Fatigue Crack Paths 2003

Liu´s Virtual Strain-Energy Model

The Liu´s virtual strain energy model [4] is an energy-based critical plane model.

This model considers two possible failure modes: a modefor tensile failure, ΔWI, and a

mode for shear failure, ΔWII. Failure is expected to occur on the plane è in the material

having the maximumVSEquantity. ΔWI is computed by firstly identifying the plane on

which the axial work is maximized and then adding the respective shear work on that

same plane:

( ) ()γτ ε σ θ Δ Δ + Δ Δ = Δ m a x n n I W

(4)

Similarly, ΔWII is computed by firstly identifying the plane on which the shear work is

maximized and then adding the axial work on that same plane:

( ) ()θγτ ε σ max Δ Δ + Δ Δ = Δ n n I I W

(5)

where Δτ and Δγ are the shear stress range and shear strain range, respectively, Δσn and

Δεn are the normal stress range and normal strain range, respectively.

Application of the Liu´s model for the six loading cases show the variations of the

Virtual Strain Energy on different plane orientations as presented in Fig. 6 for ΔWIand

Fig. 7 for ΔWII. For each loading case, the plane angle è with the maximumΔWIand

ΔWII parameters can be identified and they are summarized in Table 5.

01.024680246-90

-70

-50

-30

-10

10

30

50

Case6 Case2 Case3 Case4 Case5 Case1

I

p a r a m e t e r W

L iu

70

90

Plane angle [º]

Figure 6. Variations of the Liu´s Δ W I parameter on different plane.

-50 Case6 Case2 Case4 Case3 Case5 Case1 -30 -10 10 30 50

1.46 -90

-70

70

90

I I

p a r a m e t e r W

01.0246802

L iu

Plane angle [º]

Figure 7. Variations of the Liu´s ΔWII parameter on different plane.