Line-integral solution for the stress and displacement fields of an arbitrary dislocation segment in isotropic bi-materials in 3D space

The solutions for the stress and displacement fields due to an arbitrary dislocation segment in an isotropic bi-material medium consisting of joined three-dimensional (3D) half spaces are derived and expressed in terms of line integrals, integrands of which are given in an exact analytical form that, in turn, can also be integrated to yield analytical expressions for the stress–displacement field. The solution is constructed by employing a general solution derived by Walpole [Int. J. Eng. Sci. 34 (1996) p.629] for any elastic singularity in joined isotropic half space, and combining it with Mura's integral formula for the displacement gradient of an arbitrary dislocation segment in homogeneous medium. The resulting new solution provides a framework for deriving analytical expressions for stress and displacement fields of dislocation curves of arbitrary shapes and orientations. The benefit of the method developed, as compared with other methods found in the literature, is that the new solution presented is naturally divided into two components, a homogenous component representing the field of a dislocation in an infinitely homogenous medium, and an image component. This makes it easy and straightforward to modify existing dislocation dynamics codes that already include the homogenous part. To illustrate the accuracy of the method, the stress field expressions of an edge dislocation with Burgers vector perpendicular to the bi-material interface are derived as a degenerate case of the general result. It is shown that our solution is identical to that found in the literature for this case.     

A study of the hot and cold deformation of twin-roll cast magnesium alloy AZ31

Recent advances in twin-roll casting (TRC) technology of magnesium have demonstrated the feasibility of producing magnesium sheets in the range of widths needed for automotive applications. However, challenges in the areas of manufacturing, material processing and modelling need to be resolved in order to fully utilize magnesium alloys. Despite the limited formability of magnesium alloys at room temperature due to their hexagonal close-packed crystalline structure, studies have shown that the formability of magnesium alloys can be significantly improved by processing the material at elevated temperatures and by modifying their microstructure to increase ductility. Such improvements can potentially be achieved by processes such as superplastic forming along with manufacturing techniques such as TRC. In this work, we investigate the superplastic behaviour of twin-roll cast AZ31 through mechanical testing, microstructure characterization and computational modelling. Validated by the experimental results, a novel continuum dislocation dynamics-based constitutive model is developed and coupled with viscoplastic self-consistent model to simulate the deformation behaviour. The model integrates the main microstructural features such as dislocation densities, grain shape and grain orientations within a self-consistent viscoplasticity theory with internal variables. Simulations of the deformation process at room temperature show large activity of the basal and prismatic systems at the early stages of deformation and increasing activity of pyramidal systems due to twinning at the later stages. The predicted texture at room temperature is consistent with the experimental results. Using appropriate model parameters at high temperatures, the stress–strain relationship can be described accurately over the range of low strain rates.     

Spectral Observables for Two- and Three-Fold Symmetry Breaking

We investigate the spectral statistics of a random matrix model for symmetry breaking. It is pointed out that the spectral rigidity distinguishes more clearly the breaking of two- and three-fold symmetries than does the nearest-neighbour spacing distribution.     

A multiscale approach for modeling scale-dependent yield stress in polycrystalline metals

Modeling of scale-dependent characteristics of mechanical properties of metal polycrystals is studied using both discrete dislocation dynamics and continuum crystal plasticity. The initial movements of dislocation arc emitted from a Frank-Read type dislocation source and bounded by surrounding grain boundaries are examined by dislocation dynamics analyses system and we find the minimum resolved shear stress for the FR source to emit at least one closed loop. When the grain size is large enough compared to the size of FR source, the minimum resolved shear stress levels off to a certain value, but when the grain size is close to the size of the FR source, the minimum resolved shear stress shows a sharp increase. These results are modeled into the expression of the critical resolved shear stress of slip systems and continuum mechanics based crystal plasticity analyses of six-grained polycrystal models are made. Results of the crystal plasticity analyses show a distinct increase of macro- and microscopic yield stress for specimens with smaller mean grain diameter. Scale-dependent characteristics of the yield stress and its relation to some control parameters are discussed.     

Rheological study of heterogeneities in melt blends of ZN-LLDPE and LDPE: Influence of M<Subscript>w</Subscript> and comonomer type,and implications for miscibility

The influences of molecular weight and LLDPE comonomer type on the heterogeneity (immiscibility) of Ziegler-Natta LLDPE and LDPE blends are investigated with rheological methods. Dynamic and steady shear measurements were carried out in a Rheometrics Mechanical Spectrometer 800.Blends of low-M_w (<10⁵)LLDPE (butene) and LDPE are likely homogeneous and miscible as revealed by the dependence of their on blend composition at 140 °C. Blends of high-M_w (10⁵)LLDPE (butene) and LDPE mixed and tested at 190 °C were only partially miscible; heterogeneity and immiscibility was likely to occur around the 50/50 composition and in the LDPE-rich blends. Blends were likely miscible in the LLDPE-rich range. Increasing the LLDPE branch length (comonomer) from butene to octene slightly increased the miscibility of LLDPE/LDPE blends. It is suggested that the molecular order in polyethylenes (see Hussein and Williams (1999) J Non-Newtonian Fluid Mech 86:105–118; (1998) Macromol Rapid Commun 19:323–325) and mismatch of the molecular conformations of different polyethylene structures provide explanations for the immiscibility of polyethylenes. Agreement was observed between the measured G() and G() and theoretical predictions of Palierne and Bousmina-Kerner models, which are based on two-phase emulsion behavior.     

Development of Microwave-Assisted Extraction of Trigonelline Biomarker from Trigonella foenum-graecum Seeds Followed by High-Performance Thin-Layer Chromatographic and High-Performance Liquid Chromatographic Analyses

JPC – Journal of Planar Chromatography – Modern TLC - An efficient and fast microwave-assisted extraction (MAE) technique was developed for extracting trigonelline as an indicative...     

Temperature distribution in a storage tank

In this work the temperature distribution in a vertical storage tank fed at its top with warmer fluid at constant flow rate is investigated. The flow rate is considered to be so small that laminar flow conditions are established. The temperature of the admitted fluid is allowed to vary with time where step and ramp time functions are used in this work. A rigorous analytical solution is obtained which describes the temperature as function of vertical depth and time. Graphical representation of the temperature distribution is given for selected values of the flow parameter and the time constant. Special reference is made in selecting these numerical values to solar water heating systems. The results are discussed and also limitations are recalled.     

Synthesis and characterisation of asymmetrical mesogenic materials based on 2,5-disubstituted-1,3,4-oxadiazole

New mesogenic homologous series bearing 1,3,4-oxadiazole ring with a nitro terminal group, 4-(5-(4-nitrophenyl)-1,3,4-oxadiazol-2-yl)phenyl 4-((4-methoxybenzylidene)amino)benzoate (G₁–G₁₁), were synthesised. Their chemical structures are identified by fourier transform infrared spectroscopy (FT-IR), proton nuclear magnetic resonance (¹H-NMR) and elemental analysis. The liquid crystalline properties of the series G_n and their precursory F_n were screened by differential scanning calorimetry and optical polarising microscopy (OPM). The compounds of the series G_n were screened by thermogravimetric analysis to observe their thermal stability. The target compounds (G_n) in this study, were displayed different liquid crystalline mesophase, the first two homologous (G₁ and G₂) did not show any liquid crystalline behaviour, the homologous (G₃–G₁₀) which have an alkoxy terminal group (n = 3–10) exhibited nematic phase, whilst the last derivative of the series (G₁₁), n = 12, displayed SmA phase. The mesomorphic properties of these derivatives were affected by the presence of the nitro group at the end of the molecules which was classified as a strong polar group. Also, the role of alkoxy terminal chain and the bent heterocyclic ring (1,3,4-oxadiazole) in the liquid crystalline properties of these molecules were debated.     

Synthesis of Hg metal complex and its application to reduce the optical band gap of polymer

This study explored a new approach to fabricate the Schiff base ligand system from both ethylenediamine and 3-chloro-2-butanone. Through coordination chemistry, the mercury Hg (II) complex was achieved from the ligand and then embedded in the polyvinyl alcohol (PVA) host using a solution casting technique to prepare polymer composites (PCs). Both UV–visible and Fourier-transform infrared (FTIR) spectroscopies highlighted the formation of the Hg (II) metal complex. These techniques confirmed the synthesis of the Hg (II) metal complex. The X-ray diffraction (XRD) pattern of the polymer composite has shown a significant enhancement in its amorphous nature compared to the pure PVA host. The thermal analysis spectra for the Hg (II) complex revealed high thermal stability. The occurrence of the complexation between the Hg (II) and host matrix of the PVA was identified from the wide shifting of UV–vis absorption and peak shifting with intensity reduction of the FTIR spectra. Tauc's method has been employed to evaluate the optical band gap, and determine the types of electronic transitions. The results have shown that the samples were exhibiting an indirect forbidden electron transition, with a significant reduction in the optical band gap of a doped sample that approaching inorganic semiconductor based-materials. In addition, the optical study has exposed the role of the Hg (II) complex in tuning the refractive index of the host polymer. Ultimately, the absorption edge was found to be shifted to the lower photon energy upon the insertion of the Hg (II) complex. The PVA doped sample displayed a substantial shift in band gap from 6.2 eV to 1.2 eV.