• Korean Journal of Metals and Materials
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• v.47 no.2
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• pp.121-128
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• 2009

The strain, microstructure and mechanical properties through thickness of an oxygen free copper(OFC) processed by differential speed rolling(DSR) were investigated in detail. The OFC sample with thickness of 1 mm was rolled to 35% reduction at ambient temperature without lubrication changing the differential speed ratio from 1.0:1 to 2.2:1. The shear strain introduced by the conventional rolling showed positive values at positions of upper roll side and negative values at positions of lower roll side. However, it showed zero or positive values at all positions for the samples rolled by the DSR. The effects of strain distribution through thickness of the coper sheets on microstructure, texture and mechanical properties are discussed in the present study.

• Journal of Power System Engineering
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• v.12 no.2
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• pp.35-40
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• 2008

This paper deals with the free vibrations of conical shells with linearly variable thickness by the transfer influence coefficient method. The classical thin shell theory based upon the Flugge theory is assumed and the governing equations of a conical shell are written as a coupled set of first order matrix differential equations using the transfer matrix. The Runge-Kutta-Gill integration method is used to solve the governing differential equation. The natural frequencies and corresponding mode shapes are calculated numerically for the conical shells with linearly variable thickness and various boundary conditions at the edges. The present method is applied to conical shells with linearly varying thickness, and the effects of the semi-vertex angle, the number of circumferential waves and thickness ratio on vibration are studied.

• Structural Engineering and Mechanics
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• v.91 no.2
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• pp.197-209
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• 2024

The vibration of elastically supported bidirectional functionally graded (BDFG) sandwich beams on an elastic foundation is investigated. The sandwich structure is composed of upper and lower layers of BDFG material and the core layer of isotropic material. Material properties of upper and lower layers are assumed to vary continuously along the length and thickness of the beam with a power-law function. Hamilton's principle is used to deduce the vibration equations of motion of the sandwich Timoshenko beam. Then, the partial differential equation of motion is spatially discretized into a time-varying ordinary differential equation in terms of Chebyshev differential matrices. The eigenvalue equation associated with the free vibration is formulated to study the influence of various slenderness ratios, material gradient indexes, thickness ratios, foundation and support spring constants on the vibration frequency of BDFG sandwich beams. The present method can provide researchers with deep insight into the impact of various geometric, material, foundation and support parameters on the vibration behavior of BDFG sandwich beam structures.

• Korean Journal of Metals and Materials
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• v.48 no.1
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• pp.77-84
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• 2010

Annealing characteristics of an oxygen free copper (OFC) processed by differential speed rolling (DSR) were investigated in detail. An OFC sample with a thickness of hum was rolled to 35% reduction at ambient temperature without lubrication, varying the differential speed ratio from 1.0:1 to 2.2:1, and then annealed for 0.5h at various temperatures from 100 to $400^{\circ}C$. Different recrystallization behavior was observed depending on the differential speed ratio, especially in the case of annealing at $200^{\circ}C$ Complete recrystallization occurred in the specimens annealed at temperatures above $250^{\circ}C$ regardless of the differential ratios. The hardness distribution in the thickness direction of the rolled OFC sheets varied depending on the differential speed ratios. These annealing characteristics were explained by the magnitude of shear strain introduced during rolling.

• Journal of Magnetics
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• v.15 no.4
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• pp.204-208
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• 2010

Local wall thinning in pipelines affects the structural integrity of industries like nuclear power plants (NPPs). In the present study, a pulsed eddy current (PEC) differential probe with two excitation coils and two Hall-sensors was fabricated to measure the wall thinning in insulated pipelines. A stainless steel test sample was prepared with a thickness that varied from 1 mm to 5 mm and was laminated by plastic insulation to simulate the pipelines in NPPs. The excitation coils in the probe were driven by a rectangular current pulse, the difference of signals from two Hall-sensors was measured as the resultant PEC signal. The peak value of the detected signal is used to describe the wall thinning. The peak value increased as the thickness of the test sample increased. The results were measured at different insulation thicknesses on the sample. Results show that the differential PEC probe has the potential to detect wall thinning in an insulated NPP pipelines.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.3
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• pp.245-256
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• 2014

This work is focused on the boundary layer and heat transfer characteristics of hydromagnetic flow over a stretching sheet with variable thickness. Steady, two dimensional, nonlinear, laminar flow of an incompressible, viscous and electrically conducting fluid over a stretching sheet with variable thickness and power law velocity in the presence of variable magnetic field and variable temperature is considered. Governing equations of the problem are converted into ordinary differential equations utilizing similarity transformations. The resulting non-linear differential equations are solved numerically by utilizing Nachtsheim-Swigert shooting iterative scheme for satisfaction of asymptotic boundary conditions along with fourth order Runge-Kutta integration method. Numerical computations are carried out for various values of the physical parameters and the effects over the velocity and temperature are analyzed. Numerical values of dimensionless skin friction coefficient and non-dimensional rate of heat transfer are also obtained.

• Advances in concrete construction
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• v.15 no.5
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• pp.349-358
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• 2023

Aim of this work is investigating effect of thickness-stretching formulation on the quasi three-dimensional analysis of micro plate based on a thickness-stretched and shear deformable model through principle of virtual work and micro-scale dependent constitutive relations. Governing differential equations are derived in terms of five unknown functions and the analytical solution is derived using Navier's technique. To explore effect of thickness stretching model on the static results, a comparison between the results with and without thickness stretching effect is presented.

• Korean Journal of Materials Research
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• v.28 no.5
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• pp.295-300
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• 2018

Effects of annealing temperature on the microstructure and mechanical properties through thickness of a Cu-3.0Ni-0.7Si alloy processed by differential speed rolling are investigated in detail. The copper alloy with a thickness of 3 mm is rolled to a 50 % reduction at ambient temperature without lubricant and subsequently annealed for 0.5 h at $200-900^{\circ}C$. The microstructure of the copper alloy after annealing is different in the thickness direction depending on the amount of the shear and compressive strain introduced by the rolling; the recrystallization occurs first in the upper roll side and center regions which are largely shear-deformed. The complete recrystallization occurs at an annealing temperature of $800^{\circ}C$. The grain size after the complete recrystallization is finer than that of the conventional rolling. The hardness distribution of the specimens annealed at $500-700^{\circ}C$ is not uniform in the thickness direction due to partial recrystallization. This ununiformity of hardness corresponds well to the amount of shear strain in the thickness direction. The average hardness and ultimate tensile strength has the maximum values of 250 Hv and 450 Mpa, respectively, in the specimen annealed at $400^{\circ}C$. It is considered that the complex mode of strain introduced by rolling directly affects the microstructure and the mechanical properties of the annealed specimens.

• Transactions of Materials Processing
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• v.16 no.7
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• pp.516-520
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• 2007

As the springback of sheet metal during unloading nay cause deviation from a desired shape, accurate prediction of springback is essential for the design of sheet stamping operations. On the removal of the applied load the specimen loses its elastic strain by contracting around the contour of the block, the radius $\rho$ can be determined by the residual differential strain. Therefore in this study the springback estimated by the residual differential strain is experimentally validated through the comparison with those obtained by U-bending test. The springback characteristics of two analytical models are also estimated at various processing conditions such as thickness, curvature of radius and drawing strain. The model based on residual differential strain has an applied transition strain where the springback undergoes a dramatic decrease. Both models show that springback decreases with increased strip thickness and with decreased radius of curvature. For no applied tension, the model based on residual differential strain predicts more springback as compared to the moment based model.

• Korean Journal of Materials Research
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• v.23 no.7
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• pp.392-398
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• 2013

A two-pass differential speed rolling(DSR) was applied to a deoxidized low-phosphorous copper alloy sheet in order to form a homogeneous microstructure. Copper alloy with a thickness of 3 mm was rolled to 75 % reduction by two-pass rolling at $150^{\circ}C$ without lubrication at a differential speed ratio of 2.0:1. In order to introduce uniform shear strain into the copper alloy sheet, the second rolling was performed after turning the sample by $180^{\circ}$ on the transverse direction axis. Conventional rolling(CR), in which the rotating speeds of the upper roll and lower roll are identical to each other, was also performed by two-pass rolling under a total rolling reduction of 75 %, for comparison. The shear strain introduced by the conventional rolling showed positive values at positions of the upper roll side and negative values at positions of the lower roll side. However, samples processed by the DSR showed zero or positive values at all positions. {100}//ND texture was primarily developed near the surface and center of thickness for the CR, while {110}//ND texture was primarily developed for the DSR. The difference in misorientation distribution of grain boundary between the upper roll side surface and center regions was very small in the CR, while it was large in the DSR. The grain size was smallest in the upper roll side region for both the CR and the DSR. The hardness showed homogeneous distribution in the thickness direction in both CR and DSR. The average hardness was larger in CR than in DSR.