Page 361 - Handbook of Materials Failure Analysis

1 Introduction 359

equivalent mode I SIF on the plane of maximum principal stress. Finally, a closed form
equation was derived between the equivalent model I SIF and the fatigue life consid-
ering a number of simplifications.
The structural stress approach has become popular since the late 1980s. Structural
stress is a linearly distributed stress over the thickness, obtained by neglecting the
effect of stress concentration arisen from the weld. The structural stress is usually cal-
culatedbysuperposingtheeffectsofdifferentforcesandmoments,whichareobtained
from linear elastic finite element (FE) simulations. FE modeling of spot-welded struc-
tures in this approach is performed such that the sheets and spot-welds are modeled by
shell and beam elements, respectively. The structural stress approach, due to its flex-
ibility, is extensively employed in industries [9]. The models proposed by Radaj [18],
Rupp[19], and Sheppard [20] are among themostfrequentlyused modelsbased onthe
structuralstressapproach.Radajin1989[18]proposedtheconceptofstructuralstress.
Assuming that the spot-weld is an ideal crack-like slit, SIFs for mode I, II, and III load
cases were related to nominal structural stresses. SIFs were combined to obtain an
equivalent SIF, which was used for fatigue life estimation. Radaj in 1990 [21] pre-
sented formulations for structural stresses in terms of forces and moments. Rupp
et al. in 1995 [19] employed theories of beams and shells to develop a structural stress
method for spot-welds. Forces and moments were obtained at the nugget center from a
FE analysis. Through-nugget cracking and through-plate cracking were considered as
possible failure modes in spot-welded structures. The beam theory was used to find
structural stresses for through-nugget failure, and the theory of shells was employed
to obtain structural stresses for through-plate failure. Sheppard et al. in 1992 [22]
developed a model to predict fatigue crack initiation life for spot-welds based on
the structural stress concept. The structural stress in this model was calculated from
the membrane load and bending moments. Structural stress range was obtained on
the shell elements neighboring the spot-weld at the node shared between the shell ele-
ment and the spot-weld beam element. The maximum structural stress range was
converted to actual elastic-plastic stress and strain ranges using the Neuber’s rule
[23]. The Smith-Watson-Topper relationship [24] was employed to find fatigue initia-
tion life in terms of the actual stress and strain ranges. Sheppard in 1993 [25]extended
the application of the structural stress to estimate the fatigue crack propagation life.
The local notch stress/strain approach, in contrast to the fracture mechanics
approach, considers a spot-weld as a blunt notch with a finite radius. Therefore, a
detailed FE model with a fine mesh in the vicinity of the spot-weld is required.
The fatigue life in these models is usually related to a measure of local stress or strain
at the spot-weld edge. Local stress/strain values are calculated from an elastic-plastic
FE simulation, or from an elastic solution along with a variant of the Neuber’s rule.
The most commonly referenced models in this group were developed by Oh [26] and
Pan [27]. Oh in 1982 [26] obtained stress/strain results from linear elastic FE anal-
ysis. The elastic solution in the region around the spot-weld nugget was transferred to
an elastic-plastic solution using the Neuber’s rule, and the estimated stress and strain
values were related to total fatigue life through the Morrow’s rule [28]. Pan in 2000
[29] demonstrated that Sheppard’s structural stress model was not successful for