Design Stress

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Design Stress Fatigue

• MET 210W
• E. Evans

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Parts Fail When?
P
Crack initiation site
This crack in the part is very small. If the
level of stress in the part is SMALL, the crack
will remain stable and not expand. If the level
of stress in the part is HIGH enough, the crack
will get bigger (propagate) and the part will
eventually fail.
P
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Design Factor

• Analysis
• Design

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Factors Effecting Design Factor

• Application
• Environment
• Loads
• Types of Stresses
• Material
• Confidence

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Factors Effecting Design Factor

• Application
• Environment
• Loads
• Types of Stresses
• Material
• Confidence

• How many will be produced?
• What manufacturing methods will be used?
• What are the consequences of failure?
• Danger to people
• Cost
• Size and weight important?
• What is the life of the component?
• Justify design expense?

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Factors Effecting Design Factor

• Application
• Environment
• Loads
• Types of Stresses
• Material
• Confidence

• Temperature range.
• Exposure to electrical voltage or current.
• Susceptible to corrosion
• Is noise control important?
• Is vibration control important?
• Will the component be protected?
• Guard
• Housing

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Factors Effecting Design Factor

• Application
• Environment
• Loads
• Types of Stresses
• Material
• Confidence

• Nature of the load considering all modes of
  operation
• Startup, shutdown, normal operation, any
  foreseeable overloads
• Load characteristic
• Static, repeated reversed, fluctuating, shock
  or impact
• Variations of loads over time.
• Magnitudes
• Maximum, minimum, mean

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Factors Effecting Design Factor

• Application
• Environment
• Loads
• Types of Stresses
• Material
• Confidence

• What kind of stress?
• Direct tension or compression
• Direct shear
• Bending
• Torsional shear
• Application
• Uniaxial
• Biaxial
• Triaxial

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Factors Effecting Design Factor

• Application
• Environment
• Loads
• Types of Stresses
• Material
• Confidence

• Material properties
• Ultimate strength, yield strength, endurance
  strength,
• Ductility
• Ductile E ? 5
• Brittle E lt 5
• Ductile materials are preferred for fatigue,
  shock or impact loads.

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Factors Effecting Design Factor

• Application
• Environment
• Loads
• Types of Stresses
• Material
• Confidence

• Reliability of data for
• Loads
• Material properties
• Stress calculations
• How good is manufacturing quality control
• Will subsequent handling, use and environmental
  conditions affect the safety or life of the
  component?

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Design Factor
Adapted from R. B. Englund
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Design Factor
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Predictions of Failure Static Loads

• Brittle Materials
• Maximum Normal Stress - Uniaxial
• Modified Mohr - Biaxial
• Ductile Materials
• Yield Strength - Uniaxial
• Maximum Shear Strength - Biaxial
• Distortion Energy - Biaxial or Triaxial

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Predictions of Failure Fluctuating Loads

• Brittle Materials
• Not recommended
• Ductile Materials
• Goodman
• Gerber
• Soderberg

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Maximum Normal Stress

• Uniaxial Static Loads on Brittle Material
• In tension
• Kt s ? sd Sut / N
• In compression
• Kt s ? sd Suc / N

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Modified Mohr

• Biaxial Static Stress on Brittle Materials

s2
Sut
45 Shear Diagonal
s1
s2
Sut
Suc
s1
Stress concentrations applied to stresses before
making the circle
s1, s2
Often brittle materials have much larger
compressive strength than tensile strength
Suc
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Yield Strength Method

• Uniaxial Static Stress on Ductile Materials

• In tension
• s ? sd Syt / N
• In compression
• ? sd Syc / N
• For most ductile materials, Syt Syc

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Maximum Shear Stress

• Biaxial Static Stress on Ductile Materials

tmax ? td Sys / N 0.5(Sy )/ N
Ductile materials begin to yield when the maximum
shear stress in a load-carrying component exceeds
that in a tensile-test specimen when yielding
begins.
Somewhat conservative use Distortion Energy for
more precise failure estimate
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Distortion Energy

• Static Biaxial or Triaxial Stress on Ductile
  Materials

Shear Diagonal
s2
Best predictor of failure for ductile materials
under static loads or completely reversed normal,
shear or combined stresses.
Sy
Sy
s1
Sy
s von Mises stress Failure s gt Sy Design
s ? sd Sy/N
Sy
Distortion Energy
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von Mises Stress

• Alternate Form
• For uniaxial stress when sy 0,
• Triaxial Distortion Energy (s1 gt s2 gt s3)

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Fluctuating Stress

• Varying stress with a nonzero mean.

salternating sa
smax
Stress Ratio,
Stress
smean
Time
-1 ? R ? 1
smin
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Fluctuating Stress Example

• Bending of Rocker Arm

Valve Spring Force
Valve Open
Valve Closed

• Tension in Valve Stem

Valve Closed
Valve Spring Force
Valve Open
RBE 2/1/91
Adapted from R. B. Englund
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Fatigue Testing

• Bending tests
• Spinning bending elements most common
• Constant stress cantilever beams

Top View
Front View
Applied Deformation Fully Reversed, R
-1
Fixed Support
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Fatigue Testing
Test Data
Stress, s (ksi)
Number of Cycles to Failure, N
Data from R. B. Englund, 2/5/93
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Endurance Strength

• The stress level that a material can survive for
  a given number of load cycles.
• For infinite number of cycles, the stress level
  is called the endurance limit.
• Estimate for Wrought Steel
• Endurance Strength 0.50(Su)
• Most nonferrous metals (aluminum) do not have an
  endurance limit.

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Typical S-N Curve
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Estimated Sn of Various Materials
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Actual Endurance Strength

• Sn Sn(Cm)(Cst)(CR)(CS)
• Sn actual endurance strength (ESTIMATE)
• Sn endurance strength from Fig. 5-8
• Cm material factor (pg. 174)
• Cst stress type 1.0 for bending
• 0.8 for axial tension
• 0.577 for shear
• CR reliability factor
• CS size factor

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Actual Sn Example

• Find the endurance strength for the valve stem.
  It is made of AISI 4340 OQT 900F.

From Fig. A4-5. Su 190 ksi
From Fig. 5-8. Sn 62 ksi (machined)
62 ksi
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Actual Sn Example Continued

• Sn Sn(Cm)(Cst)(CR)(CS)
• 62 ksi(1.0)(.8)(.81)(.94) 37.8 ksi

Sn,Table 5-8
Wrought Steel
Actual Sn Estimate
Axial Tension
Reliability, Table 5-1
Size Factor, Fig. 5-9
99 Probability Sn is at or above the
calculated value
Guessing diameter ? .5
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Goodman Diagram
sa
Yield Line
Sy
FATIGUE FAILURE REGION
Sn
Goodman Line
NO FATIGUE FAILURE REGION
sm
Sy
Su
0
-Sy
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Goodman Diagram
sa
Safe Stress Line
Yield Line
Sy
FATIGUE FAILURE REGION
Sn
Goodman Line
Sn/N
SAFE ZONE
sm
Sy
Su
0
Su/N
-Sy
Safe Stress Line
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Example Problem 5-53. Find a suitable titanium
alloy. N 3
1.5 mm Radius
30 mm DIA
42 mm DIA
F varies from 20 to 30.3 kN

MAX 30.3
FORCE
MIN 20
TIME
-
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Example Problem 5-53 continued.

• Find the mean stress
• Find the alternating stress
• Stress concentration from App. A15-1

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Example Problem 5-53 continued.

• Sn data not available for titanium so we will
  guess! Assume Sn Su/4 for extra safety factor.
• TRY T2-65A, Su 448 MPa, Sy 379 MPa

(Eqn 5-20)
Size
Reliability 50
Tension
3.36 is good, need further information on Sn for
titanium.
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Example Find a suitable steel for N 3 90
reliable.
3 mm Radius
50 mm DIA
30 mm DIA
T
T
T varies from 848 N-m to 1272 N-m

MAX 1272 N-m
TORQUE
MIN 848 N-m
TIME
-
T 1060 212 N-m
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Example continued.

• Stress concentration from App. A15-1
• Find the mean shear stress
• Find the alternating shear stress

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Example continued.

• So, t 200 40 MPa. Guess a material.
• TRY AISI 1040 OQT 400F
• Su 779 MPa, Sy 600 MPa, E 19
• Verify that tmax ? Sys
• tmax 200 40 240 MPa ? Sys ? 600/2 300MPa
• Find the ultimate shear stress
• Sus .75Su .75(779 MPa) 584 MPa

Ductile
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Example continued.

• Assume machined surface, Sn ? 295 MPa
• Find actual endurance strength
• Ssn Sn(Cm)(Cst)(CR)(CS)
• 295 MPa(1.0)(.577)(.9)(.86) 132 MPa

(Fig. 5-8)
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Example continued.

• Goodman

(Eqn. 5-28)
No Good!!! We wanted N ? 3 Need a material with
Su about 3 times bigger than this guess or/and a
better surface finish on the part.
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Example continued.

• Guess another material.
• TRY AISI 1340 OQT 700F
• Su 1520 MPa, Sy 1360 MPa, E 10
• Find the ultimate shear stress
• Sus .75Su .75(779 MPa) 584 MPa
• Find actual endurance strength
• Ssn Sn(Cm)(Cst)(CR)(CS)
• 610 MPa(1.0)(.577)(.9)(.86) 272 MPa

Ductile
Sn
shear
size
wrought
reliable
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Example continued.

• Goodman

(Eqn. 5-28)

• No Good!!! We wanted N ? 3
• Decision Point
• Accept 2.64 as close enough to 3.0?
• Go to polished surface?
• Change dimensions? Material? (Cant do much
  better in steel since Sn does not improve much
  for Su gt 1500 MPa

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Example Combined Stress Fatigue
RBE 2/11/97
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Example Combined Stress Fatigue Contd
PIPE TS4 x .237 WALL MATERIAL ASTM A242
Equivalent DEAD WEIGHT SIGN ARM POST
1000 (Compression)
Reversed, Repeated
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Bending
RBE 2/11/97
Repeated one direction
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Example Combined Stress Fatigue Contd Stress
Analysis
Dead Weight
(Static)
Vertical from Wind
(Cyclic)
Bending
(Static)
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Example Combined Stress Fatigue Contd Stress
Analysis
Torsion
(Cyclic)
Stress Elements (Viewed from y)
CYCLIC
STATIC
315.5 psi
63.09 psi Repeated One Direction
9345.8 psi
t 3115.3 psi Fully Reversed
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Example Combined Stress Fatigue Contd
Mean Stress
Alternating Stress
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Example Combined Stress Fatigue
Contd Determine Strength
Try for N 3 ? some uncertainty Size Factor?
OD 4.50 in, Wall thickness .237 in ID
4.50 2(.237) 4.026 in Max. stress at OD.
The stress declines to 95 at 95 of the OD
.95(4.50) 4.275 in. Therefore, amount of steel
at or above 95 stress is the same as in 4.50
solid. ASTM A242 Su 70 ksi, Sy 50 ksi, E
21
t ? 3/4
Ductile
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Example Combined Stress Fatigue Contd
We must use Ssu and Ssn since this is a combined
stress situation. (Case I1, page 197) Sus
.75Su .75(70 ksi) 52.5 ksi Ssn
Sn(Cm)(Cst)(CR)(CS) 23 ksi(1.0)(.577)(.9)(.745
) 8.9 ksi
Hot Rolled Surface
Size 4.50 dia
Wrought steel
90 Reliability
Combined or Shear Stress
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Example Combined Stress Fatigue Contd
Safe Line for Goodman Diagram ta Ssn / N
8.9 ksi / 3 2.97 ksi tm Ssu / N 52.5
ksi / 3 17.5 ksi
10
Alternating Stress, ta
5
Ssn/N
0
Su/N
0
15
10
5
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Mean Stress, tm