Materials Science

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Week 4MECHANICAL PROPERTIES AND TESTS

• Materials Science

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Stress

• Stress is a measure of the intensity of the
  internal forces acting within a deformable body.
• Mathematically, it is a measure of the average
  force per unit area of a surface within a the
  body on which internal forces act
• The SI unit for stress is Pascal (symbol Pa),
  which is equivalent to one Newton (force) per
  square meter (unit area).
• Three types of stresses -gt Tensile Compressive
  Shear

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Mechanism of Stress (Tensile)
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Strain

• Strain is deformation of a physical body under
  the action of applied forces
• It is the geometrical measure of deformation
  representing the relative displacement between
  particles in the material body
• Strain is a dimensionless quantity
• Strain accounts for elongation, shortening, or
  volume changes, or angular distortion
• Normal stress causes normal strain (tensile or
  compressive)
• Shear strain is defined as the change in angle
  between two originally orthogonal material lines

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Types of Strains
tensile load produces an elongation and positive
linear strain.
compressive load produces contraction and a
negative linear strain.
torsional deformation
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• Tensile Test and Stress-strain relationship

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Tensile Test

• Used for determining UTS, yield strength, age
  elongation, and Youngs Modulus of Elasticity
• The ends of a test piece are fixed into grips.
  The specimen is elongated by the moving
  crosshead load cell and extensometer measure,
  respectively, the magnitude of the applied load
  and the elongation

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Stress-Strain Relationship
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Important Terms (Stress-Strain Rel.)

• Elastic Limit -gt Maximum amount of stress up to
  which the deformation is absolutely temporary
• Proportionality Limit -gt Maximum stress up to
  which the relationship between stress strain is
  linear.
• Hookes Law -gt Within elastic limit, the strain
  produced in a body is directly proportional to
  the stress applied.
• s E e

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Important Terms (Stress-Strain Rel.)

• Youngs Modulus of elasticity -gt the ratio of the
  uniaxial stress over the uniaxial strain in the
  range of stress in which Hooke's Law holds
• Elasticity -gt the tendency of a body to return to
  its original shape after it has been stretched or
  compressed
• Yield Point -gt the stress at which a material
  begins to deform plastically

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Important Terms (Stress-Strain Rel.)

• Plasticity -gt the deformation of a material
  undergoing non-reversible changes of shape in
  response to applied forces
• Ultimate Strength -gt It is the maxima of the
  stress-strain curve. It is the point at which
  necking will start.
• Necking -gt A mode of tensile deformation where
  relatively large amounts of strain localize
  disproportionately in a small region of the
  material

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Important Terms (Stress-Strain Rel.)

• Fracture Point -gt The stress calculated
  immediately before the fracture.
• Ductility -gt The amount of strain a material can
  endure before failure.
• Ductility is measured by percentage elongation or
  area reduction

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Important Terms (Stress-Strain Rel.)

• A knowledge of ductility is important for two
  reasons
• It indicates to a designer the degree to which a
  structure will deform plastically before
  fracture.
• It specifies the degree of allowable deformation
  during fabrication

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Engineering stress strain behavior for Iron at
three temperatures
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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) is the strain energy
  per unit volume required to stress a material
  from an unloaded state up to the point of
  yielding.

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Resilience

• Assuming a linear elastic region
• For SI units, this is joules per cubic meter
  (J/m3, equivalent to Pa)
• Thus, resilient materials are those having high
  yield strengths and low moduli of elasticity
  such alloys would be used in spring applications

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Shear and Torsional Tests

• Shear Stress
• The shear strain ? is defined as the tangent of
  the strain angle ?
• Torsion is a variation of pure shear, wherein a
  structural member is twisted in the manner of the
  figure
• Torsional stress -gt The shear stress on a
  transverse cross section resulting from a
  twisting action
• Torsional forces produce a rotational motion
  about the longitudinal axis of one end of the
  member relative to the other end

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ANELASTICITY

• In most engineering materials, there also exists
  a time-dependent elastic strain component.
• This time-dependent elastic behavior is known as
  anelasticity
• For metals the anelastic component is normally
  small and is often neglected
• For some polymeric materials its magnitude is
  significant in this case it is termed
  viscoelastic behavior

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EXAMPLE PROBLEM 6.1

• A piece of copper originally 305mm (12 in.) long
  is pulled in tension with a stress of 276MPa
  (40,000psi). If the deformation is entirely
  elastic, what will be the resultant elongation?
• Magnitude of E for copper from Table 6.1 is 110GPa

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Poissons Ratio

• Poissons ratio is defined as the ratio of the
  lateral and axial strains
• Theoretically, Poissons ratio for isotropic
  materials should be 1/4 furthermore, the maximum
  value for ? is 0.50
• For isotropic materials, shear and elastic moduli
  are related

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EXAMPLE PROBLEM 6.2

• A tensile stress is to be applied along the long
  axis of a cylindrical brass rod that has a
  diameter of 10mm. Determine the magnitude of the
  load required to produce a 0.0025mm change in
  diameter if the deformation is entirely elastic.
• For the strain in the x direction

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EXAMPLE PROBLEM 6.2
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True Stress and Strain

• The decline in the stress necessary to continue
  deformation past the point M, indicates that the
  metal is becoming weaker.
• Material is increasing in strength.
• True stress sT is defined as the load F divided
  by the instantaneous cross-sectional area Ai over
  which deformation is occurring
• True strain ?T is defined as

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True Stress and Strain

• If no volume change occurs during
  deformationthat is, if Aili A0l0
• Then true and engineering stress and strain are
  related according to
• The equations are valid only to the onset of
  necking beyond this point true stress and strain
  should be computed from actual load,
  cross-sectional area, and gauge length
  measurements

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Assignment

• (a) Completely describe Compression Test. (b)
  How is it different from Tensile test? (c) What
  are the effects of Friction and Workpieces
  height-to-diameter ratio on the test? (d) Derive
  relationship between true stress/strain and
  engineering stress/strain for compression test
  (also show by stress-strain curve)
• Only hand-written assignments

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EXAMPLE PROBLEM 6.4

• A cylindrical specimen of steel having an
  original diameter of 12.8mm is tensile tested to
  fracture and found to have an engineering
  fracture strength sf of 460MPa. If its
  cross-sectional diameter at fracture is 10.7mm,
  determine
• (a) The ductility in terms of percent reduction
  in area
• (b) The true stress at fracture
• Ductility is computed as

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EXAMPLE PROBLEM 6.4

• True stress is defined by Equation
• where the area is taken as the fracture area Af
• However, the load at fracture must first be
  computed from the fracture strength as
• And the true stress is calculated as

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Elastic Recovery after Plastic Deformation

• Upon release of the load during the course of a
  stressstrain test, some fraction of the total
  deformation is recovered as elastic strain
• During the unloading cycle, the curve traces a
  near straight-line path from the point of
  unloading (point D), and its slope is virtually
  parallel to the initial elastic portion of the
  curve
• The magnitude of this elastic strain, which is
  regained during unloading, corresponds to the
  strain recovery

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Hardness

• Hardness is the property of material by virtue of
  which it resists against surface indentation and
  scratches.
• Macroscopic hardness is generally characterized
  by strong intermolecular bonds
• Hardness is dependent upon strength and ductility
• Common examples of hard matter are diamond,
  ceramics, concrete, certain metals, and superhard
  materials (PcBN, PcD, etc)

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Hardness Tests (BRINELL HARDNESS TEST)

• Used for testing metals and nonmetals of low to
  medium hardness
• The Brinell scale characterizes the indentation
  hardness of materials through the scale of
  penetration of an indenter, loaded on a material
  test-piece
• A hardened steel (or cemented carbide) ball of
  10mm diameter is pressed into the surface of a
  specimen using load of 500, 1500, or 3000 kg.

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BRINELL HARDNESS TEST

• where
• P applied force (kgf)
• D diameter of indenter (mm)
• d diameter of indentation (mm)
• The resulting BHN has units of kg/mm2, but the
  units are usually omitted in expressing the
  numbers

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Rockwell Hardness Test

• Rockwell test determines the hardness by
  measuring the depth of penetration of an indenter
  under a large load compared to the penetration
  made by a preload
• A cone shaped indenter or small diameter ball (D
  1.6 or 3.2mm) is pressed into a specimen using
  a minor load of 10kg
• Then, a major load of 150kg is applied
• The additional penetration distance d is
  converted to a Rockwell hardness reading by the
  testing machine.

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Rockwell Hardness Test
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Vickers Hardness Test

• Uses a pyramid shaped indenter made of diamond.
• It is based on the principle that impressions
  made by this indenter are geometrically similar
  regardless of load.
• The basic principle, as with all common measures
  of hardness, is to observe the questioned
  material's ability to resist plastic deformation
  from a standard source.
• Accordingly, loads of various sizes are applied,
  depending on the hardness of the material to be
  measured

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Vickers Hardness Test

• Where
• F applied load (kg)
• D Diagonal of the impression made the indenter
  (mm)
• The hardness number is determined by the load
  over the surface area of the indentation and not
  the area normal to the force

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Knoop Hardness Test

• It is a microhardness test - a test for
  mechanical hardness used particularly for very
  brittle materials or thin sheets
• A pyramidal diamond point is pressed into the
  polished surface of the test material with a
  known force, for a specified dwell time, and the
  resulting indentation is measured using a
  microscope
• Length-to-width ratio of the pyramid is 71

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Knoop Hardness Test (contd)

• The indenter shape facilitates reading the
  impressions at lighter loads
• HK Knoop hardness value F load (kg) D
  long diagonal of the impression (mm)

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Hardness of Metals and Ceramics
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Hardness of Polymers
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TOUGHNESS

• It is a property of material by virtue of which
  it resists against impact loads.
• Toughness is the resistance to fracture of a
  material when stressed
• Mathematically, it is defined as the amount of
  energy per volume that a material can absorb
  before rupturing
• Toughness can be determined by measuring the area
  (i.e., by taking the integral) underneath the
  stress-strain curve

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Toughness (contd)

• Toughness
• Where
• e is strain
• ef is the strain upon failure
• s is stress
• The Area covered under stress strain curve is
  called toughness

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Toughness (contd)

• Toughness is measured in units of joules per
  cubic meter (J/m3) in the SI system
• Toughness and Strength -gt A material may be
  strong and tough if it ruptures under high
  forces, exhibiting high strains
• Brittle materials may be strong but with limited
  strain values, so that they are not tough
• Generally, strength indicates how much force the
  material can support, while toughness indicates
  how much energy a material can absorb before
  rupture

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Effect of Temperature on Properties

• Generally speaking, materials are lower in
  strength and higher in ductility, at elevated
  temperatures

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Hot Hardness

• A property used to characterize strength and
  hardness at elevated temperatures is Hot Hardness
• It is the ability of a material to retain its
  hardness at elevated temperatures

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Numerical Problems

• Problems 6.3 to 6.9
• 6.14 to 6.23
• 6.25 to 6.33
• 6.46 to 6.48