Page 123 - Biaxial Multiaxial Fatigue and Fracture

108 G.B. MARQUIS AND I! KAWALAINEN-ROIKONEN

The stress term in this model makes it suitable for describing mean stresses during multiaxial
loading and it also takes into account the significant non-proportional hardening effects that
occur in materials like stainless steel.
The virtual strain energy (VSE) model of Liu [18] is a straightforward generalization of a
uniaxial energy based fatigue life prediction model. However, it differs from most other
energy type models in that work quantities are defined for specific planes within the material,
and it can therefore be classified as a critical plane approach. The virtual strain energy quantity,
AW, on a plane is divided into elastic and plastic work components. Elastic work, Awe, is the
sum of the two darker shaded regions in Fig. 1, AoAE~, while the plastic work, AWP, is
approximated as the product, ACAEP. Figure 1 shows that the product AoAEP is larger than the
plastic hysteresis energy, i.e. the area inside the hysteresis loop. The difference is the non-
shaded area outside the hysteresis loop and is commonly termed the complementary plastic
work. The axial work per cycle AWI is defined as the sum:

AWI = AWP + AWe (3)

Similarly, the shear work per cycle AWII is defined by substituting AT, AyP and Af for the
corresponding normal stress / strain terms.

+
i,
E

Fig. 1. Elastic and plastic strain energies for the VSE approach.

For proportional multiaxial loading, the VSE model considers two possible failure modes, i.e.,
a mode for tensile failure and a mode for shear failure. In tension-torsion loading, AW is the
sum of axial and shear work, AWI and AWII acting on a plane: