{ "id": "763dfc1da20ac2ffe3925c448a246069ee3b9d58", "text": "XVIII. Experiments on the elasticity and strength of hard and soft steel. In a Letter to Thomas Young, M. D. For. Sec. R. S. By Mr. Thomas Tredgold, Civil Engineer.\n\nRead March 25, 1824.\n\nSir,\n\nLondon, Dec. 16, 1823\n\nIf a piece of very hard steel be softened, it is natural to suppose that the operation will produce a corresponding change in the elastic power, and that the same load would produce a greater flexure in the soft state than in the hard one, when all other circumstances were the same. Mr. Coulomb inferred from some comparative experiments on small specimens, that the state of temper does not alter the elastic force of steel; and your Experiments on Vibration led to the same conclusion (Nat. Philos. II. 403). But the subject appeared to require further investigation, and particularly because it afforded an opportunity of ascertaining some other facts respecting steel, which had not been before examined.\n\nIn making the experiments which I am about to describe, each bar was supported at its ends by two blocks of cast iron. These blocks rested upon a strong wooden frame. The scale to contain the weights was suspended from the middle of the length of the bar, by a cylindrical steel pin of about \\( \\frac{3}{8} \\)ths of an inch in diameter. And as in experiments of this kind it is desirable to have the means of raising the weight from the bar, without altering its position, in order to know when the load is sufficient to produce a permanent change of structure, I have a powerful screw with a fine\nthread fixed over the center of the apparatus, by which the scale can be raised or lowered, when the cords on which the screw acts are looped on to the cross pin by which the scale is suspended.\n\nTo measure the flexure, a quadrantal piece of mahogany is fixed to the wooden frame; two guides are fixed on one edge of the mahogany, in which a vertical bar slides, and gives motion to an index. The bar and index are so balanced, that one end of the bar bears with a constant pressure on the specimen, and the graduated arc over which the index moves is divided into inches, tenths, and hundredths; and thousands are measured by a vernier scale on the end of the index. There is a screw at the lower end of the vertical bar, by which the index is set to zero, when necessary. Plate XX.\n\nThe first trials were made with a bar of blistered steel of a very good quality. It was drawn out by the hammer to the width and thickness I had fixed upon, and then filed true and regular. It was then hardened, and tempered to the same degree of hardness as common files.\n\nThe total length of the bar was 14 inches; the distance between the supports 13 inches; the breadth of the bar 0.95 inches, and the depth 0.375 inches; the thermometer varied from $55^\\circ$ to $57^\\circ$ at the times of trial.\n\n| lbs. | inches |\n|------|--------|\n| 54 | 0.02 |\n| 82 | 0.03 |\n| 110 | 0.04 |\n\nThe last load remained on the bar some hours, but produced no permanent alteration of form.\nThe temper of the bar was then lowered to a rather deep straw yellow, and it was tried again; when the same loads produced exactly the same flexures as before.\n\nThe temper was then lowered till the colour was an uniform blue, or spring temper; and the trials were repeated with the same loads; but the flexures were still the same.\n\nIt was now heated to redness and very slowly cooled. In this state the same loads still produced the same flexures; and the load of 110 lbs. caused no permanent change of form.\n\nThe bar was hardened again, and made very hard; in this state the same loads produced the same flexures; and\n\n| lbs. | inches |\n|------|--------|\n| 300 | 0.115 |\n| 350 | 0.130 |\n| 580 | broke |\n\nWhen the bar was relieved from the load of 350 lbs. it retained a permanent flexure of 0.005 inches, which increased to 0.01 with the addition of 10 lbs. to the load.\n\nI found that a bar of much greater length might be tempered without difficulty, and therefore had another bar made of the same kind of steel; the length of which being 25 inches, about double the flexure could be given with the same strain upon the material, and therefore any small degree of difference in the elastic force might be more easily detected, for the preceding experiments are sufficient to show that if there be any difference, it must be extremely small.\n\nThe breadth of this bar was 0.92 inches; the depth 0.36 inches; and the distance between the supports 24 inches. It was soft, so as to yield easily to the file.\nwith a load of 18.6 the depression in the middle was 0.05\n\n| lbs. | inches. |\n|------|---------|\n| 37.0 | 0.10 |\n| 47.0 | 0.127 |\n\nThe bar was then hardened, so that a file made no impression on any part of it, and the same loads did not produce flexures that were sensibly different from those in the soft state.\n\nI then lowered the temper till it assumed an uniform straw colour;\n\n| lbs. | inches. |\n|------|---------|\n| 47 | 0.127 |\n| 85 | 0.230 |\n| 130 | 0.350 |\n| 150 | 0.400 |\n\nThe load of 150lbs. produced a permanent set of 0.012, but 130lbs. produced no sensible effect. The loading was continued, and with 185 the depression in the middle was 0.50\n\n| lbs. | Inches. |\n|------|---------|\n| 385 | 1.04 |\n\nWhen 385lbs. had been upon the bar about a minute, it emitted a faint creaking sound, and consequently I ceased to add fresh weights; in about fourteen minutes the bar broke, exactly in the middle of the length.\n\nOn comparing the fractures of the specimens, there was no apparent difference except in colour. The grain was fine, and equal; the small sparkles of metallic lustre abundant, and equally diffused; but in the harder specimen they had a whiter ground.\n\nFrom these experiments it appears that the elastic force of steel is sensibly the same in all states of temper.\n\nThe height of the modulus of elasticity, calculated by the\nformula you have given in your Nat. Phil. (Vol. II. p. 48) is, according to the first experiment, $8,827,300$ feet. And according to the second experiment $8,810,000$ feet.\n\nNow the height of the modulus, as you had determined it for steel by Experiments on Vibration, is $8,530,000$ feet. (Nat. Phil. II. p. 86.) The modulus for cast steel calculated from Duleau's experiments (Essai Théorique et Experimental sur le Fer Forcé, p. 38) is $9,400,000$ feet, and for German steel $6,600,000$ feet.\n\nThe force which produces permanent alteration is to that which causes fracture in hard steel, as $350:580$; or as $1:1.66$ in the same steel of a straw yellow temper as $150:385$, or as $1:2.56$.\n\nWhen the tension of the superficial particles at the strain which causes permanent alteration, is calculated by the formula given in my Essay on the Strength of Iron, p. 146, 2nd Edition, it is $45,000$ lbs. upon a square inch in tempered steel; and the absolute cohesion $115,000$ lbs. Mr. Rennie found the direct cohesion of blistered steel to be $133,000$ lbs. (Philosophical Transactions for 1818.)\n\nBut in the very hard bar, the strain which produced permanent alteration was $51,000$ lbs. for a square inch, and the absolute cohesion only $85,000$ lbs.\n\nFrom these comparisons I think it will appear, that in the hardening of steel, the particles are put in a state of tension among themselves, which lessens their power to resist extraneous force. The amount of this tension should be equal to the difference between the absolute cohesion in different states. Taking Mr. Rennie's experiment as the measure of cohesion in the soft state, it will be $133,000 - 115,000 =$\n18,000lbs. for the tension with a straw yellow temper; and \n\\[133,000 - 85,000 = 48,000\\]lbs. for the tension in hard steel. \nAnd if this view of the subject be correct, the phenomena of \nhardening may be explained in this manner, which nearly \nagrees with what you have observed in your Lectures I, \np. 644: after a piece of steel has been raised to a proper \ntemperature, a cooling fluid is applied capable of abstracting \nheat more rapidly from the surface than it can be supplied \nfrom the internal parts of the steel. Whence the contraction \nof the superficial parts round the central ones which are ex-\npanded by heat; and the contraction of the central parts in \ncooling, while they are extended into a larger space than they \nrequire at a lower temperature, produces that uniform state \nof tension, which diminishes so much the cohesive force in \nhard steel. The increase of bulk by hardening agrees with \nthis explanation; and it leads one to expect, that any other \nmetal might be hardened if we could find a means of \nabstracting heat with greater velocity than its conducting \npower.\n\nI am, Sir,\n\nYour most obedient Servant,\n\nTHOMAS TREDGOLD.\n\nTo Dr. Thomas Young,\n&c. &c.", "source": "olmocr", "added": "2026-01-12", "created": "2026-01-12", "metadata": { "Source-File": "/home/jic823/projects/def-jic823/royalsociety/pdfs/107720.pdf", "olmocr-version": "0.3.4", "pdf-total-pages": 8, "total-input-tokens": 12728, "total-output-tokens": 2536, "total-fallback-pages": 0 }, "attributes": { "pdf_page_numbers": [ [ 0, 0, 1 ], [ 0, 1526, 2 ], [ 1526, 2997, 3 ], [ 2997, 4509, 4 ], [ 4509, 4509, 5 ], [ 4509, 5881, 6 ], [ 5881, 7552, 7 ], [ 7552, 8736, 8 ] ], "primary_language": [ "en", "en", "en", "en", "None", "en", "en", "en" ], "is_rotation_valid": [ true, true, true, true, true, true, true, true ], "rotation_correction": [ 0, 0, 0, 0, 0, 0, 0, 0 ], "is_table": [ false, false, false, false, false, false, false, false ], "is_diagram": [ false, false, false, false, true, false, false, false ] }, "jstor_metadata": { "identifier": "jstor-107720", "title": "Experiments on the Elasticity and Strength of Hard and Soft Steel", "authors": "Thomas Tredgold", "year": 1824, "volume": "114", "journal": "Philosophical Transactions of the Royal Society of London", "page_count": 8, "jstor_url": "https://www.jstor.org/stable/107720" } }