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Lecture # 6 Mechanical Properties of Metals

Lecture # 6 Mechanical Properties of Metals. Intended learning Outcomes: After the end of this lecture the student should be able to: Define stress –strain relation. State Hooke’s law. Modules of elasticity . Tensile strength ,percent elongation ,Ductility

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Lecture # 6 Mechanical Properties of Metals

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  1. Lecture # 6Mechanical Properties of Metals • Intended learning Outcomes: • After the end of this lecture the student should be able to: • Define stress –strain relation. • State Hooke’s law. • Modules of elasticity . • Tensile strength ,percent elongation ,Ductility • Hardness and the different tests methods for measuring it.

  2. TENSION TESTS:

  3. ENGINEERING STRESS • Tensile stress, s: • Shear stress, t: Stress has units: N/m2 or lb/in2 4

  4. COMMON STATES OF STRESS • Simple tension: cable ϵ= Strain. Io= original length Ii= instantaneous length ΔI= deformation elongation or change in length • Simple shear: Note: t = M/AcR here. 5

  5. ENGINEERING STRAIN • Tensile strain: • Lateral strain: • Shear strain: Strain is always dimensionless. 8

  6. STRESS-STRAIN TESTING • Typical tensile specimen • Typical tensile test machine Adapted from Fig. 6.2, Callister 6e. • Other types of tests: --compression: brittle materials (e.g., concrete) --torsion: cylindrical tubes, shafts. Adapted from Fig. 6.3, Callister 6e. (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.) 9

  7. ELASTIC DEFORMAT ION STRESS–STRAIN BEHAVIOR For most metals that are stressed in tension and at relatively low levels, stress and strain are proportional to each other through the relationship: • Modulus of Elasticity, E: (also known as Young's modulus) • Hooke's Law: s = Ee Units: E: [GPa] or [psi]

  8. Elastic Deformation Linear Behavior Behavior of most metals (E)

  9. Non Linear Elastic Behavior (Secant and Tangent Modulus) Eg: Gray cast iron ,concrete,polymers

  10. EXAMPLE:1 A piece of copper originally 305 mm (12 in.) long is pulled in tension with a stress of 276 MPa (40,000 psi). If the deformation is entirely elastic, what will be the resultant elongation?

  11. MECHA NICAL BEHAVIOR of META LS Typical stress–strain behavior for a metal showing elastic and plastic deformations, the proportional limitP, and the yield strengthy, as determined using the 0.002 strain offset method.

  12. PLASTIC (PERMANENT) DEFORMATION (at lower temperatures, T < Tmelt/3) • Simple tension test: 14

  13. YIELD STRENGTH, sy • Stress at which noticeableplastic deformation has occurred. when ep = 0.002 15

  14. YIELD STRENGTH: COMPARISON Room T values 16

  15. TENSILE STRENGTH, TS • Maximum possible engineering stress in tension. Adapted from Fig. 6.11, Callister 6e. • Metals: occurs when noticeable necking starts. • Ceramics: occurs when crack propagation starts. • Polymers: occurs when polymer backbones are aligned and about to break. 17

  16. Example 2: From the tensile stress–strain behavior for the brass specimen shown in the following Figure determine the following: (a) The modulus of elasticity. (b) The yield strength at a strain offset of 0.002. (c) The maximum load that can be sustained by a cylindrical specimen having an original diameter of 12.8 mm (0.505 in.). (d) The change in length of a specimen originally 250 mm (10 in.) long that is subjected to a tensile stress of 345 MPa (50,000 psi).

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