Page 491 - Biaxial Multiaxial Fatigue and Fracture

Faiigue Assessment of Mechanical Components Under Complex Multiaxial Loading 475

history and superimposed to obtain the combined varying stress time histories under multiaxial
loading. For high-cycle fatigue problem, the elastic stresses can be used directly for fatigue
assessment. For low-cycle fatigue problem, the elastic-plastic stress/strain must be calculated
based on the elastic stress solutions, and the local strain approach should be used.
The implementation of the numerical approach resorted to the capabilities available in the
ANSYS optimization module. To compute R, for arbitrary multiaxial stress histories, an
internal optimization problem is defined using ADPL and the ANSYS optimizer is called for
searching the minimum values of R, and Rb as formulated in Eqs (1 5,16).
Then, the fatigue damage parameter & is evaluated based on the effective shear stress
amplitude and the maximum hydrostatic stress throughout a loading cycle (see Eq. (17)).

EXAMPLES

In this section, two engineering examples are used to illustrate that the MCE approach
reviewed in this paper can efficiently be applied in conjunction with a commercial finite
element code to provide for a general tool for fatigue damage evaluation of structural
components, under complex multiaxial loads.

Automotive Suspension Torque Arm - 3-0 Model
In this first example, fatigue analysis of a torque arm component of an automotive rear
suspension is considered. As shown in Fig. 5, the ANSYS model is fixed at the rim of the
larger hole and loaded at the edge of the smaller hole with in-plane cyclic forces Fx(t) and Fy(t).
Linear static finite element analysis was performed using unit load vectors and solid elements.
The stress influence coefficients obtained from these analyses were then superposed with the
cyclic loads Fx(t) and Fy(t) to compute the stress time histories at each nodal point. Then, nodal
fatigue damage evaluation is carried out, by post-processing the FE results, according to the
algorithm presented in the above sections.
Figure 5 shows the comparison of the fatigue damage distributions under two different
loading conditions: on the left under proportional loading and on the right under 90 degrees
out-of-phase shift. It is shown that the loading mode and the loading combination have large
influence on the fatigue damage distributions. Conventional design methodologies, based on
static criteria, may lead to unsafe and potentially dangerous design predictions if complex
fatigue loading conditions are present.

Train Car under Real Service Loading
In this example, a train car was monitored during a typical route and acceleration signals along
the x-, y-, and z-directions were recorded by transducers, totalling a number of 1559 sampling
points, see Figs 7-9.