THE INFLUENCE OF SIZE

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:

FIG. 55.—Effect of size on heating.

"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:

TABLE 20.—SPHERE
Diameter of sphere	Surface per pound of steel
X	Y
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.

TABLE 21.—ROUND
Diameter of round	Surface per pound of steel
X	Y
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.

TABLE 22.—FLAT
Diameter of flat	Surface per pound of steel
X	Y
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 abscissæ, 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 equal.

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.

For example:

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.