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ENME382 S2010 0201 ch07

ENME382 S2010 0201 ch07 - Chapter 7 Mechanical Properties...

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ISSUES TO ADDRESS... Stress and strain : What are they and why are they used instead of load and deformation? Elastic behavior: When loads are small, how much Chapter 7: Mechanical Properties Chapter 7 - ENME 382 Spring 2010 Section 0201 1 deformation occurs? What materials deform least? Plastic behavior: At what point does permanent deformation occur? What materials are most resistant to permanent deformation? Toughness and ductility : What are they and how do we measure them?
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Elastic Deformation 2. Small load δ bonds stretch 1. Initial 3. Unload return to initial Chapter 7 - ENME 382 Spring 2010 Section 0201 2 Elastic means reversible ! F F δ Linear- elastic Non-Linear- elastic
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Plastic Deformation (Metals) 1. Initial 2. Small load 3. Unload planes still sheared bonds stretch & planes shear Chapter 7 - ENME 382 Spring 2010 Section 0201 3 Plastic means permanent ! F δ linear elastic linear elastic δ plastic F δ elastic + plastic δ plastic
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Engineering Stress Shear stress, τ : Area, A o F t F s F Tensile stress, σ : Area, A o F t Chapter 7 - ENME 382 Spring 2010 Section 0201 4 Stress has units: N/m 2 or lb f /in 2 F t F F s τ = F s A o original area before loading σ = F t A o 2 f 2 m N or in lb = F t
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Simple tension: cable Common States of Stress o σ = F A σ σ A o = cross sectional area (when unloaded) F F Chapter 7 - ENME 382 Spring 2010 Section 0201 5 τ Note: τ = M / A c R here. o τ = F s A M M A o 2 R F s A c Torsion (a form of shear): drive shaft Ski lift (photo courtesy P.M. Anderson)
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Simple compression: OTHER COMMON STRESS STATES (i) A o Chapter 7 - ENME 382 Spring 2010 Section 0201 6 (photo courtesy P.M. Anderson) Canyon Bridge, Los Alamos, NM o σ = F A Note: compressive structure member ( σ < 0 here). (photo courtesy P.M. Anderson) Balanced Rock, Arches National Park
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Bi-axial tension: Hydrostatic compression: OTHER COMMON STRESS STATES (ii) Chapter 7 - ENME 382 Spring 2010 Section 0201 7 Pressurized tank σ < 0 h (photo courtesy P.M. Anderson) (photo courtesy P.M. Anderson) Fish under water σ z > 0 σ θ > 0
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Tensile strain: Lateral strain: Engineering Strain ε = δ L o δ /2 L o w o - δ ε L = L w o δ /2 Chapter 7 - ENME 382 Spring 2010 Section 0201 8 Strain is always dimensionless. Shear strain: θ 90º 90º - θ y Δ x θ γ = Δ x / y = tan Adapted from Fig. 7.1 (a) and (c), Callister & Rethwisch 3e. L
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Stress-Strain Testing • Typical tensile test machine specimen extensometer • Typical tensile specimen Adapted from Fig. 7.2, Callister & Rethwisch 3e. Chapter 7 - ENME 382 Spring 2010 Section 0201 9 Adapted from Fig. 7.3, Callister & Rethwisch 3e. (Fig. 7.3 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.) gauge length
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Linear Elastic Properties Modulus of Elasticity, E : (also known as Young's modulus) Hooke's Law : σ = E ε σ E F Chapter 7 - ENME 382 Spring 2010 Section 0201 10 Linear- elastic ε F simple tension test
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Poisson's ratio, ν Poisson's ratio, ν : ε L ε - ν ε ν = - L ε metals : ν ~ 0.33 Chapter 7 - ENME 382 Spring 2010 Section 0201 11 Units: E : [GPa] or [psi] ν : dimensionless ν > 0.50 density increases ν < 0.50 density decreases (voids form) ceramics : ν ~ 0.25 polymers : ν ~ 0.40
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