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 Hardness and the different tests methods for measuring it.

TENSION TESTS:

4 Tensile stress,  : Shear stress,  : Stress has units: N/m 2 or lb/in 2 ENGINEERING STRESS

5 Simple tension: cable Simple shear: Note:  = M/A c R here. COMMON STATES OF STRESS ϵ= Strain. I o = original length I i = instantaneous length Δ I= deformation elongation or change in length

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

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

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: ELASTIC DEFORMAT ION Modulus of Elasticity, E: (also known as Young's modulus) Hooke's Law:  = E  Units: E: [GPa] or [psi]

Elastic Deformation Linear Behavior Behavior of most metals (E)

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

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?

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 strain offset method.

14 Simple tension test: (at lower temperatures, T < T melt /3) PLASTIC (PERMANENT) DEFORMATION

15 Stress at which noticeable plastic deformation has occurred. when  p = YIELD STRENGTH,  y

16 Room T values YIELD STRENGTH: COMPARISON

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

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 (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).