# mechanical properties of metal.pptx

1 Jun 2023
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### mechanical properties of metal.pptx

• 2. • Mechanical Properties refers to the behavior of material when • external forces are applied • Stress and strain ⇒ fracture • For engineering point of view: allows to predict the ability of a component or a structure to withstand the forces applied to it 2 For science point of view: what makes materials strong →helps us to design a better new one
• 3. 3 Elastic means reversible! Elastic Deformation 2. Small load F d bonds stretch 1. Initial 3. Unload return to initial F d Linear- elastic Non-Linear- elastic Grey iron, concrete, polymers)
• 4. 4 Plastic means permanent! Plastic Deformation (Metals) F d linear elastic linear elastic dplastic 1. Initial 2. Small load 3. Unload planes still sheared F d elastic + plastic bonds stretch & planes shear d plastic
• 5. Direct Stress Examples Load, P P Area Ao Lo L/2 L/2 Direct Stress - Tension Load, P P Area Ao Lo L/2 L/2 Direct Stress - Compression S  P Ao e  L Lo Engineering Stress Engineering Strain 5
• 6. 6  Stress has units: N/m2 or lbf /in2 Engineering Stress • Shear stress, t: Area, Ao Ft Ft Fs F F Fs t = Fs Ao • Tensile stress, s: original area before loading s = Ft Ao 2 f 2 m N or in lb = Area, Ao Ft Ft
• 7. 7 • Simple tension: cable Note: t = M/AcR here. Common States of Stress o s  F A o t  Fs A s s M M Ao 2R Fs Ac • Torsion (a form of shear): drive shaft Ski lift (photo courtesy P.M. Anderson) Ao = cross sectional area (when unloaded) F F
• 8. 8 (photo courtesy P.M. Anderson) Canyon Bridge, Los Alamos, NM o s  F A • Simple compression: Note: compressive structure member (s < 0 here). (photo courtesy P.M. Anderson) OTHER COMMON STRESS STATES (i) Ao Balanced Rock, Arches National Park
• 9. 9 • Bi-axial tension: • Hydrostatic compression: Pressurized tank s < 0 h (photo courtesy P.M. Anderson) (photo courtesy P.M. Anderson) OTHER COMMON STRESS STATES (ii) Fish under water s z > 0 s q > 0
• 10. 10 • Tensile strain: • Lateral strain: Strain is always dimensionless. Engineering Strain • Shear strain: q 90º 90º - q y x q g = x/y = tan e  d Lo Adapted from Fig. 6.1(a) and (c), Callister & Rethwisch 8e. d /2 Lo wo -d eL  L wo d L/2 𝛿 = 𝐿-𝐿°
• 11. 11 Stress-Strain Testing • Typical tensile test machine Adapted from Fig. 6.3, Callister & Rethwisch 8e. (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 & Rethwisch 8e. gauge length
• 13. Raw Data Obtained Load, P (kN) Elongation, L (mm) Uniform Deformation Total Elongation Elastic Deformation X Maximum Load, Pmax Load, Pf 13
• 14. Engineering Stress-Strain Curve Elongation 0.2% offset yield stress Proportional Limit E E (Ultimate) Engineering Strain, e = L/Lo) Engineering Stress, S=P/Ao Sy Su 14
• 15. 15 Linear Elastic Properties • Modulus of Elasticity, E: (also known as Young's modulus) • Hooke's Law: s = E e s Linear- elastic E e F F simple tension test • Elastic deformation is not permanent; it means that when the load is removed, the part returns to its original shape and dimensions. • For most metals, the elastic region is linear. For some materials, including metals such as cast iron, polymers, and concrete, the elastic region is non-linear.
• 16. Modulus of Elasticity -stiffness 0.010 0.008 0.006 0.004 0.002 0.000 0 100 200 300 400 500 CONTINUED Stress (MPa) Strain E  S e  (300- 0)MPa (0.015- 0.0)  2x105 MPa 16
• 17. The elastic modulus is proportional to the slope of the interatomic force-separation curve at the equilibrium spacing The magnitude of modulus of elasticity is a measure of the resistance to separation of adjacent atoms, that is interatomic 17
• 18. Modulus of elasticity- Temperature 18 Values of the modulus of elasticity for ceramic materials are about the same as for metals; for polymers they are lower. These differences are a direct consequence of the different types of atomic bonding in the three materials types. Furthermore, with increasing temperature, the modulus of elasticity diminishes, as is shown for several metals in Figure.
• 21. Elastic Properties of Materials • Poisson’s ratio: When a metal is strained in one direction, there are corresponding strains in all other directions. • For a uniaxial tension strain, the lateral strains are constrictive. • Conversely, for a uniaxial compressive strain, the lateral strains are expansive. • i.e.; the lateral strains are opposite in sign to the axial strain. • The ratio of lateral to axial strains is known as Poisson’s ratio, n. 21
• 22. 22 Poisson's ratio, n • Poisson's ratio, n: Units: E: [GPa] or [psi] n: dimensionless n > 0.50 density increases n < 0.50 density decreases (voids form) eL e -n e n  - L e metals: n ~ 0.33 ceramics: n ~ 0.25 polymers: n ~ 0.40 Ratio of lateral and axial strains
• 23. Poisson’s Ratio, n n  - ex ez  - ey ez For most metals, 0.25 < n < 0.35 in the elastic range Furthermore: ) 1 ( 2 n   G E 23
• 24. 24 • Elastic Shear modulus, G: t G g t = G g Other Elastic Properties simple torsion test M M • Special relations for isotropic materials: 2(1  n) E G  3(1 - 2n) E K  • Elastic Bulk modulus, K: pressure test: Init. vol =Vo. Vol chg. = V P P P P = -K V Vo P V K Vo
• 25. 25 (at lower temperatures, i.e. T < Tmelt/3) Plastic (Permanent) Deformation • Simple tension test: engineering stress, s engineering strain, e Elastic+Plastic at larger stress ep plastic strain Elastic initially Adapted from Fig. 6.10(a), Callister & Rethwisch 8e. permanent (plastic) after load is removed
• 26. Plastic Deformation Stress Strain 0.002 0.002 0.002 Sy Sy Sy Elastic Plastic Most Metals - Al, Cu Clad Al-Alloys Low carbon Steel Elastic Plastic Elastic Plastic 26
• 27. 27 • Stress at which noticeable plastic deformation has occurred. when ep = 0.002 Yield Strength, sy sy = yield strength Note: for 2 inch sample e = 0.002 = l/l  z = 0.004 in Adapted from Fig. 6.10(a), Callister & Rethwisch 8e. tensile stress, s engineering strain, e sy ep = 0.002
• 28. 28 Room temperature values Based on data in Table B.4, Callister & Rethwisch 8e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered Yield Strength : Comparison Graphite/ Ceramics/ Semicond Metals/ Alloys Composites/ fibers Polymers Yield strength, s y (MPa) PVC Hard to measure , since in tension, fracture usually occurs before yield. Nylon 6,6 LDPE 70 20 40 60 50 100 10 30 200 300 400 500 600 700 1000 2000 Tin (pure) Al (6061) a Al (6061) ag Cu (71500) hr Ta (pure) Ti (pure) a Steel (1020) hr Steel (1020) cd Steel (4140) a Steel (4140) qt Ti (5Al-2.5Sn) a W (pure) Mo (pure) Cu (71500) cw Hard to measure, in ceramic matrix and epoxy matrix composites, since in tension, fracture usually occurs before yield. HDPE PP humid dry PC PET ¨
• 29. 29 Tensile Strength, TS • Metals: occurs when noticeable necking starts. • Polymers: occurs when polymer backbone chains are aligned and about to break. Adapted from Fig. 6.11, Callister & Rethwisch 8e. sy strain Typical response of a metal F = fracture or ultimate strength Neck – acts as stress concentrator engineering TS stress engineering strain • Maximum stress on engineering stress-strain curve.
• 30. 30 Tensile Strength: Comparison Si crystal <100> Graphite/ Ceramics/ Semicond Metals/ Alloys Composites/ fibers Polymers Tensile strength, TS (MPa) PVC Nylon 6,6 10 100 200 300 1000 Al (6061) a Al (6061) ag Cu (71500) hr Ta (pure) Ti (pure) a Steel (1020) Steel (4140) a Steel (4140) qt Ti (5Al-2.5Sn) a W (pure) Cu (71500) cw LDPE PP PC PET 20 30 40 2000 3000 5000 Graphite Al oxide Concrete Diamond Glass-soda Si nitride HDPE wood ( fiber) wood(|| fiber) 1 GFRE(|| fiber) GFRE( fiber) CFRE(|| fiber) CFRE( fiber) AFRE(|| fiber) AFRE( fiber) E-glass fib C fibers Aramid fib Based on data in Table B.4, Callister & Rethwisch 8e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered AFRE, GFRE, & CFRE = aramid, glass, & carbon fiber-reinforced epoxy composites, with 60 vol% fibers. Room temperature values
• 31. Microstructural Origins of Plasticity • Slip, Climb and Slide of atoms in the crystal structure. • Slip and Climb occur at Dislocations and Slide occurs at Grain Boundaries. t t 31
• 32. 32 • Plastic tensile strain at failure: Ductility • Another ductility measure: 100 x A A A RA % o f o - = x 100 L L L EL % o o f -  Lf Ao Af Lo Adapted from Fig. 6.13, Callister & Rethwisch 8e. Engineering tensile strain, e Engineering tensile stress, s smaller %EL larger %EL , ductility is defined by the degree to which a material can sustain plastic deformation under tensile stress before failure.
• 33. Ductile Vs Brittle Materials • Only Ductile materials will exhibit necking. • Ductile if EL%>8% (approximately) • Brittle if EL% < 5% (approximately) Engineering Stress Engineering Strain 33
• 34. Typical Mechanical Properties Material Yield Stress (MPa) Ultimate Stress (MPa) Ductility EL% Elastic Modulus (MPa) Poisson’s Ratio 1040 Steel 350 520 30 207000 0.30 1080 Steel 380 615 25 207000 0.30 2024 Al Alloy 100 200 18 72000 0.33 316 Stainless Steel 210 550 60 195000 0.30 70/30 Brass 75 300 70 110000 0.35 6-4 Ti Alloy 942 1000 14 107000 0.36 AZ80 Mg Alloy 285 340 11 45000 0.29 Metals in annealed (soft) condition 34
• 35. 35 Summary • Stress and strain: These are size-independent measures of load and displacement, respectively. • Elastic behavior: This reversible behavior often shows a linear relation between stress and strain. To minimize deformation, select a material with a large elastic modulus (E or G). • Toughness: The energy needed to break a unit volume of material. • Ductility: The plastic strain at failure. • Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches sy.
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• 38. Problems 38 A cylindrical metal specimen having an original diameter of 12.8 mm (0.505 in.) and gauge length of 50.80 mm (2.000 in.) is pulled in tension until fracture occurs. The diameter at the point of fracture is 8.13 mm (0.320 in.), and the fractured gauge length is 74.17 mm(2.920 in.). Calculate the ductility in terms of percent reduction in area and percent elongation.