Study of the effect of grain size on the dynamic mechanical properties of microalloyed steels

In the present paper the effect of grain refinement on the dynamic response of ultra fine-grained (UFG) structures for C–Mn and HSLA steels is investigated. A physically based flow stress model (Khan-Huang-Liang, KHL) was used to predict the mechanical response of steel structures over a wide range of strain rates and grain sizes. However, the comparison was restricted to the bcc ferrite structures. In previous work [K. Muszka, P.D. Hodgson, J. Majta, A physical based modeling approach for the dynamic behavior of ultra fine-grained structures, J. Mater. Process. Technol. 177 (2006) 456–460] it was shown that the KHL model has better accuracy for structures with a higher level of refinement (below 1 μm) compared to other flow stress models (e.g. Zerrili-Armstrong model). In the present paper, simulation results using the KHL model were compared with experiments. To provide a wide range of the experimental data, a complex thermomechanical processing was applied. The mechanical behavior of the steels was examined utilizing quasi-static tension and dynamic compression tests. The application of the different deformation histories enabled to obtain complex microstructure evolution that was reflected in the level of ferrite refinement.

Mechanical behaviour of irregular fibre materials

This work investigates the effect of fibre irregularities on the mechanical behaviour of the irregular fibres using the finite element method (FEM). The first part of this work examines that the effect of fibre dimensional irregularities on the linear and non-linear tensile behaviour of the fibres, using a two-dimensional (2D) finite element models. In the linear simulation, a concept of method Young’s modulus is introduced. The method Young’s modulus, breaking load and breaking extension are affected by the magnitude and frequency of diameter variation in the fibre specimen. Fibre dimensional variation and the gauge length effect are also simulated. In the non-linear analysis, some additional information is obtained on changes in the yield and post-yield regions, which are clearly shown in the load-extension curves. Further investigation is focused on the flexural buckling behaviour of fibres with dimensional irregularities. A three-dimensional (3D) finite element model is used to simulate the buckling deformation of dimensionally irregular fibres, and the critical buckling load of the simulated fibre is calculated. Two parameters, the effective length and the average diameter within the effective length of an irregular fibre, are considered to be the key factors that influence the buckling behaviour of the fibre. An important aspect of this work is the calculation of the effective length of an irregular fibre specimen during buckling. This method has not been reported before. The third part of this work is on the combined tensile and torsional behaviour of fibres with dimensional irregularities, using a three-dimensional (3D) finite element model. Two types of fibres, polyester and wool, are simulated with sine waves of different level (magnitude) and frequency at different twist levels. For the polyester fibre, experiment verification of the simulation results has been carried out, and the results indicate the FE model is well acceptable for the simulation. The final part of this work examines the combined effect of dimensional and structural irregularities on the fibre tensile behaviour. Three-dimensional (3D) finite element models are used to simulate the cracks (transverse, longitudinal, combined transverse and longitudinal cracks) and cavities distributed in uniform fibres and fibres with 30% level of diameter variation, respectively. One of important conclusions is that under the simulated conditions, the dimensional irregularity of fibre influences the tensile behaviour of fibres more than the fibre structural irregularity. The fibre dimensional irregularity affects not only the values of the breaking load and breaking extension, but also the shape of load-extension curves. However, the fibre structural irregularity simulated in the study appears to have little effect on the shape of the load-extension curves. In addition, the effect of crack or cavity size, type and distribution on fibre tensile properties is also investigated.

Computational aspects of the numerical solution of SDEs

In the last 30 to 40 years, many researchers have combined to build the knowledge base of theory and solution techniques that can be applied to the case of differential equations which include the effects of noise. This class of ``noisy'' differential equations is now known as stochastic differential equations (SDEs). Markov diffusion processes are included within the field of SDEs through the drift and diffusion components of the Itô form of an SDE. When these drift and diffusion components are moderately smooth functions, then the processes' transition probability densities satisfy the Fokker-Planck-Kolmogorov (FPK) equation -- an ordinary partial differential equation (PDE). Thus there is a mathematical inter-relationship that allows solutions of SDEs to be determined from the solution of a noise free differential equation which has been extensively studied since the 1920s. The main numerical solution technique employed to solve the FPK equation is the classical Finite Element Method (FEM). The FEM is of particular importance to engineers when used to solve FPK systems that describe noisy oscillators. The FEM is a powerful tool but is limited in that it is cumbersome when applied to multidimensional systems and can lead to large and complex matrix systems with their inherent solution and storage problems. I show in this thesis that the stochastic Taylor series (TS) based time discretisation approach to the solution of SDEs is an efficient and accurate technique that provides transition and steady state solutions to the associated FPK equation. The TS approach to the solution of SDEs has certain advantages over the classical techniques. These advantages include their ability to effectively tackle stiff systems, their simplicity of derivation and their ease of implementation and re-use. Unlike the FEM approach, which is difficult to apply in even only two dimensions, the simplicity of the TS approach is independant of the dimension of the system under investigation. Their main disadvantage, that of requiring a large number of simulations and the associated CPU requirements, is countered by their underlying structure which makes them perfectly suited for use on the now prevalent parallel or distributed processing systems. In summary, l will compare the TS solution of SDEs to the solution of the associated FPK equations using the classical FEM technique. One, two and three dimensional FPK systems that describe noisy oscillators have been chosen for the analysis. As higher dimensional FPK systems are rarely mentioned in the literature, the TS approach will be extended to essentially infinite dimensional systems through the solution of stochastic PDEs. In making these comparisons, the advantages of modern computing tools such as computer algebra systems and simulation software, when used as an adjunct to the solution of SDEs or their associated FPK equations, are demonstrated.

Adhesion performance of polymer nanofibres under shear loading

Geckos have extraordinary wall-climbing ability because of the millions of hairs with micro/nano fibrillar structures on their feet. Mimicking gecko's feet is of scientific and engineering importance for development of physical adhesion materials and devices. The design of gecko-inspired physical adhesives seems to be geometry dominated. In this study, Finite Element Method (FEM) has been used to analyse the vertical peel-off force of polyporpylene (PP) nanofibres having different fibre dimensions, inclining angels and contact areas on a flat glass substrate. It has been found that the main parameters affecting the frictional adhesion are fibre diameter and fibre aspect ratio, the inclining angle between the fibre and the substrate surface, and the intimate contact areas. Our analysis has shown that PP nanofibres with a diameter of less than 200nm can generate less peel-off force than fibres of larger diameters, indicating more stable adhesion with the glass substrate for thinner fibres. A bent fibre with more intimate contact area can bear more shear force than a straight fibre with less contact area. Also, under the same shear loading, fibres with an inclining angle of less than 30° provide a low peel off force.

A new solution method for homogenization of effective properties of electromagnetic honeycombs

In this paper, an analytical model and its new numerical solution using the homogenization method are developed to determine the effective electromagnetic characteristics of honeycombs. Based on the proposed solution method, the electromagnetic properties are obtained by employing the multi-scale homogenization theory and periodical electric (magnetic) potential boundary conditions. Further, the effect of geometry of honeycomb's unit cell on effective electromagnetic properties is investigated with the use of the proposed method. The numerical results are compared with analytic results using the Smith-Scarpa's semi-empirical formula.

Physically based simulation of heterogeneous deformable models using XFEM

This paper addresses the problem of heterogeneous deformable model accuracy using the finite element methods (FEM). Classic FEM uses predefined shape functions for interpolation and does not account easily for regions of discontinuities. Extended finite element methods (XFEM) use enrichment functions to compensate for the change in an element degrees of freedom (DoFs) in deformable objects. The XFEM is an accurate and fast method as no remeshing is required. In this study we investigate the performance of XFEM and demonstrate how it may be applied to discontinuities of materials that exist in heterogeneous (piece-wise homogeneous) models. The results show realistic stress prediction compared to modeling the same objects with classic FEM.

Transient temperature distribution in functionally graded graphite/Polymer nanocomposites based on temperature dependent properties

Transient heat conduction in a functionally graded graphite/polymer nanocomposite (FGN) plate is analyzed using finite element method (FEM). Stepwise gradient structure consisted of four different nanocomposite layers with 0, 5, 10 and 20 wt% of graphite. Thermal conductivity and specific heat capacity of the individual layers were determined using C-Therm TCi Thermal Conductivity Analyzer (Canada) in temperature range of -20 to 100 °C. Temperature history and temperature distribution across the thickness of the plate with two different configurations for two positive and negative temperature gradients are presented.

Multi-layer implantable antenna for closed loop deep brain stimulation system

A multi-layer circular planar inverted-F antenna is designed and simulated at the industrial, scientific, and medical (ISM) band of 915 MHz for closed loop deep brain stimulation implant. The ISM band is considered due to the capabilities of small antenna size, high data rate, and long transmission range. In the proposed four-layer antenna, the top three radiating layers are meandered, and a high permittivity substrate and superstrate materials are used to limit the radius and the height of the antenna to 3.5 mm and 2.2 mm, respectively. The bottom layer works as a ground plate. The Roger RO3210 of εr = 10.2 and δ = 0.003 is used as a dielectric substrate and superstrate. The resonance frequency of the proposed antenna is 915 MHz with a bandwidth of 12 MHz at the return loss of -10 dB in free space. The stacked layered structure reduces the antenna size, and the circular shape makes it easily implantable into the human head. The antenna parameters (e.g. 3D gain pattern), SAR value, and electric field distribution within a six layers spherical head model are evaluated by using the finite element method (FEM). The feasibility of the wireless transmission of power, control and command signal to the implant in the human head is also examined. © 2012 IEEE.