Craze growth and healing in polystyrene

The kinetics of craze growth and craze healing were studied by dark-field optical microscopy in monodisperse molecular weight polystyrene (PS) that varied in molecular weight from 88,000 to 1,334,000. The following observations were made. (1) G₁ the virgin growth rate, decreased rapidly with increasing molecular weight until M_n ～ 200,000 and then remained constant. (2) G₁ decreased with increasing craze density. (3) The growth rates of approaching craze tips decreased when the craze tips overlapped, and the effect was less for crazes whose parallel growth paths were greater than 40 μm apart. (4) Complete craze healing was observed by comparison of the nucleation times, τ₂, and growth rates, G₂, of healed individual crazes with the craze kinetics of the virgin sample. (5) The extent of healing was characterized using four cases in which τ and G were measured as a function of healing time, temperature, constant stress, and molecular weight. (6) Craze healing times were found to increase with molecular weight and were analyzed in terms of the modified molecular weight of the craze zone. (7) Significant bond rupture was determined to occur during crazing by comparison of healing times with stress relaxation and diffusion data. (8) Craze healing studies provide insight into both crack healing and fracture of glassy polymers.     

Fracture toughness of nylon‐6 blends with maleated rubbers

The fracture toughness of blends of nylon‐6 with maleated ethylene–propylene rubber and maleated styrene/hydrogenated butadiene/styrene triblock copolymer was investigated with a single‐edge‐notched three‐point‐bending instrumented Dynatup test. The blends for which the rubber particle size was less than 0.7 μm fractured in a ductile manner over the whole range of ligament lengths, whereas the blends with particles larger than 0.7 μm showed a ductile‐to‐brittle transition with the ligament length. In this regime, ductile fracture was observed for specimens with short ligaments, whereas brittle fracture was seen for those with long ligaments. The ductile fracture behavior was analyzed with the essential‐work‐of‐fracture model, whereas linear elastic fracture mechanics techniques were used to analyze the brittle fracture behavior. The fact that the ductile fracture energy was larger for the blends with the styrene/hydrogenated butadiene/styrene triblock copolymer than for those with ethylene–propylene rubber was due to the larger dissipative energy density of the blends based on the styrene/hydrogenated butadiene/styrene triblock copolymer. Both the critical strain energy release rate (G_IC) and the plane‐strain critical stress intensity factor (K_IC) increased as the rubber particle size decreased for both blend systems. The G_IC and K_IC parameters had similar values, regardless of the rubber type, when the rubber particle size was fixed. The transition ligament length was near the size criterion for plane‐strain conditions for both blend systems. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1739–1758, 2004     

Growth kinetics of solvent crazes in glassy polymers

The kinetics of craze growth from sharp cracks in polystyrene (PS) and poly(methyl methacrylate) (PMMA) in contact with liquid methanol were measured with time-lapse photography as a function of the stress intensity factor K_I. At high K_I the craze length in both systems increases as √t if the sides of the craze are protected from methanol and as t if they are not, where t is the elapsed time after loading. If such a side-protected craze is dried under load and then methanol is reintroduced to the crack tip, the methanol front advances with the same kinetics as the original craze growth. This experiment Proves that solvent crazing velocities are limited by the hydrodynamic transport of solvent through the porous craze structure under a capillary pressure driving force (which can be as high as 100 atm). An improved model of fluid flow through the craze is developed and shown to predict craze growth kinetics in good agreement with those observed. The hydraulic permeability of methanol crazes in PS was found to be independent of craze length at small craze length and to be independent of K_I except at very low K_I. Although increases in molecular weight in the range M_w = 200,000 to M_w = 670,000 do not markedly affect the crazing kinetics, they greatly increase the time to fracture of the craze.     

Effect of molecular entanglements on craze microstructure in glassy polymers

Thin films of ten glassy polymers are bonded to copper grids and strained in tension to produce crazes, which are then examined in the transmission electron microscope. The average craze fibril extension ratio λ for each polymer is determined from microdensitometer measurements of the mass thickness contrast of the crazes. The extension ratio λ is found to increase approximately linearly with the chain contour length l_e between entanglements, as determined from melt elasticity measurements of the entanglement molecular weight of these polymers. These results are analyzed by comparing them with λ_max, the maximum extension ratio of an entanglement network in which polymer chains neither break nor reptate (i.e., permanent entanglement crosslinks are assumed). The values of λ_max are given by l_e/d where d, the entanglement mesh spacing in the unoriented glass, is computed from d = k(M_e)^1/2 with k determined either from small-angle neutron scattering results on isolated chains in the glass or from coil size measurements in dilute solutions of a θ solvent. The craze extension ratios fall somewhat below λ_max at low λ but increase to well above λ_max for polymers with high l_e. This comparison suggests a significant contribution due to chain breakage (or reptation) in the higher-λ crazes of large-l_e polymers, which may arise from the higher true stresses in the craze fibrils (which for a given applied stress increase proportionally to λ). The results also imply that a useful way to increase the “brittle” fracture stress and decrease the ductile-to-brittle transition temperature of a glassy polymer is to decrease its entanglement contour length l_e.     

Chain scission in polystyrene by impact fracture

The number of chain scissions n_s per unit fracture area by impact in high-molecular weight polystyrene is determined to be approximately 3.3 × 10¹⁴/cm² at room temperature. This is almost 20 times larger than would be expected if chain scissions took place only at, or very close to, fracture surfaces. This result was obtained by measuring the molecular weight decrease and the total fracture area of the impact fragments by using size exclusion chromatography and statistical particle size measurements, respectively. The large n_s strongly indicates that significant chain breakage occurs during crazing before the propagation of cracks. An average craze thickness before breakdown under impact is estimated from n_s to be around 2 μm. In a diluted polymer, n_s is found to be significantly lower than the extrapolated value, assuming a linear dilution of entangled chain crossings at the fracture surface. This low chain scission density, however, can be explained by taking into account the reduction of craze breakdown strain in the diluted polymers. Finally, the broken chain ends of polystyrene appear to be stable under ambient conditions. © 1992 John Wiley & Sons, Inc.     

Brittle‐ductile transition in uniaxial compression of polymer glasses

We carried out a large set of tests to establish a correlation between the molecular (network) structure (influenced by molecular weight, molecular weight distribution, and melt predeformation) and mechanical responses of several glassy polymers to uniaxial compression at different temperatures and different compression speeds. The experimental results show that to have ductile responses there must be an adequate chain network, afforded by the interchain uncrossability among sufficiently long chains. Specifically, polystyrene (PS) and poly(methyl methacrylate) of sufficiently low molar mass do not have chain network and are found to be very brittle. Binary PS mixtures are brittle at room temperature when the volume fraction of the high‐molecular‐weight component is sufficiently low (e.g., at and below 27.5%). Moreover, sufficiently melt‐stretched PS mixtures show brittle fracture when compressed along the same direction, along which melt stretching was made. All the experimental findings confirm that a robust chain network is also a prerequisite for yielding and ductile cold compression of polymer glasses, as is for extension. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 758–770     

硬脂酸改性纳米羟基磷灰石表面性能的研究

采用硬脂酸(C₁₇H₃₅COOH)对纳米羟基磷灰石(n-HA)表面进行处理,并研究了n-HA与C₁₇H₃₅COOH的界面作用。透射电子显微镜(TEM)、傅立叶红外光谱(FTIR)以及X光电子能谱(XPS)分析表明,C₁₇H₃₅COOH在n-HA表面黏附,其中羧酸根离子(-COO^-)与钙离子(Ca^2＋)之间形成了稳定的离子键,以羧酸钙形式存在。C₁₇H₃₅COOH改性后的n-HA与聚碳酸酯(PC)复合后,复合材料的力学性能与未改性n-HA相比有明显提高。扫描电子显微镜(SEM)结果显示,经处理后的HA微粒在PC中分散均匀,两者间结合紧密,无明显界面,复合材料的断裂呈明显的韧性断裂,随着n-HA无机粒子含量增加,复合材料的断裂也逐渐向韧性与脆性断裂共存转变。     

The temperature‐dependent ballistic performance and the ductile‐to‐brittle transition in polymer networks

The temperature dependence of the ballistic impact performance of a series of transparent polymer networks is evaluated. A systematic series of homogeneous epoxy/propylene‐oxide‐based thermosets, a nanoscale phase‐separated epoxy/dual amine thermoset, and two homogeneous, completely aliphatic materials synthesized via ring‐opening metathesis polymerization are examined. The Vogel temperature (T_o) and the Kauzmann temperature (T_K) are critical parameters for scaling the temperature‐dependent ballistic impact performance of each class of materials. The ductile‐to‐brittle transition temperature in a series of propylene‐oxide amine‐cured epoxies occurs at the material T_K, corresponding to a sharp drop in fracture toughness and ballistic impact performance. Two aliphatic, ring‐opening metathesis polymerized materials are found to exhibit no clear transition from purely ductile to purely brittle behavior, but the temperature dependence is still scaled to a single curve when normalized by T_o. The cooperatively rearranging region (CRR) or the volume of this region is related to the breadth of temperatures over which these materials exhibit purely ductile deformation both quasi‐statically and at higher rates. The temperature‐dependent performance is discussed in the context of the configurational entropy. The breadth of the ductility window is related to the size of the CRR, calculated from calorimetric measurements at the resin T_g. Published 2019. This article is a U.S. Government work and is in the public domainin the USA. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 511–523     

Effect of ionic additives on deformation behavior of bisphenol a polycarbonate

The deformation behavior of bisphenol A polycarbonate containing only a small amount of oligoionomeric additives in the range of a few parts per hundred parts of resin was examined. The impact strength of polycarbonate markedly decreased as the content of additive increased, and brittle fracture of polycarbonate was observed in tensile tests when the concentration of additive was above 2.5 phr. The ductile‐to‐brittle transition that was determined using a comparison of the critical shear yield stress and the critical craze stress appeared to exist in the range of 2.5–3.5 phr of additive. The measured entanglement density was also found to decrease significantly with the addition of a few parts per hundred parts of resin of additives, and the change of the dominant deformation mechanism from ductile to brittle failure was recognized as a result of the change of the entanglement density of polycarbonate. Therefore, it was concluded that the presence of a small amount of ionomeric additives caused the loss of entanglement density that induced transition of the deformation mechanism of polycarbonate from ductile to brittle failure and led to the corresponding deterioration of impact strength. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2635–2643, 2001     

A ductile-brittle zone in polyimides depending on the reaction temperature

The mechanical and optical properties of polyimides were studied in this paper and the influence of the variation of the reaction temperature on the physico-chemical properties of the polymers was evaluated. From this the dependence of the stress-strain diagrams on the reaction temperature, as well as the stresses and strains at fracture were experimentally determined. Moreover, the elastic moduli and Poisson's ratios, as well as the refractive index of the polymers were evaluated for different temperatures of imidization. In order to define also the behaviour of the polymers as thin membranes at fracture, simple tension tests with edge-cracked thin strips were executed up to fracture. The method of caustics was used, with the specimens loaded inK _I mode of deformation at different stress-levels to evaluate the stress intensity factors of the materials in the non-linear zone of loading. TheK _I -factor was evaluated by applying the simple Dugdale-Barenblatt model for the ductile materials, whereas for brittle samples the elastic theory was used. Interesting results concerning the physico-mechanical properties of the polyimides were derived.     

Discussion of craze formation and growth in amorphous polymers in terms of the multiplicity of glass transition at low temperatures

A craze, the typical deformation zone in an amorphous polymer, can be divided into a precraze and a proper craze. A better understanding of the two corresponding formation processes is possible in terms of glass transition multiplicity.The precraze is associated with the molecular mobility in the confined flow zone, which is part of the main transition. The proper craze corresponds to the mobility in the flow transition zone (terminal zone for shear). A negative pressure generated by nonuniaxial stress is considered to be important for the maintainance of the molecular mobility in these zones belowT _g . The behavior of the zones at negative pressure and low temperatures Tg is considered using a pressure-temperature diagram. The fibril structure of crazes is discussed by a defect diffusion model for the proper glass transition; it is correlated with the sequential physical aging of the corresponding frozen structural defects. Typical mode lengths of the molecular mobilities in the different zones are compared with typical craze parameters. The structure of the craze material is considered to result from confined flow processes which cannot percolate because in the main transition the flow is confined by entanglements, and in the flow transition zone the flow is stopped by releasing the negative pressure due to crack propagation.     

Low-angle electron diffraction from high temperature polystyrene crazes

Low-angle electron diffraction (LAED) was used to study the microstructure of crazes produced at different temperatures T and strain rates in thin films of monodisperse polystyrene (PS). At a slow strain rate of 4.1 × 10^?6 s^?1 both the fibril diameter D and the fibril spacing D₀ of crazes in 1800k molecular weight PS remained constant with temperature up to T ≈ 70°C and then sharply increased as T approaches T_g. At a higher strain rate of ～ 10^?2 s^?1, both D and D₀ increase only slightly with T. The values of D and D₀ over a range of temperature are in very good agreement with those values obtained in bulk samples using small-angle x-ray scattering. The crazing stress was measured as a function of temperature in the thin films of the 1800k molecular weight PS strained at the same slow strain rate used for the LAED measurements. These measurements were analyzed using a simple model of craze growth to reveal the temperature and strain rate dependence of the craze surface energy Γ. At room temperature Γ ≈ 0.076 J/m² (versus Γ ≈ 0.087 J/m² predicted) and was observed to remain constant up to T ≈ 70°C and then decrease by approximately a factor of two at T = 90°C. This decrease in Γ is believed to result from chain disentanglement to form fibril surfaces at sufficiently high temperatures and occurs in the same temperature range in which the craze fibril extension ratio λ was observed to increase.     

The role of disclinations in two phase changes induced by temperature and pressure in crystalline solids: melting and the brittle–ductile transition

It has long been known that the melting temperature T _m of close-packed metals correlates well with the mono-vacancy formation energy. However, with the possible exception of the face-centered-cubic metals, there is a prior phase transition from a mechanically brittle solid phase to a ductile phase. Here the likely role of disclinations in the brittle-ductile phase change is stressed. The present picture may help to understand the brittle–ductile transition not only in crystalline materials but also in amorphous phases. The structure of such phases can probably be characterized in terms of a disordered disclination network. As examples of elemental crystalline solids, Si and graphite are finally discussed, with the melting under pressure of graphite being quantified.     

Correlation between the fractal dimension of fracture surfaces and fracture toughness for ductile polymer materials

A microcrack-shear band chain model for the fracture of ductile materials is proposed. The fractal dimension (D) of the fracture surfaces is derived and correlated with the fracture toughness (K_Ic) of ductile materials. The fractal dimension of the fracture surface is predicted to have an inverse trend with the fracture toughness. The theoretical results are consistent with the experimental results of some polymers and metals. © 1994 John Wiley & Sons, Inc.     

Brittle–ductile transition of polypropylene/ethylene–propylene–diene monomer blends induced by size,temperature, and time

To study the brittle–ductile transition (BDT) of polypropylene (PP)/ethylene–propylene–diene monomer (EPDM) blends induced by size, temperature, and time, the toughness of the PP/EPDM blends was investigated over wide ranges of EPDM content, temperature, and strain rate. The toughness of the blends was determined from the tensile fracture energy of the side‐edge notched samples. The concept of interparticle distance (ID) was introduced into this study to probe the size effect on the BDT of PP/EPDM blends, whereas the effect of time corresponded to that of strain rate. The BDT induced by size, temperature, and time was observed in the fracture energy versus ID, temperature, and strain rate. The critical BDT temperatures for various EPDM contents at different initial strain rates were obtained from these transitions. The critical interparticle distance (ID_c) increased nonlinearly with increasing temperature, and when the initial strain rate was lower, the ID_c was larger. Moreover, the variation of the reciprocal of the initial strain rate with the reciprocal of temperature followed different straight lines for various EPDM contents. These straight lines were with the same slope. Furthermore, a diagram at critical BDT points in three dimensions (ID, T, and initial strain rate) was given for the PP/EPDM blends. The brittle and ductile zones are clearly shown in this diagram. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1433–1440, 2004     

Polysiloxanes: paradigm or paradox

Spherulitic growth rates and physical properties of polysiloxanes are well correlated for a wide range of molecular weights. Below the zero shear entanglement molecular weight, M_c, chain folding is probably the norm and fractions are brittle, but after M_c is traversed there is a significant decrease in crystallinity, increase in interfacial surface energy and change in lamellar morphology as polymer fractions go from brittle to tough. The chain folded crystallization model with reptation, as a chain folding facilitator, fails to account for this behavior. Appropriate property data for polyethylene and polyisoprene fractions also supports this thesis which now appears to be more of a paradigm than a paradox.     

Synthesis of hydroxyl‐terminated poly(ether ether ketone) with pendent tert‐butyl groups and its use as a toughener for epoxy resins

Hydroxyl‐terminated poly(ether ether ketone) with pendent tert‐butyl groups (PEEKTOH) was synthesized by the nucleophilic substitution reaction of 4,4′‐difluorobenzophenone with tert‐butyl hydroquinone with potassium carbonate as a catalyst and N‐methyl‐2‐pyrrolidone as a solvent. Diglycidyl ether of bisphenol A epoxy resin was toughened with PEEKTOHs having different molecular weights. The melt‐mixed binary blends were homogeneous and showed a single composition‐dependent glass‐transition temperature (T_g). Kelley–Bueche and Gordon–Taylor equations gave good correlation with the experimental T_g. Scanning electron microscopy studies of the cured blends revealed a two‐phase morphology. A sea‐island morphology in which the thermoplastic was dispersed in a continuous matrix of epoxy resin was observed. Phase separation occurred by a nucleation and growth mechanism. The dynamic mechanical spectrum of the blends gave two peaks corresponding to epoxy‐rich and thermoplastic‐rich phases. The T_g of the epoxy‐rich phase was lower than that of the unmodified epoxy resin, indicating the presence of dissolved PEEKTOH in the epoxy matrix. There was an increase in the tensile strength with the addition of PEEKTOH. The fracture toughness increased by 135% with the addition of high‐molecular‐weight PEEKTOH. The improvement in the fracture toughness was dependent on the molecular weight and concentration of the oligomers present in the blend. Fracture mechanisms such as crack path deflection, ductile tearing of the thermoplastic, and local plastic deformation of the matrix occurred in the blends. The thermal stability of the blends was not affected by blending with PEEKTOH. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 541–556, 2006     

The effects of annealing on fatigue crack propagation in polyethylene

Fatigue crack propagation tests on annealed and quenched medium-density polyethylene showed the annealed specimens to have much lower resistance to crack initiation and subsequent propagation. Although the same fracture mechanism, in which the brittle crack gradually becomes more ductile, prevailed in both cases, the voided and fibrillated crack tip root craze in the annealed material was much weaker that the nonfibrillated quenched root craze. Microstructural analyses indicate that the annealed material had separate crystallite populations, whereas the quenched material had a more homogeneous morphology. The highest melting fraction of the annealed material was composed of lamellae that were about 270 Å thick, and the quenched lamellae were estimated to be 160 Å thick. The reduced fatigue crack propagation resistance of the annealed material was suggested to be a result of a lower concentration of tie molecules and its reduced damping capability, compared to the quenched material. © 1995 John Wiley & Sons, Inc.     

Effects of radiation and chain ends on fatigue behaviour of polystyrene

Fatigue lifetimes, under a given alternating stress amplitude, have been determined for a series of linear and branched polystyrenes. The branched polymers were obtained by a crosslinking reaction using γ-irradiation from a Co⁶⁰ source. By control of irradiation time, a series of branched samples of progressively increasing weight average molecular weight ($\text{M}$_w), with little change in number average molecular weight ($\text{M}$_n, were obtained. From comparison of fatigue data for these irradiated and branched samples with fatigue data obtained on a series of linear polystyrenes of increasing molecular weight, it may by concluded that appreciable increases in fatigue endurance can be achieved by increase in $\text{M}$_n and reduction in chain end density. For the irradiated samples, whether irradiated in air or in vacuum, fatigue lifetimes were comparable to or less than lifetimes to fracture for the unirradiated polymer, even though significant increases in $\text{M}$_w had occurred. It is suggested that the improved fatigue performance with increase of $\text{M}$_n is a consequence of increased craze stability resulting from the greater degree of chain entanglement and the smaller proportion of chain end defects.     

Modification of poly(vinyl chloride). XIII. Crosslinking of poly(vinyl chloride) with dithiols and properties of the crosslinked products

PVC was crosslinked by immersing PVC–dithiol blends in ethylenediamine at 30°C. Properties of the products depended on the chain length and chemical structure of the crosslinkage and on the molecular weight of the polymer chain between crosslinks M_c. Crosslinking by the agent of soft structure and long molecular chain resulted in high tensile strength at break and impact strength and low brittle temperature. The use of the crosslinking agent of short molecular chain gave high yield strength, Young's modulus, and heat distortion temperature. The relation of M_c and the chemical structure of the crosslinks to the properties of the crosslinked rigid polymer was discussed in regard to the crosslinking effect and plasticizing effect.