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MECH466-Lecture-5

# MECH466-Lecture-5 - MECH 466 Systems University of Victoria...

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1 MECH 466 Microelectromechanical Systems University of Victoria Dept. of Mechanical Engineering Lecture 5: Stress and Strain Mechanics of Beams May 24th, 2007 Mech 466, N. Dechev, UVic 2 Stress and Strain Bending of Beams Overview Mech 466, N. Dechev, UVic

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3 Graphical Relation Between Stress and Strain Mech 466, N. Dechev, UVic Linear Region Ceramics, Crystal Silicon, Polysilicon Metals, Gold, Aluminum, Certain Plastics Linear Region 4 Movie of Tensile Testing of Steel The relationship of stress and strain for steel can be observed in the following movie: Mech 466, N. Dechev, UVic Tensile Testing A36 mild steel, (speed = 4X), [Civil Engineering, University of New Mexico]
5 Values for E (modulus of elasticity) Some typical values for E for common MEMS materials are listed below: Note: Appendix A lists numerous material properties for typical MEMS materials. Mech 466, N. Dechev, UVic Material E (GPa) Yield Strength (MPa) Fracture Strength (MPa) Single Crystal Silicon: <100> <110> <111> 130 168 187 N/A 600 to 7700 Polysilicon 120 to 175 N/A 1000 to 3000 Silicon Nitride (SiN) <100> <110> 385 254 N/A 6400 to 14000 Silicon Oxide 73 N/A 8400 Silicon Carbide (SiC) 700 N/A 21000 Stainless Steel 200 - 2100 Gold 78 250 - Aluminum 70 170 - When you strain a body along one axis, it will change shape along the other axes. For example, consider the rectangular body below: If it is in tension, its cross-sectional area will become reduced. We can define Poisson’s ratio as: Note for Si: (See Appendix A for other materials) 6 Definition of Poisson’s Ratio Mech 466, N. Dechev, UVic

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7 Definition of Stress Tensor Consider a solid body (as shown below) with an arbitrary shape, subjected to a set of arbitrary forces.
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