Analysis of the limiting plastic state of a thick-walled bent pipe

We propose an engineering approach to the determination of the limiting state of a bent pipe. In the first stage, the influence of some groups of external loads is analyzed separately. Then it is necessary to determine the coefficient of reduction of internal moments under the combined action of external bending moments and internal pressure. In the final stage, we use a specially developed general approach to the analysis of the limiting state at a given point of the cross-section of a bent pipe for the obtained system of internal forces, namely, for the bending moment, the tensile force acting in the circumferential direction, and longitudinal and tangential forces. We also demonstrate the possibility of application of the obtained results to the approximate analysis of cracks and three-dimensional defects appearing in a bent pipe. Scientific and Engineering Center of Materials-Science Support of the Production and Certification of Equipment of Nuclear Power Plants at the Institute for Problems of Strength of the National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 131 – 150, March – April, 1998.     

On stress-strain state in thick-walled cylindrical shells bounded by corrugated surfaces

Applying the second variant of the boundary-shape perturbation method and using three-dimensional equations and relations of the elasticity theory including the first three approximations the author has obtained an analytical solution to the problem of elastic equilibrium for noncanonical near-cylindrical shells subjected to fluctuating axial external forces. The influence of individual shapes of noncanonical shells, amplitude and parameter of oscillation of boundary surfaces in the axial or circumferential directions on the value of maximum stresses has been clarified. An almost numerical convergence is demonstrated, based on contribution (in absolute magnitude) of each of the approximations to the sum total. For a shell in the form of bellows, which is under a permanent external pressure, a comparison is made between the hoop stress values as found by the boundary-shape perturbation method and the data obtained by the finite-difference method using equations of the Vekua theory of shells.     

Approximate calculation of the elastoplastic stress-strain state of a pipe with a helical corrugation

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Problemy Prochnosti, No. 1, pp. 82–86, January, 1988.     

Chirality dependence of carbon single-walled nanotube material properties: axial Young's modulus

The potential use of individual carbon nanotubes as nano devices warrants detailed investigation of their mechanical behavior based on structural and geometrical configurations. The objective of this paper is to unravel the structural and chirality dependence of the axial Young's modulus of a carbon single-walled nanotube by analytical and numerical approaches. In this work, we employ the general homogenization composite shell model developed based on the asymptotic homogenization technique for analytical modeling of single-walled nanotubes. We derive the working formulae for the effective elastic properties of carbon single-walled nanotube of any chirality and predict the structural and chiral dependence of the effective axial Young's modulus of the nanotube. Also, a finite element analysis on the chirality dependence of the axial Young's modulus of the carbon nanotube is reported. The outcomes of our analyses are compared with available experimental and simulation results.     

A compensation of Young's modulus in polysilicon structure with discontinuous material distribution

This paper is concerned with the effect of material discontinuities, such as porosity, on the modulus of elasticity and attempts to simulate the effects of porosity in polysilicon using a finite element model. The proposed Young's modulus model is applied to the simulation of a polysilicon MEMS gyro. When the compensated Young's modulus is used in this simulation, we can reduce the difference between the simulation and the actual experimental result.     

Young's modulus of porous materials

The Young's modulus of porous alumina was determined by both sonic and bending tests. The pore structure of the specimens changes from interconnected at high porosities to disconnected at low porosities. The Young's modulus data can best be treated by the correlation proposed in Part 1 of this paper.     

Young's modulus,density and material properties in cancellous bone over a large density range

Data on the compressive properties of cancellous bone cubes with a large range of densities (relative densities compared with compact bone of 0.04–0.60) show that the exponent relating the Young's modulus to the density is close to quadratic and that it is improbable that the material Young's modulus of our specimens was less than 8 GPa, and was probably considerably higher.     

Young's modulus and shear modulus of a composite shaft from resonance measurements

A simple method which uses axial and torsional vibration resonance for the measurement of Young's modulus, E, and shear modulus, G, of shafting is described. The moduli are used to calculate the resonance frequency of transverse vibration for comparison with a measured value. The agreement is extremely good so the measurements of E and G, and the theory used to calculate the transverse resonant frequency, must be precise.This method can be used in materials research but its simplicity also commends it for the quality control of composite material components in production.     

Young's modulus of porous brittle solids

A new equationE =E ₀ (1 –aP) ⁿ whereE andE ₀ are the Young's moduli at porosity,P, and zero, respectively, a andn are material constants, has been derived semi-empirically for describing the porosity dependence of Young's modulus of brittle solids. The equation satisfies quite well the exact theoretical solution for the values of Young's moduli at different porosities for model systems with ideal and non-ideal packing geometry. The equation shows excellent agreement with the data On- and-alumina over a wide range of porosity. Unlike the existing porosity-elastic modulus equations, the proposed equation satisfies the boundary conditions and is inherently capable of treating isometric closed pores as well as non-isometric interconnected pores. The parameters a and n provide information about the packing geometry and pore structure of the material.     

Measurement of Young's modulus in an elastic material using 3D digital holographic interferometry

Digital holographic interferometry using three different illumination directions is applied to quantify in full field of view the deformation of an elastic membrane under a given vibration frequency. The technique allows the separation of the object microdisplacements components in the x, y, and z directions, and the resulting data is used to find the membrane Young's modulus. The latter was compared with the result obtained using the theory of thin plates for a clamped circular membrane under a uniformly distributed load, reaching a 95% agreement. Validation of the results between these methods shows the reliability of DHI to measure the mechanical properties of an elastic material.     

Young's modulus of lignin from a continuous indentation test

The deformation of lignin in a continuous ball indentation test was almost entirely elastic up to a stress of 2.2 × 10⁸ Pa (22 kg mm^–2). The load versus depth of indentation curve of the lignin followed closely the classical Hertz equation thus enabling the Young's modulus of lignin to be calculated. From these results a stress-strain curve for lignin was drawn.Visitor from Mechanical Engineering Department, University of Maryland, College Park, Md 20742, USA.     

Effect of structure on the Young's modulus of Al-Cu-Ni alloys

Experimental measurements of the dynamic Young's modulus of a wide range of wrought Al-Cu-Ni alloy compositions have shown this property to depend not only on the volume fraction of the phases present in the alloy but also on the microstructure. The results can be described by the simple relationship: $$E = 76.6 + 94.6 V{_d} - 1.3d + 0.06\lambda$$ whereE is Young's modulus of the alloy (in GN m^?2),V _d is the volume fraction of all the dispersed phases, andd and λ are the respective average particle size and mean free path of all dispersed phases (inμm). In view of the wide range of alloys tested in the present work, the above equation is expected to apply reasonably well to most wrought aluminium alloys.