Singular behaviour near the tip of a sharp V-notch in a power law hardening material

This paper presents an asymptotic analysis of the near-tip stress and strain fields of a sharp V-notch in a power law hardening material. First, the asymptotic solutions of the HRR type are obtained for the plane stress problem under symmetric loading. It is found that the angular distribution function of the radial stress sigma(r) presents rapid variation with the polar angle if the notch angle beta is smaller than a critical notch angle; otherwise, there is no such phenomena. Secondly, the asymptotic solutions are developed for antisymmetric loading in the cases of plane strain and plane stress. The accurate calculation results and the detailed comparisons are given as well. All results show that the singular exponent s is changeable for various combinations of loading condition and plane problem.

Asymptotic solutions to a class of nonlinear oscillation systems

In this paper, we present an asymptotic method for the analysis of a class of strongly nonlinear oscillators, derive second-order approximate solutions to them expressed in terms of their amplitudes and phases, and obtain the equations governing the amplitudes and phases, by which the amplitudes of the corresponding limit cycles and their behaviour can be determined. As an example, we investigate the modified van der Pol oscillator and give the second-order approximate analytical solution of its limit cycle. The comparison with the numerical solutions shows that the two results agree well with each other.

Stiffness behaviour of injection moulded short glass fibre/impact modifier/polypropylene hybrid composites

The stiffness behaviour of injection moulded short glass fibre/impact modifier/polypropylene hybrid composites has been investigated in this work by theoretical predictions and experiments. Predictions from the self-consistent method were found to be in good agreement with test results for the impact modifier/polypropylene blends. By taking into account of the fibre orientation distributions in the skin and core layers, the values of Young's modulus for the skin and core layers were predicted by employing Eshelby's equivalent inclusion method and the average induced strain approach. The prediction of the values of Young's modulus for the whole sample was obtained by applying the simple mixture theory of laminated composites to the predicted results for the skin and core layers. Good correlation between predicted and experimental Young's modulus values were found.

Thermal-mechanical interface crack behaviour of a surface mount solder joint

The effect of thermal-mechanical loading on a surface mount assembly with interface cracks between the solder and the resistor and between the solder and the printed circuit board (PCB) was studied using a non-linear thermal finite element analysis. The thermal effect was taken as cooling from the solder eutectic temperature to room temperature. Mechanical loading at the ends of the PCB was also applied. The results showed that cooling had the effect of causing large residual shear displacement at the region near the interface cracks. The mechanical loading caused additional crack opening displacements. The analysis on the values of J-integral for the interface cracks showed that J-integral was approximately path independent, and that the effect of crack at the solder/PCB interface is much more serious than that between the component and solder.

Microstructure and mechanical behaviour of a SiC particles reinforced Al-5Cu composite under dynamic loading

The mechanical behaviour of a composite of Al–5Cu matrix reinforced with 15% SiC particles was studied at different strain rates from 1×10−3 to 2.5×103 s−1 using both a conventional universal testing machine (for low strain-rate tests) and a split Hopkinson bar (for tests at dynamic strain rates). Whilst the yield stress of the composite increases as the strain rate increases, the maximum flow stresses, 440 MPa for compression and 450 MPa for tension, are independent of strain rate. The microstructures and defect structures of the deformed composite were studied with both scanning electron microscopy and transmission electron microscopy and were correlated to the observed mechanical behaviour. Fracture surface studies of samples after dynamic tensile testing indicates that failure of the composite is controlled by ductile failure of the aluminium matrix by the nucleation, growth and coalescence of voids.

Effect of structural relaxation on deformation behaviour of Zr-based metallic glass

Structural relaxation through isothermal annealing at tempertature below glass transition is conducted on Zr46.75Ti8.25Cu7.5Ni10Be27.5 (Vitreloy-4) bulk metallic glass. Defect concentration is correlated with the annealing time t according to differential scanning calorimetry thermalgrams. The effects of structural relaxation on mechanical properties and deformation behaviour are investigated by using instrumented nanoindentation. It is found that as-cast alloy exhibits pronounced serration flow during the loading process of nanoindentation, and the size and number of serrations decrease with the annealing time. The change of the deformation behaviour with structural relaxation is explained using a free volume model.

Behaviour of a puff of resuspended sediment: a conceptual model

The particulate matter concentration above the seabed is usually assumed to decrease with height, following an exponential or Rouse profile. Many particulate matter concentration profiles with a peak were found on the North Mediterranean bottom water at a few tens of metres above the bottom. A particle size signal at the same altitude was found in this area and on the New York Eight shelf. It is assumed that this unexpected shape is due to a cloud of resuspended cohesive sediments originating from an impulse resuspension process. A simplified three-dimensional numerical model is proposed to describe the behaviour of resuspended particulate matter that originates from a sediment impulse vertically injected in the bottom water. This model reproduces the concentration profile shape observed, and it gives indications concerning the length and time characteristics of such a cloud, depending on the water velocity and bottom boundary layer properties.

Interfacial microstructure and mechanical behaviour in laser clad TiCp/Ni alloy coatings

Coatings of TiCp reinforced composite have been produced by laser cladding. Two kinds of coating with different TiCp origins were investigated, i.e. undissolved TiCp and in situ TiCp. For undissolved TiCp, epitaxial growth of TiC, precipitation of CrB, and a chemical reaction occur at phase interfaces, and nanoindentation loading curves show pop in marks caused by the plastic deformation associated with crack formation or debonding of TiCp from the matrix. As for in situ TiCp, no pop in mark appears. Meanwhile, in situ TiCp produces hardness and elastic modulus values that are higher than those produced by the coating that contains undissolved TiCp.

Transition to Chaos in the Floating Half Zone Convection

The transition process from steady convection to chaos is experimentally studied in thermocapillary convections of floating half zone. The onset of temperature oscillations in the liquid bridge of floating half zone and further transitions of the temporal convective behaviour are detected by measuring the temperature in the liquid bridge. The fast Fourier transform reveals the frequency and amplitude characteristics of the flow transition. The experimental results indicate the existence of a sequence of period-doubling bifurcations that culminate in chaos. The measured Feigenbaum numbers are delta(2) = 4.69 and delta(4) = 4.6, which are comparable with the theoretical asymptotic value delta = 4.669.

Asymptotic analysis for a crack on interface of damaged materials

An asymptotic analysis for a crack lying on the interface of a damaged plastic material and a linear elastic material is presented in this paper. The present results show that the stress distributions along the crack tip are quite similar to those with HRR singularity field and the crack faces open obviously. Material constants n, mu and mo are varied to examine their effects on the resulting stress distributions and displacement distributions in the damaged plastic region. It is found that the stress components sigma(rr), sigma(theta theta), sigma(r theta) and sigma(e) are slightly affected by the changes of material constants n, mu and m(0), but the damaged plastic region are greatly disturbed by these material parameters.

Behaviour of Gaseous Chlorine and Alkali Metals During Biomass Thermal Utilisation

The behaviour of gaseous chlorine and alkali metals of three sorts of biomass (Danish straw, Swedish wood, and sewage sludge) in combustion or gasification is investigated by the chemical equilibrium calculating tool. The ranges of temperature, air-to-fuel ratio, and pressure are varied widely in the calculations (T=400-1800 K, gimel=0-1.8, and P=0.1-2.0 MPa). Results show that the air excess coefficient only has less significant influence on the release of gaseous chlorine and potassium or sodium during combustion. However, in biomass gasification, the influence of the air excess coefficient is very significant. Increasing air excess coefficient enhances the release of HCl(g), KOH(g), or NaOH(g) as well as it reduces the formation of KCl(g), NaCl(g), K(g), or Na(g). In biomass combustion or straw and sludge gasification, increasing pressure enhances the release of HCl(g) and reduces the amount of KCI(g), NaCl(g), KCI(g), or NaOH(g) at high temperatures. However, during wood gasification, the pressure enhances the formation of KOH(g) and KCI(g) and reduces the release of K(g) and HCl(g) at high temperatures. During wood and sewage sludge pyrolysis, nitrogen addition enhances the formation of KCN(g) and NaCN(g) and reduces the release of K(g) and Na(g). Kaolin addition in straw combustion may enhance the formation of potassium aluminosilicate in ash and significantly reduces the release of KCl(g) and KOH(g) and increases the formation of HCl(g).

Mode I and Mode II Crack Tip Asymptotic Fields with Strain Gradient Effects

The strain gradient effect becomes significant when the size of fracture process zone around a crack tip is comparable to the intrinsic material length l, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dominant strain field is irrotational. For mode I plane stress crack tip asymptotic field, the stress asymptotic field and the couple stress asymptotic field can not exist simultaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode II plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode II plane stress and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode I and mode II, because the present theory is based only on the rotational gradient of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient.

A New Modified Expanding Cavity Model for Characterizing the Spherical Indentation Behaviour of Bulk Metallic Glass with Pile-up

Spherical nanoindentation tests were performed on Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass and pile-ups were observed around the indenter. A new modified expanding cavity model was developed to characterize the indentation deformation behavior of strain-hardening and pressure-dependent materials. By using this model, the representative stress-strain response of this bulk metallic glass to hardness and indentation in the elastic-plastic regime were obtained taking into consideration the effect of pile-up.

Behaviour analysis of numerical solutions and simulation of coherent structures in compressible mixing layers

For understanding the correctness of simulations the behaviour of numerical solutions is analysed, Tn order to improve the accuracy of solutions three methods are presented. The method with GVC (group velocity control) is used to simulate coherent structures in compressible mixing layers. The effect of initial conditions for the mixing layer with convective Mach number 0.8 on coherent structures is discussed. For the given initial conditions two types of coherent structures in the mixing layer are obtained.