Читать книгу Sticking Together - Steven Abbott - Страница 35
ОглавлениеCHAPTER 4
How Stuck Is Stuck?
It seems very easy to know how well two things are stuck together. You measure the area of overlap then measure the force needed to pull them apart. Force divided by area in standard units is N m−2, also known as a Pascal, Pa. Because a Newton is rather small and a square metre is rather large, a Pa is small and adhesion values tend to be quoted in MPa or GPa.
Let us start with the system we introduced in the chapter above, with gecko-style, glueless, surface energy adhesion. Take two pieces of smooth rubber (rubber strips can be cast onto glass to produce super-smooth surfaces) and place them together so they spontaneously stick to each other.
We can pull them apart in three ways (Figure 4.1):
Pull up one end and peel the samples apart: Peel test
Pull along the join and try to shear them apart: Lap shear test
Attach something strong to the back of one piece and pull it up vertically while holding the lower piece in place: Butt test
Figure 4.1 The three types of adhesion tests: Peel, Shear and Butt. Even for the same material the force need to separate them differs by factors of 100s or 1000s.
Rubber typically has a surface energy around 40 mJ m−2 which, via a bit of manipulation, can be seen to be equivalent to a peel force of 40 mN m−1. If we have a sample width of 25 mm (0.025 m) then we find that the peel force is 40×0.025=1 mN. With an overlap length of 25 mm, the area is 0.0252=0.000625 m2 so the adhesion value in N m−2=0.001/0.000625=1.6 N m−2, a very small adhesion value. Readers may notice that including the overlap length is a cheat; it is the only way to get a value in the same units as the others. This is an early indication of the problems ahead. I am cheating deliberately and openly; many in the adhesion world are unaware that these numbers are meaningless.
If you measure the force required to fail the same joint by pulling in shear mode, you find it needs a force that depends not only on the surface energy but on the thickness and the modulus of the rubber, i.e. how much stretch you get divided by the force required to create that stretch. Using typical values, we find that F=1.25 N (not the mN of peel!) giving a N m−2=2000.
If you now try to pull it apart vertically, in the butt joint test mode, it requires F=27 N and a N m−2=55 000, 30 000 times more than the peel. This now explains why the two strong men could not pull two pieces of rubber apart (butt joint) while the little girl had no problem (peel joint). Although the men were stronger, they weren't 30 000 times stronger!
You can find all the formulae (which come from Prof. Kendall) and play with the key values in an app I wrote: https://www.stevenabbott.co.uk/practical-adhesion/weak-strong.php. More important is the message that Adhesion is a Property of the System. If your system is one where the forces are always equivalent to a butt joint, then the 55 000 N m−2 might be good enough. Yet if there is any risk of some peel forces, then the 1.6 N m−2 is likely to be very worrying.
Why do the values change by more than 30 000? Because joints fail whenever the local forces exceed a limit. In the peel test, the forces are focussed exactly at one point – the point where the joint will fail. With the lap and butt joints, the work put in to breaking the joint is also expended in stretching and distorting the material layers involved in the joint so that the force at the edge of the joint is much smaller.
