The essential work of plane stress ductile fracture of linear polyethylenes

The specific essential works of plane stress ductile tearing of several high- and ultrahigh-molecular-weight polyethylenes were obtained from deeply edge-notched tension specimens, with either single or double notches, by extrapolating the straight line relationship between the total specific fracture work and ligament length to zero ligament. Provided the fracture morphologies of the torn ligament are not widely different, the specific essential work (w_e) is a material property dependent on thickness but independent of specimen geometry. The specific essential fracture work also can be identified with J_c the critical value of the J-integral along a contour immediately bordering the fracture process zone at the crack tip. There is good agreement between the experimental we values and theoretical J_c estimates for these polyethylene materials.     

Ethylene polymerization with methylaluminoxane/(nBuCp)2ZrCl2 catalyst supported on silica and silica‐alumina at different AlMAO/Zr molar ratios

Methylaluminoxane (MAO)/(nBuCp)₂ZrCl₂ metallocene catalytic system was supported on silica and silica‐alumina. The Zr loading was varied between 0.2–0.4 wt %, and the MAO amount was calculated to get (Al_MAO/Zr) molar ratios between 100 and 200, suitable for the industrial ethylene polymerization of supported metallocene catalysts. Catalytic activity was statistically analyzed through the response surface method. Within the ranges studied, it was found that Zr loading had a negative effect on polymerization activity, which increases with the (Al_MAO/Zr) molar ratio. Catalysts supported on silica‐alumina are more active than those supported on silica, needing less MAO to reach similar productivity, which constitutes an important advantage from an economical and environmental point of view. Supported catalysts were characterized by ICP‐AES, SEM‐energy‐dispersive X‐ray spectrometer, and UV‐Vis spectroscopy, whereas polyethylenes were characterized by GPC and DSC. Molecular weight and crystallinity are not influenced by Zr loading or (Al_MAO/Zr) ratio, in the range studied. In general, silica‐supported MAO/(nBuCp)₂ZrCl₂ catalysts give polyethylenes with higher molecular weight and polydispersity but lower crystallinity. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Temperature effect on impact fracture toughness and fracture mechanism of phenolphthalein poly(ether ketone)

Phenolphthalein poly(ether ketone) (PEK-C) was tested using an instrumented impact tester to determine the temperature effect on the fracture toughness K_c and critical strain energy release rate G_c. Two different mechanisms, namely the relaxation processes and thermal blunting of the crack tip were used to explain the temperature effect on the fracture toughness. Examination of the fracture surfaces revealed the presence of crack growth bands. It is suggested that these bands are the consequence of variations in crack growth along crazes that are formed in the crack tip stress field. As the crack propagates, the stress is relaxed locally, decreasing the growth rate allowing a new bundle of crazes to nucleate along which the crack advances.     

Ethylene polymerization using a novel MgCl2/SiO2‐supported Ziegler–Natta catalyst

A novel MgCl₂/SiO₂‐supported Ziegler–Natta catalyst was prepared using a new one‐pot ball milling method. Using this catalyst, polyethylenes with different molecular weight distributions were synthesized. The effects of the [Si]/[Mg] ratio, polymerization temperature and [Al]/[Ti] ratio on the catalytic activity, the kinetic behaviour and the molecular weight and the polydispersity of the resultant polymer were studied. It was found that the polydispersity index of the polymer could be adjusted over a wide range of 5–30 through regulating the [Si]/[Mg] ratio and polymerization temperature, and especially when the [Si]/[Mg] ratio was 1.70, the polydispersity index could reach over 25. This novel bi‐supported Ziegler–Natta catalyst is thus useful for preparing polyethylene with a required molecular weight distribution using current equipment and technological processes. Copyright © 2005 Society of Chemical Industry     

Time-dependent fracture toughness measure for polyethylene

Because of their extraordinary cracking resistance, medium-density polyethylenes (MDPEs) do not fail in a brittle manner when tested with conventional fracture toughness procedures, but brittle fractures and J_1c values can be obtained for these materials by utilizing fatigue loading. However, because brittle fracture in polyethylene is a result of low stresses (energy) applied over long periods of time, and since J_1c neglects time, J_1c is incapable of differentiating MDPEs on the basis of their fracture resistance. Thus, the power to fracture method, which incorporates both energy and time, has been developed. During increments of crack growth, the product of the potential energy and the number of elapsed cycles is used to calculate the power to fracture. Within limits that assure a similar failure mechanism, the power to fracture for a particular resin is constant despite varied fatigue conditions. The power to fracture is capable of differentiating between resins on the basis of their brittle cracking resistance. © 1994 John Wiley & Sons, Inc.     

Sequences of fracture toughness micromechanisms in PP/CaCO3 nanocomposites

Mechanical properties and fracture toughness micromechanisms of copolypropylene filled with different amount of nanometric CaCO₃ (5–15 wt %) were studied. J‐integral fracture toughness was incorporated to measure the effect of incorporation of nanoparticle into PP matrix. Crack‐tip damage zones and fracture surfaces were studied to investigate the effect of nanofiller content on fracture toughness micromechanisms. It was found that nanofiller acted as a nucleating agent and decreased the spherulite size of polypropylene significantly. J‐integral fracture toughness (J_c) of nanocomposites was improved dramatically. The J_c value increased up to approximately two times that of pure PP at 5 wt % of nano‐CaCO₃. The fracture micromechanisms varied from rubber particles cavitation and shear yielding in pure PP to simultaneous existence of rubber particles cavitation, shear yielding, filler particles debonding, and crazing in PP/CaCO₃ nanocomposites. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Gross melt fracture elimination: The role of surface energy of boron nitride powders

Boron nitride (BN) is an effective processing aid for the extrusion of polyethylenes. It postpones the onset of gross melt fracture to significantly high shear rates not previously attained with conventional fluoropolymers. However, BN particles containing relatively high amounts of boron oxide (B₂O₃) do not perform well as processing aids. A reliable procedure has been developed for measurement of surface energy of powders using the capillary rise technique through the use of Washburn's equation. It is based on finding the contact angle from liquid penetration experiments with polar and non‐polar liquids. Both the dispersive and non‐dispersive components of surface energy are determined. With this technique, the surface energy of a number of different powders has been assessed. These results of the surface energy of BN powders have been found to correlate well with the critical shear rate for the onset of melt fracture, indicating the important role that surface energy plays in gross melt fracture elimination.     

Determination of fracture toughness of epoxy using fractography

Fracture toughness of epoxy was determined by quantitative fractography, one of the techniques for brittle materials based on fracture mechanics. Two different epoxy systems, an anhydride‐cured and an amine‐cured epoxy based upon diglycidyl ether of bisphenol A (DGEBA) were studied. Epoxies with different average molar mass between crosslinks (M_c) or crosslink density were prepared by varying the cure profiles. The materials were characterized using differential scanning calorimetry (DSC), dynamic mechanical spectroscopy (DMS), and density measurements. Optical microscopy was used to measure the dimensions of the different regions on the fracture surfaces of unnotched samples that were tested to failure under tension. The fracture toughness values were calculated from the relationship between the measured sizes and fracture stress. Epoxies with lower M_c values or higher crosslink densities have lower fracture toughness values. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 72: 257–268, 1999     

A study of extrudate distortion in controlled-rheology polypropylenes

The melt fracture characteristics of controlled-rheology polypropylenes (CRPP) were studied by means of capillary rheometry experiments. CRPPs were produced through reactive extrusion of a commodity polypropylene resin using various peroxide concentrations. These materials exhibited lower molecular weights and narrower molecular weight distributions than those of the starting commodity resin. The CRPP materials studied were found to exhibit only gross melt fracture. At extremely high shear rates and relatively low temperatures, a sigmoidal flexure was observed in the flow curve of certain CRPPs. Generally, it was found that the severity of melt fracture decreased with increasing shear rate for a given material and temperature and in some cases, the extrudates exhibited completely smooth surfaces. Also, the severity of surface distortions was reduced when high L/D dies were employed at a given shear rate. The critical shear stress for the melt fracture onset was found to increase with decreasing molecular weight and polydispersity, and correlations have been developed between the critical stress values and the polymer polydispersity and shear compliance.     

Fracture characteristics of concrete at early ages

The purpose of this study is to experimentally investigate, at early ages, the fracture characteristics of concrete such as critical crack tip opening displacement, critical stress intensity factor, fracture energy, and bilinear softening curve based on the concepts of the effective-elastic crack model and the cohesive crack model.A wedge-splitting test for Mode I was performed on cubical specimens with an initial notch at the edge. By taking various strengths and ages, load-crack mouth opening displacement (CMOD) curves were obtained and these curves were evaluated by linear elastic fracture mechanics and finite element analysis.The results from the test and analysis indicate that critical crack tip opening displacement decreases and critical stress intensity factor and fracture energy increase with concrete ages from Day 1 to Day 28. By numerical analysis, four parameters of bilinear softening curves from Day 1 to Day 28 were obtained. In addition, it was observed that the parameters f_t and f₁ increase and the parameters w₁ and w_c decrease with increasing age. The obtained fracture parameters and bilinear softening curves at early ages may be used as a fracture criterion and an input data for finite element analysis of concrete at early ages.     

Silane grafting and moisture crosslinking of polyethylene: The effect of molecular structure

The silane grafting and moisture crosslinking of different grades of polyethylene have been investigated. Three types of polyethylene (HDPE, LLDPE, and LDPE) with different molecular structures and similar melt flow indices were selected. The initiator was dicumyl peroxide (DCP), and the silane was vinyltrimethoxysilane. The grafting reaction was carried out in an internal mixer. The extent of grafting and the degree of crosslinking were determined, and hot‐set tests were carried out to evaluate the crosslink structure of the different polyethylenes. The LLDPE had the highest degree of grafting, while the LDPE had the least. The rate of crosslinking for LDPE was higher than that of HDPE and LLDPE. The gel content of LDPE was higher than that of HDPE and LLDPE. Hot‐set elongation and the number‐average molecular weight between crosslinks (M_c) were lower for LLDPE and LDPE than for HDPE. Increasing the silane/DCP percentage led to peroxide crosslinking, thereby decreasing the M_c and hot‐set elongation. The number‐average molecular weight (M_n), molecular weight distribution, and number of chain branches were the most important parameters affecting the silane grafting and moisture crosslinking. J. VINYL ADDIT. TECHNOL., 2009. © 2009 Society of Plastics Engineers     

Fracture toughness and mechanical properties of poly(n-pentyl-n-alkylsilanes)

The mechanical properties and fracture toughness of thin films of a series of poly(n-pentyl-n-alkylsilanes) were investigated. Poly(n-butyl-n-pentylsilane) is the strongest of these polymers with an elastic modulus of 2.96 × 10⁸ Pa and a fracture strain of 85% at 25°C. The hexagonal mesophases of these polymers generally show elastic moduli on the order of 10⁷ Pa and are often quite extensible. A J-integral analysis of the ductile tearing of thin films of poly(n-butyl-n-pentylsilane) and poly(n-propyl-n-pentylsilane) using an Instron tensile testing machine and specimens in the single edge notch (SEN) geometry yielded plane stress J_1c (critical value of J for fracture initiation) of 1745 J/m² and 205 J/m², respectively. Both values are significantly higher than the plane stress G_1c (critical energy release rate) value of 109 J/m² obtained for poly(di-n-hexylsilane) with a residual stress analysis using the same apparatus and testing procedure.     

Fracture behavior of bimodal polyethylene: Effect of molecular weight distribution characteristics

A series of bimodal polyethylenes with different molecular weight distribution characteristics were prepared by melt blending, and the fracture behavior of these bimodal polyethylenes was studied by the method of essential work of fracture. The results show that specific essential work of fracture, w_e, increases obviously with the molecular weight distribution characteristic, A_L/U, indicating the improvement of the resistance to crack propagation. By means of successive self-nucleation and annealing analysis, obvious variations in the crystal structures of bimodal polyethylenes with increasing A_L/U have been found. That is, the crystal size and the amount of relatively thick lamellas increase with A_L/U, but no large variation of crystallinities has been observed. So, the influence of A_L/U is mainly on the crystal perfection, the improvement of which produces an enhancement of fracture toughness since more energy would be dissipated in the superior network structure constructed from crystalline zones and amorphous zones.     

On the measurement of fracture toughness of soft biogel

In this study, the rate dependent energy dissipation process and the fracture toughness of physical gels were investigated using agarose as a sample material. Both the J‐integral and Essential work of Fracture (EWF) methods were examined. To assess the quasi‐static fracture toughness of gels, linear regression was performed on critical J (J_c) values at different loading rates resulting in a quasi‐static J_c value of 6.5 J/m². This is close to the quasi‐static EWF value of 5.3 J/m² obtained by performing EWF tests at a quasi‐static loading rate (crosshead speed of less than 2 mm/min). Nearly constant crack propagation rates at low loading rates, regardless of crack length, suggest viscoplastic chain pull‐out is the fracture mechanism. At high loading rates failure was highly brittle, which is attributed to sufficient elastic energy accumulation to precipitate failure by chain scission. We conclude that in physical gels quasi‐static fracture toughness can be evaluated by both the J‐integral and EWF methods provided the effects of loading rate are investigated and accounted for. POLYM. ENG. SCI., 2011. © 2011 Society of Plastics Engineers     

Internal stresses and adhesion of thin silicon oxide coatings on poly(ethylene terephthalate)

The effect of internal stresses on the cohesion and adhesion of a thin silicon oxide (SiO_x) oxygen-barrier coating, evaporated on a poly(ethylene terephthalate) (PET) film substrate was studied. Internal stresses were generated during annealing in the temperature range for recrystallization of the PET,during calendering in a multilayer structure where two SiO_x /PET films were laminated together with a polypropylene film, and during long-term thermal aging below the glass transition temperature of the polymer. The cohesion of the coating and its adhesion to the polymer substrate were derived from fragmentation tests, in which the failure of the oxide coating was analyzed as a function of the applied stress during uniaxial tensile loading of the substrate. The intrinsic coating strength at critical length and the interfacial shear strength were found to be equal to 1350 MPa and 73 MPa, respectively. It was found that none of the thermal treatments investigated altered the interfacial interactions. Rather, these treatments induced shrinkage of the PET substrate, which increased the coating internal compressive stress and the SiO_x /PET interfacial shear strength. A linear relationship between the SiO_x /PET interfacial shear strength and the coating internal stress was determined from a stress transfer analysis. The coefficient of this linear relationship, equal to-1.34 · h _c/l _c, where h _c is coating thickness and l _c is the critical stress transfer length, reproduces the experimental data with good accuracy.     

Effect of molecular weight between crosslinks on the fracture behavior of rubber‐toughened epoxy adhesives

The effect of molecular weight between crosslinks, M_c, on the fracture behavior of rubber‐toughened epoxy adhesives was investigated and compared with the behavior of the bulk resins. In the liquid rubber‐toughened bulk system, fracture energy increased with increasing M_c. However, in the liquid rubber‐toughened adhesive system, with increasing M_c, the locus of joint fracture had a transition from cohesive failure, break in the bond layer, to interfacial failure, rupture of the bond layer from the surface of the substrate. Specimens fractured by cohesive failure exhibited larger fracture energies than those by interfacial failure. The occurrence of transition from cohesive to interfacial failure seemed to be caused by the increase in the ductility of matrix, the mismatch of elastic constant, and the agglomeration of rubber particles at the metal/epoxy interface. When core‐shell rubber, which did not agglomerate at the interface, was used as a toughening agent, fracture energy increased with M_c. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 79: 38–48, 2001     

α‐Crystallin Modulates its Chaperone Activity by Varying the Exposed Surface

The α‐crystallin family of small heat shock proteins possesses chaperone activity in response to stress and is involved in several neurological, muscular, and ophthalmic pathologies. This family includes the vertebrate lens protein α‐crystallin, associated with cataract disease. In this study, by combining small‐angle X‐ray and light scattering techniques, the structure and shape of α‐crystallin was revealed in its native state and after a transition caused by heat stress. Below critical temperature (T_c), α‐crystallin appears as an ellipsoid with a central cavity; whereas at high temperatures the cavity almost disappears, and the protein rearranges its structure, increasing the solvent‐exposed surface while retaining the ellipsoidal symmetry. Contextually, at T_c, α‐crystallin chaperone binding shows an abrupt increase. By modelling the chaperone activity as the formation of a complex composed of α‐crystallin and an aggregating substrate, it was demonstrated that the increase of α‐crystallin‐exposed surface is directly responsible for its gain in chaperone functionality.     

Influence of molecular structure on the rheological and processing behavior of polyethylene resins

The rheological and processing behavior (melt fracture performance) of linear lowdensity polyethylenes (LLDPEs) is studied as a function of both the weight average molecular weight (M_w) and its distribution (MWD). A number of LLDPE resins having different molecular characteristics were tested, with essentially one characteristic (M_w or MWD) changing at a time. The first series of resins consisted of nine samples having a wide range of polydispersities (3.3–12.7) and nearly constant M_w and short chain branching. The second series had six resins with varying M_w (51,000–110,000) but fixed MWD (about 4). The influence of M_w and MWD on the viscosity profiles, linear viscoelastic moduli as expressed by means of a discrete spectrum of relaxation times, extrudate swell, and melt fracture behavior for these resins is reported. Correlations between the molecular characteristics of the resins and their rheological and processing behavior are also reported. It is found that for a given molecular weight, the optimum melt fracture performance is obtained at a specific polydispersity value, and it is characterized by a minimum relaxation time for the resin defined in terms of recoverable shear.     

Rheology and enhancement of extrusion of linear and branched polyethylenes using low amount of organoclay

Interaction between 0.05 wt % organoclay and polyethylenes of different short chain branching (SCB) was studied. Linear rheology (van Gurp‐Palmen plot) was used to study the effect of organoclay on the rheology of polyethylenes. Organoclay had effect only on the van Gurp‐Palmen plot of linear polyethylene. Fourier transform (FT) rheology, extrusion at high‐shear rates in a slit rheometer, transient stress growth analysis, and extensional rheology were conducted to examine the potential of organoclay as a processing aid. Organoclay reduced the transient stress overshoot, normal stress difference, ηo, onset of shear thinning, and extrusion pressure of polyethylene. The reduction was more pronounced in linear polyethylene without branching. Such effects gradually decreased as the branch content increased. The trend was independent of the type of flow (shear or extensional). It was interesting to note that FT rheology was not effective in explaining the impact of organoclay on polyethylene. The work concluded with the proposition that organoclay (as low as 0.05 wt %) was a good processing aid for linear polyethylene and polyethylenes with low content of SCB. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Statistical modeling for the accumulation of transverse matrix cracking in cross‐ply laminates

A statistical model has been proposed to predict the evolution of matrix cracking in the transverse lamina of cross‐ply laminates subjected to longitudinal tensile loading. The analytical model is based on a fracture mechanics approach which considers that the critical fracture toughness G_c of the 90° layers is not a constant but follows a Weibull distribution. Monte‐Carlo simulation technique is applied to predict the initiation and propagation of transverse cracking in terms of applied stress versus crack density. The effects of the thickness of the 90° layers on progressive damage and failure are also discussed in this study. Good agreements are reached between simulation and experimental results. POLYM. COMPOS., 2012. © 2012 Society of Plastics Engineers