CHAPTER 6: MECHANICAL PROPERTIES

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CHAPTER 6 MECHANICAL PROPERTIES
ISSUES TO ADDRESS...
Stress and strain What are they and why are
they used instead of load and deformation?
Elastic behavior When loads are small, how
much deformation occurs? What materials
deform least?
Plastic behavior At what point do
dislocations cause permanent deformation?
What materials are most resistant to
permanent deformation?
Toughness and ductility What are they and
how do we measure them?
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Chapter 6 Mechanical Properties of Metals6.1
Introduction

• Why Study the Mechanical Properties of Metals ?
• It is important for engineers to understand
• How the various mechanical properties are
  measured, and
• What these properties represent
• The role of structural engineers is to determine
  stresses and stress distributions within members
  that are subjected to well-defined loads
• By experimental testing
• Theoretical and mathematical stress analysis.
• Design structures/components using predetermined
  materials such that unacceptable levels of
  deformation and/or failure will not occur.

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6.2 Concepts of Stress and Strain

• Static load ? changes relatively slowly with time
  
• Applied uniformly over a cross-section or surface
  of a member.
• Tension
• Compression
• Shear
• Torsion

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6.2 Concepts of Stress and Strain (Contd.)

• TENSION TEST
• Most common mechanical stress-strain test
• Used to ascertain several mechanical properties
  that are important in design
• A specimen is deformed, usually to fracture, with
  a gradually increasing tensile load that is
  applied uniaxially along the long axis of the
  specimen.
• A standard specimen is shown in Figure 6-2.

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6.2 Concepts of Stress and Strain (Contd.)

• The specimen is mounted by its ends into the
  holding grips of the testing apparatus (Figure
  6-3).
• Tensile testing machine
• To elongate the specimen at a constant rate
• To continuously and simultaneously measure the
  instantaneous load and the resulting extension
• Load using load cell
• Extension using extensometer
• Takes few minutes and is destructive.

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6.2 Concepts of Stress and Strain (Contd.)

• Engineering Stress (s) Instantaneous applied
  load (F) / Original Area (Ao)
• Unit MPa, GPa, psi
• Engineering strain (e)
• li instantaneous length
• lo original length
• COMPRESSION TESTS
• Similar to tensile test, compressive load
• Sign convention, compressive force is taken
  negative ? stress negative
• Since lo gt li , negative strain

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6.2 Concepts of Stress and Strain (Contd.)

• SHEAR AND TORSIONAL TESTS
• Shear stress t F / Ao
• F Load or force imposed parallel to the upper
  and lower faces
• Ao shear or parallel area
• Shear strain (g) is defined as the tangent of the
  strain angle q.

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6.2 Concepts of Stress and Strain (Contd.)

• GEOMETRIC CONSIDERATIONS OF THE STRESS STATE
• Stress is a function of orientations of the
  planes

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ELASTIC DEFORMATION
1. Initial
2. Small load
3. Unload
Elastic means reversible!
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ELASTIC DEFORMATION6.3 Stress-Strain Behavior

• Elastic deformation
• Non-permanent, completely reversible,
  conservative
• Follow same loading and unloading path
• Linear elastic deformation
• Hookes Law
• Modulus of elasticity or Youngs Modulus ?
  stiffness or a materials resistance to elastic
  deformation

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6.3 Stress-Strain Behavior (Contd.)
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• Nonlinear Elastic Behavior
• Gray cast iron, concrete, many polymers
• Not possible to determine a modulus of elasticity
• Either tangent or secant modulus is normally used.

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6.3 Stress-Strain Behavior (Contd.)

• On an atomic scale, macroscopic elastic strain is
  manifested as small changes in the interatomic
  spacing and the stretching of interatomic bonds.
• ? E is a measure of the resistance to separation
  of adjacent atoms
• Modulus is proportional to the slope of the
  interatomic force-separation curve (Fig 2.8a) at
  equilibrium spacing

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6.3 Stress-Strain Behavior (Contd.)

• With increasing temperature, the modulus of
  elasticity diminishes
• Shear stress and strain are proportional to each
  other
• Shear modulus or modulus of rigidity ( Table 6.1)

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6.4 Anelasticity

• Up to this point, it is assumed that
• Elastic deformation is time-independent
• An applied stress produces an instantaneous
  elastic strain
• Strain remains constant over the period of time
  the stress is maintained
• Upon release of the load, strain is totally
  recovered (immediately returns to zero)
• In most engineering materials, there will also
  exist a time-dependent elastic strain component ,
  i.e.
• elastic deformation will continue after stress
  application
• Upon load release some finite time is required
  for complete recovery
• Loading and unloading path are different
• Anelasticity time-dependent elastic behavior
• For metals, the anelastic component is normally
  small and neglected.
• For some polymers, it is significant and known as
  viscoelastic behavior (Sec. 16.7)

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6.5 Elastic Properties of Materials

• Poissons ratio
• E 2G(1 n)
• Example 6.1
• Example 6.2

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PLASTIC DEFORMATION

• For most metals, elastic deformation persists
  only to strains of about 0.005
• Plastic deformation
• Stress not proportional to strain (Hookes law
  cease to be valid)
• Permanent
• Nonrecoverable
• Non-conservative
• Transition from elastic to plastic deformation
• Gradual for most metals
• Some curvature results at the onset of plastic
  deformation

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PLASTIC DEFORMATION (METALS)
1. Initial
2. Small load
3. Unload
Plastic means permanent!
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PLASTIC (PERMANENT) DEFORMATION
(at lower temperatures, T lt Tmelt/3)
Simple tension test
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Plastic deformation (Contd.)

• From as atomic perspective
• Plastic deformation corresponds to the breaking
  of bonds with original atom neighbors
• Reforming bonds with new neighbors
• Large number of atoms and molecules move relative
  to one another
• Upon removal of stress, they do not return to
  their original position
• Mechanism of plastic deformation
• Crystalline Solids
• accomplished by a process called slip
• Involves the motion of dislocations (Sec 7.2)
• Non-crystalline solids (as well liquids)
• Occurs by a viscous flow mechanism (Sec 13.9)

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YIELD STRENGTH, sy
Stress at which noticeable plastic deformation
has occurred.
when ep 0.002
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6.6 Tensile Properties

• YIELDING and YIELD STRESS
• Typical stress strain behavior (Figure)
• Proportional Limit (P)
• Yielding
• Yield strength
• In most cases, the position of yield point may
  not be determined precisely.
• Established convention a straight line is
  constructed parallel to the elastic portion at
  some specified strain offset, usually 0.002
  (0.2) Fig. 6.10a ? corresponding intersection
  point gives yield strength.

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6.6 Tensile Properties (Contd.)

• Some steels and other materials exhibit the
  behavior as shown in Fig 6.10b
• The yield strength is taken as the average stress
  that is associate with the lower yield point.
• Magnitude of yield strength is a measure of its
  resistance to plastic deformation
• Range from 35 MPa to 1400 MPa
• 35 MPa for low-strength aluminum
• 1400 MPa for high-strength steel

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6.6 Tensile Properties (Contd.)

• TENSILE STRENGTH
• Tensile strength TS (MPa or psi) is the stress at
  the maximum on the engineering stress-strain
  curve
• All deformation up to this point is uniform.
• Onset of necking at this stress at some point ?
  all subsequent deformation at this neck.
• Range 50 - 3000 MPa
• 50 MPa for aluminum
• 3000 MPa for high strength steel

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DUCTILITY, EL
Plastic tensile strain at failure
Adapted from Fig. 6.13, Callister 6e.
Another ductility measure
Note AR and EL are often comparable.
--Reason crystal slip does not change material
volume. --AR gt EL possible if internal
voids form in neck.
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• Effect of Temperature
• As with modulus of elasticity (E), the magnitudes
  of both yield and tensile strengths decline with
  increasing temperature
• Ductility usually increases with temperature
• Figure shown stress-strain behavior of iron

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RESILIENCE

• Resilience is the capacity of a material to
  absorb energy when it is deformed elastically and
  then, upon unloading, to have this energy
  recovered.
• Modulus of resilience (Ur)
• Associated property
• Area under the engineering stress-strain curve
• Strain energy per unit volume required to stress
  from an unloaded state to yielding
• Mathematically,

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TOUGHNESS
Energy to break a unit volume of material
Approximate by the area under the stress-strain
curve.
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TOUGHNESS

• A measure of the ability of a material to absorb
  energy up to fracture.
• Specimen geometry and the manner of load
  application are important in toughness
  determination
• Notch toughness dynamic (high strain rate)
  loading, specimen with notch (or point of stress
  concentration) (Sec 8.6)
• Fracture toughness property indicative of a
  materials resistance to fracture when crack is
  present (Sec 8.5)
• For static (low strain rate) condition, modulus
  of toughness is equal to the total area under the
  stress-strain curve (up to fracture )
• For Ductile Material For Brittle Material

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6.7 True Stress and Strain

• Engineering stress-strain curve beyond maximum
  point (M) seems to indicate that the material is
  becoming weaker.
• Not true, rather it becomes stronger.
• Since cross-sectional area is decreasing at the
  neck ? reduces load bearing capacity of the
  material
• True stress Actual or current or instantaneous
  force divided by the instantaneous
  cross-sectional area.
• True Strain Change in length per unit
  instantaneous length

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6.7 True Stress and Strain (Contd.)

• Relation between two definitions
• Above equations are valid only to the onset of
  necking beyond this point true stress and strain
  should be computed from actual load, area and
  gauge length.
• Schematic comparison in Figure 6.16
• Corrected takes into account complex stress state
  with in neck region.

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6.7 True Stress and Strain (Contd.)

• For some metals and alloys, the true
  stress-strain curve is approximated as
• Parameter n
• strain-hardening exponent
• A value less than unity
• Slope on log-log plot
• Parameter K
• Known as strength coefficient
• True stress at unit true strain

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6.8 Elastic Recovery During Plastic Deformation

• Upon release of load, some fraction of total
  strain is recovered as elastic strain
• During unloading, straight path parallel to
  elastic loading
• Reloading
• Yielding at new yield strength

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• Solve Examples in Class
• 6.3
• 6.4
• 6.5
• 6.6
• Design Example 6.1