The Influence Of Size
Category: HEAT TREATMENT OF STEEL
The size of the piece influences the physical properties obtained in
steel by heat treatment. This has been worked out by E. J. Janitzky,
metallurgical engineer of the Illinois Steel Company, as follows:
With an increase in the mass of steel there is a corresponding
decrease in both the minimum surface hardness and depth hardness,
when quenched from the same temperature, under identical conditions
of the quenching medium. In other words, the physical properties
obtained are a function of the surface of the metal quenched for
a given mass of steel. Keeping this primary assumption in mind, it
is possible to predict what physical properties may be developed in
heat treating by calculating the surface per unit mass for different
shapes and sizes. It may be pointed out that the figures and chart
that follow are not results of actual tests, but are derived by
calculation. They indicate the mathematical relation, which, based
on the fact that the physical properties of steel are determined
not alone by the rate which heat is lost per unit of surface, but
by the rate which heat is lost per unit of weight in relation to
the surface exposed for that unit. The unit of weight has for the
different shaped bodies and their sizes a certain surface which
determines their physical properties.
For example, the surface corresponding to 1 lb. of steel has been
computed for spheres, rounds and flats. For the sphere with a unit
weight of 1 lb. the portion is a cone with the apex at the center
of the sphere and the base the curved surface of the sphere (surface
exposed to quenching). For rounds, a unit weight of 1 lb. may be
taken as a disk or cylinder, the base and top surfaces naturally do
not enter into calculation. For a flat, a prismatic or cylindrical
volume may be taken to represent the unit weight. The surfaces
that are considered in this instance are the top and base of the
section, as these surfaces are the ones exposed to cooling.
The results of the calculations are as follows:
Diameter Surface per
of sphere pound of steel
8 in. 2.648 sq. in.
6 in. 3.531 sq. in.
4 in. 5.294 sq. in.
3 in. 7.062 sq. in.
2 in. 10.61 sq. in.
XY = 21.185.
Diameter Surface per
of round pound of steel
8.0 in. 1.765 sq. in.
6.0 in. 2.354 sq. in.
5.0 in. 2.829 sq. in.
4.0 in. 3.531 sq. in.
3.0 in. 4.708 sq. in.
2.0 in. 7.062 sq. in.
1.0 in. 14.125 sq. in.
0.5 in. 28.25 sq. in.
0.25 in. 56.5 sq. in.
XY = 14.124.
Thickness Surface per
of flat pound of steel
8.0 in. 0.8828 sq. in.
6.0 in. 1.177 sq. in.
5.0 in. 1.412 sq. in.
4.0 in. 1.765 sq. in.
3.0 in. 2.345 sq. in.
2.0 in. 3.531 sq. in.
1.0 in. 7.062 sq. in.
0.5 in. 14.124 sq. in.
0.25 in. 28.248 sq. in.
XY = 7.062.
Having once determined the physical qualities of a certain specimen,
and found its position on the curve we have the means to predict the
decrease of physical qualities on larger specimens which receive
the same heat treatment.
When the surfaces of the unit weight as outlined in the foregoing
tables are plotted as ordinates and the corresponding diameters as
abscissae, the resulting curve is a hyperbola and follows the law
XY = C. In making these calculations the radii or one-half of
the thickness need only to be taken into consideration as the heat
is conducted from the center of the body to the surface, following
the shortest path.
The equations for the different shapes are as follows:
For flats XY = 7.062
For rounds XY = 14.124
For spheres XY = 21.185
It will be noted that the constants increase in a ratio of 1, 2,
and 3, and the three bodies in question will increase in hardness
on being quenched in the same ratio, it being understood that the
diameter of the sphere and round and thickness of the flat are
Relative to shape, it is interesting to note that rounds, squares,
octagons and other three axial bodies, with two of their axes equal,
have the same surface for the unit weight.
Size Length Surface Weight Surface for 1 lb.
2 in. Sq. 12 in. 96.0 sq. in. 13.60 lb. 7.06 sq. in.
2 in. Round 12 in. 75.4 sq. in. 10.68 lb. 7.06 sq. in.
Although this discussion is at present based upon mathematical
analysis, it is hoped that it will open up a new field of investigation
in which but little work has been done, and may assist in settling
the as yet unsolved question of the effect of size and shape in
the heat treatment of steel.
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