by the hysteresis method is indeed the displacement at the onset of true crack initiation and the corresponding J_1c represents a physical event of crack initiation. The fracture toughness, K_1c value, based on linear elastic fracture mechanics (LEFM), was determined by using K_Q analysis (ASTM E399–78), and the obtained K_Q value decreases with the increase of the test temperature. The K_Q value is not the real LEFM K_1c value because the criterion of P_max/P_Q < 1.1 has not been satisfied. However, the corresponding J_Q obtained from the K_Q analysis is comparable to the J_1c obtained from the E813–81 method at lower temperature (−45 or −60°C), an indication of LEFM behavior at lower temperature. The various schemes and size criterion based on LEFM and the J-method are explored for the validity of J_1c and K_1c values. © 1996 John Wiley & Sons, Inc.     

Lignocellulose–polymer composite. III

A linear relationship was achieved between the polymer load and the monomer concentration up to 200% when china clay or talc replaced the glass in the initiating system, sodium bisulfite–soda lime glass, for the free-radical graft polymerization reactions using semichemical pulp of bagasse as substrate. The results showed that china clay is better than talc, which may be contributed to the difference in their network structure. The properties of the composites prepared from the cografted semichemical pulp–polymethyl methacrylate revealed that the china clay leads to composites with high compression strength and hardness. Deformation percent increased with increasing polymer load. However, decreasing or increasing the polymer load affects the properties of the composites up to a limit, where there is a maximum or minimum for both compression strength and hardness at china clay ratio of 2 or 3. Composites were also prepared from poly(methyl methacrylate)-cografted-pith of bagasse using the initiating system sodium bisulfite in the absence or presence of soda lime glass. Compression strength, deformation percent, and hardness increased on decreasing the glass ratio from 1 to 0, at nearly the same polymer load. The presence of waxes and resins decreased the compression strength of the composites prepared by impregnation of the lignocellulose in polymer solution. The hardness of these composites increased on removing waxes and resins. Removal of part of hemicellulose by alkali treatment of the lignocellulose has increased the effect on hardness. Alkali treatments of the substrates lead to a high deformation percentage. The compression strength of alkali-treated lignocellulose are lower than the untreated ones. The change of compression strength to deformation percent and the compressibility due to complete removal of waxes and resins by the extraction with methanol–benzene or partial removal of the waxes, resins, and hemicellulose through alkali treatment followed the change of both the compression strength and percent of deformation. Water uptake of the composites prepared in this work was ranged between 6.8 and 7%. After 48 h the water uptake increased to the range 8.5–14.1%. Impregnation of the composites in water for 72 h increased the water uptake to the range 10.2–18.1%. © 1993 John Wiley & Sons, Inc.     

The association constant of macrocyclic ether–cation interactions in 1,4-dioxane/water mixtures. III. Effect of temperature on the binding

The association constant, K_a of Na⁺ with [12]crown-4, [15]crown-5 and [18]crown-6 crown ethers were determined in a binary mixture, 1,4-dioxane/water (50/50) using a Na⁺ ion selective electrode at different temperatures. K_a values were determined with the relationship, 1/K_a [L_o]^n+m–1 = (1–nP′)ⁿ(1–mP′)^m/P′, for various stoichiometries, (n:m), where P′ is the mole fraction of the complexed cation. The exothermic association constants and the thermodynamic data for cation–macrocycle complexes explained in terms of Eigen–Winkler binding mechanism are given. The binding power found for Na⁺, however, was the highest with [18] crown-6.     

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.     

Application of an extended Tool–Narayanaswamy–Moynihan model.Part 2. Frequency and cooling rate dependence of glass transition from temperature modulated DSC

In the first part of this paper a Tool–Narayanaswamy–Moynihan-model (TNM) extended by non-Arrhenius temperature dependence of the relaxation time was applied to describe results from temperature modulated DSC (TMDSC). The model is capable to describe the features of the heat capacities measured in TMDSC scan experiments in the glass transition region of polystyrene (PS). In this part the model is applied to bisphenol A-polycarbonate (PC). Both aspects of glass transition, vitrification as well as the dynamic glass transition are again well described by the model. The dynamic glass transition above T_g can be considered as a process in thermodynamic equilibrium. The non-linearity parameter (x) of the TNM model is not needed to describe complex heat capacity as long as the dynamic glass transition is well separated from vitrification. Under such conditions the relation between cooling rate (q₀), and the corresponding frequency (ω) can be found from the two independently observed glass transitions. Fictive temperature and the maximum of the imaginary part of complex heat capacity are used for comparison here. The measurement as well as the TNM-model confirm the relation derived from Donth's fluctuation approach to glass transition, ω=q₀/aδT, where a=5.5±0.1 (confirmed previously experimentally as 6±3) and δT is mean temperature fluctuation of the cooperatively rearranging regions (CRRs).     

Glass transition temperature of methyl methacrylate–ethyl α‐benzoyloxymethylacrylate copolymers

Poly(ethyl α‐benzoyloxymethylacrylate) (EBMA) and copolymers of methyl methacrylate (MMA) with EBMA have been prepared by free radical polymerization. Monomer precursors of ethyl α‐benzoyloxymethylacrylate have likewise been polymerized. Glass transition temperatures (T_g) of homo and copolymers have been determined by differential scanning calorimetry. The Johnston equation, which considers the influence of monomeric unit distribution on the copolymer glass transition temperature, has been used to explain the T_g behaviour. T_g12 has been calculated by the application of the Johnston equation, which gave a value markedly lower than the average value expected from the additive contribution of the T_g of the corresponding homopolymers. © 2000 Society of Chemical Industry     

Novel effect of barbituric acid on glass transition temperature of bismaleimide–epoxy resin systems

Barbituric acid (BTA) has a novel influence on glass transition temperature (T_g) of bismaleimide (BMI)–epoxy resin systems. It causes the T_g of a BMI–epoxy resin system to rise significantly. The BTA's influence on T_g was investigated by changing the molar ratio of the reactants. In addition, the influence of benzoperoxide (BPO) on T_g was compared with that of BTA. The reaction selectivity of BTA and diamino-diphenyl sulfone (DDS) toward BMI and epoxy individually in the BMI–epoxy blended systems were studied using the DSC and GPC. By controlling the amount of DDS and BTA, epoxy and BMI could form intercrosslinking networks.