Page 490 - Biaxial Multiaxial Fatigue and Fracture

414 1L.Z SANTOS ET AL.

where R, and Rb are the major and minor semi-axis of the minimum ellipse circumscribing the
shear loading traces, respectively. The ratio P = Rb/& represents the factor of non-
proportionality of the multiaxial fatigue loading.
According to the MCE approach [14, 151, R, and Rb are obtained from the solution of the
following optimization problems with the coordinates of the MCC center point w (w,, w2, w3.
w4, w5) as design variables:

Minimize R,
Subject to maxllS(t) - will R,
t
and
Minimize Rh

5) Calculate the fatigue damage indicator DN for the point under consideration:
When the effective shear stress amplitude ./J2u and the maximum hydrostatic stress PH,,,~~
during a loading cycle are computed, the fatigue damage indicator DN, for a specified number
N of lifetime cycles, can be calculated using the Crossland’s criterion of Eq. (8):

where

A negative DN value means safety, while a positive value means failure. The greater DN is,
the larger the fatigue damage. If all the DN values, computed at critical component locations are
less than zero, then the design predicts that the component is able to undergo the multiaxial
fatigue loads for N cycles without crack initiation.

ZNPLEMENTATION OF THE MCE APPROACH IN THE COMMERCIAL FEM CODE
ANSYS

To make full use of the capabilities available in ANSYS [19], the MCE approach was
implemented as a post-processing step, using the ANSYS Parametric Design Language
(APDL), the flowchart of the implemented procedure on the platform of ANSYS is shown in
Fig. 4.
A unit accelaration field is applied in each of the coordinate directions x, y, z. A linear static
finite element analysis is carried-out for each of the unit accelaration fields. The response
stresses associated with each of the unit accelaration fields are scaled by the accelaration time