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# lecture3 - ENGR 2220 Structure Properties of Materials...

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ENGR 2220 ENGR 2220 – Structure & Properties of Materials Lecture 3 Overview of material properties hapter 6 ontinued Chapter 6 Chapter 6 - Continued Continued

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Normal & Shear Stresses on Other lanes Planes o A F = σ + = = 2 cos 1 cos 2 ' θ o o o i l l l l l Δ = = ε 2 o A F = τ = = 2 2 sin cos sin '
Engineering Strain Tensile strain: Lateral strain: δ /2 ε= δ L o δ ε L = L w o L o w o Shear strain: Strain is always dimensionless. δ L /2 θ Δ x θ γ = Δ x / y = tan 90º - θ y γ τ G = 90º Adapted from Fig. 6.1 (a) and (c), Callister 7e. G is shear modulus

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Lateral Strains y x ε ε= For isotropic materials y x z z υ = = is Poisson’s ratio ) 1 ( 2 ν + = G E
Linear Elastic Properties Modulus of Elasticity, E : (also known as Young's modulus) Hooke's Law : σ = E ε σ E F Linear- ε elastic F simple tension st test

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Poisson's ratio, ν Poisson's ratio, ν : ε L ε ε ν =− L ε - ν metals : ν ~ 0.33 eramics ~025 ceramics : ν 0.25 polymers : ν ~ 0.40 Units: E : [GPa] or [psi] dimensionless ν > 0.50 density increases ν < 0.50 density decreases oids form) ν : (voids form)
Ex Problem 6.2 d o = 10 mm = 2 5x10 m Δ d = 2.5x10 -3 mm F = ? Material is brass

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OTHER ELASTIC PROPERTIES • Elastic Shear modulus, G: τ G M simple 1 γ τ = G γ torsion test • Elastic Bulk modulus, K: P P M P= - K Δ V V o Δ V -K V o P P pressure test: Init. 1 • Special relations for isotropic materials: E E vol =V o . Vol chg. = Δ V G = 2(1 ) K = 3(1 2 ν )
YOUNG’S MODULI: OMPARISON 1200 Metals Alloys Graphite Ceramics Semicond Polymers Composites /fibers E eramics COMPARISON antalum Steel, Ni Molybdenum Si nitride Al oxide Carbon fibers only 0 600 800 1000 400 Tungsten 111> Si carbide Diamond CFRE(|| fibers)* E(GPa) ceramics > E metals >> E olymers Magnesium, Aluminum Platinum Silver, Gold Tantalum Zinc, Ti Si crystal Glass-soda oncrete Glass fibers only Aramid fibers only 40 60 80 100 200 Tin Cu alloys <100> <111> GFRE(|| fibers)* AFRE(|| fibers)* polymers Based on data in Table B2, Callister 6e . omposite data based on 8 Graphite Concrete AFRE( fibers)* CFRE* GFRE* 6 10 20 olyester CFRE( fibers)* GFRE( fibers)* 10 9 Pa Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CFRE), aramid (AFRE), or l ( G F R E ) 1 PC Epoxy only 0.8 2 4 HDPE PP

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lecture3 - ENGR 2220 Structure Properties of Materials...

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