Application of a hybrid finite element method to determine stress intensity factors in unidirectional composites

In this paper a hybrid finite element method is applied in evaluation of the stress intensity factors K _I and K _II of unidirectional fiber reinforced composites. In order to satisfy the stress singularity at the crack tip a singular super-element based on a modified complementary energy principle is developed. The stress and displacement fields in the super-element are expressed in terms of polynomials of two complex variables ₁ and ₂ in the transformed -plane. The stiffness matrix of the super-element was determined by using a line integral along the boundary of the super-element. The displacement vector was expressed in terms of the element nodal displacement vector {q} and a properly selected shape function defined along the element boundary.Numerical results for K _I and K _II of glass-epoxy and graphite-epoxy unidirectional composites with cracks along the diameter of a circular cut out as well as elliptical cut outs were evaluated

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Résumé On applique, dans la présente étude, une méthode d'éléments finis hybrides à l'évaluation des facteurs d'intensité de contrainte K_I et K_II pour des composites renforcés de fibres unidirectionnelles. Pour tenir compte de la singularité de la contrainte à l'extrémité de la fissure, on développe un super élément singulier en se basant sur un principe modifié d'énergie complémentaire. Les champs de contraintes et de déplacements dans le super-élément sont exprimés sous forme polynormale de deux variables complexes ₁, et ₂ dans le plan de la transformée. La matrice de rigidité du super élément est, quant à elle, définie en utilisant une intégrale linéaire le long du contour de l'élément. Le vecteur de déplacement est exprimé par un vecteur (9) de déplacement nodal de l'élément, et par une fonction de forme appropriée, définie le long du contour de l'élément.On évalue les résultats numériques pour K_I et K_II, correspondant à des composites à fibres unidirection-nelles de types verre-epoxy et graphite-epoxy, oú des fissures se situeraient sur le diamètre de découpes circulaires et elliptiques

     

Analytical studies on the temperature distribution in spiral plate heat exchangers: Straightforward design formulae for efficiency and mean temperature difference

The temperature distribution in spiral plate heat exchangers has been calculated numerically to obtain the efficiency and the logarithmic mean temperature difference (LMTD) correction factors F as a function of the number of transfer units N, the number of turns n, and the heat capacity rate ratio C. It has been found that the LMTD correction factors, when plotted against the number of transfer units per turn N/n, fall approximately on a single curve. That curve for balanced countercurrent operation (C = −1) can be very closely represented by the simple formula F = (n/N)tanh(N/n). From that simple analytic representation of our numerical results it was concluded that a simpler physical model might exist to represent the overall behaviour of a spiral plate heat exchanger equally well. In fact, a countercurrent cascade of n cocurrent heat exchangers does result exactly in the above-mentioned formula for the LMTD correction factor. From that model the F-factors for other heat capacity rate ratios C (−1 < C 0) can also be calculated and they are in sufficient agreement with the numerical results.     

Antimicrobial protection of cotton and cotton/polyester fabrics by radiation and thermal treatments. I. Effect of ZnO formulation on the mechanical and dyeing properties

Cotton and cotton/polyester fabrics were treated against microbial attack by applying a formulation based essentially on ZnO under high‐energy radiation and thermal curing. To achieve the homogeneity and the reactivity of the treating formulation, a binder (Impron MTP) and a dispersing agent (Setamol WS) were used with ZnO. The antimicrobial property of the fabrics was evaluated, in terms of mechanical properties, by a soil burial test. Moreover, the effect of antimicrobial finishing on the dyeing properties in terms of color strength was investigated. It was found that the best composition that affords the best antimicrobial protection to cotton fabrics contains 2% ZnO, 2% binder, and 1% dispersing agents. For the cotton/polyester blend, the best results were achieved at the same conditions except the ZnO was 1%. It was found that the treatment under the effect of electron‐beam irradiation is better than that of gamma irradiation and thermal curing. The results showed that when the finishing process was carried out before dyeing with a reactive dye, it affects the color strength rather than performing the finishing after the dyeing process. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 1129–1137, 2003     

Anodic oxidation of bismuth in H2SO4 solutions

Anodic charging curves have been measured on polycrystalline Bi in H₂SO₄ solutions (0·01–6·0 N) at 30°C. The effect of various experimental procedures, eg electrode treatment and stirring, has been established. The anodic behaviour of Bi depends markedly on the acid concentration. In the high range, the results indicate dissolution which follows a Tafel relation. However, in dilute solutions, growth of oxide film occurs, and the potential rises rapidly with time, reaching over 100 V at high cds. Sparking and oxide breakdown start at about 150 V. Oxide growth follows the high field ionic conduction. The reciprocal capacitance is linearly related to the logarithm of cd. The constants of the exponential law, the half-barrier width, and the field strength have been calculated The last lies between 1 and 3 × 10⁶ V/cm at 1 mA/cm². The effect of F⁻ and Cl⁻ ions on oxide growth in H₂SO₄ has been also investigated.     

Pentavalent vanadium ion-induced grafting of methyl methacrylate onto cotton cellulose

Graft polymerization of methyl methacrylate (MMA) onto cotton cellulose using vanadium pentanitrate as initiator was studied under a variety of conditions. The graft yield increased with increasing initiator concentration up to 8 mmole/l. and then decreased upon further increase in initiator concentration. Increasing MMA concentration from 1 to 5% was accompanied by a significant increase in the degree of grafting. The latter was also affected by the kind and concentration of the acid incorporated in the polymerization medium. Based on graft yields, the efficiency of the acids follows the order H₂SO₄ > HNO₃ > HClO₄. Replacement of the acid with isopropyl alcohol was also examined. An isopropyl alcohol concentration of 10% constitutes the optimal concentration for grafting. Maximum graft yield depends upon the polymerization temperature; it follows the order 50°C ≥ 60°C > 40°C > 30°C > 70°C. Reaction mechanisms for grafting in the presence of acid as well as in the presence of isopropyl alcohol are proposed.     

Electrodeposition of catalytically active nickel powders from sulphate baths. I. Effect of bath constituents

A detailed study was made of the influence of the sulphate bath constituents: 0.3 - 0.0125 NiSO₄·7H₂O (I), 0.05 – 0.23 (NH₄)₂SO₄ (II), 0.1 – 0.4 H₃BO₃ (III) and 0.07 – 0.35 mol l^?1 Na₂SO₄·10H₂O (IV) on the electrodeposition of nickel powder. The cathodic polarization, current efficiency, growth morphology, crystallite size and catalytic activity of the electrodeposited nickel powders were affected to different extents by the bath constituents. A highly pure nickel powder characterized by a small crystallite size (776 Å) and moderate catalytic activity was obtained from a bath containing: 0.0125 (I), 0.23 (II), 0.1 (III) and 0.07 mol l^?1 (IV) at a current density of 10 A dm^?2 and electrolysis time 60 min. at 25 °C. Structural studies with a scanning electron microscope are given and a reaction mechanism for the electrolytic powder deposition is discussed.     

Behavior of cellulose graft copolymer towards persulphate oxidation. III. Poly(acrylonitrile) graft copolymers

Cotton cellulose was graft copolymerized with poly(acrylonitrile) to different levels. The copolymers so obtained together with the nongrafted cellulose were oxidized at different pH's (4–10) and temperatures (50–70°C) with potassium persulphate. The oxidation reaction was studied with respect to oxygen consumption, mass loss, and changes in copper number and carboxyl content of the cellulosic materials. It was found that the rates of oxidation at pH 4 for the copolymers are substantially higher than that of the nongrafted cellulose and the rate of oxidation is higher the higher the level of grafting. The reverse is the case at pH 10. The mass loss increases as the oxygen consumption increases irrespective of the substrate used and the pH employed. The magnitude of the mass loss is substantially lower in the case of grafted cellulose than in the case of nongrafted cellulose. The cellulosic copolymers with higher graft levels show lower mass loss than those having lower graft levels. However, the copper number and carboxyl content of the oxidized grafted cellulose are higher than those of the nongrafted cellulose at the same oxygen consumption. It is believed that the presence of poly(acrylonitrile) graft in the molecular structure of cellulose impedes cellulosic chain scission without necessarily preventing oxidation of cellulose hydroxyls.     

Grafting of nylon 66 with methyl methacrylate using dimethylaniline–benzyl chloride–acetic acid initiating system

Grafting of nylon 66 with methyl methacrylate (MMA) under the initiating influence of dimethylaniline (DMA)–benzyl chloride (BC)–acetic acid (AC) mixture was studied to discover optimal conditions for grafting. Results of this investigation showed that a mixture of water/ethanol at a ratio of 90:10 constitutes the most favorable medium for the grafting reaction. Optimal grafting occurred when a concentration of 0.16 mole/l. DMA plus 0.17 mole/l. BC plus 0.2 mole/l. AC was used. Using lower or higher concentrations of this initiator led to lower grafting. On the other hand, increasing MMA concentration brings about a significant increase in the graft yield. The same holds true for reaction time and temperature, though an induction period was observed at a lower temperature (65°C) and when lower monomer concentration (2%) was used.     

Graft copolymerization of vinyl monomers on modified cottons. VI. Vinyl graft copolymerization initiated by manganese (IV)

The ability of potassium permanganate in the presence of different acids to induce grafting of methyl methacrylate and acrylonitrile onto sodium hydroxide-treated cotton, partially carboxymethylated cotton, partially cyanoethylated cotton, and partially acetylated cotton was investigated. The copolymerization reaction was carried out under a variety of conditions. The graft yields are greatly enhanced by increasing concentration of monomer, reaction time, and temperature. The opposite holds true for initiator at higher concentrations. The effectiveness of the acids was: nitric acid > sulfuric acid > perchloric acid > hydrochloric acid. The change in the physical and/or chemical structure of cellulose by its modification via etherification reaction or esterification reaction had a significant effect on the susceptibility of cellulose toward grafting. While partial carboxymethylation or partial cyanoethylation of cellulose prior to grafting increased the graft yield, partial acetylation caused a decrease.     

Graft polymerization of methyl methacrylate onto wool using dimethylaniline/copper(II) system

Dimethylaniline (DMA)/Cu^II-induced grafting of methyl methacrylate (MMA) onto wool fibres was studied under different conditions. The grafting reaction was found to be influenced by Cu^II, DMA, and MMA concentrations as well as polymerization temperature, reaction time, and polymerization medium. While the graft yield increased by increasing the amount of MMA from 100 to 500 mmol/L, maximum grafting occurred at 0.5 mmol/L CuSO₄, 10 mmol/L DMA. The graft yield increased by increasing the reaction time from 15 to 150 min and by raising the polymerization temperature from 60 to 80°C. Using dimethylformamide/water and ethyl alcohol/water mixture as a medium for grafting decreased the graft yield, while using isopropyl alcohol/water mixtures increased the graft yield as compared to pure aqueous medium.