Chapter 7 - Mechanical properties

# Chapter 7 - Mechanical properties - Chapter 7 Mechanical...

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1 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? Chapter 7: Mechanical Properties

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2 Elastic means reversible ! Elastic Deformation 2. Small load F δ bonds stretch 1. Initial 3. Unload return to initial F δ Linear- elastic Non-Linear- elastic
3 Plastic means permanent ! 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

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5 Stress has units: N/m 2 or lb f /in 2 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 σ = F t A o 2 f 2 m N or in lb = Area, A F t F t

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6 Simple tension: cable Common States of Stress o σ = F A σ σ Ski lift (photo courtesy P.M. Anderson) A o = cross sectional area (when unloaded) F F
7 (photo courtesy P.M. Anderson) (photo courtesy P.M. Anderson) Canyon Bridge, Los Alamos, NM o σ = F A Simple compression: Note: compressive structure member ( σ < 0 here). A o Balanced Rock, Arches National Park

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8 Tensile strain: Lateral strain: Strain is always dimensionless. Engineering Strain Shear strain: θ 90º 90º - θ y x θ γ = x / y = tan ε = δ L o Adapted from Fig. 7.1 (a) and (c), Callister & Rethwisch 3e. δ /2 L o w o - δ ε L = L w o δ L /2
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10 Stress-Strain Testing • Typical tensile test machine 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.) specimen extensometer • Typical tensile specimen Adapted from Fig. 7.2, Callister & Rethwisch 3e. gauge length
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12 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
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14 Mechanical Properties Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal Adapted from Fig. 7.7, Callister & Rethwisch 3e.
c07f08 c07f08 Q: Modulus of elasticity decreases as temperature increases…Why? A: At higher temps atoms are less strongly bonded

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17 Metals Alloys Graphite Ceramics Semicond Polymers Composites /fibers E (GPa) Based on data in Table B.2, Callister & Rethwisch 3e.

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