Page 360 - Handbook of Materials Failure Analysis

358 CHAPTER 14 Fatigue failure analysis of welded structures

application can be extended to any spot joint, such as friction stir spot-welds and self-
piercing rivets, due to the similarity of the geometry and stress analyses as well as
flexibility of the fatigue models.
Fatigue modeling of weldments, in general, and spot-welds, in particular, is based
on the comparison of loads, stresses, or strains with their critical or strength values
which cause a defined damage or total fracture [9]. These models can be categorized
into global and local approaches. The global approaches assess the fatigue strength
using the external forces and moments, or using the nominal stress at the critical
cross-section calculated from the external forces. Fatigue life is determined by com-
paring this value with the corresponding critical value related to a global failure such
as fully yielding or total rupture. The local approaches, in contrast, use local param-
eters at the critical point to evaluate the fatigue damage. Local approaches are capa-
ble to follow the fatigue crack initiation and crack propagation processes. To predict
the crack initiation behavior, local notch approach is applied, that is, a measure of
local notch stress or strain is utilized as the damage parameter. Crack propagation
behavior may be modeled by fracture mechanics approach in which stress intensity
factor (SIF) or J-integral is the fatigue parameter. The transition between the global
and local approaches is called the structural stress approach, which is sometimes con-
sidered as a local approach [9]. The structural stress is calculated from the internal
forces at the weld (as opposed to external forces in the global approach), but does not
explicitly account for the weld notch stress concentration.
Up until the 1970s, the global approaches were being used for fatigue assessment of
spot-welds, that is, the fatigue strength was represented by specimen-dependent quan-
tities, such as the load amplitude. These approaches required an extensive library of
fatigue strength data for different spot-weld configurations and loading conditions.
Also, the global approaches are not capable of following the fatigue process which
has a local nature. These drawbacks have limited the application of global approaches,
although they are very simple to apply. Local approaches on the other hand have
attracted attentions since then, and have been widely applied to spot-welds.
The fracture mechanics approach considers the spot-weld as a sharp notch, and
treats it as a crack [11–13]; therefore, the crack initiation life is often assumed to be
insignificant in this approach. The fatigue models based on the fracture mechanics
use a measure of SIF or J-integral as the fatigue damage parameter and relate this
parameter to the fatigue life or the crack growth rate. Pook in 1975 [14]derived for-
mulations for the modes I and II SIFs for spot-welds under tensile-shear loading,
Figure 14.2a, and the range of mode I SIF, △K I , was introduced as a fatigue damage
parameter. Swellam in 1992 [15] developed a fatigue model for spot-welds, combining
the effects of mode I and mode II SIFs. This model considered spot-welds under a gen-
eral load case. Forces and moments at the spot-weld center were found from static equi-
librium equations, and SIFs were calculated according to the work by Tada et al. [16].
Assuming that the SIFs are independent of the crack length, fatigue life was calculated
from the SIFs through the well-known Paris’ equation. Newman in 1998 [17] developed
a fatigue model for spot-welds under the tensile-shear load case. Formulations proposed
by Pook [14] for mode I and II SIFs were employed and combined to obtain an