Page 367 - Handbook of Materials Failure Analysis

2 Fatigue Modeling of Welded Structures by Local Approaches 365

comprehensive formulation for calculating the stress concentration factor for spot-
welds; this is a challenge in the application of Neuber’s rule under a general load
case. Furthermore, similar to other models based on the structural stress approach,
effects of material anisotropy and yield asymmetry were not taken into account.

2.3 LOCAL NOTCH STRESS/STRAIN APPROACH
Some studies, in contrast to the fracture mechanics approach, consider a spot-weld as
a blunt notch with a finite radius. Therefore, a detailed FE model with a fine mesh at
the vicinity of the spot-weld is required. A measure of local notch strain at the spot-
weld edge is often assumed to control fatigue failure in this approach. Local stress/
strain values are calculated from an elastic-plastic FE simulation or from an elastic
solution along with the Neuber’s rule [23]. An advantage of this approach is that the
effect of the spot-weld notch is considered. Also, cyclic characteristics of materials,
for example, anisotropy and hardening asymmetry, may be accounted for. On the
other hand, crack propagation is not considered in the local notch models. Moreover,
complexities of the FE model preparation as well as the intensive FE calculations
restrict the applicability of this approach for real-life problems. One of the most com-
monly referenced models in this group has been developed by Pan [27].
Panin2000 [29] showed that the Sheppard’s model is capable of successfully pre-
dicting the fatigue life of steel spot-welds, as long as the sheets being welded have the
samethickness;however,theSheppard’smodelfailsfordissimilarthicknesses.Totackle
this problem, Pan in 2002 [27] proposed a model based on the local strain concept. A
detailed FE model of spot-weld specimens with a nominal radius at the nugget edge
was employed in this model. The nominal radius was selected according to experimental
observationsofthespot-weldcross-sections.Nonlineargeometryandnonlinearmaterial
propertieswereincludedintheFEanalyses.Becausetheheataffectedzoneofspot-welds
containsagradientof materialproperties,thisregionwassplitintoseveralsubzoneswith
corresponding nonlinear properties. Local stress and strain values at the spot-weld edge
were obtained from three-dimensional elastic-plastic FE simulations. The critical point
was identified as the location with the maximum local principal strain at the end of the
first reversal. The maximum principal strain range at the critical point was used as the
fatigue damage parameter. Maximum principal strain range, according to Pan [27], is
the difference in the principal strain at the end of the loading and unloading reversals.
Behravesh in 2013 [10] proposed a local fatigue model based on strain energy.
The advantage of energy-based fatigue models over stress- and strain-based models
is that energy is a scalar quantity. Therefore, the energy values corresponding to
different axial and shear components of stress and strain tensors can be simply
manipulated without the concern of dissimilar nature or direction [10]. The total
strain energy, as the damage parameter in this model, includes the plastic strain
energy. The plastic energy dissipates in each cycle as a result of plastic deformation.
To take the effect of mean stress into account, positive elastic strain energy was
added to the plastic strain energy. Moreover, the positive elastic energy term helps
to distinguish the data points in the high-cycle regime. Figure 14.5a schematically
displays the equivalent stress versus total strain in the first three reversals.