### Fall 2019 Contents:                                                                                                Issue No. 44

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Nugget Size in Resistance Welding

(Below is text of the article without figures; if you would like to download pdf copy with figures, please click on the link above)

Resistance welding is a widely used process for lap welding foils and sheets in automotive, aerospace, and many other industries where structures have to be fabricated out of metal sheets.  In its most common incarnation, two metal sheets are squeezed between two welding electrodes and a weld is made by passing electrical current through the electrodes and sandwiched sheets.   Variations include multiple sheets, dissimilar metals, and dissimilar thicknesses; the discussion below is applicable to those conditions as well with suitable modifications.  Combination of flow of current and application of welding force produces a fusion zone that originates at the weld interface and grows to the required height and diameter; see Figure 1 for a typical resistance weld section.  Size and shape of the nugget is dictated by rate of energy delivery, cooling effect of electrodes, and material properties of the sheets being welded.

Diameter of the weld nugget (d) typically defines weld strength in sheets of given thickness (t); conventional expectation of relation between the two is given by the formula d = 4√t.  You might find other variants of this formula with the constant anywhere between 4 and 5; most of these ratios are borrowed from riveting process, which was the precursor to resistance spot welding process.   The square-root based formula gives non-linear relationship between the two and may not be rational at extremes of sheet thickness.  For example, at a thickness of 0.1 mm, the nugget diameter required is 1.26 mm, which is 12.6 times the sheet thickness, which is huge; while at thickness of 2 mm, the nugget diameter required is 5.6 mm, which is only 2.82 times the sheet thickness.

Data from tables in RWMA Welding Handbook does not indicate such a strong non-linear relation within thickness ranges covered, and different materials seem to have different ratios.  For example, for HSLA (calculated by trendline curve fitting in excel) the relation is d = 1.9t; for Stainless Steel it is d = 3.2t, and for Aluminum it is d = 2.9t.  It is not clear if such relationships are based on experimental data, stress analysis, or modeling studies.

In most resistance welding applications for welding metal sheets, the testing procedure is fairly straight-forward as the two sheets are pried away from each other.  Typical expectation is that the weld will not separate cleanly at the interface but will transfer material from one sheet to the other which in extreme cases leaves a hole in one of the sheets.  Essentially, the weld has to be stronger than the strength of the base material surrounding the weld nugget.  Competition between weld strength and base metal strength can be setup for the two test modes as follows:

Pull Test (Weld in Shear)

In pull test mode (see Figure 2A), tensile shear strength of a nugget of diameter d will be compared to the shear strength of a cylinder around the nugget of diameter d and sheet thickness t; material shear strength, σs, of nugget and base material is assumed to be the same, though such strengths may not be equal.  During testing, if the nugget is strong enough, the tabs will bend and allow the base metal to fail in shear around the weld nugget leaving a button of diameter d and thickness t.  The relation between shear strength of nugget and the base metal can be setup as follows:

2 * σ= πd * t* σS , solving the equation gives

d = 4t

Cross-Tension Test (Weld in Tension)

In cross-tensile method (see Figure 2B) the weld is theoretically in pure tension as long as the sheets do not bend during the test.   Comparing tensile strength of weld to shear strength of cylindrical surface of diameter, d, and thickness, t, with material properties of tensile strength, σT, material shear strength σs, and assuming a simple relation between tensile and shear strength of σS = 0.5 σT, we get the following equation:

2 * σT  * t * σS, solving the equation gives

d = 2t

The above analysis indicates that welds in pure tension are lot stronger (need a smaller weld nugget) to cause parent metal failure.

In typical metal sheets, which are not very thick, the welded tabs will bend and distort (again, assuming the weld is intact) during testing to a point where the actual failure mode is likely to be peeling of the nugget from one edge as the nugget experiences high stress concentration.  In many welding applications, the weld is directly tested in peel mode (Figure 2C) and measured weld strength is much lower than the other two modes due to high stress loading on the front edge of the nugget.   It is not uncommon to have peel strength of the order of 25 % of tensile-shear strength of the weld.  Figure 3 shows a peel test sample where the test was interrupted and the failure in parent metal is evident.

Given all the options for diameter-to-thickness relations, an engineer has to be careful in determining which ratio is relevant and applicable to any particular weld being analyzed based on anticipated loading in service conditions and material properties of the welded region including the heat affected zone (HAZ).  An engineer should not completely depend on conventional wisdom, data from handbooks, or simplistic stress analysis to define what is good or bad for a specific weld.  If the relevant diameter/thickness ratio is chosen incorrectly, the weld diameter may end up being too large thus putting in too much energy and causing related collateral damage.  If the weld diameter chosen is too small, it can lead to premature failure of the weld in service.

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