ch07_Mechanical-Properties

# ch07_Mechanical-Properties - CHAPTER 7: MECHANICAL...

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CHAPTER 7: MECHANICAL PROPERTIES

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CHAPTER 7: MECHANICAL PROPERTIES ISSUES TO ADDRESS. .. Stress and strain Elastic behavior Plastic behavior Toughness and ductility Ceramic Materials Stress Strain Elasticity Strength Tensile Elongation Ductile Fracture Tension Flexural Plasticity
4 Tensile stress, σ : Shear stress, τ : Area, A F t F t σ = F t A o original area before loading Area, A F t F t F s F F F s τ = F s A o Stress has units: N/m 2 or lb/in 2 7.2 STRESS & STRAIN

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c07f01 Tensile load Compressive load Shear strain γ = tan θ Torsional deformation angle of twist, φ o σ = F A Stress ( σ ) for tension and compression ε = δ L o Strain ( ε ) for tension and compression Shear stress o τ = F s A
5 Simple tension: cable o σ = F A Simple shear: drive shaft A o = cross sectional Area (when unloaded) F F σ σ o τ = F s A τ Ski lift (photo courtesy P.M. Anderson) 7.2 COMMON STATES OF STRESS M M A o 2R F s A c

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Canyon Bridge, Los Alamos, NM 6 Simple compression: A o Balanced Rock, Arches National Park o σ = F A Note: compressive structure member ( σ < 0 here). (photo courtesy P.M. Anderson) (photo courtesy P.M. Anderson) OTHER COMMON STRESS STATES
7 Bi-axial tension: Hydrostatic compression: Fish under water Pressurized tank σ z > 0 σ θ > 0 σ < 0 h (photo courtesy P.M. Anderson) (photo courtesy P.M. Anderson) OTHER COMMON STRESS STATES

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8 Tensile strain: Lateral strain: Shear strain: θ /2 π /2 π /2 - θ θ /2 δ /2 δ /2 δ L /2 δ L /2 L o w o ε = δ L o ε L = - δ L w o γ = tan θ Strain is always dimensionless. ENGINEERING STRAIN
• Typical tensile specimen 9 • Other types of tests: --compression: brittle materials (e.g., concrete) --torsion: cylindrical tubes, shafts. gauge length (portion of sample with reduced cross section) = • Typical tensile test machine load cell extensometer specimen moving cross head Adapted from Fig. 6.2, Callister 6e. Adapted from Fig. 6.3, Callister 6e. (Fig. 6.3 is taken from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials , Vol. III, Mechanical Behavior , p. 2, John Wiley and Sons, New York, 1965.) 7.2 STRESS-STRAIN TESTING

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c07f04 Normal and shear stresses on an arbitrary plane Stress is a function of the orientation On plane p-p’ the stress is not pure tensile There are two components Tensile or normal stress σ ’ (normal to the pp’ plane) Shear stress τ ’ (parallel to the pp’ plane)
Modulus of Elasticity, E : (also known as Young's modulus) 10 Hooke's Law : σ = E ε Poisson's ratio, ν : metals: ν ~ 0.33 ceramics: ~0.25 polymers: ~0.40 ε ν = - L ε ε L ε 1 - ν F F simple tension test σ Linear- elastic 1 E ε Units: E: [GPa] or [psi] ν : dimensionless ELASTIC DEFORMATIONS 7.3 Stress-strain behavior

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c07f05
Elastic modulus , E Energy ~ curvature at r o cross sectional area A o L length, L o F undeformed deformed L F A o = E L o Elastic modulus r larger Elastic Modulus

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## This note was uploaded on 03/08/2010 for the course CHEN 313 taught by Professor Seminario during the Fall '07 term at Texas A&M.

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ch07_Mechanical-Properties - CHAPTER 7: MECHANICAL...

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