Page 220 - Biaxial Multiaxial Fatigue and Fracture

204 A. YARVANI-FARAHANI

incremental plasticity theory to predict fatigue life under complex non-proportional multiaxial
loading conditions [6], however the approach did not successfully correlate the uniaxial and
torsional fatigue data. In another attempt [7-81, a ratio of axial strain to maximum shear strain
has been introduced as a correction factor to the energy approach. This ratio has been criticized
because the hysteresis energy method used in Refs [7-81 does not hold any terms to reflect this
strain ratio.
Fatigue analysis using the concept of a critical plane of maximum shear strain is very
effective because the critical plane concept is based on the fracture mode or the initiation
mechanism of cracks. In the critical plane concept, after determining the maximum shear strain
plane, many researchers have defined fatigue parameters as combinations of the maximum
shear strain (or stress) and normal strain (or stress) on that plane to explain multiaxial fatigue
behavior [9-131. Some researchers [ 14-18] used the energy criterion in conjunction with the
critical plane approach. Energy-critical plane parameters are defined on specific planes and
account for states of stress through combinations of the normal and shear strain and stress
ranges. These parameters depend upon the choice of the critical plane and the stress and strain
ranges acting on that plane. For instance, Liu [14] calculated the virtual strain energy (WE) in
the critical plane by the use of crack initiation modes. The critical plane in Liu’s parameter is
associated with two different physical modes of failure and the parameter consists of Mode I
and Mode 11 energy components. The Mode I energy is computed by first identifying the plane
on which the axial energy is maximized and adding the shear energy on that plane. Similarly,
the Mode II energy is calculated by first identifying the plane on which the shear energy is
maximized and then adding the axial energy component. In the calculation of VSE, Liu
induced both elastic energy and plastic energy while the elastic energy was not considered in
Garud’s model [6]. Chu et al. [ 151 formulated normal and shear energy components based on
Smith-Watson-Topper parameter. They determined the critical plane and the largest damage
parameter from the transformation of strains and stresses onto planes spaced at equal
increments using a generalized Mroz model [19]. Glinka et ai. [I61 presented a multiaxial life
parameter based on the summation of the products of shear and normal strains and stresses on
the critical shear plane.
In a recent study [ 171, a multiaxial fatigue parameter for various in-phase and out-of-phase
loading paths has been proposed. The parameter is given by the integration of the normal
energy range and the shear energy range calculated for the critical plane at which the stress and
strain Mohr’s circles are the largest during the reversals of a cycle. The maximum shear strains
for in-phase and out-of-phase paths are numerically calculated at small increments through a
fatigue cycle. The parameter has taken into account both elastic and plastic strain components
in fatigue damage analysis. The normal and shear energies in this parameter have been
weighted by the tensile and shear fatigue properties, respectively, and the parameter requires
no empirical fitting factors. The parameter has taken into account the effect of mean stress
applied normal to the critical plane and has also shown an increase when there is additional
hardening, caused by out-of-phase loading, while strain-based parameters fail to take into
account this effect. The present paper further extends the Varvani’s damage parameter [ 171 for
fatigue life assessment under biaxial loading condition by accumulating damage on a cycle-by-
cycle basis within an entire two-axis block loading history, where the stress-time axes are at
different frequencies.

MATERIAL AND FATIGUE TESTS
Table 1 tabulates the chemical composition and fatigue properties of EN 24 steel studied in the
present paper.