Stress intensity factors for spot welds between plates of unequal thickness

Abstract

The stress intensity factors for spot welds between plates of unequal thickness are derived as a basis for fatigue strength assessments for spot-welded specimens and components. As a first step, the structural stress state at the weld spot edge is determined, in this case by the finite element method. Then the stress state is decomposed, edge point by edge point, into symmetrical and antisymmetrical components of membrane, bending, transverse shear and longitudinal shear stresses. Different decomposition modes can be used, on the basis of stresses or resultant forces. A mixed decomposition mode which deletes those components which cause no stress singularity is preferred. The internal stress or force states are transferred to a strip model with slits representing the cross sectional contour of the weld spot edge (extended to a strip plate model for longitudinal shear loading). The resulting equivalent stress intensity factor is determined, applying the J integral on a path identical to the outside contour of the model. To deal with the antiplane shear loading case connected with K III , a J ∗ integral is defined analogous to the J integral. The boundary element method for plane and antiplane stress fields is used to determine K I , K II and K III . The dependence of the stress intensity factors on the thickness ratio of the two strips is stated by simple formulae, which are derived on the basis of the J and J ∗ integral solutions. The fundamental structure of the formulae, “structural stress multiplied by square root of thickness” is maintained including a coefficient which depends on the thickness ratio. The content of the formulae is illustrated in relevant diagrams. Comparisons with values from the literature in special cases of the strip model showed complete correspondence. The generally derived procedure is applied to the tensile shear and cross tension specimen with a thickness ratio of 4.0. The change of the maximum stress intensity factors versus a thickness ratio of 1.0 is small. The maximum stress intensity can be assessed on the basis of a simple engineering formula.