Papers by Keyword: Elasticity

Abstract: This paper is a continuation of earlier publications of the authors related to the analysis of mechatronic systems including piezoelectric materials used as sensors or actuators for stabilization and damping of mechanical vibration. It was demonstrated that only very accurate mathematical model of the system with the piezoelectric transducers and external electric circuit attached to a mechanical system like a beam or a shaft by a glue layer allows the engineers to design the system with required dynamic parameters. Geometrical and material parameters of all the components have to be taken into account because neglecting the influence of one of them results in erroneous analysis results [1-4]. The paper presents the improved mathematical model of the considered mechatronic system. The assumption of pure shear of the connection layer is rejected during modeling and deformation of the layer is taken into consideration. The purpose of the reported enhancement of the mathematical model of the considered mechatronic system is to improve accuracy of computational results.

Abstract: A finite element simulation of a plasma sprayed thermal barrier coating(TBC) system was conducted. Plasma sprayed thermal barrier ceramic coating was treated as either a simple elastic model or an advanced viscoplastic model which includes rate dependence and unequal flow stresses in tension and compression. Predicted tensile stresses emerging in the ceramic plane at the elevated temperature never become large enough to cause surface cracks based on elastic analysis, so does using the viscoplastic model. At the low temperature, these two models identically show that the ceramic coat will locally cracks at the “peak” location. It is shown that although there are some numerical differences in these two models’ predictions, elastic analysis predicts accurate in failure mechanism analysis based on stresses

Abstract: Many nanocomposite materials are obtained by dispersing a charge in a matrix. Due to the conditions of mixing, the arrangement of the charge usually presents some heterogeneity at different scales. In order to predict the effective properties of such composites (like the dielectric permittivity or the elastic moduli), it is necessary to know the properties of the two components (charge and matrix), and their spatial distribution. To fulfil this project, we developed a general methodology in several steps: the morphology is summarized by multi-scale random models accounting for the heterogeneous distribution of aggregates. The identification of models is made from image analysis. It is then used for the prediction of effective properties by estimation, or by numerical simulations. Our approach is illustrated by various examples of multi-scale models: Boolean random sets based on Cox point processes and various random grains (spheres, cylinders), showing a very low percolation threshold and therefore a high conductivity or elastic moduli for a low charge content; multi-scale iterations of random media.

Abstract: In this work, the mechanical properties of randomly folded thin sheets in the hydrostatic and non-hydrostatic stress states were studied. It is pointed out that under the hydrostatic compression the sheet, rigidity is governed by the volume dependence of its enthalpy, whereas in a non-hydrostatic stress state, the rigidity of folded sheets is controlled by the shape dependence of the Edwards entropy of the network of crumpling creases. Furthermore, the stress relaxation in folded sheets after uni-axial compression was studied. It was found that stress relaxation in folded elasto-plastic sheets differs from this in the folded predominantly plastic sheets and obeys an unusual relaxation law with the universal characteristic exponent.

Abstract: This paper determined the torsional strength of steel reinforcements used in the construction industry in Nigeria and compares their Modulus of Rigidity with available standards. Fifteen test specimens were examined from the reinforcing steel of various sizes ranging from 8mm to 20mm diameter which were sourced randomly. The samples were tested with the Torsion Testing Machine until failure. The initial parameters such as gauge length and diameter were considered before the application of torque. The failure torque for the 8mm, 10mm, 12mm, 16mm and 20mm steel reinforcements obtained from the test are 15Nm, 28.81Nm, 77.09Nm, 191.89Nm and 368.99Nm respectively. The result showed that the torsional strength of reinforcement available in the construction industry is below the standard modulus of rigidity of 21000N/mm2 by about 15%.

Abstract: The asymptotic method is used to solve the three-dimensional dynamic problem of the elasticity theory on forced vibrations of multi-layered orthotropic plate under full contact conditions between the layers. The analysis of the obtained mathematically exact solutions is conducted and the usage of seismoisolators is proved. For a three-layered packet (foundation-seismoisolator-base) it is shown that in case the layers are rigid enough, the displacements imparted to the lower layer are basically transmitted to the upper layers, and when the middle layer is considerably soft, the amplitudes of the upper layer vibrations are essentially diminishing. The results prove the necessity of using seismic isolators, particularly in the construction of especially responsible buildings, such as schools, hospitals etc., with the aim of decreasing negative influence of earthquakes. The simple algorithm is built in order to calculate the amplitudes of forced vibrations in case of any quantity and configurations of layers. The behavior of the multi-layered packets under various layers configurations is graphically illustrated.

Abstract: Cast iron and steel conveying rollers used in hot rolling mills must be changed very frequently because conveyed strips with high temperature induces wear on the roller surface in short periods. This failure automatically stops the production line for repair and maintenance of conveying rollers. In this study a new type of roller is considered where a ceramics sleeve is connected with two short shafts at both ends by shrink fitting. Here, a ceramics sleeve provides longer life and therefore reduces the cost for the maintenance. However, for the hollow ceramics rollers, care should be taken for maximum tensile stresses appearing at both edges of the sleeve. In particular, because fracture toughness is extremely smaller compared with the value of steel, stress analysis for the roller is necessary for ceramics sleeve. In this study FEM analysis is applied to the structure, and the maximum stress has been investigated with varying the dimensions of the structure. It is found that the maximum tensile stress appearing at the end of sleeves takes a minimum value at a certain amount of shrink fitting ratio.

Abstract: A traditional approach to increasing fatigue resistance of many assemblies involves the creation of regions of compressive residual stress. For example, riveting holes used in modern passenger aircraft are currently subjected to cold expansion using split mandrel tools. The method is relatively expensive and not entirely problem-free. In the present study we consider a method of creating residual stresses around drilled holes referred to as ‘dimpling’, that itself is a variation of a novel technique known as the StressWaveTM process. An experimental procedure is described for the creation of localised regions of significant plastic deformation and residual stress by ‘dimpling’, allowing the production of cold-worked and residually-stressed specimens. The overall aims of this study were to determine thickness-average residual stresses by two different techniques, namely, one destructive technique (Sachs boring) and one non-destructive (high energy X-ray diffraction); and to compare the results. In Sachs boring experiments the variation of strain gauge readings with increasing diameter of the central hole was recorded. A classical elastic-ideally plastic axisymmetric model for plane stress conditions was used in the analysis. Energy dispersive synchrotron X-ray diffraction experiments were performed for non-destructive assessment of residual elastic strains. The two different stress evaluation techniques used in this project led to consistent results. Good correlation was found between the stresses obtained from X-ray diffraction results and those deduced from Sachs boring experiments.

Abstract: Most models based on continuum mechanics do not account for inhomogeneities at the micro-scale. This can be achieved by considering a representative volume of material and using (poly)crystal elasto-plastic deformation theory to model the effects of grain morphology and crystallographic orientation. In this way, the relationship between the macroscopic stress state and the stress state at the grain level can be investigated in detail. In addition, this approach enables the determination of the inhomogeneous fields of plastic strain, the identification of regions of localised plasticity (persistent slip bands), grain level shakedown, and the prediction of fatigue crack initiation using energy dissipation at the micro-scale. Elastic anisotropy is known to promote earlier onset of yielding, and to increase the magnitude of intergranular residual stresses. The effect of hardening behaviour of different slip systems on intergranular residual stresses is more subtle, as discussed in the text. The present study focuses on the analysis average intergranular residual strains and stresses that arise within the polycrystal aggregate following the application of single or cyclic external loading. These residual strains can also be evaluated experimentally using diffraction of penetrating radiation, e.g. neutrons or high energy X-rays, allowing comparisons with the model predictions to be made.

Abstract: The sin2ψ technique for near-surface and bulk stress evaluation is frequently considered to be the method of reference, largely due to the historical reason of being established early on in the development of experimental study of residual stress, and due to the widespread availability of laboratory X-ray facilities equipped with goniometers allowing ψ-tilting to be carried out. In recent years other diffraction-based techniques of residual strain and residual stress evaluation have been developed, some of them based at large facilities such as synchrotrons, neutron reactors or spallation sources, and others becoming available in the laboratory setting. It is therefore perhaps relevant and timely to review the strengths and shortcomings of the sin2ψ technique in today’s context. In the present study this task is addressed through the use of polycrystal elasto-plastic modelling that allows the determination of equivalent average elastic lattice strains following complex deformation history, and by post-processing of the model results in order to extract the parameters measurable in diffraction experiments. In particular, it is possible to extract the simulated strain values that would be measured at different tilt angles, and to build a family of sin2ψ plots for different reflections. It then becomes possible to assess the degree to which the hypotheses underpinning the principle of this method are enforced or violated; to select the most suitable reflections; and to discuss how the method could be improved or varied to provide more reliable residual stress measurement procedures.