This is a picture of an assembly that is part of my full scale (human size) quad-copter rotor blade.
For background, the FlexElement is the structural member that will connect the rotor blade to the rotor hub or head. (shaft). The leading edge rod is an internal structure to give the leading edge of the rotor blade airfoil durability for small impacts. The composite beam is a composite layup which holds it all together, but mainly its function is to transfer the centrifugal forces of the rotor blade (which extends to the left off the page) to the FlexElement.
Originally I did a simple calculation to determine how much surface area I needed for the glue joint between the FlexElement and the composite beam. This was based on the shear strength of the epoxy resin I was using.
A = F / U where U is the maximum stress I want the glue to experience.
In my case F=1600 Lb
U = 5000/4 psi (Lb/in^2) (divide by safety factor of 4:1)
A (minimum) = 1600 / 1250 = 1.28 in^2
My FlexElement rod has an OD of 5/16" or 0.3125", so the circumference is pi * .3125 = 0.982"
So every 1" of bond length along the rod, will give 0.982 in^2 of bond area, so my bond length needs to be at least:
1.28 / 0.982 = 1.30" long. That's how much the rod must insert into the composite beam to provide enough bonding area.
In actual fact, I made the joint length about 4" because of other design factors, so I theoretically had 12 x more area than I needed (safety factor of 4 * (4"/1.3") ~ 12)
I was VERY surprised when this joint failed in simple tension at well below 1600 Lbs of tension.
Lets look why.
My simple bond joint area calculation made one very innocent, but deadly assumption:
That the force or stress would be evenly distributed across the full area of the joint.
WRONG WRONG WRONG WRONG!!
Lets look at a simpler geometry to help understand.
Here is a cut-away of a simple rod glued into a larger cylindrical rod.
The problem with this design is that it produces a concentration of stresses in the glue joint at the point where the rod first enters the cylinder. This is because of the huge, and sudden difference in cross sectional area between the rod, and the rod/cylinder combination at that point.
All materials have elasticity and deform (stretch or compress) when a force is applied to them.
The rod is being pulled in tension, so it is stretched longer than it's normal relaxed length.
Since the glue joint between these two parts is very very thin, we assume that the rod and cylinder dont move relative to each other. But that is not the case here, because the rod is a small diameter, so it is under much greater stress (force per unit cross sectional area) than the green cylinder. So... the rod will be stretching more, so it MUST deform more than the cylinder which is under less stress because the tensile force is spread across a much larger cross sectional area.
When you pull the rod in tension, you quickly cause a stress concentration in the glue joint at the spot indicated.
When the rod pulls to the right, all of that force is concentrated to a small portion of the glue joint. That section of the glue joint fails, and the rod stretches a minute amount. But now, the portion of the glue joint just to the left of the stress concentration area becomes the new stress concentration area, and so on until the joint failure/ stress concentration has moved all the way along the glue joint, and the rod simply pulls out of the cylinder.
This is very hard to describe and visualize because it happens essentially instantaneously, but seeing the results (failure of the joint WAY below what was expected) make it impossible to deny.
The solution to the problem is to design the two parts (or for simplicity in this case - the cylinder) so that there is a very gradual change in cross sectional area, so that there is a gradual change in the stress, and hence a gradual change in the stretch (strain).
Care must be taken to make this transition gradually so that at no point along the glue joint, does the stress excess the shear strength of the cured glue material.
So back to the stress concentration area, the glue joint only needs to transfer enough force to the "cylinder" (now a cone) to make that tiny, thin green area on the far right to stretch along with the rod which is under full stress.
This force transfer keeps happening along the length of the glue joint until eventually all of the force is tranferred to the green cylinder.
Thanks for taking the time to "bond" with me. :)