The burning process that happens where the wire broke, fouls
the surfaces. Sometimes the wire is surrounded by a rubber
compound, and the fouling material is burned rubber.
I do not recommend acid core flux.
The rosin core solder, is more gentle than acid core flux, long term.
Even so, if you can manage it (with propanol as a cleaner), you
should try to remove excess flux in any case.
Even though acid core flux would likely clean up the wire enough
to make the solder joint, I would be afraid of what would happen
long term.
*******
You should not be soldering mains wires together,
because of the risk the wire gets really hot, makes
the solder melt and the wires separate. There are
various weaving procedures for making stranded wire
cables "hold together". You should only use procedures
that insurance companies approve.
If I was repairing the Hoover cord here, I would:
1) Pull grommet where cord passes through. That is
where the wire is broken. You have to compress the two-piece
grommet thingy, to get it to pull out of the chassis material.
It is the devil to compress.
2) Pull unbroken wire through where the grommet goes.
The grommet is a two piece assembly that "compresses"
onto the cord, as you shove the grommet back into the
chassis of the vacuum. It helps prevent the vacuum operator
from yanking the cord right out of the chassis (sparks and all).
3) Now you have a foot or a foot and a half of new cord
inside the vacuum. Strip the nice clean wires and consider
your next option.
4) If the wires are fitted with spade lugs or screw
terminations, you fit similar items to the fresh cord.
Primary fix-ment, is via compression or crimping of the
fastener to the stranded wire. Again, it's not really
recommended to be soldering the wire to the lug, but if
your crimper isn't very good, you might not have any
choice in terms of firming things up.
As long as the solder joint is not under stress or
mechanical vibration, probably nothing bad would
happen to it. It's preferably to just do a good job
with your crimper.
Some of these things, have two crimp sections on them.
One section holds the wire (part nearest the screw head).
The section further away can help secure the wire insulation.
https://media-dali.azureedge.net/2827/dali-spade-lugs-background.png
They can also have a plastic cover that goes over the crimps.
In these examples, the two on the left are the kinds I stock here.
And they must match the dimensions of the one being replaced.
https://www.powerandcables.com/wp-content/uploads/2019/04/pvc-insulated-crimp-terminals-min-1.jpg
Anyway, there's probably a lot more safety tips to go with
this subject, and maybe someone else can list more of them.
But suffice to say, doing this, in this way, is "not recommended".
This is a good effort... but if the house burns down, this
is what the insurance company will be looking for. Bodgery.
And wrapping that with electric tape? NO. Use shrink wrap,
as it is an alternative insulation method, and comes in a
variety of diameters. You can slide the shrink wrap up the wire,
do something sinful, then slide the shrink wrap over the
exposed bits. Having left sufficient diameter for the bodge.
Shrink wrap is better than electrical tape, but has its own
set of issues with the skills needed to do a good job. For example,
you can melt the 70C rated wire insulation the wrap sits on top of,
if you're careless.
https://knowhow.napaonline.com/wp-content/uploads/2015/08/Solder__lead.jpg
This is not a proper weaving. It's imaginative though.
https://www.instructables.com/Soldering-Tutorial-Inline-Splicing/
This is an example of a proper splice. Someone here posted
a similar idea in this group, a while back. That's the only reason I have
seen the more exotic method. I've never done one with
this much attention to detail, but I still think you
should see what they have in mind. You start with significantly
more stripped wire, to be doing all the winds involved in a good
splice.
https://en.wikipedia.org/wiki/Western_Union_splice
Soldered wires need to be strain relieved, because where
the solder stopped flowing in the stranded wire, is a
stress point. The wire "wants to flex" right at the point
where the solder stops. The wire should not be allowed to
flex at that point. For example, you would not put a
soldered joint right inside the strain relief grommet on
the vacuum cleaner. That would be asking for "instant failure".
Sometimes, even fitting several layers of shrink wrap,
incites flexure failure. Right where the shrink wrap stops.
It's definitely a topic with a lot of "learn by doing"
and "smoke testing". And over the years, discovering
what were bad ideas, and what were successes. I can tell
you, there are *lots* of bad things you can do.
We had "soldering police" at work, who would check workmanship,
and I would never pass one of their examinations. They are
police, only because they were sent on course and trained at
it. You can't argue with those dickheads, it's a waste of time.
Just sit there and take your lumps. I do OK at soldering,
because I've done thousands of joints (think HeathKit :-) ).
There are even techniques for taking care of the tip of
your soldering iron. If you foul it with too much burnt
crap, it'll never work right again. You can't use it for
wood burning one morning and soldering the next. You have
to take care of those, and the modern tips are much better
fabricated than the ones fifty years ago.
Paul