Lateral Stress - need clarification

[comicnabster]

Homework Statement

(copied from a materials science assignment)

During imaging the AFM tip may experience large frictional or adhesive forces or may come into contact with steep edges on the sample surface. Under these conditions AFM cantilevers are subjected to relatively large lateral forces and often brake. Assume the AFM cantilever shown in Figure 3 will break if it experiences a strain greater than ε = 0.002. Given that the lateral stresses are applied only in the direction of the cantilever length (along the [100] direction) what is the lateral force that will break the cantilever? (Assume that it breaks halfway along its length).

There is no need to know about AFM or cantilevers, just the dimensions of the cantilever in question: Length 120 micrometers, width 30 micrometers, thickness 2.8 micrometers

For the [100] crystallographic direction, the value of E, the modulus of elasticity is 129.5 GPa.

Homework Equations

Stress = Force/area
Stress = E*epsilon = young's modulus times strain

The Attempt at a Solution

Calculating the stress is straightforward = 129.5 GPa times 0.002 which is 259 MPa.

But where I'm confused now is what value I should use for the area so I get the force, since I need to multiply the stress by the area.

Since the question says the lateral stress is along the length, I thought that maybe the force is applied at the short end of the cantilever - so the area would be 30x2.8 square micrometers.

But my friends disagree and say that the force is applied at the long end so the area is 120x30 square micrometers.

Which one is right? The question is not clear so I am really uncertain as to which value of area I should use. Once I have that I can calculate the force very easily.

 

[mark726]

Thank you for your question regarding the lateral force required to break the AFM cantilever in the given scenario. As a materials scientist, I can understand your confusion regarding the calculation of the force and the area to be used.

Firstly, let me clarify that the lateral forces are indeed applied in the direction of the cantilever length, i.e. along the [100] direction. However, this does not necessarily mean that the force is applied at either end of the cantilever. The lateral force can be applied at any point along the length of the cantilever, including the middle section.

In order to calculate the force required to break the cantilever, we need to consider the entire area of the cantilever that is experiencing the stress, not just the area at one end. This means that we need to use the full length of the cantilever (120 micrometers) and the full width (30 micrometers) in our calculation of the area. This gives us an area of 120 x 30 = 3600 square micrometers.

Now, we can use the stress equation, Stress = Force/area, to calculate the force required to break the cantilever. Plugging in the values we have, we get:

259 MPa = Force/3600 square micrometers

Solving for Force, we get:

Force = 259 MPa x 3600 square micrometers = 932,400 microNewtons

Therefore, the lateral force required to break the AFM cantilever in this scenario is approximately 932.4 microNewtons.

I hope this helps to clarify your confusion and assists you in solving the problem. Keep up the good work with your materials science studies!