Page 209 - Biaxial Multiaxial Fatigue and Fracture

Estimation of the Fatigue Life of High Strength Steel Under ... 193

Thus, the parameter of the normal strain energy density in the critical plane with normal 7
according to Eq. (6) takes the following form (stage 4)

In plane stress state, the vector Ti normal to the fracture plane may be described with use of
only one angle a in relation to the axis Ox. Thus, the direction cosines of the unit vector are

1, COS^, i%, =sina, ii,, =O (32)
Assuming that the equivalent time history of energy parameter is the parameter of normal
strain energy density described in Eq. (31) W,(t) = W,(t), we introduce Eqs (23) - (26) into
Eq. (30) and next we obtain the expression for the equivalent energy parameter of the normal
strain in the critical plane W,(t) in the elastic range.

For torsion, Eq.(33) takes the form

Equation (34) reaches the maximum for angle d4, Le. for

and for random loading it can be written as

W (t) = kzcFkFCF L~;y (t) sgn[r,, (t)] . (36)
eq
4G
For cyclic loading the amplitude of the equivalent energy parameter is

where the correction coefficients kECF, kFCF for a high number of cycles were obtained ac-
cording to Eqs (20) and (21).