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Chapter2_props - Chapter 2 Properties and Behaviour...

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Chapter 2 Properties and Behaviour
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Required Reading Stress and Strain - Callister, p.133-153 Hardness - Callister, p. 154-160 Environmental – Callister, p. 237 – 238 Polymers – Callister, p. 524 – 532
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Typical tensile specimen. For metals use ASTM E8, E8M and for polymers use ASTM D638. Note there is a difference in standards. g a u g e le n g th (p o rtio n o f s a m p le with re du ce d cro s s s e ctio n ) = Typical tensile test machine loa d ce ll e xte nsome ter s pe cime n moving cros s he ad Recall: Tensile Test, elastic and plastic deformation, engineering stress and strain, true stress and strain
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• Maximum possible engineering stress in tension. • Why does the curve decrease after UTS? Metals: occurs when noticeable necking starts – see above for metals Ceramics: occurs when crack propagation starts -see ceramic stress vs. strain . • Polymers: occurs when polymer backbones are aligned and about to break – see polymer stress vs. strain Recall: Tensile Strength (TS) or Ultimate TS (UTS) s t r a in e n g in e e r in g s t r e s s T S T y p ic a l r e s p o n s e o f a
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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 units: MPa or psi (N/m 2 or lb/in 2) Recall: Engineering Stress
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Tensile or longitudinal strain ε = (l f –l o )/l o = Δ l/l o p. 135 Shear strain: γ = tan θ Strain is always dimensionless – think of it as m/m or mm/mm Recall: Engineering Strain l o l f Lateral strain ε lateral = Δ w/w o ν = -lateral strain/longitudinal strain w f
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Modulus of Elasticity, E : (also called Young's modulus) Hooke's Law p. 137 : σ = E ε Poisson's ratio, ν : p. 141 ν = -lateral strain x/longitudinal strain z or ν = - ε x / ε z metals: ν ~ 0.33 ceramics: ν ~0.25 polymers: ν ~0.40 σ Linear- elastic 1 E ε Units: E: [GPa] or [psi] ν : dimensionless Linear Elastic Property-Review
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• Elastic Shear modulus, G: τ 1 G γ τ = G γ • Elastic Bulk modulus, K: P= - K Δ V V o P Δ V 1 -K V o • Special relations for isotropic materials: E= 2G(1+ ν ) G=E/(2(1+ ν )) and K = E/(3(1-2 ν )) P P P M M simple torsion
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