Materials Science 101
03 Mechanical Behavior
Chapter 08

Failure

Two views on how materials break — the S–N curve that predicts cyclic life, and the Paris-law growth of a single crack from sub-critical flaw to final rupture.

380

The S–N (Wöhler) curve plots stress amplitude σa against cycles to failure Nf. Slide σa to read off life. Ferrous alloys show a true endurance limit — below it, life is effectively infinite. Aluminum and most non-ferrous alloys do not.

Predicted Life

High-cycle fatigue
Material
Steel 1045
σa
380 MPa
Nf
~1.2 × 10⁵
σUTS
625 MPa
σe (10⁷)
310 MPa
Basquin b
−0.085

High-cycle fatigue: stress is below yield, life dominated by crack initiation. Reduce σa below σe for unlimited life.

Center-Cracked Plate

Paris Law — a vs. N

dadN = C · (ΔK)m,  ΔK = Y · Δσ · π·a
200
1.0
Cycle N
0
a
1.00 mm
ΔK
11.2 MPa·m
da/dN
9.7e-9 m/cyc
Nf
~ 4.2 × 10⁵
ac
9.0 mm