SME
Biomaterials · Problem type
Fatigue safety factor
Use this for “A Ti alloy stem with a 500 MPa endurance limit sees 180 MPa. What is its safety factor?”
Diagram
36% of 500 MPa is 180 MPa.
This is an example. Type your own values to start a new problem.
SF
=
Sₑ (MPa)
σ (MPa)
p
Stress as a share of the limit
worked out (not typed) · %
Formulas
SF
=
Sₑ
σ
2.78
=
500
180
p
=
100
×
σ
Sₑ
36
=
100
×
180
500
Assumptions
•
Below its endurance limit the alloy survives about 10⁷ load cycles or more without a fatigue crack.
•
The peak stress is the largest stress in each cycle, at the stem’s worst spot.
•
SF above 1 means the stem should last; implant designs often ask for 2 or more.
Step-by-step
WE KNOW
Sₑ = 500 MPa, σ = 180 MPa
FIND
safety factor (SF), stress as a share of the limit (p)
Step 1 · Find safety factor (SF)
Use SF = Sₑ ÷ σ
The safety factor is how many times the peak stress fits into the endurance limit.
SF
=
500
180
SF = 2.78
Step 2 · Find stress as a share of the limit (p)
Use p = 100 × σ ÷ Sₑ
The peak stress as a percent of the endurance limit.
p
=
100
×
180
500
p
=
18,000
500
p
=
36%
Check
Put the numbers back in. Both sides should match.
2.78
=
500
180
✓
36
=
100
×
180
500
✓
Topic check
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