Optimal Design of Thickness and Young’s Modulus of Multi-Layered Foldable Structure Considering Bending Stress, Neutral Plane and Delamination under 2.5 mm Radius of Curvature

2018 ◽  
Vol 19 (8) ◽  
pp. 1143-1154 ◽  
Author(s):  
Yunsik Chae ◽  
Gee Sung Chae ◽  
Yeo O Youn ◽  
Sangwook Woo ◽  
Sang Hak Shin ◽  
...  
Keyword(s):  
Optimal Design ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Neutral Plane ◽  
Radius Of Curvature ◽  
Bending Stress

Optimal Design of a Nonhomogeneous Annular Disk Under Pressure Loadings

1994 ◽  
Vol 116 (4) ◽  
pp. 989-996
Author(s):  
Chung-Yun Gau ◽  
Souran Manoochehri
Keyword(s):  
Optimal Design ◽  
Young’S Modulus ◽  
Variable Thickness ◽  
Volume Fraction ◽  
Young's Modulus ◽  
Yield Criterion ◽  
Constant Thickness ◽  
Annular Disk ◽  
Disk Thickness ◽  
Thickness Variations

A method for the design of nonhomogeneous, variable-thickness, annular disks under internal and external pressures satisfying Tresca yield criterion is presented in this paper. The effects of varying the disk thickness and stiffness properties to achieve a fully stressed design are investigated. Analytical solutions for distributions of Young’s modulus and disk thickness variations have been developed for the case of fully stressed designs. Examples are given for three different cases, namely, constant thickness with variable Young’s modulus, variable thickness with constant Young’s modulus, and variable thickness with variable Young’s modulus. In the last case, due to the existence of many alternative solutions, optimal design techniques have been utilized. Application of the developed methodology for optimal designs of short fiber composites with random fiber orientations is discussed. The optimization results of fiber volume fraction distributions and thickness variations for a disk made of nylon 66 matrix with E glass fiber are given under specified pressure loadings.

Analytical Modeling of Top Roller Position for Multiple Pass (3-Roller) Cylindrical Forming of Plates

2006 ◽  
Author(s):  
A. H. Gandhi ◽  
H. K. Raval
Keyword(s):  
Young’S Modulus ◽  
Analytical Model ◽  
Young's Modulus ◽  
Material Behavior ◽  
Analytical Models ◽  
Radius Of Curvature ◽  
Single Pass ◽  
Multiple Pass ◽  
Efficient Performance ◽  
Constant E

As forming of the double or multiple curvature surfaces, includes roller forming at least once in the sequential process; its efficient performance is of great importance for controlling the final product dimensions. Most efficient and economical way to produce the cylinder is to roll the plate through the roller in single pass. Literature review revels that, most of the reported analytical models for the prediction of springback were developed with the assumption of zero initial strain. However, in practice multiple pass bending is recommended to work within the power limitation of the machine and to improve the accuracy of the final product. An attempt is made to develop the analytical model for estimation of top roller position as a function of desired radius of curvature, for multiple pass 3-roller forming of cylinders, considering real material behavior. Due to the change of Young's modulus of elasticity (E) under deformation, the springback is larger than the springback calculated with constant E. Developed analytical model was modified to include the effect of change of Young's modulus during the deformation. Developed multiple pass analytical models were compared with the single pass analytical model and experiments (on pyramid type 3-roller bending machine).

Optimal Shape and Nonhomogeneity of a Timoshenko Beam for Maximum Load

1979 ◽  
Vol 23 (04) ◽  
pp. 229-234
Author(s):  
Sarp Adali ◽  
Ibrahim Sadek
Keyword(s):  
Optimal Design ◽  
Young’S Modulus ◽  
Timoshenko Beam ◽  
Young's Modulus ◽  
Maximum Load ◽  
Optimal Shape ◽  
Graphical Form ◽  
Sectional Area ◽  
Cross Sectional ◽  
Closed Form Solutions

The best possible distributions of Young's modulus or the cross-sectional area or both are determined explicitly for a cantilevered Timoshenko beam which, for a given volume and end deflection, carries the maximum possible load at its free end. Closed-form solutions are given for the optimal height, width and/or Young's modulus functions. Numerical results are presented in graphical form. It is found that the inclusion of shear deformation decreases the efficiency of the optimal design, and that optimization with respect to Young's modulus in addition to shape increases the efficiency considerably in comparison with optimization of the shape only.

Near Surface Measurement of Mechanical Properties Using Instrumented Indentation Measurements

2005 ◽  
Author(s):  
K. Farhang ◽  
L. E. Seitzman ◽  
B. Feng
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Surface Measurement ◽  
Accurate Estimation ◽  
Radius Of Curvature ◽  
Instrumented Indentation ◽  
Near Surface ◽  
Parameter Function ◽  
Two Parameter ◽  
Indentation Measurement

A two-parameter function for estimation of projected area in instrumented indentation measurement is obtained to account for indenter tip imperfection. Imperfection near indenter tip-end is modeled using a spherical function and combined with a linear function describing the edge boundary of the indenter. Through an analytical fusion technique the spherical and linear functions are combined into a single function with two unknown geometric parameters of tip radius of curvature and edge slope. Data from indentation measurement of force and displacement, using a Berkovich tip and single crystal alumina and silica samples, are implemented in the proposed area function yielding estimated values of Young’s modulus. Results were compared with that obtained from Oliver and Pharr technique for deep as well as shallow indentation regimes. The estimates for Young’s modulus were found to agree quite favorably. More importantly, in contrast to the Oliver-Pharr technique, the use of the two-parameter function resulted in a significantly more accurate estimation of Young’s modulus for shallow indentation depth of 0 to 100 nm. The error in estimation of Young’s modulus was found to be within 10 percent for indentation depths 25 nm to 50 nm and within 20 percent for indentation depths 0 to 25 nm.

Mechanical Property Measurement of 0.5-µm CMOS Microstructures

1998 ◽  
Vol 518 ◽  
Author(s):  
M. S.-C. Lu ◽  
X. Zhu ◽  
G. K. Fedder
Keyword(s):  
Young’S Modulus ◽  
Composite Structures ◽  
Young's Modulus ◽  
Stress Gradient ◽  
Radius Of Curvature ◽  
Cmos Process ◽  
Out Of Plane ◽  
Property Measurement ◽  
Micromechanical Structures ◽  
Repetitive Stress

AbstractMeasurements are reported on the mechanical properties of high-aspect-ratio micromechanical structures formed using a conventional 0.5-µm CMOS process. Composite structures are etched out of the CMOS dielectric, aluminum, and gate-polysilicon thin films using a post-CMOS CHF3:O2 reactive-ion etch and followed by a SF6 :O2silicon etch for release. Microstructures have a height of 5 µm and beam widths and gaps down to 1.2 µm. Properties are strongly dependent on the relative metal and dielectric content of the beams. Beams with three metal conductors and polysilicon have an effective Young's modulus of 62 GPa, residual stress of -29 MPa, and an average out-of-plane radius of curvature of 1.9 mm. Maximum Young's modulus variation is 3 GPa die-todie, and is 9 GPa between two runs. Die-to-die variation of stress and stress gradient is poor for many beam compositions, however local matching on a die is very good. Cracking is induced in a resonant fatigue structure at 620 MPa of repetitive stress after over 50 million cycles.

scholarly journals An Elastic Moduli Independent Approximation to the Radius of Curvature of the Bimetallic strip

2017 ◽  
Vol 14 (1) ◽  
pp. 68-78
Author(s):  
Amol Khatkhate ◽  
R Singh ◽  
P. T Mirchandani
Keyword(s):  
Ambient Temperature ◽  
Young’S Modulus ◽  
Coefficient Of Thermal Expansion ◽  
Young's Modulus ◽  
Order Approximation ◽  
Radius Of Curvature ◽  
Parametric Approach ◽  
First Order ◽  
Bimetallic Materials ◽  
First Order Approximation

A parametric approach has been used to derive an approximate formula for the prediction of the radius of curvature of a thin bimetallic strip that at initial ambient temperature, is both flat and straight, but at above ambient temperature, forms into an arc of a circle. The formula enables the evaluation of the radius of curvature of the strip as a function of heating or cooling. A formula for calculating the radius of curvature of a bimetallic strip already exists, and was produced by Timoshenko in his paper on Bimetallic Thermostats. The formula by Timoshenko has been vigorously tested, tried and proven and accepted in countless papers and journals since its original publication. The parametric approach solution introduced in this work gives an approximate solution to the Timoshenko formula for equal thicknesses of two mating metals within the bimetallic. The Khatkhate Singh Mirchandani (KSM) formula presented here is taken from the first order approximation derived by Angel and Haritos by incorporating the ratio of Young's modulus of the bimetallic materials. Furthermore, researchers in this area have proven that the Young's modulus does not have a significant effect on the radius of curvature. Taking this fact into consideration, the authors have suitably incorporated a correction modifier purely based on the coefficient of thermal expansion (CTE) of the materials. The simulation results and the overall close agreement with the Timoshenko formula has been put forward here. Also, the solution derived by the authors Khatkhate et.al shows better prediction as compared to the solutions derived by other researchers.

A Two-Parameter Function for Nanoscale Indentation Measurement of Near Surface Properties

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
K. Farhang ◽  
L. E. Seitzman ◽  
B. Feng
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Linear Functions ◽  
Accurate Estimation ◽  
Radius Of Curvature ◽  
Near Surface ◽  
Tip Radius ◽  
Parameter Function ◽  
Two Parameter ◽  
Indentation Measurement

A two-parameter function for estimation of projected area in instrumented indentation measurement is obtained to account for indenter tip imperfection. Imperfection near indenter tip is modeled using a spherical function and combined with a linear function describing the edge boundary of the indenter. Through an analytical fusion technique, the spherical and linear functions are combined into a single function with two unknown geometric parameters of tip radius of curvature and edge slope. Data from indentation measurement of force and displacement, using a Berkovich tip and single crystal alumina and silica samples, are implemented in the proposed area function yielding estimated values of Young’s modulus. Results were compared with that obtained from Oliver and Pharr technique for deep as well as shallow indentation regimes. The estimates for Young’s modulus were found to agree quite favorably. More importantly, in contrast to the Oliver–Pharr technique, the use of the two-parameter function resulted in a significantly more accurate estimation of Young’s modulus for shallow indentation depth of 0–50nm. The error in estimation of Young’s modulus was found to be within 10% for indentation depths of 25–50nm and within 20% for indentation depths of 0–25nm.

Mechanical properties of FeAlSi powders prepared by mechanical alloying from different initial feedstock materials

2019 ◽  
Vol 107 (2) ◽  
pp. 207 ◽  
Author(s):  
Jaroslav Čech ◽  
Petr Haušild ◽  
Miroslav Karlík ◽  
Veronika Kadlecová ◽  
Jiří Čapek ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Mechanical Alloying ◽  
Young’S Modulus ◽  
Milling Time ◽  
Young's Modulus ◽  
Element Model ◽  
X Ray Diffraction ◽  
X Ray ◽  
Powder Particles ◽  
Complete Homogenization

FeAl20Si20 (wt.%) powders prepared by mechanical alloying from different initial feedstock materials (Fe, Al, Si, FeAl27) were investigated in this study. Scanning electron microscopy, X-ray diffraction and nanoindentation techniques were used to analyze microstructure, phase composition and mechanical properties (hardness and Young’s modulus). Finite element model was developed to account for the decrease in measured values of mechanical properties of powder particles with increasing penetration depth caused by surrounding soft resin used for embedding powder particles. Progressive homogenization of the powders’ microstructure and an increase of hardness and Young’s modulus with milling time were observed and the time for complete homogenization was estimated.

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