Plane strain fracture toughness testing of high density polyethylene

The concepts of linear elastic fracture mechanics (LEFM) are applied to three grades of high density polyethylene in an attempt to determine their fracture behavior in terms of a linear elastic fracture toughness, K_c. The effect of specimen size (thickness and width), crack length and the mode of loading on K_c has been investigated in order to determine the plane strain fracture toughness, K_Ic, of these materials. The effect of temperature (between +23 and ?180°C) on their fracture behavior has also been investigated and compared in terms of their plane strain fracture toughness values.     

Anodic formation of polypyrrole/tungsten trioxide composites

The anodic codeposition of WO₃ and polypyrrole at constant current densities was studied. The powdery solid was dispersed in the electrolyte (0.1m pyrrole, 0.1m LiClO₄) under strong convection at c _L = 0.01–30 g dm⁻³. Water or wet acetonitrile were employed as solvents. Various modes of convection were developed. The resulting WO₃ Concentrations in the PPy/WO₃ composites were up to c _C = 53 wt%. c _C was found to increase with increasing convection intensity and with decreasing current density. Quantitative evaluation leads to a relationship c _C = K log c _E/c _E.0, where K is a constant,and c _E.0 is a threshold concentration. This equation was derived from a model assuming a Temkin type adsorption of the impinging particles and their field enhanced final incorporation into the polypyrrole matrix K is proportional to j ⁻¹. The new model complements the older theory of Guglielmi originally developed for systems with metal matrices, and it also holds for these very well known composites. The homogeneous distribution of WO₃ in PPy is demonstrated by the linear increase of the WO₃ mass with the thickness of the composite in combination with SEM techniques.     

Evaluation of methods of determining fracture parameters for a glassy polymer: Poly(methyl methacrylate)

Fracture criteria for the brittle fracture of a glassy thermoplastic, poly(methyl methacrylate), have been evaluated using three test piece geometries; the double cantilever beam (DCB), three-point bend (TPB), and compact tension (CT). For the DCB good agreement is obtained with published estimates of the fracture parameters using either a compliance calibration calculation for the critical energy release rate, G_1c, or a polynomial function for the critical stress intensity factor, K_1c. Anamolously high values of G_1c or K_1c were obtained using the TPB test piece. These high values of K_1c may be partially due to the difficulty of “sharpening” the crack, but there is a test piece size effect which also contributes to the over estimation of K_1c. For the CT test piece use of either a new compliance calibration for the determination of G_1c or a standard polynomial function for K_1c, good agreement was obtained with our own DCB and other published data. The range of applicability of the CT test geometry is discussed critically, and with some reservations it is considered suitable for the evaluation of either G_1c or K_1c.     

Crack propagation in polycarbonate

Crack velocity measurements and fracture toughness tests have been carried out on extruded sheets of bisphenol-A polycarbonate. Slow bend tests provided quasi-static K_1c data while dynamic initiation values were obtained from instrumented Charpy impact tests. In both types of tests high-speed crack velocity measurements were made using conductive silver grids applied to the specimens. The variation of K_1c with strain rate and temperature was found to be small and in general agreement with expectations from the relaxation properties of polycarbonate. Notch acuity was found to have little effect in that values of K_1c and crack velocity from specimens having the standard Charpy notch were similar to values obtained from sharp-cracked specimens. Some anisotropy was present in the material and gave rise to a small variation in K_1c values with direction of crack propagation. Crack velocity and also the fracture mode transition temperature showed considerable dependence upon orientation. It was thought that dynamic toughness K_d, was influenced more than K_1c by partial orientation of amorphous regions in the material and that the relaxation time for re-orientation was probably significant here.     

The fracture behavior of rubber-toughened,short-fiber composites of nylon 6,6

This study critiques the use of both rubber particles and short-glass fibers for the improvement of polymer fracture toughness (K_c). Although dry neat nylon is brittle with only a moderate K_c value (4.2 Mpa√m), additions of either second phase produce rising K_R-curves and associated high K_c values (8.1 Mpa√m for rubber-toughened nylon, and 10.0Mpa√m for 17 vol% Glass-fiber neat nylon). In the rubber -modified resin, the high K_c value is associated with extensive plastic blunting at the crack tip. In the fiber-reinforced neat resin, K_c is improved due to a combination of fiber-bridging and increased strength, the latter being associated with additional load carrying capacity of the fibers. When both rubber and fibers are added, however, no further increase in K_c is noted (K_c = 9.3 Mpa√m for 17 vol% glass-fiber rubber-modified nylon). The extent of ductile blunting in the rubber + fiber resin is not as great as in the rubber-only resin. Furthermore, the fracure strength of the rubber + fiber resin is not as high as the fiber-only resin. The net result is a balance of properties for the rubber-toughened composite.     

Flow of water through highly swollen membranes

The difference between the hydraulic permeability K under a pressure gradient and the diffusive permeability P under a concentration gradient can be explained by the incipient viscous flow at high degree of swelling. This flow is opposed by the friction resistance of the macromolecules of the highly swollen membrane. It comes to an end at a critical swelling H_c when the number of permeant molecules is not more sufficient for a complete solvation of the macromolecules of the membrane. Below this swelling, K equals PV₁/RT, where V₁ is the molar volume of the permeant, and above it the difference K ? PV₁/RT is proportional to H/(1 ? H) ? H_c/(1 ? H_c). The proportionality factor depends on the friction coefficient of the macromolecular segments and on the average lateral chain clustering. The data on poly(glycerol methacrylate) suggest that on the average the aggregates contain two chains.     

Improvements to C-ring fracture toughness test for poly(vinyl chloride) pipes

Abstract

Examination of the published procedure for performing calculations on data obtained from the C-ring fracture toughness test for unplasticised poly(vinyl chloride) reveals a major flaw. The dimensions of the specimens do not satisfy the ASTM criteria for plane strain conditions and correction factors are therefore introduced. However, there is an error in the calculation procedure, which results in variations in the severity of the test with pipe wall thickness. An improved approach is proposed and recommendations are made for changing the ISO/DIS 11673·2 test standard, to allow for variations in the yield strength of unplasticised poly(vinyl chloride) and to identify the calculated data as K _c rather than K _1c.     

Failure criterion for brittle materials with U-notches: Unification of characteristic length-based and grain size-based criteria

Here, the limitations of characteristic length-based (L_chb) and grain size-based (G_b) criteria with two or three parameters were pointed out employing the apparent toughness tests of 12 different ceramics at a large span range of U-notch root radius (ρ) values. After comprehensively considering the potential influencing factors of stress intensity factor (K_c), ρ divided by critical notch tip radius (ρ_c) was proposed as the independent variable, and the data of 21 materials (covering ceramics, plastics, resins, rocks, and metals) was summarized and discussed to establish a simple and more applicable K_c prediction model. Results indicated that K_c/K_Ic was a power function of ρ/ρ_c with a power exponent n of 0.5 for ideal materials and less than 0.5 for actual materials. It was also found that ρ_c can be calculated simply by K_Ic²/(πσ₀²), where σ₀ represented the inherent strength. This semiempirical criterion succeeded in unifying the L_chb and G_b criteria without introducing more parameters to increase the prediction accuracy of the K_c at the U-notch root for brittle materials like ceramics.     

Thermal expansivity and bulk modulus of polymer composites: Experiment versus theory

Correlations between the thermal expansivity, α_c, and the compressibility, K_c, of particulate-filled polymer melts are explored in terms of two different theories and in connection with experiments. Both theories employed [an interlayer approach based on micromechanics (IM), and a molecular one starting from the statistical thermodynamics of mixtures (MM)] account for the effect of filler-matrix interactions, viewed as a system-dependent parameter. The concentration dependences of α_c and K_c calculated using either IM or MM agree well with experiments on polyurethane and epoxy composites, and it is possible to predict α_c based on K_c experimentation. In MM this is always true, but in IM it depends on a knowledge of relations between α and K of the constituents. This point remains to be explored further.     

Partitioning of polymer chains in solution with a square channel: lattice Monte Carlo simulations

Cubic lattice Monte Carlo simulation studies were conducted to examine the effect of confinement on dilute and non-dilute solutions of polymer chains in a channel with a square cross section. In dilute solutions, the partition coefficient K_c with channels of different widths d followed the scaling-law prediction, and was close to the square of the partition coefficient K_s with a slit of the same d. The chain with its bulk radius of gyration greater than ∼d/2 adopted a conformation extending along the channel and, with a decreasing channel width, the chain ends were forced to face outside. The chain conformation in broader channels was a compressed random coil. The K_c increased with an increasing polymer concentration φ_E in the exterior solution equilibrated with the channel. In a weak confinement, K_c closely followed K_s² of the same φ_E and d. The chains contracted at higher concentrations as they did in the bulk solutions. In a strong confinement, K_c was smaller than K_s² at the same φ_E in the semidilute regime, and, at higher concentrations, sharply increased to the value close to K_s².     

Fatigue crack propagation in poly(methyl methacrylate): Effect of molecular weight and internal plasticization

In spite of the importance of fatigue behavior in engineering plastics, relatively few fundamental studies have been made of the effects of polymer structure, molecular weight, composition, and morphology on fatigue crack propagation (FCP). As, part of a broad program for the study of such effects, the role of molecular weight and internal plasticization has been studied in poly(methyl methacrylate) (PMMA) which had been specially prepared and characterized with respect to molecular weight, dynamic mechanical behavior, and, in some cases, stress-strain response. As expected, values of fracture toughness, K_c, varied considerably as the molecular weight was rai ed, from 0.7 MPa, √m at M _v = 1.0 × 10⁵ to 1.1 at M_v, = 4.8 × 10⁶. However, a specific effect of fatigue was noted: over the same range of K_c, values of FCP rate decreased by two orders of magnitude as molecular weight was; increased. It is proposed that this high sensitivity is due to differences in the degree of chain disentanglement effected by the cyclic loading, with consequent differences in the strength of the craze preceding the crack. With PMMA plasticized internally with a low level (10 percent) of n-butyl acrylate (nBA), the FCP rate and K_c, were similar to those of controls, with very high rates shown. At higher nBA levels (up to 30 percent), the sensitivity of FCP rate to stress intensity factor range decreased considerably, K_c, increased by 30 percent and the pre-exponential constant in the growth rate law increased. Plasticization weakens the polymer but at high degrees leads to enough hysteretic heating to induce local creep and crack blunting.     

Impact fracture toughness tests on polymers

A series of impact tests are described in which the plane strain fracture toughness, K_c1, of five different polymers is measured using a three point bend specimen at striker speeds up to 5m/s. At low speeds K_c1 is determined using the maximum load and a static analysis, but at speeds greater than 1 m/s the dynamic effects render the load signal unusable. For the higher speeds the fracture is timed using contact and crack propagation gages and the analysis is performed using the striker displacement at fracture. A dynamic analysis is used to convert this measurement to the true specimen displacement and K_c1 is determined from this. The apparent downward trends in the K_c1 results obtained, especially at speeds above 3m/s, are discussed.     

The fracture mechanics of polymers at high rates

Instrumented pendula have been applied to investigate the fracture toughness of some polymeric materials—homopolymers and composites—by fracture mechanics. The method is simple, and can be easily used for routine testing or research work. The load transducer is such that it allows the achievement of very accurate stress-time curves. Data are reported which clearly show the dependence of K_c on speed, temperature, and molecular weight. K_c is the critical stress intensity factor. It has also been found that the K_c experimental values can be correlated with a peculiar feature of the fracture surface for the determination of the intrinsic value of K_c/1 by the use of both the Dugdale model and a simple graphic correlation.     

2‐Amino[1,2,4]triazolo[1,5‐c]quinazolines and Derived Novel Heterocycles: Syntheses and Structure–Activity Relationships of Potent Adenosine Receptor Antagonists

2‐Amino[1,2,4]triazolo[1,5‐c]quinazolines were identified as potent adenosine receptor (AR) antagonists. Synthetic strategies were devised to gain access to a broad range of derivatives including novel polyheterocyclic compounds. Potent and selective A₃AR antagonists were discovered, including 3,5‐diphenyl[1,2,4]triazolo[4,3‐c]quinazoline ( 17 , K_i human A₃AR 1.16 nm ) and 5′‐phenyl‐1,2‐dihydro‐3′H‐spiro[indole‐3,2′‐[1,2,4]triazolo[1,5‐c]quinazolin]‐2‐one ( 20 , K_i human A₃AR 6.94 nm ). In addition, multitarget antagonists were obtained, such as the dual A₁/A₃ antagonist 2,5‐diphenyl[1,2,4]triazolo[1,5‐c]quinazoline ( 13 b , K_i human A₁AR 51.6 nm , human A₃AR 11.1 nm ), and the balanced pan‐AR antagonists 5‐(2‐thienyl)[1,2,4]triazolo[1,5‐c]quinazolin‐2‐amine ( 11 c , K_i human A₁AR 131 nm , A_2AAR 32.7 nm , A_2BAR 150 nm , A₃AR 47.5 nm ) and 9‐bromo‐5‐phenyl[1,2,4]triazolo[1,5‐c]quinazolin‐2‐amine ( 11 q , K_i human A₁AR 67.7 nm , A_2AAR 13.6 nm , A_2BAR 75.0 nm , A₃AR 703 nm ). In many cases, significantly different affinities for human and rat receptors were observed, which emphasizes the need for caution in extrapolating conclusions between different species.     

An oscillating baffle column fitted with stator rings IV. interfacial area and mass-transfer coefficients

Studies are reported on an oscillating baffle column fitted with stator rings with special reference to interfacial area. Pseudo point values of interfacial area are given along the extractor which together with values of mass-transfer coefficient, Ka, enable pseudo point values of the coefficient for continuous and disperse phases, K_c and K_d, to be evaluated. The dependence of point and overall values of K_c, K_a and a (the overall interfacial area) on operating parameters are considered.     

A Specific Feature in the Fracture of Polycrystalline Zirconia Ceramic

The effect of indentor load F and V-notch tip radius r on the crack resistance factor K _Ic of ZrO₂ + 3 mol.% Y₂O₃ ceramic is studied by microindentation and bending methods. Materials composed of 100% tetragonal phase (T-phase) and 70 – 80% T-phase were used. In both materials, an increase in F and a decrease in r cause a decrease in K _Ic . The higher sensitivity of K _Ic to F and r is observed in 100% T-phase specimens. This effect is explained by the involvement of martensite-type phase transformations.     

Impact of geometry on the critical values of the stress intensity factor of adhesively bonded joints

Several studies have dealt with the application of the generalized stress intensity factor (GISF) on the failure load prediction of adhesive joints. However, the effect of geometry on the critical value of the GSIF (H_c) is complex and limits its application. Due to the effect of multiple geometrical features and the limited success in the field of adhesive joints, a statistical analysis is a possibility. This paper investigates the impact of different geometrical features on the H_c in single lap adhesive joints. To achieve this, the statistical response surface methodology (RSM) was used to design the experiments and for the statistical analysis. According to the RSM, 31 arrangements of single lap joints were manufactured and tested. In this analysis, the adhesive thickness, adherend thickness, overlap length and also the free length, each in five different levels, were considered. The effect of linear, quadratic and two-way interactions of the geometrical parameters on the H_c and failure load were also studied. It was shown that H_c is most affected by the overlap length. Variation of H_c in term of the free length is by far higher at lower adhesive thicknesses. Also, the effect of substrate thickness on H_c is more considerable for thinner bondlines. The interactions of overlap length/free length and overlap length/adhesive thickness affect the failure load more considerably than the other studied interactions. The effect of free length on the failure load increases with the bondline thickness, while the effect of substrate thickness is stronger for a lower adhesive thickness.     

Hydrodynamic Performance of a Ring-Style High-Shear Impeller in Newtonian and Shear-Thinning Fluids

Laminar mixing of Newtonian and shear-thinning fluids induced by a Hockmeyer®-type impeller was investigated. Two unbaffled tanks at three impellers off-bottom clearances (c) were studied. Six geometric combinations, i.e., two d/T and three c/T, were examined where d and T are the impeller and tank diameters, respectively. Determination of the Metzner-Otto constant (K_s) was undertaken. The effects of d/T, c/T, and fluid rheology on K_s, power demand, pumping, shear and viscous dissipation were analyzed. The evaluated geometric ratios and rheology do not significantly affect K_s and power demand, only the rheology had an impact on the remaining hydrodynamic parameters. Pumping was favored with the Newtonian fluid, and shear and viscous dissipation increased with the shear-thinning fluid.     

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.