PSI - Issue 75

Jörg Baumgartner et al. / Procedia Structural Integrity 75 (2025) 538–545 Jo¨rg Baumgartner / Structural Integrity Procedia 00 (2025) 000–000

539

2

a non-conservative dimensioning and subsequently to failure in service in cases where in-plane or out-of-plane shear dominates. The aim of this paper is to present a methodology that is easily applicable based on a standard simulation model but also able to capture the influence of all loading modes (I, II and III) on the stresses at the weld. With this approach, a higher assessment reliability is expected.

Nomenclature

t

thickness

w F

width of the sheets

d

diameter of spot weld

cutting forces M cutting moments

r

notch radius

2. Fatigue and assessment of spot-welded structures

Various di ff erent approaches exist for the fatigue assessment of spot-welded structures. The main approaches have been summarized almost 30 years ago as the structural stress approaches, the notch stress approaches, and fracture mechanics [17].

2.1. Structural stress approach

The advantage of using structural stresses for fatigue assessment is primarily due to the simplicity of finite element models. The structural connection is modeled using a connector element, which can simply be a bar or beam element that exhibits the same diameter as the spot weld, Fig. 1. In case of a bar or beam element, two nodes need to be positioned exactly on the opposite sites of the sheets. Another commonly applied approach is the use of a hexahedron element as spot weld, which is connected with RBE3 connectors (spider) to the shell elements. This configuration e ff ectively distributes the loads from the shell elements to the joining element. With this approach, the nodes of the shell mesh do not need to be adapted to the connector. In addition, this approach allows a better mapping of the sti ff ness of the spot weld.

Shellmesh Spider

7

8

Beam

5

6

3

4

Hexahedron

1

2

Fig. 1. Representation of a spot-weld with a beam (left) and a hexahedron and spider element (right)

Di ff erent analytical formulae to derive all structural stress components at a spot weld are available [14, 20]. These are primarily determined by the three cutting forces F x , F y and F z as well as three cutting moments M x , M y and M z at the spot weld, which is represented as a beam element. These cutting forces and moments are then used for a fatigue assessment [18, 8]. Another approach is to use stresses measured at a certain distance from the spot weld on the sheet surface [22]. The most common approach to assess the fatigue strength of spot-welded structures is the so-called FESPOW (fatigue evaluation of spot welds) approach that was published in 1995 [18] as a result of a joint research project from the automotive industry in Germany [19]. The approach uses radial stresses determined at two bar elements that represent the spot weld as the main parameter for the fatigue assessment.