Page 364 - Handbook of Materials Failure Analysis

362 CHAPTER 14 Fatigue failure analysis of welded structures

a combination of modes I and II SIFs (such as double-shear and tensile-shear
configuration, Figure 14.2). The parameter β should be found such that the best cor-
; when plotted versus the
relation is achieved for equivalent stress intensities, K I eq
fatigue life for all specimen configurations.
A geometrical correction factor, G, was defined to incorporate the effects of spec-
imen and nugget size

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2

t W 9t 2
G ¼ +1 ; (14.4)
r 3 4r 2
where t is the sheet thickness, and W is the specimen width. To account for the effect
of load ratio, R, the general stress intensity parameter, K i , was defined as
p
K I eq ffiffiffiffiffiffiffiffiffiffiffi
K i ¼ 1 R: (14.5)
G
The parameter K i was related to the fatigue life by a linear relationship in the log-
log scale.
The fracture mechanics approach in general has a number of advantages and
drawbacks. The main advantage of this approach is that the crack propagation pro-
cess may be closely followed. A drawback of this approach is that the nugget edge is
considered a crack and therefore crack initiation life is assumed insignificant, which
is not supported by experimental observations and analysis. The work by Swellam
et al. [15] shows that crack initiation life in spot-welds of a low-carbon steel over-
whelms the crack propagation life in the high-cycle fatigue regime, that is, life > 10 5
cycles. McMahon et al. [34] demonstrated that up to 55% of the total fatigue life of
spot-welds can be consumed by crack initiation. This ratio in the work by Sheppard
et al. [22] is 30%. It should be mentioned that the crack initiation life is the number of
cycles required for the crack to reach a length of 18% of the sheet thickness in Swel-
lam’s work [15], and 0.25 mm in the studies by McMahon et al. and Sheppard et al.
[22,34]. Another deficiency associated with the fracture mechanics approach is that
the formulations are based on the assumption that the crack is along the faying sur-
face, while according to experiments, through-thickness cracking is the most com-
mon fatigue failure mode for tensile-shear specimens [13,35–37]. Moreover, in
contrast to the assumption in this approach, primary cracks in some cases do not ini-
tiate from the nugget edge [29,37].

2.2 STRUCTURAL STRESS APPROACH
Since 1989, a number of fatigue models have been developed for spot-welds based
on the structural stress concept. The structural stress takes into account all the stress
concentrations, except the stress concentrations originating from the weld [9,38].
Structural stress reflects the effects of forces and moments at the spot-weld center
or edge, and theoretically may be defined in the plate or nugget depending on the
mode of failure. Therefore, structural stress has been considered as the factor which
controls the fatigue failure. The structural stress approach, as opposed to many