The Influence Of Size

: The Working 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
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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.

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.