From: bercov@bevsun.bev.lbl.gov (John Bercovitz)
Subject: Cast bullet hardness (medium long)
Organization: Lawrence Berkeley Laboratory

I recently bought 2K of the #68 BB H&G 200 gn semi-wadcutter from Western
Nevada Bullet Company.  The attraction was that they're cheap: $40/K delivered
anywhere.  I got good groups from these bullets when I tested them in my GC 
which was held in a Ransom Rest.  Best grouping came at a little over 800 fps
with Unique and anywhere in the 800 to 900 fps area with Bullseye.  I got
no barrel leading even at velocities over 900 fps.  Groups were about twice
the size of what I get with the Hornady #4515 which is a jacketed version of 
the same bullet.  Defintely more than good enough for practice - you do your
part and most of them will be in the X-ring with some in the 10-ring at 25 yds.

Western Nevada's literature says that their cast bullets are 7 1/2% alloy.
I felt that was a little cryptic so I called them (702-885-0310) to find out 
what the alloy is.  They said it was about 6% antimony and 1% tin. I wanted
to make a check of the bullet hardness to see if it corresponded with this
alloy but I don't have a Brinell hardness tester.  So I looked up how to do
hardness testing in "Marks' Std Hdbk for Mech Engrs" and found it was pretty
easy to do.  I used a 1/8 inch (actually .1249) diameter ball because I wanted
to make a very small impression since the nose of the bullet isn't all that
big.  I used a good spring scale to put 9 pounds of force on the ball for 30
seconds.  With an optical comparator (magnifying glass and a scale) I got
an impression diameter of 0.65 mm.  This calculates out to a BHN of 12 which
is about what it should be for this alloy:

D = .125" = 3.17 mm
P = 9 lb = 4.08 kg
d = .65 mm

BHN = 4.08/{(pi*3.17/2)*[3.17-(3.17^2-.65^2)^0.5]} = 12

I didn't do an error analysis to see how sensitive the equation is, but I
should since it would be edifying and it's trivial to do so.

I found that the .65 mm diameter of the impression was hard to read so
next time I will go to a 3/16 inch or even 1/4 inch ball with correspondingly
higher P to drive it.

Disclaimer: I have nothing to do with Western Nevada other than I bought 
some bullets from them.

Clip and save:
----------------------------------------------------------------------------
Below is what I've cribbed from "Marks' Std Hdbk for Mech Engrs":

BHN = P/{(pi*R)*[D-(D^2-d^2)^0.5]}

Where:
BHN = Brinell Hardness Number
P = load on the indenter in kilograms
D = diameter of the indenter in mm
R = radius of the indenter in mm
d = diameter of the impression in mm

The load should be kept on the indenter for 15 seconds for most 
materials but 30 seconds for soft materials.  Longer periods are 
required for materials which exhibit creep at room temperature
(for example, lead).

Standard loads are 3000, 1500, 500 kg with 250, 125, & 100 kg 
sometimes used for softer materials.

The normal indenter diameter is 10 mm.  If another indenter diameter 
is used, the diameter and load should be noted in the report.

If another indenter diameter is used, load P should be approximately 
30 D^2 for iron or steel, 5 D^2 for brass, bronze and other soft metals, 
and D^2 for extremely soft materials.

A hardened steel bearing ball is an adequate indenter up to a material 
hardness of 450.

The depth of the impression should not exceed 1/10th of the sample 
thickness.

No part of the plastic flow around the impression should reach a free 
edge of the sample.

The official rules are found in ASTM E10-61T, "Methods of Brinell Hardness 
Testing".

      JHBercovitz@lbl.gov    (John Bercovitz)

From: bercov@bevsun.bev.lbl.gov (John Bercovitz)
Subject: Z Re: Cast bullet hardness
Organization: Lawrence Berkeley Laboratory

In article <36804@mimsy.umd.edu> bercov@bevsun.bev.lbl.gov 
(John Bercovitz) writes:
[........]
#Below is what I've cribbed from "Marks' Std Hdbk for Mech Engrs":
#
#BHN = P/{(pi*R)*[D-(D^2-d^2)^0.5]}
#
#Where:
#BHN = Brinell Hardness Number
#P = load on the indenter in kilograms
#D = diameter of the indenter in mm
#R = radius of the indenter in mm
#d = diameter of the impression in mm
#
#  The load should be kept on the indenter for 15 seconds for most 
#materials but 30 seconds for soft materials.  Longer periods are 
#required for materials which exhibit creep at room temperature
#(for example, lead).
#  Standard loads are 3000, 1500, 500 kg with 250, 125, & 100 kg 
#sometimes used for softer materials.
#  The normal indenter diameter is 10 mm.  If another indenter diameter 
#is used, the diameter and load should be noted in the report.
#  If another indenter diameter is used, load P should be approximately 
#30 D^2 for iron or steel, 5 D^2 for brass, bronze and other soft metals, 
#and D^2 for extremely soft materials.
#  A hardened steel bearing ball is an adequate indenter up to a material 
#hardness of 450.
#  The depth of the impression should not exceed 1/10th of the sample 
#thickness.
#  No part of the plastic flow around the impression should reach a free 
#edge of the sample.
#  The official rules are found in ASTM E10-61T, "Methods of Brinell Hardness 
#Testing".

One of you told me that your LBT hardness tester works by measuring the
depth of the indentation rather than the diameter.  I thought that was
interesting so I used a little geometry to figure out what the relation-
ship between diameter of the impression and the depth of the impression
is.  Using the same symbols as above but adding:
h = depth of impression in mm
I found that h = (1/2)[D-(D^2-d^2)^0.5]
which is mighty convenient since then the formula for Brinell Hardness
Number reduces to:

BHN = P/( pi * D * h )

this is surely a lot easier to calculate than the previous formula,
and, since it's linear, it lends itself to direct readout from a 
measuring device sans computer.  You just have to be a little more
careful in your measuring since you're measuring much smaller
numbers.  However, a dial indicator measures these sorts of numbers
easily.  Also, good surface preparation would be advisable since
you won't have several diameters to measure for an average.

I then went on to calculate the area of the indenter ball which is in
contact with the impression it has made in the lead.  This is called
a "spherical segment" in geometry: the area of the curved surface of
a sphere which is inside the boundary of a circle drawn on the sphere.
It turns out that the area of a spherical segment is:
    A = pi * D * h
So Brinell hardness is just the load on the ball divided by the area
of the lead sample in contact with the surface of the ball.

Since 1/8" bearing balls and spring scales reading in pounds are readily
available in this country, I made up a little chart for BHN using a 20#
load on a 1/8" ball:

P = 20 pounds = load on indenter ball
d = diameter of impression in millimeters
h = depth of impression in millimeters
BHN = Brinell Hardness Number

      d                h                BHN
     .60             .029               31.8 
     .65             .034               27.0
     .70             .039               23.3
     .75             .045               20.2
     .80             .051               17.8
     .85             .058               15.7
     .90             .065               14.0
     .95             .073               12.5
    1.00             .081               11.3
    1.05             .089               10.2
    1.10             .098                9.2
    1.15             .108                8.4
    1.20             .118                7.7

    JHBercovitz@lbl.gov    (John Bercovitz)