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Mechanical properties of metals by malj

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									     Mechanical properties of
            metals


    How do metals respond to external loads?
•Stress& strain
•Elastic deformation.
•Plastic deformation.
  STRESS-STRAIN TESTING
• Typical tensile specimen                     • Typical tensile
                                                  test machine
         Adapted from Fig. 6.2,
          Callister 6e.




            • Other types of tests:            Adapted from Fig. 6.3, Callister 6e.
                                               (Fig. 6.3 is taken from H.W. Hayden,
               --compression: brittle          W.G. Moffatt, and J. Wulff, The
                                               Structure and Properties of
                 materials (e.g., concrete)    Materials, Vol. III, Mechanical
                                               Behavior, p. 2, John Wiley and Sons,
               --torsion: cylindrical tubes,   New York, 1965.)
                 shafts.                                                       9
                   Raw Data Obtained
                       Total Elongation
               Uniform Deformation
Load, P (kN)




                                                   X

                                    Maximum
                                    Load, Pmax
                  Elastic
                                                 Load,
                  Deformation                    Pf




                                  Elongation, DL (mm)
                             Engineering Stress-Strain Curve
                                                 Elongation

                             Sy
Engineering Stress, S=P/Ao



                             0.2% offset
                             yield stress




                                       E                  (Ultimate)

                                                                       Su
                                E

                                    Proportional Limit




                                              Engineering Strain, e = DL/Lo)
Stress-strain behavior
                Elastic behavior
• In brittle materials   • In ductile materials
• Non linear elastic     • Linear elastic behavior
  behavior
               Hooke’s Law
            Elastic Deformation
• 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.
• If the behavior is linear elastic, or nearly linear-elastic,
  Hooke’s Law may be applied:
                         S  Ee
• Where E is the modulus of elasticity (MPa)
 Elastic properties of materials
• Poisson’s ratio:
  When a metal is
  strained in one
  direction, there are
  corresponding
  strains in all other
  directions.
    ex  ey
          For most metals,
    ez  ez
                0.25 <  < 0.35
               in the elastic range
Stress-strain behavior
        • Elastic deformation
        • Reversible: when the stress is
          removed, the material returns to
          the dimension it had before the
          loading. Usually strains are small
          (except for the case of plastics).
        • Plastic deformation
        • Irreversible: when the stress
        • is removed, the material
        • does not return to its
        • previous dimension.
                   Elastic Recovery
         Loading               Loading
                                                   Reloading
Stress




                               Unloading


                   Unloading


                   Strain                                 Strain
                                         elastic strain
            Elastic and Plastic Strain
                         P (σ,Ɛ)
                                       Ɛ=Ɛe+Ɛp
                                       Total strain =
Stress




                                       elastic strain + plastic strain
                                       Ɛe= σ/E
                                       Ɛp=Ɛ- Ɛe
         Total Strain

                                              The 0.2% offset yield stress
                             Strain           is the stress that gives a plastic
         Plastic                              (permanent) strain of 0.002.
                             Elastic
            Ɛp          Ɛe
Tensile properties: Yielding

              • Yield strength σy - is chosen
                as that causing a permanent
                strain of 0.002
              • Yield point P - the strain
                deviates from being
                proportional to the stress (the
                proportional limit)
              • The yield stress is a measure
                of resistance to plastic
                deformation
Tensile properties: Yielding
                 • For a low-carbon steel,
                   the stress vs. strain
                   curve includes both an
                   upper and lower yield
                   point.

                 The yield strength is
                   defined in this case as
                   the average stress at
                   the lower yield point.
Tensile Strength
        • For structural applications,
          the yield stress is usually a
          more important property
          than the tensile strength,
          since once the it is passed,
          the structure has deformed
          beyond acceptable limits
                   Ductility
                            • Ductility is a measure
                              of the deformation at
        L f  Lo              fracture
EL%               x 100
          Lo                • Define as elongation
                              percent or reduction in
                              area
                            •        L f  Lo
                           EL%                  x 100
                                        Lo
                                     Ao  A f
                             AR%               x 100
                                        Ao
                 Ductile Vs Brittle Materials
• Only Ductile materials will exhibit
  necking.
• Ductile if EL%>8% (approximately)
• Brittle if EL% < 5% (approximately)
Engineering Stress




                           Engineering Strain
            Example problem
Determine the mechanical properties for metal which have the
stress-strain curve as shown below.
• The elastic modulus is the slope in the linear elastic
  region


For the yield strength, the 0.002 strain offset line is
 drawn dashed. It intersects the stress-strain curve at
 approximately 285 MPa
• (d) The tensile strength is approximately 370
  MPa, corresponding to the maximum stress on
  the complete stress-strain plot.
• If the gauge length (L0) = 12 cm , the length at
  fracture (Lf) = 16 cm, original diameter (d0)= 12
  mm, the diameter at fracture (df) = 8mm.
Then the ductility =

								
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