Materials Selection- Cumulative Fatigue Damage and Fatigue Crack Propagation

Question 1

Problem with fatigue data

Answer 1

Uses constant amplitude fatigue tests which are unrealistic of actual field service conditions. Many engineering structures subjected to range of load fluctuations, mean stresses and frequencies.

Question 2

What is ‘damage’ from fatigue loading in the form of?

Answer 2

Plastic deformation, fatigue crack initiation and propagation

Question 3

What is the Palmgren-Miner rule for damage?

Answer 3

Assumes the total life of a part can be estimated by summing the fraction of life consumed by each stress level, σi.
D=Σni/Ni=n1/N1+n2/N2+…+nk/Nk
Failure occurs when D=1.
k is number of stress levels in a block loading spectrum
ni is number of cycles applied at σi
Ni is fatigue life at σi

Question 4

Linear elastic fracture mechanics (LEFM) assumption

Answer 4

All engineering structures contain flaws e.g cracks

Question 5

What happens to crack length a under cyclic loading?

Answer 5

Crack grows with every cycle (N) from an initial size a0 to a critical size ac (related to fracture toughness) at which catastrophic failure occurs

Question 6

Crack length vs number of cycles graph

Answer 6

Starts at a0 and curves up to ac at number of cycles to failure nf. About 2/5 of way across is inspection. Between here and 4/5 across is retirement. Crack growth rate da/dN can be determined from slope of the curve.

Question 7

Paris law equation

Answer 7

da/dN=A(ΔK)^m
Where ΔK=YΔ σrt(πa)
A and m are material constants (2

Question 8

Integrating Paris law equation to get number of cycles to failure Nf

Answer 8

Rearrange to make dN subject and integrate between ac and a0.
Gives long expression page 18 lecture 7

Question 9

Formula to find critical crack length

Answer 9

It is when K is Kc (fracture toughness). This is at σmax.
ac=(1/π)(Kc/Yσmax)^2
Can substitute in for formula for Nf