Model description—DSSA

The development of the direct structural stress based approach was done after the observation that the previously described NSSA approach can lead to significant conservative fatigue lifetime results (up to a factor of more than 103 compared to test results). The NSSA also shows to be significantly influenced by certain modeling parameters when applying this approach for the fatigue life analysis of BIW structures. [1].

In Radaj’s concept, shown in the figure below, the structural stress σr is considered to be the fatigue relevant stress parameter for describing spot weld fatigue. The radial stress component σr, displayed in (left), is a local stress quantity that can be computed using the elastic theory of thin shell elements. [5]. When applying this concept in a fully 3D finite element (solids) representation of the spot weld there will be no stress singularity. This corresponds to the concept model because the linear stress distribution over thickness, shown in (right), also excludes the notch stress concentration at the notch in the spot weld nugget. The radial part of the stress field is thereby only influenced by the component geometry, external loading and material properties. [1].

Radaj's Concept for Spot Weld and Various Implementations Including NSSA and DSSA

Structural Elastic Stress σr (Radial) Used as the Fatigue Parameter for Radaj's Concept

The implementation of the direct structural stress approach that uses an appropriate finite element discretization is a direct implementation of this underlying mechanical model, described by Radaj’s concept. According to the authors in [1], the finite element discretization is needed to overcome the assumptions, limitations and simplifications of Rupp’s approach (NSSA), which are the following:

• The analytical engineering stress formulas are only valid under certain assumptions for the boundary conditions of the plate configurations. Two of these assumptions are that for a circular plate with a rigid inclusion under bending and transverse load the diameter and the type of constraint are fixed. To overcome these assumptions, Rupp et al proposed a case-to-case adaption of the parameter to mimic the different condition for every spot weld. This was found to be impractical for real complex structures such a vehicles BIW.

• The original concept of Radaj assumes an elastic representation of the spot weld nugget. However, the NSSA model adopts a rigid representation of the nugget. To compensate for this simplification a correction factor of was introduced. This correction factor K acts as a weighting factor of the bending portion of the structural stress and results in a different stress ratio R of the resulting equivalent stress.

• Load transfer through the individual sheets without load transfer through the weld nugget is not considered (Eigenforces). Torsion around the spot weld axis is also excluded from the model.Because the boundary conditions are very important for determining the local structural stress distribution at the spot weld, the first limitation of the NSSA approach was found by the authors of [1] to be the most significant.Detailed Model of the DSSA Spot Weld

The figure above shows the discretized spot weld model that is implemented in Specialist Durability. Convergence studies have been carried out in order to identify the best trade-off between numerical accuracy and computational cost. For these studies the results of models with different levels of discretization were compared to fine mesh models and this for multiple load cases. The level of discretization is defined by the number of shell elements that lie adjacent to the weld nugget and the type of elements (1st or 2nd order). [1]. The results of these studies showed that the best compromise between numerical accuracy and computational effort is obtained when using number of 16, evenly shaped, first order shell elements (4-nodes), along the nuggets circumference. Simulation results for the direct structural stress based approach.

In [1] the DSSA approach is validated using experimental data for proportional and non-proportional loading of box-beam structures. These box-beam specimens are also used in [2, 3] for the validation of the NSSA approach. The following figure shows the maximum structural stress amplitude σr,a, obtained with the DSSA method, vs. the experimental fatigue life for all the studied specimen and load cases [1].

Maximum Structural Stress Amplitude σr,a vs. Experimental Fatigue Life

To account for the mean stress, the equivalent stress amplitude at R = 0 is calculated using:

with

These structural stress data point match well to the three different SN-curves, each curve used for a discrete thickness value of the sheet in which cracking occurs. The SN-curves are calculated as best fits lines based on following power law relation:

The data for each SN-curve for each sheet thickness is displayed in the following figure [1]. The fatigue strength is taken at N = 106 cycles.

SN-Curve Data Each Sheet Thickness, Calculated Using the DSSA Approach

Normalizing this stress data based on the sheet thickness allows for the interpolation and extrapolation of the SN data to other thickness values. The normalization is done based on:

This normalization process leads a unique master SN-curve that can be characterized by a specific inverse slope k = 1.44 and specific strength value σr,E = 208 MPa at N = 106 cycles. This master SN-curve is shown in the following figure. The size of the scatter of the normalized SN-curve is determined as T**N,10/90 = 1:6.7, which is smaller than the scatter determined for the NSSA approach. [1, 3].

Master SN-Curve by Normalizing the Maximum Structural Stress Amplitude σr,a Displayed in the Figure Maximum Structural Stress Amplitude σr,a vs. Experimental Fatigue Life

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Comparison of the results for direct vs. nominal structural stress approach

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Model description—DSSA, Simcenter 3D 2021.1 Series

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