MFGT 290 MFGT Certification Class

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MFGT 290MFGT Certification Class
8 Strength of Materials Chapter 11 Material
Properties
Professor Joe Greene CSU, CHICO
MFGT 290
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Chap 8 Strength of Materials

• Stress and Strain
• Axial Loading
• Torsional Loading
• Beam Loading
• Column Loading
• Practice Problems

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Mechanical Test Considerations

• Normal and Shear Stresses
• Force per unit area
• Normal force per unit area
• Forces are normal (in same direction) to the
  surface
• Shear force per unit area
• Forces are perpendicular (right angle) to the
  surface
• Direct Normal Forces and Primary types of loading
• Prismatic Bar bar of uniform cross section
  subject to equal and opposite pulling forces P
  acting along the axis of the rod.
• Axial loads Forces pulling on the bar
• Tension pulling the bar Compression pushing
  torsiontwisting flexure bending shear
  sliding forces

Normal Forces
Shear Forces
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Stress-Strain Diagrams

• Equipment
• Tensile Testing machine
• UTM- Universal testing machine
• Measures
• Load, pounds force or N
• Deflection, inches or mm
• Data is recorded at several readings
• Results are averaged
• e.g., 10 samples per second during the test.
• Calculates
• Stress, Normal stress or shear stress
• Strain, Linear strain
• Modulus, ratio of stress/strain

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Stress-Strain Diagrams

• Stress-strain diagrams is a plot of stress with
  the corresponding strain produced.
• Stress is the y-axis
• Strain is the x-axis

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Modulus and Strength

• Modulus Slope of the stress-strain curve
• Can be Initial Modulus, Tangent Modulus or Secant
  Modulus
• Secant Modulus is most common
• Strength
• Yield Strength
• Stress that the material starts to yield
• Maximum allowable stress
• Proportional Limit
• Similar to yield strength and is the point where
  Hookes Law is valid
• If stress is higher than Hookes Law is not valid
  and cant be used.
• Ultimate strength
• Maximum stress that a material can withstand
• Important for brittle materials

Ultimate Strength
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Allowable Axial Load

• Structural members are usually designed for a
  limited stress level called allowable stress,
  which is the max stress that the material can
  handle.
• Equation 8-2 can be rewritten
• Required Area
• The required minimum cross-sectional area A that
  a structural member needs to support the
  allowable stress is from Equation 9-1
• Example 8-2.1 Hinged Beam
• Statics review
• Sum of forces 0
• Sum of Moments 0. Moment is Force time a
  distance to solid wall

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Strain

• Strain Physical change in the dimensions of a
  specimen that results from applying a load to the
  test specimen.
• Strain calculated by the ratio of the change in
  length, ?, and the original length, L.
  (Deformation)
• Where,
• ? linear strain (? is Greek for epsilon)
• ? total axial deformation (elongation of
  contraction) Lfinal Linitial Lf - L
• L Original length
• Strain units (Dimensionless)
• Units
• When units are given they usually are in/in or
  mm/mm. (Change in dimension divided by original
  length)
• Elongation strain x 100

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Strain

• Example
• Tensile Bar is 10in x 1in x 0.1in is mounted
  vertically in test machine. The bar supports 100
  lbs. What is the strain that is developed if the
  bar grows to 10.2in? What is Elongation?
• ? Strain (Lf - L0)/L0 (10.2 -10)/(10) 0.02
  in/in
• Percent Elongation 0.02 100 2
• What is the strain if the bar grows to 10.5
  inches?
• What is the percent elongation?

100 lbs
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Tensile Modulus and Yield Strength

• Modulus of Elasticity (E) (Note Multiply psi by
  7,000 to get kPa)
• Also called Youngs Modulus is the ratio of
  stress to corresponding strain
• A measure of stiffness
• Yield Strength (Note Multiply psi by 7,000 to
  get kPa)
• Measure of how much stress a material can
  withstand without breaking
• Modulus (Table 8-1) Yield Strength
• Stainless Steel E 28.5 million psi (196.5
  GPa) 36,000 psi
• Aluminum E 10 million psi 14,000 psi
• Brass E 16 million psi 15,000 psi
• Copper E 16 million psi
• Molybdenum E 50 million psi
• Nickel E 30 million psi
• Titanium E 15.5 million psi 120,000 psi
• Tungsten E 59 million psi
• Carbon fiber E 40 million psi
• Glass E 10.4 million psi
• Composites E 1 to 3 million psi 15,000 psi
• Plastics E 0.2 to 0.7 million psi 5,000 to
  12,000 psi

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Hookes Law

• Hookes Law relates stress to strain by way of
  modulus
• Hookes law says that strain can be calculated as
  long as the stress is lower than the maximum
  allowable stress or lower than the proportional
  limit.
• If the stress is higher than the proportional
  limit or max allowable stress than the part will
  fail and you cant use Hookes law to calculate
  strain.
• Stress modulus of elasticity, E, times strain
• Stress ? load per area, P/A
• Strain ? deformation per length, ? /L
• Rearrange Hookes law
• Solving for deformation is
• With these equations you can find
• How much a rod can stretch without breaking.
• What the area is needed to handle load without
  breaking
• What diameter is needed to handle load without
  breaking
• Example 10-1
• Example 10-3

Eqn 8-3
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Problem solving techniques

• Steps to solve most Statics problems
• Set-up problem
• Draw picture and label items (D, L, P, Stress,
  etc..)
• List known values in terms of units.
• Solve problem
• Make a Force balance with Free body diagram
• Identify normal forces
• Identify shear forces
• Write stress as Force per unit area
• Calculate area from set-up, or
• Calculate force from set-up
• Write Hookes law
• Rearrange for deflections
• Write deflections balance
• Solve for problem unknowns

Eqn 8-3
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Safety Factor

• Allowable Stresses and Factor of Safety
• Provide a margin of safety in design for bridges,
  cars, buildings, rockets, space shuttles, air
  planes, etc
• Structural members and machines are designed so
  that columns, plates, trusses, bolts, see much
  less than the stress that will cause failure.
• Ductile materials If the stress is greater than
  the yield strength or proportional limit of the
  material.
• Brittle materials If the stress is greater than
  the ultimate strength of the material.Since they
  do not show any yielding, just fracturing.

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Stress Concentrations

• Stresses can be higher near holes, notches, sharp
  corners in a part or structural member.
• Stress concentration factor, K stresses near
  hole
• 
  stresses far away from hole
• K is looked up in a table or on a graph
• Stress at hole can be calculated to see if part
  will fail.
• Where b is the net width at hole section and t is
  the thickness.

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Thermal Stresses

• Most materials expand when heated as the
  temperature increases.
• As the temperature goes up, the material expands
  and results in forces that cause stress in the
  part. As temperature increases the stresses
  increase in part.
• Examples,
• Cast iron engine block heat up to 500F and
  expands the cast iron block which causes stresses
  at the bolts. The bolts must be large enough to
  withstand the stress.
• Aluminum heats up and expands and then cools off
  and contracts.
• Sometimes the stresses causes cracks in the
  aluminum block.
• Space shuttle blasts off and heats up, goes into
  space and cools down (-200F), and reenters Earths
  atmosphere and heats up (3000F)
• Aluminum melts at 1300F so need ceramic heat
  shields
• Aluminum structure expands and cools.
• The amount the material expands is as follows
• Change in length that is causes by temperature
  change (hot or cold)
• Where,
• ? change in length
• ? the CLTE (coefficient of linear thermal
  expansion
• ?T change in temperature (Thot Tcold)
• L length of member
• Examples

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Strain and Poissons Ratio

• Axial strain is the strain that occurs in the
  same direction as the applied stress.
• Transverse strain is the strain that occurs
  perpendicular to the direction of the applied
  stress.
• Poissons ratio is ratio of lateral strain to
  axial strain.
• Poissons ratio lateral strain
• axial strain
• Example
• Calculate the Poissons ratio of a material with
  lateral strain of 0.002 and an axial strain of
  0.006
• Poissons ratio 0.002/0.006 0.333
• Example

Note For most materials, Poissons ratio is
between 0.25 and 0.5 Plastics Poissons ratio
0.3 Table 8-1 Metals Poissons ratio 0.3
steel, 0.33 Al, 0.35 Mg, 0.34 Ti
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Chapter 11 Material Properties

• Structure of Matter
• Material Testing Agencies
• Physical Properties
• Mechanical Properties and Test Methods
• Stress and Strain
• Fatigue Properties
• Hardness
• Practice Problems

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Fatigue Properties

• Fatigue Properties
• All materials that are subjected to a cyclic
  loading can experience fatigue
• Failure occurs through a maximum stress at any
  cycle.
• Test methods
• Subject the material to stress cycles and
  counting the number of cycles to failure, then
• Fatigue properties are developed.
• Table of properties for each material
• How many cycles a material can experience at a
  certain stress level before failing.
• S-N diagrams are developed (Stress and Number of
  cycles)
• Specify fatigue as a stress value
• Design for less than fatigue stress

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Fundamentals of Hardness

• Hardness is thought of as the resistance to
  penetration by an object or the solidity or
  firmness of an object
• Resistance to permanent indentation under static
  or dynamic loads
• Energy absorption under impact loads (rebound
  hardness)
• Resistance toe scratching (scratch hardness)
• Resistance to abrasion (abrasion hardness)
• Resistance to cutting or drilling (machinability)
• Principles of hardness (resistance to
  indentation)
• indenter ball or plain or truncated cone or
  pyramid made of hard steel or diamond
• Load measured that yields a given depth
• Indentation measured that comes from a specified
  load
• Rebound height measured in rebound test after a
  dynamic load is dropped onto a surface

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Hardness Mechanical Tests

• Brinell Test Method
• One of the oldest tests
• Static test that involves pressing a hardened
  steel ball (10mm) into a test specimen while
  under a load of
• 3000 kg load for hard metals,
• 1500 kg load for intermediate hardness metals
• 500 kg load for soft materials
• Various types of Brinell
• Method of load applicationoil pressure,
  gear-driven screw, or weights with a lever
• Method of operation hand or electric power
• Method of measuring load piston with weights,
  bourdon gage, dynamoeter, or weights with a lever
• Size of machine stationary (large) or portable
  (hand-held)

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Brinell Test Conditions

• Brinell Test Method (continued)
• Method
• Specimen is placed on the anvil and raised to
  contact the ball
• Load is applied by forcing the main piston down
  and presses the ball into the specimen
• A Bourbon gage is used to indicate the applied
  load
• When the desired load is applied, the balance
  weight on top of the machine is lifted to prevent
  an overload on the ball
• The diameter of the ball indentation is measured
  with a micrometer microscope, which has a
  transparent engraved scale in the field of view

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Brinell Test Example

• Brinell Test Method (continued)
• Units pressure per unit area
• Brinell Hardness Number (BHN) applied load
  divided by area of the surface indenter

Where BHN Brinell Hardness Number L
applied load (kg) D diameter of the ball (10
mm) d diameter of indentation (in mm)

• Example What is the Brinell hardness for a
  specimen with an indentation of 5 mm is produced
  with a 3000 kg applied load.
• Ans

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Brinell Test Method (continued)

• Range of Brinell Numbers
• 90 to 360 values with higher number indicating
  higher hardness
• The deeper the penetration the higher the number
• Brinell numbers greater than 650 should not be
  trusted because the diameter of the indentation
  is too small to be measured accurately and the
  ball penetrator may flatten out.
• Rules of thumb
• 3000 kg load should be used for a BHN of 150 and
  above
• 1500 kg load should be used for a BHN between 75
  and 300
• 500 kg load should be used for a BHN less than
  100
• The materials thickness should not be less than
  10 times the depth of the indentation

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Advantages Disadvantages of the Brinell
Hardness Test

• Advantages
• Well known throughout industry with well accepted
  results
• Tests are run quickly (within 2 minutes)
• Test inexpensive to run once the machine is
  purchased
• Insensitive to imperfections (hard spot or
  crater) in the material
• Limitations
• Not well adapted for very hard materials, wherein
  the ball deforms excessively
• Not well adapted for thin pieces
• Not well adapted for case-hardened materials
• Heavy and more expensive than other tests
  (5,000)

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Rockwell Test

• Hardness is a function of the degree of
  indentation of the test piece by action of an
  indenter under a given static load (similar to
  the Brinell test)
• Rockwell test has a choice of 3 different loads
  and three different indenters
• The loads are smaller and the indentation is
  shallower than the Brinell test
• Rockwell test is applicable to testing materials
  beyond the scope of the Brinell test
• Rockwell test is faster because it gives readings
  that do not require calculations and whose values
  can be compared to tables of results (ASTM E 18)

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Rockwell Test Description

• Specially designed machine that applies load
  through a system of weights and levers
• Indenter can be 1/16 in hardened steel ball, 1/8
  in steel ball, or 120 diamond cone with a
  somewhat rounded point (brale)
• Hardness number is an arbitrary value that is
  inversely related to the depth of indentation
• Scale used is a function of load applied and the
  indenter
• Rockwell B- 1/16in ball with a 100 kg load
• Rockwell C- Brale is used with the 150 kg load
• Operation
• Minor load is applied (10 kg) to set the indenter
  in material
• Dial is set and the major load applied (60 to 100
  kg)
• Hardness reading is measured
• Rockwell hardness includes the value and the
  scale letter

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Rockwell Values

• B Scale Materials of medium hardness (0 to
  100HRB) Most Common
• C Scale Materials of harder materials (gt 100HRB)
  Most Common
• Rockwell scales divided into 100 divisions with
  each division (point of hardness) equal to
  0.002mm in indentation. Thus difference between a
  HRB51 and HRB54 is 3 x 0.002 mm - 0.006 mm
  indentation
• The higher the number the harder the number

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Rockwell and Brinell Conversion

• For a Rockwell C values between -20 and 40, the
  Brinell hardness is calculated by
• For HRC values greater than 40, use
• For HRB values between 35 and 100 use

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Rockwell and Brinell Conversion

• For a Rockwell C values, HRC, values greater than
  40,
• Example,
• Convert the Rockwell hardness number HRc 60 to
  BHN
• Review Questions