http://www.mse.ncsu.edu/zhu Materials Science & Engineering • Objectives/outcomes: You will learn the following: • Stresses and strains in solids. !• Normal and shear stresses. !• Elastic and plastic deformation. !• The tensile test and the engineering stress-strain curves. !• Young’s modulus, the yield strength, the ultimate tensile strength, the percent elongation and percent reduction in area. !• True stress and true strain. Hardness and hardness testing!MSE200 Lecture 7 (CH. 6.2-6.4) Mechanical Properties I Instructor: Yuntian Zhuhttp://www.mse.ncsu.edu/zhu Materials Science & Engineering Elastic and Plastic Deformation in Metals • Elastic deformation: Metal returns to its original dimension after the force is removed. • Plastic deformation: The metal is deformed to such an extent such that it cannot return to its original dimension after the load is removedhttp://www.mse.ncsu.edu/zhu Materials Science & Engineering Engineering Stress and Strain – under tension/compression Engineering stress σ = A0 Δl A Units of Stress are N/m2 (Pascals, or Pa) or PSI Engineering strain = є € = − 00=Δ0 €  € 00Force F (N) For elastic deformation: σ = E є"E is the Young’s modulushttp://www.mse.ncsu.edu/zhu Materials Science & Engineering Poissons Ratio 0w0 w . € ν= −(lateral)(longitudinal)= −yzPoissons ratio = 00 −−−=wwνUsually poissons ratio ranges from 0.25 to 0.4. Example: Stainless steel 0.28 Copper 0.33 є є є є y zhttp://www.mse.ncsu.edu/zhu Materials Science & Engineering Shear Stress and Shear Strain Shear stress τ = S (Shear force) A (Area of shear force application) Shear strain γ = Amount of shear displacement Distance ‘h’ over which shear acts Shear Modulus G = τ / γ Tensile Shearhttp://www.mse.ncsu.edu/zhu Materials Science & Engineering Tensile test/The most common test • Strength of materials can be tested by pulling the metal to failure. Specimen Extensometer Force data is obtained from Load cell Strain data is obtained from Extensometer. Load Cell http://video.google.com/videosearch?q=tensile+testing&hl=en&emb=0&aq=0&oq=tensile+test#http://www.mse.ncsu.edu/zhu Materials Science & Engineering Tensile Test (Cont) Commonly used Test specimen ASTM standard gives more information Typical Stress-strain curve Round bar sample Flat sheet samplehttp://www.mse.ncsu.edu/zhu Materials Science & Engineering Young’s Modulus • Young’s Modulus (E) : Stress and strain are linearly related in elastic region. (Hooke’s law) • The higher the bonding strength, The higher the modulus of elasticity • Largely determined by composition • Insensitive to the grain size E = Stress Strain Linear portion of the stress strain curve Δє Δσ E = Δσ Δєhttp://www.mse.ncsu.edu/zhu Materials Science & Engineering Yield Strength • 0.2% offset yield strength is that strength at which 0.2% plastic deformation takes place. • Construction line, starting at 0.2% strain and parallel to elastic region is drawn to find 0.2% offset yield strength.http://www.mse.ncsu.edu/zhu Materials Science & Engineering Ultimate tensile strength • Ultimate tensile strength (UTS) is the maximum strength reached by the engineering stress strain curve. • Necking starts after UTS is reached. • More ductile the metal is, more is the necking before failure. • True stress level at necking section? Al 2024-Annealed Al 2024-Tempered S T R E S S MPa Eng. Strain Necking Point Engineering Stress strain curves of Al 2024 With two different heat treatments. Ductile annealed sample necks morehttp://www.mse.ncsu.edu/zhu Materials Science & Engineering Percent Elongation/Ductility • Percent elongation (elongation to failure) is a measure of ductility of a material. • It is the elongation of the metal before fracture expressed as percentage of original length. % Elongation to failure = € lf− l0l0i.e. Ductility (єf) =http://www.mse.ncsu.edu/zhu Materials Science & Engineering Percent Reduction in Area • Percent reduction area is also a measure of ductility. • Percent reduction in area in metals decreases in case of presence of porosity. % Reduction Area = Initial area – Final area Initial area Ductile Brittlehttp://www.mse.ncsu.edu/zhu Materials Science & Engineering True Stress – True Strain • True stress and true strain are based upon instantaneous cross-sectional area and length. • True Stress = σt = • True Strain = εt = F Ai (instantaneous area) € Lnlil0= LnA0Aiσt = σ (1+ є) εt = ln (1+ є)"http://www.mse.ncsu.edu/zhu Materials Science & Engineering Hardness and Hardness Testing • Hardness is a measure of the resistance of a metal to permanent (plastic) deformation. • A quick way to estimate the yield strength: σ0.2 ≈Hardness/3 • General procedure: Press the indenter that is harder than the metal Into metal surface. Withdraw the indenter Measure hardness by measuring depth or width of indentation. Rockwell hardness tester http://video.google.com/videosearch?q=hardness+testing&hl=en&emb=0&aq=1&oq=hardness#http://www.mse.ncsu.edu/zhu Materials Science & Engineering Home work • Example Problems: 6.4, 6.5, 6.6, 6.7, 6.8, • Regular Problems, Chapter 6: download from web • Reading assignment: section