Page 480 - Biaxial Multiaxial Fatigue and Fracture

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464 .I SANTOS ET AL.
In real service, engineering components and structures are generally subjected to multiaxial
fatigue loading conditions, in which the cyclic loads act in various directions, with different
frequencies and/or different phases [2]. In these non-proportional multiaxial loading
conditions, the corresponding principal directions and/or principal stress ratios vary during a
loading cycle or block. Advanced engineering designs require efficient, accurate and easy-of-
use methods for durability assessment of components/structures under complex multiaxial
loading.
Current fatigue design approaches treat both proportional and non-proportional loading with
the maximum principal or equivalent stress range, and then, they refer to the design S-N curve
obtained under uniaxial loading condition [3]. The Eurocode 3 design code recommends that
the maximum principal stress range may be used as a fatigue life damage parameter if the
loading is proportional. For non-proportional loading, the components of damage for normal
and shear stresses are assessed separately using the Palmgren-Miner rule and then combined
using an interaction equation. Maximum shear stress range is used as an equivalent stress for
non-proportional loading in the ASME code.
However, conventional multiaxial fatigue criteria were based on proportional fatigue data,
and hence not applicable to non-proportional loading, due to the changes in direction and/or
ratio of the principal stresses. This has led to a number of research studies on the multiaxial
fatigue problem over the past 20 years. Much progress has been made in understanding the
cracking modes under complex loading, and various multiaxial fatigue damage parameters
have been proposed.
Although many multiaxial fatigue models have been proposed in the literature, there still
exist gaps between the theoretical models and engineering applications. Generally, there are
many sources of error in the computational fatigue damage assessments, including uncertainties
in analysing complex service environments, complex geometries, and lack of usable material
information, etc. It is imperative to study the accuracy and improve the computational
algorithms for every step of the fatigue evaluation process.
The objective of this paper is to study the engineering approaches for crack initiation life
assessment of components under complex multiaxial loading. Firstly, current multiaxial fatigue
models are briefly reviewed and compared. Then the recent approaches for evaluating the
effective shear stress amplitude under complex loading paths are studied and compared with
example problems. It is shown that the minimum circumscribed ellipse (MCE) approach,
developed on the basis of the minimum circumscribed circle (MCC) approach, is an easy and
efficient way to take into account of the non-proportional loading effect for fatigue evaluations.
The stress invariants based multiaxial criterion, coupled with the minimum circumscribed
ellipse (MCE) approach for evaluating the effective shear stress amplitude, are shown to be a
simple and efficient methodology for handling the complex loading effects.
The implementation of the minimum circumscribed ellipse (MCE) approach in the
commercial FEM code ANSYS is discussed. Applications of the developed procedure for
engineering problems are shown for two examples: an automotive suspension torque arm, and
a train car.
In the integrated FEM based fatigue assessment procedure, the quasi-static FE analyses are
used to obtain the stress-time histories at each nodal point by stress superimposition due to
each individually applied load. Then the minimum circumscribed ellipse (MCE) approach is
used for multiaxial fatigue life evaluation at each nodal point, requiring only the knowledge of
basic material fatigue parameters.