A software system has been developed in the MSC.Fatigue environment which permits fatigue life predictions to be made for automotive spot-welds joining two steel sheets. The method uses bar element forces to calculate the “structural stresses” in each spot-weld nugget and the adjacent sheets using the methodology described by Rupp, Störzel and Grubisic. The system described here supports the use of dynamic stresses derived from road load data, using either a quasi-static or transient approach to stress history determination. The method is geometry-independent and suitable for application to large models (because it does not require local mesh refinement). The system provides a convenient way for users of MSC.Patran, MSC.Nastran, and MSC.Fatigue to predict the location and life of fatigue sensitive spot-welds. See (Ref. 32.) through (Ref. 38.) in References (Ch. 16) for more detail.

Resistance spot welds are very commonly used in the automotive industry in the fabrication of all manner of components and structures, and the durability of such structures is very often controlled by the strength of the spot welds. The cost of tooling up for a single weld spot as part of an automated manufacturing process may be around $30,000, and this can more than double if a weld spot has to be added during production to remedy a problem. These costs may be minimized if the life of spot welds can be predicted at an early stage in the design process, though the reduction in development time and improvement in quality is likely to be more significant.

Smith and Cooper addressed the problem of life prediction of shear spot welds using a fracture mechanics approach. They noted that a spot weld could be “....considered to be a circular solid surrounded by a deep circumferential crack, which when loaded in a combination of Mode I and Mode II, would grow a branch crack in the direction of maximum local Mode I”. They showed that good predictions of life could be made on the basis of calculated crack growth rates, and used their calculations to generate some simple design curves. The method was based on detailed finite element modeling of simple spot-welded lap-joints loaded in shear. This method would need further development in order to cover all the possible weld configurations used in automotive structures and to deal with the variable amplitude out-of-phase loadings to which they are subject. The results of this might be a simple design code for spot-welds along the lines of BS 7608 with families of load-life curves for different classes of spot-weld. In practical FE models of automotive structures there is no scope for such detailed modeling of individual spot welds.

In fact, load is a rather poor parameter for correlating the fatigue strength of spotwelds under different loading conditions. Radaj and Sheppard note that durability of spot welds of a variety of configurations and loadings can be better understood through numerical analysis of the local stresses at the weld spot edge on the inside of the plate - the structural stresses around the weld.

Rupp, Störzel, and Grubisic describe the calculation of these structural stresses, and also carry out fatigue life predictions based on maximum and minimum stresses and a load spectrum. The software described here is closely based on the work of Rupp et al, but combines their method for structural stress calculation with the methods of stress scaling and superposition and access to transient FE results normally used in MSC.Fatigue.

The method requires spot welds to be modeled as stiff beam elements in MSC.Nastran. The forces transmitted through these beam elements are used to calculate the structural (nominal) stresses in the weld nugget and the adjoining sheet metal at intervals around the perimeter of the nugget. These stresses can then be used to make fatigue life predictions on the spot weld using a S-N (total life) method.

The software system consists of some modified MSC.Fatigue modules and a spot-weld fatigue analyzer called SPOTW. The system currently only supports fatigue calculations on spot welds joining two sheets. In the FE model, the spot-welds should be represented by stiff beam elements joining the mid-planes of the two sheets of shell elements, and perpendicular to both. The length of the spot weld and the sheet separation should therefore be half the sum of the sheet thicknesses. There is no need for any refinement of the mesh around the spot-welds. The only requirement for the shell elements used to model the sheets is that they transmit the correct loads to the bar elements. In fact it seems that best results are achieved when the dimensions of the shell elements are quite large - more than twice the diameter of the weld nuggets.

A typical spot-weld is illustrated in Figure 9‑33. The shaded part is the spot weld “nugget”. In a finite element analysis, the weld is modeled in MSC.Nastran as a stiff beam element joining the mid-plane of two sheets. The length of the beam element will be 0.5(s1+s2) where s1 and s2 are the thicknesses of sheets 1 and 2 respectively. Point 3 is on the axis of the weld nugget and at the interface of the 2 sheets, i.e. 0.5s1 from Point 1. All forces and moments are taken to be in the MSC.Fatigue beam element co-ordinate system illustrated. This is taken to be a Cartesian system with the Z axis going from Point 1 to Point 2. This is different both from the arrangement used by Rupp et al. and that used in MSC.Nastran, but is a little more simple.

The translator extracts forces and moments Fx,y,z and Mx,y,z in the MSC.Fatigue coordinate system, and in the conventional right-handed sense, from the results in the database, for each of the three specified points. These forces and moments (except Mz) are used to calculate nominal stresses (structural stresses) on the inner surface of Sheet 1 and Sheet 2, and in the weld nugget at the interface of the two sheets, at intervals around the circumference of the spot weld (=0 degrees to 360 degrees by increments of 10 degrees). The forces and moments at points 1 and 2 are those applied by the spot welds on the sheets, and the forces and moments at point 3 will be those applied by the upper section (between point 3 and point 2) on the lower section (between point 1 and point 3).

The stresses are calculated as follows:

The equivalent stress on the inner surface of the sheet as a function of angle around the circumference of the spot weld is:

 

so that only the tensile component of the axial force in the nugget contributes to damage, and:

Note that K1 = 0.6 sqrt(s1) and d is the diameter of the weld nugget, dimensions in mm. Forces are in N and moments in Nmm.

The equivalent stress on the inner surface of the sheet as a function of angle around the circumference of the spot weld is:

 

so that only the tensile component of the axial force in the nugget contributes to damage, and:

Note that K2 = 0.6 sqrt(s2) and d is the diameter of the weld nugget, dimensions in mm. Forces are in N and moments in Nmm.

From the forces calculated for point 3, nominal stresses are calculated at intervals around the circumference of the weld nugget, say at 10 degree intervals. The method of Rupp then suggests that the direct stress be calculated on multiple planes at 10 degree intervals, i.e. use a stress-based critical plane method. This would mean 36 x 18 = 648 calculations for each weld nugget. This is very computationally intensive, especially in view of the fact that spot welds do not usually fail by cracking through the nugget. For this reason, two faster approaches are considered: to ignore the possibility of nugget failure altogether, and to use the absolute maximum principal stress as the damage parameter, as used in MSC.Fatigue (only 36 calculations). This is calculated as follows:

 

From the shear and direct stresses on the nugget, the in-plane principal stresses can be calculated from:

The principal stress with the greatest magnitude is taken as the damage parameter.

The system requires an S-N curve for each metal sheet and for the weld nugget at load ratio R=0, plus a mean stress sensitivity factor and a standard error parameter. The formulation of the S-N curve is as follows:

for Nf<Nc1 the transition life. For Nf>Nc1 a second slope b2 is used. It is possible to correct each cycle with amplitude S and mean stress Sm to calculate an equivalent stress amplitude S0 at R=0:

Rupp described generic S-N curves for sheet steel and weld nuggets. There is quite a wide-scatter band, which is partly a reflection of the fact that this data represents spot-welds in a variety of steels, including mild and high strength. Better predictions may be possible if S-N data specific to the materials being used is available.

Actual damage calculations use typical MSC.Fatigue techniques for the S-N methods as described fully in Fatigue Theory (Ch. 15).

Specific to spot weld analysis, damage calculations are carried out at 10 degree intervals around the spot weld in both sheets and in the weld nugget. There are therefore 108 fatigue calculations per spot-weld. At each calculation point, the effective stress history is calculated either directly from the force and moment results from a transient FE analysis, or by scaling and superimposing the results of a number of static load cases according to the quasi-static method. The stress history is then rainflow cycle counted to form a range-mean histogram. Rainflow cycles are converted to equivalent stress amplitude for R=0, then damage is calculated and summed using Miner’s rule. The results are written to two files: a MSC.Patran jobname.els file containing summary results for postprocessing in MSC.Patran, and a more detailed file for postprocessing by SPOTW.

The method for life prediction of spot-welds described here is somewhat computationally intensive. Computation time is roughly proportional to the number of data points in the load histories. Substantial reductions in computation time can therefore be achieved by judicious filtering of the loading inputs.

The spot weld analyzer works by using the cross-sectional forces and moments in the beam elements to calculate structural stresses in the spot weld nugget, and the two sheets being joined. These structural stresses are then used to make the fatigue calculation. More information on this is available in Spot Weld Analysis Theory, 793 in this chapter. The structural stresses are modified by empirical factors that take into account size and loading type effects. These factors are different for material types 1-99 (ferrous metals) and types 100-199 (aluminum alloys). The stress factors are applied to the stresses due to the x and y forces on the beam element, the z forces and the x and y moments. The factor takes the general form:

where F is a factor and e1 and e2 are the diameter and sheet thickness exponents. For steels these factors are by default assumed to be as follows:

For aluminium alloys, the factors are as follows:

Expert users may wish to specify their own values. This can be achieved by setting an environment keyword using the environment manipulation program MENM. See Modifying the MSC.Fatigue Environment (MENM), 1433. The keyword to be set is "SPOTWPAR" and the value it must take is the 9 values detailed in the table above, in the correct order, separated by commas:

SPOTWPAR=SFFXY,DEFXY,TEFXY,SFMXY,DEMXY,TEMXY,SFFZ,DEFZ,TEFZ