Page 443 - Biaxial Multiaxial Fatigue and Fracture

A Damage Model for Estimating Low Cycle Fatigue Lives Under Nonpmportional Multiaxial Loading 427

4 Loading
Interaction between

Fig.4. Interaction between slip systems due to nonproportional straining

AEI expresses the principal strain range applied on the plane perpendicular to the principal
direction of &lrnax (Eh,,-plane).

Nonproportional Strain Range based on Maximum Principal Strain

The dependency of nonproportional LCF lives on the material and strain history can be
explained by the slip behavior of materials. The change of the principal stress/strain directions
due to nonproportional straining increases the interaction between slip systems, which plays a
vital role in additional hardening as schematically shown in Fig.4 [ 10,111. The intensity of the
interaction has a connection with the slip behavior of a material. Strong interaction occurs in
planar slip materials and weak interaction in wavy slip materials. The slip behavior is also
related to the stacking fault energy (SFEi) of materials [ 1 I]. For materials with low SFEs such
as stainless steels and copper, planar slip occurs and causes strong interaction between slip
systems. Materials with high SFEs such as pure aluminum and aluminum alloys have wavy slip,
which shows no or small additional cyclic hardening because dislocations change their gliding
planes easily following the variation of the principal stressktrain directions.
As mentioned above, nonproportional LCF lives have a close connection with additional
hardening. Thus, nonproportional LCF parameter for life prediction must take into account the
amount of additional hardening. A couple of nonproportional parameters which include the
stress range or stress amplitude have been proposed [3,12,13], and the stress terms of these
parameters can be calculated using inelastic constitutive equations [9,14-161. However, in
general, it is not a simple procedure and requires many material constants. Therefore, a
nonproportional LCF parameter would better not include the stress term, and one of the authors
[4,8] proposed the strain range, AENP, for the life evaluation under nonproportional LCF. It is
based on the maximum principal strain and is given by the next equation.