Cubic void in center of sphere

[Nataddrho]

I want to know by how much the external compression strength is weakened by introducing a cubic void into the center of a sphere.

I am an electrical engineer with a basic but not fully functional understanding of continuum mechanics, and I figured one of you guys could probably run a few quick simulations in the time it would take me to learn the basics.

I've read a few white papers on thick spherical shells and less than 50 percent shell thickness to sphere radius not much changes compared to a solid sphere. The cubic void will probably be around 75 percent sphere radius.

The spherical material is phenolic resin, the application has to do with marine communications.

Thanks!!!

 

[TheTick]

In addition to the missing material, there will be weakness introduced by the stress concentrations at the cube corners. If I was running the simulation, I would account for that, most likely by letting auto-refinement churn away repeatedly until convergence.

 

[TheTick]

You may also take the above as a piece of design advice: eliminate sharp corners.

 

[rb1957]

if the cube side length is 3/4 of the radius, then won't the diagonal, sqrt(2)*0.75r = 1.06r, pierce the side of the sphere ?

I'd guess the maximum practical cube is about 0.5r, with the corner being sqrt(3)*.5r = 0.866r.

How'd yo make this void ? lost wax method ?

another day in paradise, or is paradise one day closer ?

 

[Nataddrho]

No. Cube length is 75% diameter of sphere. It will fit inside.

What I want is something like this: eliminate corners as suggested. Here is a quick simulation I made using a cylinder void instead of a cube void, with a static compression test, and visually it shows that the stress distribution doesn't creep near the void when there is significant thickness. I still don't have the knowledge of how to accurately model dynamic impact tests for fracture toughness, for example, if this were a drop test.

 

[rb1957]

well there's a significant difference between "The cubic void will probably be around 75 percent sphere radius." and "Cube length is 75% diameter of sphere.".

what shape do you want ? cube or cylinder ?? A cube with sharp corners should show more stress concentration.

What if you modelled your void as a sphere ?

another day in paradise, or is paradise one day closer ?

 

[Nataddrho]

Moving target has come to rest.

Final dimensions:

Sphere radius: 71.25mm
Cylinder radius: 18.75mm
Cylinder height: 22.5mm

Spherical material properties:
Compressive strength: 40
Compressive modulus: 4000
Shock impact Charpy (Kj/m^2): 12
Hardness: Shore 90D

Cylinder material properties:
Air.

Final Question: "How much weaker is axial compression with cylindrical void compared to without".

 

[rb1957]

even in compression, I suspect the sphere breaks by (tension) rupture around the diameter (normal to the load axis).

I suspect that this void has little impact on the load capacity of the sphere, maybe 10% reduction ?

the orientation of the void would have a 2nd order effect.

how are you going to make the void ?

another day in paradise, or is paradise one day closer ?

 

[Nataddrho]

You asked this question twice so you must be curious.

The void is actually a low hardness material, Shore 40A potting material. Comparatively it is negligible in compression strength. The sphere material is a thermoset that is molded and cured around the inner part for a specialized application. The casting will have to be done at low pressures or as a liquid pour to avoid deforming the inner part.

 

[rb1957]

what happens if the inner "void" deforms under loads ?

A filled "void" is not the same as an empty void.

another day in paradise, or is paradise one day closer ?

 

[Nataddrho]

Your feeling of 10% reduction is valid, because a lot of the time "feel" from someone experienced is valuable, which is what that sounds like.

Do you have the ability to run a simulation for me to verify?

Nate

 

[rb1957]

do you have FE analysis software ?

another day in paradise, or is paradise one day closer ?

 

[Nataddrho]

No, not really.

 

[rb1957]

make one and see ...

another day in paradise, or is paradise one day closer ?

 

[Nataddrho]

I don't have software. You can do it.

 

[rb1957]

I could, but I don't want to !?

Do you have "proper" material properties for the two materials ?

another day in paradise, or is paradise one day closer ?

 

[GregLocock]

If the fill material has a poissons ratio of 0.5, like most rubber like materials, then it is practically volumetrically incompressible, and so can't be ignored. It will have a stiffening effect.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[Nataddrho]

Thats good to know.

 

[rb1957]

but I think a key failure mode is tension along the diameter perpendicular to the load axis. Then it volumetric constraint of the "void" is less critical (tho' important in any case) then the connection (glue?) between the "void" and the body.

A different poission's ratio for the "void" filler would have interesting effects.

another day in paradise, or is paradise one day closer ?