Wire bonding is the primary method of making interconnections between an integrated circuit (IC) and a printed circuit board (PCB) during semiconductor device fabrication. Although less common, wire bonding can be used to connect an IC to other electronics or to connect from one PCB to another. Wire bonding is generally considered the most cost-effective and flexible interconnect technology, and is used to assemble the vast majority of semiconductor packages. Bond wires usually consist of one of the following materials: Gold - Aluminum - Copper. Wire diameters start at 15 µm and can be up to several hundred micrometers for high-powered applications. There are two main classes of wire bonding: Ball bonding and Wedge bonding. Ball bonding usually is restricted to gold and copper wire and usually requires heat. Wedge bonding can use either gold or aluminum wire, with only the gold wire requiring heat. -Wikipedia
These values (for a constant current) are typical for standard industry bond wire, and could vary from one product to another.
Here is an article gives equations for calculating fusing current when the duty cycle is very small, "Bond Wire Fusing in ICs with Pulsed Current." Note that much larger currents can be handled with very short pulses. Here is the whitepaper for the formula.
This study by Sandia National Laboratories is titled, "1 Mil Gold Bond Wire Study."
|Gold||1.00||0.79||1.16||0.6-0.7||4 x 4|
|1.30||1.33||0.693||0.9-1.0||5 x 5|
|1.50||1.77||0.521||1.2-1.4||6 x 6|
|2.00||3.14||0.294||1.6-2.0||8 x 8|
|Aluminum||1.00||0.79||1.33||0.27-0.30||3.5 x 3.5|
|1.25||1.23||0.856||0.4-0.5||4 x 4|
|1.50||1.77||0.595||0.6-0.7||6 x 6|
|2.00||3.14||0.335||1.0-1.2||6 x 8|
|3.00||7.07||0.149||2-2.5||9 x 12|
|4.00||12.57||0.0838||3.5-4.0||12 x 20|
|5.00||19.63||0.0537||5-6||15 x 25|
|8.00||50.27||0.0210||11-12||20 x 32|
|10.00||78.54||0.0134||16-18||25 x 40|
|12.00||113.10||0.0093||21-23||30 x 48|
|15.00||176.71||0.0059||20-35||40 x 60|
|20.00||314.16||0.0033||50-60||50 x 80|
99.99% purity @ 20°C