Volume Change in Tool Steel on Hardening and Tempering
Relative volume of water hardened tool steel rods of four diameters, measured before hardening, dead hard, and after tempering to yellow, blue and grey, from tests by Fromme published in 1918. A reference summary of published practice and not an Aobo Steel specification.
What the figures measure
A piece of steel always gains volume when it is hardened. The gains are small enough to be ignored on a bush or a punch, and large enough to scrap a gauge or a long die section that was finished to size before the quench. The reason is that martensite occupies more space than the annealed structure it replaces, so the harder the quench and the more of the section that transforms, the more the piece grows.
The table below is the check on how far that goes in practice. A series of steel rods of four different thicknesses was hardened under the same conditions and then tempered through a succession of colours, and their volumes were measured against the volume of the same rod in the annealed state. Volume is the figure that matters for a block or a die insert, because a change in volume shows up as a change in every dimension at once.
Volume of hardened and tempered rods
Relative volume, unhardened rod taken as unity
| Condition of rod | 7 mm rod | 4.2 mm rod | 2.65 mm rod | 2.55 mm rod |
|---|---|---|---|---|
| Unhardened | 1.00000 | 1.00000 | 1.00000 | 1.00000 |
| Dead hard | 1.00772 | 1.01000 | 1.01285 | 1.01210 |
| Tempered, yellow | 1.00347 | 1.00495 | 1.00660 | 1.00620 |
| Tempered, blue | 1.00217 | 1.00425 | 1.00370 | 1.00205 |
| Tempered, grey | 0.99957 | 1.00060 | 1.00055 | 0.99930 |
Source, the relative volume table by Fromme on printed page 39 of The Heat Treatment of Tool Steel (Harry Brearley), which is PDF page 57 of the copy consulted. Every figure was read from the 500 dpi page image, not from the OCR text layer.
Volume of the unhardened rod is taken as unity, so 1.00772 means a rise of 0.772 per cent. The rods were hardened under the same conditions and then tempered. Values below 1.00000 are a net contraction against the annealed rod. Rods are round bar of the diameter named; the source gives no length, so the figures are for the volume of the piece as a whole.
What the table shows
Quenching grows the piece, and the thin rod grows most. The 7 mm rod comes out of a dead hard quench 0.772 per cent larger than it went in. The 2.65 mm rod comes out 1.285 per cent larger, roughly two thirds more movement for a section a third of the diameter. The numbers are the whole volume of the piece, so a block three inches thick will move less than a slender insert of the same steel, which is the opposite of what a shop usually allows for.
Tempering gives part of the growth back. On the 7 mm rod a yellow temper drops the figure to 1.00347, a blue temper to 1.00217, and a grey temper to 0.99957, which is finer than the annealed rod it started from. The same sequence runs on the other three diameters. The recovery is not complete and not even: the thin rods stop further short of their original volume than the thick one, so a thin section is left larger than a thick one after the same temper.
For a shop the reading is straightforward. Leave stock for the quench on any part that has to hold size, and expect the stock to be larger on a slender section than on a heavy one. Where the temper is carried high the piece may come back under its finished size instead of over it, and that direction of error cannot be ground out. If the drawing allows it, harden first and finish afterwards; where it does not, the figure in the table is the allowance to work to.
Where this matters most
The grades most often caught by it are the ones taken to full hardness with a fast quench. O1 tool steel is water or oil quenched and moves more than the air hardening grades, and D2 is quenched from a higher temperature for the carbide it carries. A2 and the other air hardening grades are the usual answer when dimensional movement is the controlling problem, since they quench in still air and the section cools evenly.
Related reference data
Growth and shrinkage measured on the standard grades is on our tool steel size change in heat treatment page. For the quench sequences themselves see the tool steel heat treatment guide, and for the hardening problem that follows a fast quench see quench cracking in tool steel.
Compiled from The Heat Treatment of Tool Steel (Harry Brearley), the Fromme relative volume table on printed page 39, with the surrounding discussion of critical density changes on printed pages 38 and 39. The figures are reproduced from the published table and are a reference summary rather than an Aobo Steel specification.