Page 403 - Biaxial Multiaxial Fatigue and Fracture

A Multiaxial Fatigue Life Criterion fir Non-Symmetrical and Non-Proportional Elasto-Plastic ... 387

Then, the arithmetic mean value is determined by taking into account the interaction of shear
strains as following:

The equivalent axial strain amplitude is calculated according to:

5
&e%, =- (7)
4( 1 + y)
With this equivalent strain amplitude the fatigue life can be derived from the Manson-Coffin
curve obtained under uniaxial strain.

THE NEW CRITERION
Eflective shear strain

The new criterion adopts a complete calculation procedure, extending the investigation of the
interaction of shear strains to all different interference planes at a material point. For each
interference plane, completely defined by the spherical coordinates 6 and Q, of the unit
normal vector n (Fig. 2), a shear strain vector denoted as 1/27, may be obtained:

1
)
- y,, ( p, 6, = E (t ). n - [n .E (t ). n]n (8)
t
2
where ~(t) is the total stsain tensor at instant t. In the appendix, the squared intensity of 1/2y, ,
i.e. l/4(yn)' =(1/2yn).(1/2y,,) is calculated 'for the most general case where all the six
components of E(t) are present. Clearly, (7" )* is a scalar quantity.
"t

Fig. 2. Definition of the generic interference plane by means of spherical coordinates