Page 447 - Biaxial Multiaxial Fatigue and Fracture

A Damage Model for Estimating Low Cycle Fatigue Lives Under Nonpmportional Multiaxial Loading 43 I

Table 2. Cycle counting in each strain paths.
~~
I-plane 11-plane
Case
number Strain range Number of Strain, range Number of
A€:IAEI cycles &'I& cycles
0 1 1 0 0
I 1 1 0.87 1
2 1 1 0.87 1
3 1 1 1 1
0.1 1 0.1 1
1
1
4 0.1 1 0.1 1
1
1
5 1 1 1 0
6 1 1 0.18 8
0.09 2
7 I 1 0.35 3
0.16 2
8 1 1 0.5 2
9 1 1 0.5 2
10 1 1 1 1
11 1 1 0.64 1
12 1 1 0.87 1
13 1 2 0.87 2
14 1 1 0.87 1

Damage Model for Evaluation of LCF Lives

A couple of damage models for nonproportional LCF life evaluation which have been proposed
previously are usually developed based on the magnitude of stress and strain loaded on the
critical plane (fracture plane) on which cracks initiate and grow [17,18]. However, to predict
the crack direction is not so easy under nonproportional LCF because of the direction change of
the principal stresslstrain makes the crack initiation and propagation behavior more complicated.
Therefore, the &I,,,-plane (I-plane) in this model does not always correspond to the critical
plane.
As schematically shown in Fig.7, we consider that the normal and shear strains applied to the
&Imnx-plane, and yn, lead to the accumulation of damages, d1 and dIl, respectively. This model
&,,
assumes that E. and 'y,, are replaced by the principal strains EI and EI~ normal to the I and 11-planes.