Crack Paths 2006

110 1000 100 0 (a) m

0.002 λ = ∞ Torsion

tulbenggtahge wall hickness

0.000

0.001

0.003 Transition Strains Energy, εt =0.0011 Area, εt =0.0 8

0.004

tube gage l n th

50μmshear crack de ection esolution

)

m )

λ=3

tube wall hickness

1100 1000

(b)

100

TransitionStrains Energy,εt=0.0019

Area, εt =0.0011

50μmshear crack

detection resolution

0.000

0.001 Equivalent Strain Amplitude, Δε/2 0.002 0.003

0.004

Equivalent Strain Amplitude, Δε/2

tubegage length

50μmshearcrack

m )

λ=3/2

tube wall hickness

Transition Strains

Energy, εt =0.0039

Area, ε t =0.0014

detection resolution

(2)

(c)

1 1010100

Detected Crack

0.000

0.001

0.002

0.003

0.004

Equivalent Strain Amplitude, Δε/2

λ=0 Uniaxial

m

m

tube gage l n th ube w ll hickness

50μmshear crack detection resolution

tube gage tulbne wthll hickness

110 1000 )

)

(d)

Transition Strains Energy, εt = .0079 Area, εt =0.0 1 λ=3/4

100

0.000

0.001

0.002

0.003 0.007 0.008

10 100 1000

(e)

1000

TransitionStrainsEnergy,εt=0.0165

Area, ε t =0.0025

0.001 Equivalent Strain Amplitude, Δε/2 0.002

Equivalent Strain Amplitude, Δε/2

0.000

0.003 0.016 0.017

Figure 4. Experimental observations and predictions of maximumshear crack lengths

(before crack growth changes to maximumtensile planes). For strains which

exceed the transition strain (εt), models predict a shear crack that grows until it

spans the gage length (2c = 30mm).

plane and then back again to growth on a shear plane – in these cases it is the initial shear

crack half-length at the change in cracking modethat is plotted. With the exception of a

single test (λ = 3/2, Δ¯εeff/2 = 0.0008) all of the tests plotted at the 50μmdetection limit

had initial shear cracks that were not detected. While the experimental data in the figure

has a significant amount of scatter, it does show that the material exhibits increasingly

longer shear cracks as shear the strain amplitude and the biaxial strain ratio increase.

Each of the two crack growth mode transition models predicts that above a certain