I have a question about the graft healing and the strength after.

When the graft is healed, what holds the scion to the rootstock?
I think the answer maybe different for different types of grafts like bud, chip, whip, bark, and whip-and-tongue.

Would a chip/bud grafting would produce a stronger branch later in the plant's life than a whip graft?
How about whip-and-tongue? bark?
By stronger I mean harder to brake off.

What happens to the sapwood,heartwood, and pith in the case of a whip grafting? Do they heal (i.e. the scion parts attach to the rootstock)?

The old wood and pith don't heal together. The union is only formed from new growth. So a graft union will never be quit as strong as a normal branch. But after a couple yrs there won't be much difference.

A whip and tongue can be very strong. A chip bud would be a strong union. The weaklings to my thinking are bark grafts and anything that is lopsided.  But after a while they are as good as anything.

Support the graft especially if it grows very rapidly the first yr.

Thanks, Steve!
The graft support is a must in any case, esp. at the beginning. I was thinking about the people and raccoons later, in a few years.
Outside the unions may look strong and solid but I wasn’t sure what is happening inside.
It seems the earlier in the fig’s life the graft is done, the stronger it becomes later, because of the new growth volume. 

FWIW, I've had many chestnut bark grafts break .... about 2" above the graft union.  With strong growth and hard winds, the new branch would get blown around a lot while the stock was bigger and more rigid.  Even though the new growth had grown to 1" or more in diameter, it will sometimes snap in the strong winds.  The strength of the graft union has rarely been a problem.  I've done grafts of many different plants and the only time the graft union strength was an issue is when it never grew well to begin with for whatever reason.

Nice!
That is good to know. 
Have you tried to slice open a graft to see how it heals? Just curious what parts do what.

Good topic, I have always wondered about this as well.

I think I found a partial answer as to what could be found in a healed grafting union:

 
 

From here:
http://aggie-horticulture.tamu.edu/faculty/davies/pdf%20stuff/ph%20final%20galley/M11_DAVI4493_08_SE_C11.pdf

That is a really nice document, provides a lot of insight on what is really happening.
One more schematics:

 

Hi greenfig,
That first pic figure11-17 is for a root stock cut through the middle so that is the "cleft graft" technique.
The stem was split at the middle and the scion was inserted in the middle.
IMO, that graft is the most solid as the scion is "growing" in the middle of the rootstock instead of "growing" on one side of the rootstock.
The scion will then grow as big as the rootstock or sometimes the scion will overflow down on the rootstock if its diameter grows bigger than the rootstock.
You can often see that "overflow/tire effect" on cherry-trees.

A T-bud is probably the strongest because it has the least non-cambium contact. 

If you to a splice, or a whip and tongue, or wedge, the only part that is actually holding it together is the cambium layer (about as thick as a piece of paper. So you you graft 2 1/2" piees together, to two 2" pieces together, you have the same thin contact. After a couple years, you have added more hardened wood, and it is less of an issue. If you are worried, stake the grafted portion for a few years till the strength develops.

Wedge and whip+tongue grafts are "stronger" than a chip bud or splice graft because the scion and rootstock are physically locked together, so they are not depending entirely on the cambium union. Any technique that provided physical interlock will be better when the union is still tender. After a few years, it really doesn't matter.

This is an interesting topic!
What grafting methods have been found to work best with figs?

From my limited experience with figs, almost anything will work provided the proper timing and proper care conditions afterwords.
I tried the bark, chip, patch, splice, whip and tongue. With the splice, it healed so well that I would have a hard time to tell where the joint is.
I found that the grafting wax was very helpful, it seals the moisture in nicely. 
I think what method you choose depends on what size/shape of the scion and rootstock you have. 
The highest take was in the spring, when the plants start growing. The lowest, - in the middle of the summer: too hot and dry.
Early in the morning is the best time, and I keep the scions (grafting side)/buds in my mouth while preparing the rootstock (not sure if that’s how it is supposed to be done though).

Here is a great pic

http://northernpecans.blogspot.com/2011/04/anatomy-of-bark-graft.html

That is a great picture. Thanks for sharing it with us, I am really amazed by the presence of the old sun bleached wood inside the trunk.

Igor, your using the "Lick it and stick it" method, for real.

Wow! What a great image in that link, brackishfigger! Thanks!
The quality is so good that I would print a poster and hang in the guest room, a nice conversation starter :)

Calvin, you got it right! As soon as you master that, the rest is easy :D