Failure Theories

1
Failure Theories

• Stress in machine components should be accurately
  computed.
• Designer must understand material limits to
  ensure a safe design.

2
Design Factor

• Factor of Safety (N)
• Suitable values depend on inherent danger,
  certainty of calculations, certainty of material
  properties, etc.

3
Static Stresses - Brittle Materials

• Percent elongation lt 5
• for parts in tension
• for parts in compression
• for parts with general stress

4
Example

• The Gray Cast Iron (Grade 40) cylinder carries an
  axial compressive load of 75,000 lbs and a torque
  of 20,000 in lbs. Compute the resulting design
  factor.

5
Static Stresses - Ductile Materials

• Percent elongation gt 5
• Distortion Energy Theory
• Define von Mises Stress
• For nominal stress
• For localized stress

6
Static Stresses - Ductile Materials

• Percent elongation gt 5
• Maximum Shear Stress Theory
• For nominal stress
• For localized stress

7
Example

• Specify a diameter for the middle portion of the
  rod, if it is to be made from AISI 1040-hot
  rolled steel.

8
Example

• For the seat support shown, specify a standard
  structural tube to resist static loads shown. The
  tube has properties similar to AISI 1020
  hot-rolled steel. Use a design factor of 3.

9
Repeated Loads
10
Example

• The notched bar is machined from AISI 1020 steel.
  This bar is subjected to a load that varies from
  2000 lb to 3000 lb. Determine the mean and
  alternating nominal stresses.

11
Fatigue Strength

• R.R. Moore Test

12
Endurance Strength

• sn Endurance strength
• Listed in tables
• If no information is available, use
• sn ? 0.5 su (Steel)
• sn ? 0.4 su (Aluminum)

13
Adjusted Endurance Strength

• The data from the standard R.R. Moore test is
  adjusted for a particular application.
• sn Adjusted endurance strength
• (Cs) (Cm) (Cst) (CR) (sn)

14
Size and Stress Type Factors

• Cs Size Factor
• Dlt 0.4 in Cs 1.0
• 0.4 lt D 2.0 in Cs (D/0.3)-0.068
• 2.0 lt D 10.0 in Cs D-0.19
• For rectangular sections, D.808(h b)1/2
• Cst Stress Type Factor
• 1.0 for bending
• 0.80 for axial tension
• 0.50 for torsion

15
Material and Reliability Factor

• Cm Material Factor
• 1.0 for wrought steel
• 0.80 for cast steel
• 0.70 for cast iron
• CR Reliability Factor
• 50 CR 1.0
• 90 CR 0.90
• 99 CR 0.81
• 99.9 CR 0.75

16
Example

• The notched bar is machined from AISI 1020 steel.
  This bar is subjected to a load that varies from
  2000 lb to 3000 lb. Determine the endurance limit
  of the material.

17
Repeated Stresses - Ductile Materials

• Distortion Energy Theory
• Define repeated von Mises Stress
• Solderberg criterion

18
Repeated Stresses - Ductile Materials

• Maximum Shear Stress Theory

• ssy 0.5 sy
• ssn 0.5 sn

19
Example

• The notched bar is machined from AISI 1020 steel.
  This bar is subjected to a load that varies from
  2000 lb to 3000 lb. Comment on the robustness of
  the design.

20
Example

• Comment on the robustness of a 1-1/4 round bar
  made from AISI 1213 C-D steel. It carries a
  constant tensile load of 1500 lbs, a bending load
  that varies from 0 to 800 lbs at the senter of
  the 48 length and a constant torque of 1200 in
  lbs.