Fracture Mechanics in Fatigue Analysis

The stress intensity factor K:

a: the crack width and geometrical correction factor.

F: the product of a couple of factors (back crack shape factors, front face factor, finite thickness factor, finite width factor and stress gradient factor)

K a F Mods for Factor “K”

Kmax and Kmin are the maximum and minimum values of the stress intensity factor, at theupper and lower limit stresses during a cyclic loading.

Kmax= F.σmax(π.a)1/2

Kmin= F.σmin(π.a)1/2

Plastic Zone Size =

∆σ1=(σ1max-σ1min)

Semi-Crack Lenght- Number of Cycles

∆K= Kmax-Kmin=F.∆σ(πa)1/2

Plastic Zone Characterized with K

Three distinct regions are indicated: 1) the well-known threshold region2) intermediate region3) the failure region.

max min

( )mda

C KdNK K K

m: experimental constantm= 3 for steelm=3~4 for aluminum alloy

Paris Law

Paris Law in Application

Differences Between Classical Design and

Fracture Mechanics Based Design

•Classical desing predicts that the material under pressure is confident under yield criteria.

•Classical desing ignores behaviours of material. (Ductile or Brittle)

•Classical design does not consider crack in the material and the fracture roughness

Infamous Fatigue Failures

War ship: S.S. Schenectady

Infamous Fatigue Failures

Offshore platform: Alexander Kielland

Infamous Fatigue Failures

Aircraft : De Havilland Comet