Neck Tension - Bushing and Mandrel Sizes?

[Coyotefurharvester]

It is logical to move the brass past it's spring back, whether using a bushing(reducing diameter) or a mandrel(expanding diameter).

 

[dgeesaman]

Bushings...............I ordered a set from 0.242 to 0.250. I was very frustrated when the 0.244 and 0.245 bushings gave me exactly the same OD. I was able to return them and get two new ones.......

I’m not naming names but a mfr who sells by the set gave me the same issue.

As for the .002 minimum number, I think that’s more than what’s necessary. Perhaps she’s talking about the 0.2% offset definition of yielding. That means .002” per inch of feature size. On a 1/4” diameter that implies .0005. (I’m too lazy to look up the actual formulas today). My brass springs back from a mandrel or bushing less than .001”, more like .0005”.

It would be interesting to consider how much that stress strain curve changes for strain hardening, which is what annealing minimizes.

David

 

[PopCharlie]

I anneal (AMP) every time I reload.

me too, AMP as well...

 

[D-4297]

For an alternative view, I asked my mechanical engineer step-daughter about this. She's not a shooter, but does work in a metal fabrication shop and works with different metal alloys.

She sent me a stress-strain curve for 260 Grade Brass (also known as "cartridge brass"), which happens to be what most cases are made from. Her main point was that you need to stretch the brass by at least roughly 0.0020 of an inch to get out of the "elastic range". That's NOT stretching it by 0.0020" in diameter but 0.0020" in circumference. If you don't go beyond a 0.0020" stretch in circumference, the brass simply returns to its original shape/size. Beyond that, it's "plastic". So here's the math:

1. A .2240 bullet has a circumference of 0.7038" (0.2240 x 3.14159, a.k.a. diameter times pi),
2. Stretch that by 0.0020" means the circumference is 0.7058",
3. Doing the math backwards, that means the diameter is now 0.2247, and thus
4. Anything changing the ID by 0.0007" (0.2247 - 0.2240) is just enough to make that change "sort of" permanent.

Sort of? Spring back is due to the fact the stress-strain curve isn't flat, but the further you move up from the 0.0020"/200MPa point on the curve, the less the spring back.

Other interesting points she raised:

1. When I try to decide how much tension I want on the bullet, remember that there's only a marginal increase in real (force) tension beyond 0.0010 of neck tension, as we shooters know it, because the case neck is entering the plastic range (0.0010" diameter change = 0.0031" circumference change), and
2. If I try for 0.0005" tension, the case neck brass was only stretched by 0.0016" when I seat the bullet and the case neck is still in the elastic range. Given how step the stress/strain curve is, along with normal brass metallurgical quality inconsistencies, the actual "force" tension holding the bullet can vary a lot.
3. So, for my .222 Remington and .22-250 Remington, her input was it's best to stick between a minimum of (what she called "shooters neck tension") 0.0010" and a maximum of 0.0020". Little benefit beyond, and potential inconsistencies below.

These are approximately the same theories I came up with regarding the amount of "movement" for selecting a Bushing for .308 , and it was "down" to .3065 , and a .3075 Expander to give me the .307 - .3075 internal I was looking for . Since I anneal after every firing , I learned this batch of cases settled after six reloads , and I now get a very consistent .307 case-mouth . I'm normally running just .001 Interference fit , and SD averages 4 - 4.6 , with ES between 8 to 9 . Remember ; the more you move that Brass around , the more it will rebel , becoming inconsistent .

 

[RegionRat]

Her main point was that you need to stretch the brass by at least roughly 0.0020 of an inch to get out of the "elastic range".

Left out an important part of the dimension for strain. It isn't an absolute 0.002" it is a strain of 0.002 in/in

Strain on that chart is in inches per inch, meters per meter, or extension per unit length.

In your example, you are effectively translating the perspective of the sizing to one of hoop stress/strain and the circumference becomes the length.
The dimensions of the stress are in PSI or MPa and the dimensions for the strain are in length/length.

So the length of the material in the test is pulled by a stress, and the strain is calculated by dividing the length while under the stress by the length before the stress.
(In reality, this only holds in the elastic region but we still use the original length as the basis even after plastic flow begins.)

We define the Young's modulus by looking at the slope of the chart with a little parallel line that is offset by 0.002 strain. Beyond that point, we say we are into yield.
(Some materials can return to their original length to within less than 0.002 strain right up to that point if the stress is held below the yield point, but even then many materials, like brass, do not. That is because 0.002 is just a standard and doesn't always look good on every material plot.)

If you look real close at the lower scale on the inset, you can see where the 0.002 strain value comes from.

In your example, if the original circumferential length was 0.7038, it only takes a stretch of 0.0014" to get it into yield.

In reality, even the so called elastic region can be thought of as little springs and dampers, where the speed and duration of the stress has an effect we often call "creep" due to shear storage and shear loss buried inside the elastic modulus term. Brass is kinda magical in how useful it is for cartridges.

Not important in the sizing discussion since we are really using a trail and error process to size and measure with gage pins, carry on.

 

[222Jim]

For an alternative view, I asked my mechanical engineer step-daughter about this. She's not a shooter, but does work in a metal fabrication shop and works with different metal alloys.

She sent me a stress-strain curve for 260 Grade Brass (also known as "cartridge brass"), which happens to be what most cases are made from. Her main point was that you need to stretch the brass by at least roughly 0.0020 of an inch to get out of the "elastic range". That's NOT stretching it by 0.0020" in diameter but 0.0020" in circumference. If you don't go beyond a 0.0020" stretch in circumference, the brass simply returns to its original shape/size. Beyond that, it's "plastic". So here's the math:

1. A .2240 bullet has a circumference of 0.7038" (0.2240 x 3.14159, a.k.a. diameter times pi),
2. Stretch that by 0.0020" means the circumference is 0.7058",
3. Doing the math backwards, that means the diameter is now 0.2247, and thus
4. Anything changing the ID by 0.0007" (0.2247 - 0.2240) is just enough to make that change "sort of" permanent.

Sort of? Spring back is due to the fact the stress-strain curve isn't flat, but the further you move up from the 0.0020"/200MPa point on the curve, the less the spring back.

Other interesting points she raised:

1. When I try to decide how much tension I want on the bullet, remember that there's only a marginal increase in real (force) tension beyond 0.0010 of neck tension, as we shooters know it, because the case neck is entering the plastic range (0.0010" diameter change = 0.0031" circumference change), and
2. If I try for 0.0005" tension, the case neck brass was only stretched by 0.0016" when I seat the bullet and the case neck is still in the elastic range. Given how step the stress/strain curve is, along with normal brass metallurgical quality inconsistencies, the actual "force" tension holding the bullet can vary a lot.
3. So, for my .222 Remington and .22-250 Remington, her input was it's best to stick between a minimum of (what she called "shooters neck tension") 0.0010" and a maximum of 0.0020". Little benefit beyond, and potential inconsistencies below.

Thanks to everyone who took the time to offer their thoughts and feedback in the past month since I originally posted my question and the “alternative view”.

I learned a lot from all of you as I thought over your replies and feedback. Three things in particular – two of them related to technique and one to me being a little sloppy in my writing.

The two technique items? First, I now hold the press handle down for 6 – 8 seconds when I use a bushing die or a mandrel to allow time for the brass to “relax” in the bushing or around the mandrel, as the case may be. My case-to-case variation has been greatly reduced. Second, I put a small amount of grease on top of the bushing or the mandrel just to help it self-centre. This has reduced, but not eliminated, runout. For those interested, I’m now consistently shooting (20 shot groups at 100 m) with a CEP 90% of 0.25” – 0.30”, or a Mean Radius of 0.15” – 0.20” with my .22-250 firing 40 grain Sierra Blitzking and 40 grain Berger FBV, using IMR-3031 and Federal GM210M primers.

As to me being sloppy in my writing, I learned it’d help if I was more precise in how I describe brass stress/strain, and in particular the fact strain is expressed in terms of “inch per inch of length”. Why is this important? Well, if you have a 1” long piece of 260 Grade Brass, stretching it by 0.0020” will move it from the elastic into the plastic deformation range. But, if you have a 2” long piece of brass, then you need to stretch it by 0.0040” to get it into that elastic/plastic point. The fact I predominately shoot .224 caliber bullets means this “inch per inch” issue isn’t a huge issue. Why not? The circumference of a .224 caliber bullet is 0.7038, which for all practicality is equal to 1” when trying to read these stress/strain curves. And it’s even less of an issue with .308 caliber bullets because the circumference of them is 0.9676”! But I should have been more precise.

None of this changes the core message, but I’ve updated it to be more precise, and as a way to acknowledge the feedback and input many of you provided! So here we go…….

--------------

For an alternative view, I asked my mechanical engineer step-daughter about this. She's not a shooter, but does work in a metal fabrication shop and works with different metal alloys.

She sent me a stress-strain curve for 260 Grade Brass (also known as "cartridge brass"), which happens to be what most cases are made from. Her main point was that you need to stretch the brass by at least roughly 0.0020 of an inch per inch (“in/in”) of length to get out of the "elastic range". That's NOT stretching it by 0.0020 in/in of diameter, but 0.0020 in/in in circumference. If you don't go beyond a 0.0020 in/in stretch in circumference, the brass simply returns to its original shape/size. Beyond that, it's "plastic". So, here's the math:

1. A .2240 bullet has a circumference of 0.7037" (0.2240 x 3.14159, a.k.a. diameter times pi).
2. Let’s assume we want 0.0020” of “shooters tension”, i.e. the internal neck diameter is 0.0020” less than the bullet diameter, and thus the internal neck diameter is equal to 0.2220” (set through using a neck bushing, mandrel, or both). This 0.2220” diameter is equal to a circumference of 0.6974”.
3. When the bullet is seated, the neck circumference stretches from 0.6974” to 0.7037”, equal to an increase of 0.0063”. That happens to be 0.0090 in/in and is well into the plastic deformation range for 260 Grade Brass.

I built a little table to show the results for .224 and .308 bullets at typical “shooter’s tensions”:

Bullet​	0.2240​					Bullet​	0.3080​
pi​	3.1416​					pi​	3.1416​
Tension​	0.0005​	0.0010​	0.0015​	0.0020​		Tension​	0.0005​	0.0010​	0.0015​	0.0020​
Neck ID​	0.2235​	0.2230​	0.2225​	0.2220​		Neck ID​	0.3075​	0.3070​	0.3065​	0.3060​
Neck Circ.​	0.7021​	0.7006​	0.6990​	0.6974​		Neck Circ.​	0.9660​	0.9645​	0.9629​	0.9613​
Seated Circ.​	0.7037​	0.7037​	0.7037​	0.7037​		Seated Circ.​	0.9676​	0.9676​	0.9676​	0.9676​
Stretch​	0.0016​	0.0031​	0.0047​	0.0063​		Stretch​	0.0016​	0.0031​	0.0047​	0.0063​
Strain​	0.0022​	0.0045​	0.0067​	0.0090​		Strain​	0.0016​	0.0033​	0.0049​	0.0065​

I didn’t account for spring back, which is roughly 0.0008” based on the 260 Grade Brass stress/strain curve, but the net result is for “shooters tensions” above 0.0010”, we are safely in the plastic range. But, for .224 bullets a “shooters tension” of 0.0005” leaves us in the elastic/plastic transition zone, and for a .308 bullet that 0.0005” tension leaves us in the elastic range.

 

[RegionRat]

https://bisonballistics.com/articles/case-neck-tension-a-stress-analysis

Tag - @damoncali

You might also like the article above. It includes the concept of the variation in the material when you account for the cold work state.

In the end, even with All the King's Horses and All the King's Men (in the industry) we used trial and error to set up the ammo lines. We only provided analysis because we were required to demonstrate to our watchdogs that we were not doing anything stupid during reviews and audits.

Over time, climate exposure, captive carry when the ammo is exposed to extreme vibrations + hot/cold yet not used, etc., the difficulty was to make sure it was reliable when called upon after all the abuse.

 

[JFrank]

Wouldn’t it be simpler just to use a target to test bullet hold and follow the results ?

 

[222Jim]

Wouldn’t it be simpler just to use a target to test bullet hold and follow the results ?

But it wouldn't be as much fun (and yes, as an engineer, I'm sometimes accused of having a strange taste of fun).

 

[222Jim]

https://bisonballistics.com/articles/case-neck-tension-a-stress-analysis

Tag - @damoncali

You might also like the article above. It includes the concept of the variation in the material when you account for the cold work state.

In the end, even with All the King's Horses and All the King's Men (in the industry) we used trial and error to set up the ammo lines. We only provided analysis because we were required to demonstrate to our watchdogs that we were not doing anything stupid during reviews and audits.

Over time, climate exposure, captive carry when the ammo is exposed to extreme vibrations + hot/cold yet not used, etc., the difficulty was to make sure it was reliable when called upon after all the abuse.

I read that article shortly after I bought my AMP annealing machine. Helped me justify the expense!

 

[Dwubyd]

Other interesting points she raised:

1. When I try to decide how much tension I want on the bullet, remember that there's only a marginal increase in real (force) tension beyond 0.0010 of neck tension, as we shooters know it, because the case neck is entering the plastic range (0.0010" diameter change = 0.0031" circumference change), and

Wow, that is a really good point. Go step daughter!

The spring back should be in the vicinity of 0.0007". Spring back is the brass following the dotted line on the graph, reducing force as the deformation decreases. Once the dotted line reaches the x axis, it is at a different point on the Strain axis, so there is permanent deformation.

 

[SeabeeKen]

I use sac bushings and find i have to go .001 smaller than the math tells me. So far this has only applied to my sac bushings