I've puzzled over this topic for some time, and have not seen any definitive article on what happens to brass when it is fired and resized. I finally put some time into it, and this is what I came up with. This post has been made to share what I found, and will welcome any comments on whether or not it makes any sense. I'll admit the results surprised me, and I wonder if I've made a slip in my calculations/assumptions somewhere. In any case here it is.
First, I stumbled on this rather dated article on the properties of 70-30 Brass:
Tensile Stress-Strain Curves of a 70-30 Brass
It contains some rather useful data and graphs. In particular figure 4 (Adobe page 13), shows the stress-strain relationship of cartridge brass in 6 different annealed states. For this discussion I will only refer to the top normal annealed state, which is probably quite close to as supplied annealed brass. This graph shows the stress in brass as it is stretched well beyond yield. Figure 1 shows what it does before yield.
I first calculated the strain a 6BR neck undergoes when a bullet is loaded with 0.001" neck tension, and then fired in a chamber with 0.003 additional clearance. I worked that out to be simply 0.004/0.268 or 0.015 strain, for as fired, and 0.001/0.268 or 0.0037 for as seated. This is well beyond the elastic limit which would be reached at less than 0.001 strain (figure 1). What happens when you stretch brass this much is that it just follows the stress strain line up to the strain level of 0.015. This corresponds to a stress level of 28,000 psi. When the cartridge is fired this stress level is retained as the new yield limit. When you resize it, it undergoes the same stress level, but in reverse. It work hardens again, up to a stress level of 40,000 psi. The graph at the end of this post shows this graphically. The yellow highlighted lines are the first firing and resizing cycle. The green the second, and the pink the third. This is a summary of the stresses:
Starting Point - Before Seating, After Seating, After Firing, After Sizing
Annealed - 17,000, 24,000, 28,000, 40,000
Fired 1X, Sized 1X - 40,000, 47,000, 56,000, 80,000
Fired 2X, Sized 2X - 80,000, 92,000, 110,000, 150,000
What you can see is that the brass work hardens very quickly and gains higher and high yield strength. What are the conclusions?
1. Brass yields when we seat bullets. Since it is yielding the stress-strain curve is quite flat. So double the seating tension only increases stress a bit, and far from double. On the first firing 0.001" would be about 24,000 psi, while 0.002" is 26,000, or only an 8% increase in seating grip.
2. One firing and resizing cycle work hardens brass a lot. It is virtually doubling each cycle. If you mix brass of different firing cycles there will be huge differences in neck tension.
3. 150,000 yield is reached in 3 firing cycles. That is around the limit of what brass can take. It seems a miracle that it lasts much beyond that. Perhaps I have an error somewhere... But, it does suggest more frequent annealing is better than less frequent.
4. The modulus of elasticity of brass is 17 million psi. One thou neck tension results in 67,000 psi if the brass is still below yield. This will be reached after 2 firings. At that point neck tension starts to go up significantly with increased fit. For example after the third firing yield will be 150,000. One thou neck tension will give 67,000 stress, and two thou now will be double at 134,000 psi. This is because there is no yielding.
I have some other thoughts on the affect of annealing but will leave that for another post.
Comments? Questions?
Edit: Added point #4.
First, I stumbled on this rather dated article on the properties of 70-30 Brass:
Tensile Stress-Strain Curves of a 70-30 Brass
It contains some rather useful data and graphs. In particular figure 4 (Adobe page 13), shows the stress-strain relationship of cartridge brass in 6 different annealed states. For this discussion I will only refer to the top normal annealed state, which is probably quite close to as supplied annealed brass. This graph shows the stress in brass as it is stretched well beyond yield. Figure 1 shows what it does before yield.
I first calculated the strain a 6BR neck undergoes when a bullet is loaded with 0.001" neck tension, and then fired in a chamber with 0.003 additional clearance. I worked that out to be simply 0.004/0.268 or 0.015 strain, for as fired, and 0.001/0.268 or 0.0037 for as seated. This is well beyond the elastic limit which would be reached at less than 0.001 strain (figure 1). What happens when you stretch brass this much is that it just follows the stress strain line up to the strain level of 0.015. This corresponds to a stress level of 28,000 psi. When the cartridge is fired this stress level is retained as the new yield limit. When you resize it, it undergoes the same stress level, but in reverse. It work hardens again, up to a stress level of 40,000 psi. The graph at the end of this post shows this graphically. The yellow highlighted lines are the first firing and resizing cycle. The green the second, and the pink the third. This is a summary of the stresses:
Starting Point - Before Seating, After Seating, After Firing, After Sizing
Annealed - 17,000, 24,000, 28,000, 40,000
Fired 1X, Sized 1X - 40,000, 47,000, 56,000, 80,000
Fired 2X, Sized 2X - 80,000, 92,000, 110,000, 150,000
What you can see is that the brass work hardens very quickly and gains higher and high yield strength. What are the conclusions?
1. Brass yields when we seat bullets. Since it is yielding the stress-strain curve is quite flat. So double the seating tension only increases stress a bit, and far from double. On the first firing 0.001" would be about 24,000 psi, while 0.002" is 26,000, or only an 8% increase in seating grip.
2. One firing and resizing cycle work hardens brass a lot. It is virtually doubling each cycle. If you mix brass of different firing cycles there will be huge differences in neck tension.
3. 150,000 yield is reached in 3 firing cycles. That is around the limit of what brass can take. It seems a miracle that it lasts much beyond that. Perhaps I have an error somewhere... But, it does suggest more frequent annealing is better than less frequent.
4. The modulus of elasticity of brass is 17 million psi. One thou neck tension results in 67,000 psi if the brass is still below yield. This will be reached after 2 firings. At that point neck tension starts to go up significantly with increased fit. For example after the third firing yield will be 150,000. One thou neck tension will give 67,000 stress, and two thou now will be double at 134,000 psi. This is because there is no yielding.
I have some other thoughts on the affect of annealing but will leave that for another post.
Comments? Questions?
Edit: Added point #4.
