Page 365 - Handbook of Materials Failure Analysis

2 Fatigue Modeling of Welded Structures by Local Approaches 363

fracture mechanics-based models, often provides enough flexibility to be applicable
to different specimens and structures. Therefore, these models are widely employed
in industry, including the automobile industry [9]. However, some weak points are
also associated with this approach. A serious shortcoming is that the notch effect at
the spot-weld edge is ignored [9].
Sheppard and Strange in 1992 [22] studied steel spot-welds under cyclic loading
and observed that failure occurs in the through-thickness fashion. They defined the
structural stress as a function of membrane load and bending moment,

△P ij △M ij
△S ij ¼ +6 2 ; i, j ¼ 1, 2; (14.6)
ωt i t W
i
where △S ij is the structural stress range, △P ij and △M ij are membrane load and
bending moment ranges, respectively. ω is the effective sheet width and according
to Wang et al. [39] was defined as πd/3, in which d is the nugget diameter. The
subscript i represents the sheet (i¼1 for the bottom sheet, and i¼2 for the top sheet),
and the subscript j represents the side (j¼1 for the right side, and j¼2 for the left
side). Figure 14.4 illustrates the membrane forces and bending moments at the
edges of a spot-weld, that is, D ij .

z
x
P P
Faying surface t
: spot weld with
A y A
P diameter d
x P

(a)
Section A-A
M 22 M 21
P 22 PA 22 PA 21 P 21
t
D 22 D 21
D 12 D 11
P 12 P 11
t
PA 12 d PA 11

M 12 M 11
(b)
FIGURE 14.4
Forces and moments at a spot-weld nugget edge for Sheppard’s structural stress
calculation [22].