Lecture 9 updated

# Lecture 9 updated - Mechanical Properties Mechanical...

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1 Mechanical Properties Mechanical Properties 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 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? Mechanical Properties Mechanical Properties

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2 Elastic means reversible ! Elastic Deformation Elastic Deformation 1. Initial 2. Small load 3. Unload F δ bonds stretch return to initial F δ Linear- elastic Non-Linear- elastic Plastic means permanent ! Plastic Deformation (Metals) Plastic Deformation (Metals) F δ linear elastic linear elastic δ plastic 1. Initial 2. Small load 3. Unload planes still sheared F δ elastic + plastic bonds stretch & planes shear δ plastic
3 Stress has units: N/m 2 or lb f /in 2 Engineering Stress Engineering Stress Shear stress, τ : Area, A F t F t F s F F F s τ = F s A o Tensile stress, σ : original area before loading Area, A F t F t σ = F t A o 2 f 2 m N or in lb = Simple tension: cable τ Note: τ = M / A c R here. Common States of Stress Common States of Stress A o = cross sectional area (when unloaded) F F o σ = F A o τ = F s A σ σ 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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4 (photo courtesy P.M. Anderson) Canyon Bridge, Los Alamos, NM o σ = F A Simple compression: Note: compressive structure member ( σ < 0 here). (photo courtesy P.M. Anderson) OTHER COMMON STRESS STATES (1) OTHER COMMON STRESS STATES (1) A o Balanced Rock, Arches National Park Bi-axial tension: Hydrostatic compression: Pressurized tank σ < 0 h (photo courtesy P.M. Anderson) (photo courtesy P.M. Anderson) OTHER COMMON STRESS STATES (2) OTHER COMMON STRESS STATES (2) Fish under water σ z > 0 σ θ > 0
5 Tensile strain: Lateral strain: Shear strain: Strain is always dimensionless. Engineering Strain Engineering Strain θ 90º 90º - θ y x θ γ = x / y = tan ε= δ L o δ ε L = L w o Adapted from Fig. 6.1 (a) and (c), Callister 7e. δ /2 δ L /2 L o w o = L-L o L o Stress Stress -Strain Testing Strain Testing • Typical tensile test machine Adapted from Fig. 6.3, Callister 7e. (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.) specimen extensometer • Typical tensile specimen Adapted from Fig. 6.2, Callister 7e. gauge length

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6 Linear Elastic Properties Linear Elastic Properties Modulus of Elasticity, E : (also known as Young's modulus) Hooke's Law : σ = E ε σ Linear- elastic E ε F F simple tension test Poisson's ratio, Poisson's ratio, ν Poisson's ratio, ν : Units: E : [GPa] or [psi] ν : dimensionless ν > 0.50 density increases ν < 0.50 density decreases (voids form) ε L ε - ν ε ν =− L ε metals : ν ~ 0.33 ceramics : ν ~ 0.25 polymers : ν ~ 0.40
7 Mechanical Properties Mechanical Properties

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Lecture 9 updated - Mechanical Properties Mechanical...

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