Page 22 - Biaxial Multiaxial Fatigue and Fracture

Assessment of Welded Structures by a Structural Multiaxial Fatigue Approach 7

dispose at the present time of reliable and sufficiently accurate methods for predicting the
fatigue life, with regard to the results obtained by modern finite elements methods. To
overcome this difficulty, we come back to the structural approach with a clear definition of the
design stress which can be transposed to multiaxial structural problems.
The classical introduction of the design stress is based on the extrapolation of far field
stresses with unclear rules. In order to clarify the description of this design stress we propose
an approach deriving from an analogy with the concepts which are at the origin of the Fracture
Mechanics. It is known that the mechanical state in the highly damaged crack tip zone, called
by H.D. Bui [9,10] the process zone, is inaccessible by the usual mechanics of solids. In this
zone, the material is neither really continuous nor homogeneous and the local strains are not
small. Nevertheless, the stress solution obtained from linear homogeneous and isotropic
elasticity in small strains allows the correct description of the mechanical state outside the
process zone. Although it is erroneous at the vicinity of the crack tip, it makes sense in terms of
an asymutotic solution which allows the correct control and the interpretation of the
phenomena produced in the process zone. Likewise, we will look for a way to build the
asymptotic solution which allows the correct control and interpretation of the phenomena
produced in the critical zone of the weld. For that purpose we adopt an approach which
combines testing and calculations with meshing rules taking into account the local rigidity due
to the weld instead of the local geometry of the weld itself which is a very hazardous data.
Therefore, the fatigue design can be based on a structural stress calculation from a finite
element analysis. On this basis we can establish design rules for welded structures [ 1 11 with a
structural approach and an unique S-N curve where S is a local equivalent stress defined from T
and p at the Hot Spot as described in the next paragraph.

Computing procedure and applications

Welding is one of the most important manufacturing process in the mechanical industry. In the
present industrial context, engineers need some fast and efficient tools to achieve the design of
such welded structures. Some computational methods applicable to the prediction of fatigue
strength have been proposed by different researchers [ 1,121. In the automotive industry,
J.L. Fayard et al. [ll] developed an efficient numerical tool to evaluate the asymptotic
mechanical field which defines precisely the design stress state and allows the prediction of the
fatigue strength of continuous arc-welded structures. In most of the cases, components are
usually made of metal sheets of approximately 2 to 5 mm thick joined by automatic metal
active gas (MAG) welding. Thus, the thin shell theory was considered to be the most
appropriate calculation method to solve the fatigue life prediction problem of automotive
welded structures.
However, in a thin shell finite element model, sheets are described by their mean surfaces.
The outstanding difficulty in using such meshes lies in the modelling of the mean surface
intersection. In fact, this zone exhibits 3D behaviour, whereas a thin shell model only produces
biaxial stresses. Moreover, at the intersection of thin shells, where hot spots commonly appear,
the stress gradient can be rather steep, so that stress calculations are very sensitive to the mesh
size. It is therefore necessary to define a meshing methodology which can be systematically
applied to any welded connection. On this basis, a design rule was established [I 1,13,14]. The
first idea was to reproduce as precisely as possible the local rigidity induced by the weld to the
joint, which modifies the local stress distribution. The other principal idea that supports the
meshing strategy was to simulate the stress flow from one sheet to another through the weld.
For that purpose, rigid body elements were used to link the two shells. The <<good den,
associated with a design stress representing faithfully the fatigue phenomenon and with an