attaching two materials of different modulus of elasticity
attaching two materials of different modulus of elasticity
(OP)
Hi everybody,
I have the following problem:
I use two component epoxy to attach ceramic (270000 N/mm2) to a brick (14000 N/mm2). The ceramic piece is very thin and small with respect to the brick.
When the brick is subject to compressive stress, the brick will have a strain that follows Hooks low. What will be the strain in the ceramic piece?
I would assume that the epoxy has also its deformation and plays important role in transmitting the strain to the ceramic
I attach a simple drawing.
Any hint on how to make this calculation?
Thank you
I have the following problem:
I use two component epoxy to attach ceramic (270000 N/mm2) to a brick (14000 N/mm2). The ceramic piece is very thin and small with respect to the brick.
When the brick is subject to compressive stress, the brick will have a strain that follows Hooks low. What will be the strain in the ceramic piece?
I would assume that the epoxy has also its deformation and plays important role in transmitting the strain to the ceramic
I attach a simple drawing.
Any hint on how to make this calculation?
Thank you





RE: attaching two materials of different modulus of elasticity
Once you have the load, you can work out the strain using Hooke's Law.
You just need to ensure you have sufficient overlap to enable the shear stress distribution to decay to near-zero in the centre of the joint for this calculation to be valid. (Do NOT use an average shear stress calculation. It is totally meaningless and has no relationship with the real world. Pity 78% of aircraft manufacturers use average shear stress to design aircraft joints.)
Regards
blakmax
RE: attaching two materials of different modulus of elasticity
The ceramic piece is a thick film sensor.
The result of strain calculated this way is much bigger from the sensor reading.
I think the relationship you suggest is valid if the cross sectional areas of ceramic and brick is the same.
It seems that some geometrical factor is missing.
What do you think?
Jabir
RE: attaching two materials of different modulus of elasticity
Let me be clear: Are the strain readings from the sensor higher or lower than those calculated?
RE: attaching two materials of different modulus of elasticity
I think in this scenario the sensor has shear strain.
RE: attaching two materials of different modulus of elasticity
There will be several possible causes of inefficient bonds: inadequate overlap length, poor adhesive properties due to poor mixing of the adhesive, inadequate surface preparation, excessive service temperatures etc.
I'd need more details of all of the above issues to help you.
RE: attaching two materials of different modulus of elasticity
RE: attaching two materials of different modulus of elasticity
Adhesive shear stresses peak at both ends of a bonded doubler, and if the overlap length is large enough, the shear stresses decay to zero in the middle of the joint. The reason they decay to zero is that the strain in both adherends is the same and will be a value as calculated above. There will be a strain ditribution in the ceramic from zero at the ends (no load in the adherends there) to the maximum once the shear stresses decay to zero.
Now if the overlap length is inadequate (or if the adhesive shear modulus is too low) and the shear stresses do not decay to zero, then your assertions may be correct.
Regards
blakmax
RE: attaching two materials of different modulus of elasticity
when you say strain distribution in the ceramic, I think you mean from the joint up, in the Y direction right?
I understand that the shear strain in the two joints should be the same. So it is the same as that of the brick.
What is the relation between F1 and F2 in the attached image?
the joint area on brick is A2 and the joint area on ceramic is A1. The cross section of ceramic is a1.
RE: attaching two materials of different modulus of elasticity
The strain in the ceramic is NOT uniform and it appears that your model assumes that it is. In reality where you have F1, there can be no force in the ceramic. The force will increase from zero at the end to a maximum towards the centre. That force is generated by adhesive shear transfer.
I will try to give a "canned" lesson in bonded joint mechanics. When your brick is loaded, a strain will develop in the brick. That causes a difference in displacements at the END of the ceramic between the brick and the ceramic (which at that point has no load so it is not strained). The relative DISPLACEMENT between the brick and the ceramic at the end of the ceramic will cause a shear strain in the adhesive. That shear strain causes a shear stress which will cause SOME load to be transferred from the brick into the ceramic. The ceramic, now being under load, will start to strain. I stress that this is not a uniform strain. The additional strain in the ceramic then actually reduces the displacement difference between the brick and the ceramic, so the shear strain in the adhesive (caused by the displacement difference) gradually reduces. So does the shear stress.
Eventually the adhesive transfers load until the strain in the ceramic matches the strain in the brick, and then there is no displacement difference accross the adhesive layer, so ther shear strains and shear stresses are zero. (There is a corresponding reduction in strain in the brick, but given the thickness that will not be significant.)
The same effect is occurring at the other end of the ceramic as load is transferred out of the ceramic. In between the two locations where the shear stress in the adhesive decays to zero, the strain in the ceramic will be uniform.
I suggest that you try reading Hart-Smith, L.J., Design and Analysis of Adhesive Bonded Joints, Air Force Conference on Fibrous Composites in Flight Vehicle Design, Dayton OH, Sep 26-28 1972.
Failing that I can send some lecture material I have which explains this better than I can by text alone.
www.adhesionassociates.com
Regards blakmax