A New Finite Element Method for Strain Gradient Theories and Applications to Fracture Analyses

A new compatible finite element method for strain gradient theories is presented. In the new finite element method, pure displacement derivatives are taken as the fundamental variables. The new numerical method is successfully used to analyze the simple strain gradient problems – the fundamental fracture problems. Through comparing the numerical solutions with the existed exact solutions, the effectiveness of the new finite element method is tested and confirmed. Additionally, an application of the Zienkiewicz–Taylor C1 finite element method to the strain gradient problem is discussed. By using the new finite element method, plane-strain mode I and mode II crack tip fields are calculated based on a constitutive law which is a simple generalization of the conventional J2 deformation plasticity theory to include strain gradient effects. Three new constitutive parameters enter to characterize the scale over which strain gradient effects become important. During the analysis the general compressible version of Fleck–Hutchinson strain gradient plasticity is adopted. Crack tip solutions, the traction distributions along the plane ahead of the crack tip are calculated. The solutions display the considerable elevation of traction within the zone near the crack tip.

Improved Procedure on the Microscopic Approach to Determine Colloidal Stability

We present an improved procedure on the approach to determine the stability of polystyrene spheres at microscopic particle levels by means of artificially induced particle collisions with the aid of optical tweezers [J.Chem.Phys. 119, 2399(2003)]. The basic consideration on this new development is that the major contribution to the sticking probability for a particle pair caught into the optical trap for a short period is from its single collision; therefore, if the trapping duration for the pair is taken to be short, the accumulated sticking probability will be a good approximation for the single collision. The experimental procedure associated with this approximation does not resort to exactly controlling the short trapping duration or request the trapping duration correction as previously reported and therefore it is more practical and applicable for broader range of the stability ratio. The experimental results under different electrolyte concentrations by the new procedure are consistent with those from the turbidity measurements.

Performance analyses of flowing chemical oxygen-iodine laser

A modified simplified rate-equation model that utilizes the Voigt profile function and another gain saturation model deduced from the kinetic equations are presented for performance analyses of a flowing chemical oxygen-iodine laser. Both models are adapted to both the condition of homogeneous broadening and that of inhomogeneous broadening being of importance and the condition of inhomogeneous broadening being predominant. Effects of temperature and iodine density on the output power and on variations of output power, optical intensity, and saturation intensity with flow distance are presented as well. There are differences between results of two models, but both qualitatively agree with known results.

Measurement of Microscopic Deformation in a Cualni Single Crystal Alloy by Nanoindentation with a Heating Stage

Thermally induced recovery of nanoindents in a CUAINi single crystal shape memory alloy was studied by nanoindentation in conjunction with a heating stage. Nanoindents formed by a Berkovich indenter at room temperature were heated to 40, 70 and 100 degrees C. Partial recovery was observed for the nanoindents. The recovery ratio depended on the heating temperature. Indentation of CuAlNi can induce inelastic deformation via dislocation motion and a stress-induced matensitic transformation. The percentages of dislocation-induced plastic strain would affect the thermal deformation of CuAlNi, because the induced dislocations could stabilize stress-induced martensite plates even when the temperature above austenite finish temperature, A(f). When the applied indentation load is low (less than 10,000 mu N), the shape recovery strain is predominant, compared with the dislocation-induced plastic strain. Therefore, the degree of indent recovery in the depth direction, delta(D), is high (about 0.7-0.8 at 100 degrees C).

Statistical and stochastic description of microvoid evolution observed in dynamic failure of ductile materials

A brief review is presented of statistical approaches on microdamage evolution. An experimental study of statistical microdamage evolution in two ductile materials under dynamic loading is carried out. The observation indicates that there are large differences in size and distribution of microvoids between these two materials. With this phenomenon in mind, kinetic equations governing the nucleation and growth of microvoids in nonlinear rate-dependent materials are combined with the balance law of void number to establish statistical differential equations that describe the evolution of microvoids' number density. The theoretical solution provides a reasonable explanation of the experimentally observed phenomenon. The effects of stochastic fluctuation which is influenced by the inhomogeneous microscopic structure of materials are subsequently examined (i.e. stochastic growth model). Based on the stochastic differential equation, a Fokker-Planck equation which governs the evolution of the transition probability is derived. The analytical solution for the transition probability is then obtained and the effects of stochastic fluctuation is discussed. The statistical and stochastic analyses may provide effective approaches to reveal the physics of damage evolution and dynamic failure process in ductile materials.

Study of the surface structure of butterfly wings using the scanning electron microscopic moire method

Scanning electron microscopic (SEM) moire method was used to study the surface structure of three kinds of butterfly wings: Papilio maackii Menetries, Euploea midamus (Linnaeus), and Stichophthalma how-qua (Westwood). Gratings composed of curves with different orientations were found on scales. The planar characteristics of gratings and some other planar features of the surface structure of these wings were revealed, respectively, in terms of virtual strain. Experimental results demonstrate that SEM moire method is a simple, nonlocal, economical, effective technique for determining which grating exists on one whole scale, measuring the dimension and the whole planar structural character of the grating on each scale, as well as characterizing the relationship between gratings on different scales of each butterfly wing. Thus, the SEM moire method is a useful tool to assist with characterizing the structure of butterfly wings and explaining their excellent properties. (c) 2007 Optical Society of America.

Numerical analyses for the material bifurcation in plane sheet under tension

The various patterns (shear banding, surface wrinkling and necking) of material bifurcation in plane sheet under tension are investigated in this paper by means of a numerical method. It is found that numerical analysis can provide better ground for searching for the lowest critical loads. The inhomogeneity caused by void damage and the nonuniformity in the stress distribution across sheet thickness are proved to have detrimental effects on the material bifurcation. Nevertheless, material stability can be promoted by any means of depressing void damage or alleviating stress, even locally across the thickness. Besides, the peculiar behaviour of material bifurcation under slight biaxiality state is demonstrated. Copyright (C) 1996 Elsevier Science Ltd

Micromechanics analyses of interface crack

A new mechanics model based on Peierls concept is presented in this paper, which can clearly characterize the intrinsic features near a tip of an interfacial crack. The stress and displacement fields are calculated under general combined tensile and shear loadings. The near tip stress fields show some oscillatory behaviors but without any singularity and the crack faces open completely without any overlapping when remote tensile loading is comparable with remote shear loading. A fracture criterion for predicting interface toughness has been also proposed, which takes into account for the shielding effects of emitted dislocations. The theoretical toughness curve gives excellent prediction, as compared with the existing experiment data.

Analyses of the mechanical properties and microstructure of bamboo epoxy composites

Bamboo reinforced epoxy possesses reasonably good properties to waarrant its use as a structural material, and is fabricated by utilizing bamboo, an abundant material resource, in the technology of fibre composites. Literature on bamboo-plastics composites is rare. This work is an experimental study of unidirectional bamboo-epoxy laminates of varying laminae number, in which tensile, compressive, flexural and interlaminar shear properties are evaluated. Further, the disposition of bamboo fibre, the parenchymatous tissue, and the resin matrix under different loading conditions are examined. Our results show that the specific strength and specific modulus of bamboo-epoxy laminates are adequate, the former being 3 to 4 times that of mild steel. Its mechanical properties are generally comparable to those of ordinary glass-fibre composites. The fracture behaviour of bamboo-epoxy under different loading conditions were observed using both acoustic emission techniques and scanning electron microscopy. The fracture mode varied with load, the fracture mechanism being similar to glass and carbon reinforced composites. Microstructural analyses revealed that natural bamboo is eligibly a fibre composite in itself; its inclusion in a plastic matrix will help solve the problems of cracking due to desiccation and bioerosion caused by insect pests. Furthermore, the thickness and shape of the composite can be tailored during fabrication to meet specific requirements, thereby enabling a wide spectrum of applications.

Microscopic theory of chemical-reaction rate

In this paper we deduce the formulae for rate-constant of microreaction with high resolving power of energy from the time-dependent Schrdinger equation for the general case when there is a depression on the reaetional potential surface (when the depression is zero in depth, the case is reduced to that of Eyring). Based on the assumption that Bolzmann distribution is appropriate to the description of reactants, the formula for the constant of macrorate in a form similar to Eyring's is deduced and the expression for the coefficient of transmission is given. When there is no depression on the reactional potential surface and the coefficient of transmission does not seriously depend upon temperature, it is reduced to Eyring's. Thus Eyring's is a special case of the present work.

Elastic-plastic finite element analyses of short cracks

Stress and strain distributions and crack opening displacement characteristics of short cracks have been studied in single edge notch bend and centre cracked panel specimens using elastic–plastic finite element analyses incorporating both a non strain hardening and a power law hardening behaviour. J contour integral solutions to describe stress strain conditions at crack tips for short cracks differ from those for long cracks. The analyses show that (i) short cracks can propagate at stress levels lower than those required for long cracks and (ii) a two-parameter description of crack tip fields is necessary for crack propagation.

Association analyses of DNA polymorphisms in bovine SREBP-1, LXRα,FADS1 genes with fatty acid composition in Canadian commercial crossbred beef steers

Two previously reported DNA polymorphisms of sterol regulatory element binding transcription factor 1 (SREBP1) and liver X receptor alpha (LXRα) and two DNA polymorphisms of fatty acid desaturase 1 (FADS1) were evaluated for associations with fatty acids in brisket adipose tissue of Canadian cross-bred beef steers. The polymorphism of 84 bp insert/deletion in intron 5 of SREBP1 was significantly associated with the concentration of 9c C17:1 (P=0.013). The G>A single nucleotide polymorphism (SNP) in the exon 4 of LXRα gene was associated with the concentration of 9c, 11t C18:2 (P=0.04), sum of conjugated linoleic acids (CLA) (P=0.025) and 11c C20:1(P=0.042). Two DNA polymorphisms in the promoter region of FADS1, deletion/insertion of ->GTG in rs133053720 and SNP A>G in rs42187276, were significantly associated with concentrations of C17:0 iso, C17:0 ai, total branched chain fatty acids (BFA), 12t C18:1, 13t/14t C18:1, 15t C18:1, and 13c C18:1 (P<0.05). Further studies are needed to validate the associations and to delineate the roles of the gene polymorphisms in determining the fatty acid composition in beef tissues.

Numerical Analyses of Transonic Fluid/Structure interaction in Aircraft Engineering

Through the coupling between aerodynamic and structural governing equations, a fully implicit multiblock aeroelastic solver was developed for transonic fluid/stricture interaction. The Navier-Stokes fluid equations are solved based on LU-SGS (lower-upper symmetric Gauss-Seidel) Time-marching subiteration scheme and HLLEW (Harten-Lax-van Leer-Einfeldt-Wada) spacing discretization scheme and the same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Transfinite interpolation (TFI) is used for the grid deformation of blocks neighboring the flexible surfaces. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between fluid and structure. The developed code was fort validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. In the subsonic and transonic range, the calculated flutter speeds and frequencies agree well with experimental data, however, in the supersonic range, the present calculation overpredicts the experimental flutter points similar to other computations. Then the flutter character of a complete aircraft configuration is analyzed through the calculation of the change of structural stiffness. Finally, the phenomenon of aileron buzz is simulated for the weakened model of a supersonic transport wing/body model at Mach numbers of 0.98 and l.05. The calculated unsteady flow shows, on the upper surface, the shock wave becomes stronger as the aileron deflects downward, and the flow behaves just contrary on the lower surface of the wing. Corresponding to general theoretical analysis, the flow instability referred to as aileron buzz is induced by a stronger shock alternately moving on the upper and lower surfaces of wing. For the rigid structural model, the flow is stable at all calculated Mach numbers as observed in experiment