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FORMULA FOR ELONGATION OF RAILS IN THE
By M. H. WICKHORST
The drop test of rails is primarily a means of testing their ductility and, when first used, the height of drop that the rails would stand without breaking was naturally used as the measure of ductility. In 1891 Dr. P. H. Dudley developed a means of determining directly the ductility by measuring the stretch between a series of prick punch marks placed on the part of the rail placed in tension. This method has come into general use but the simple height of drop is thought by some to be perferable as the operation of testing can be carried out more quickly and the height of drop can be adjusted more accurately than the per cent. of stretch in one inch can be measured. This paper is a discussion of the relation between the height of drop and the elongation of the outermost fibers in tension, and presents also a formula by which the height of drop necessary to produce a given elongation, or the elongation that will be produced by a given height of drop, can be calculated.
The factors of which the elongation is a function, and which need consideration in the present discussion, are the height and weight of drop, the weight and section of the rail and the composition of the steel, mainly the carbon content.
The elongation within the elastic limit would increase directly as the foot-pounds of load applied, which for a tup of 2,000 pounds would be a height of drop of less than one foot. Beyond the elastic limit and for heights of drop usual for the first blow, the elongation would be expected also to vary about as the height of drop and this has been confirmed by experimental determinations. (See Report 1, Proceedings American Railway Engineering Association for 1911, Vol. 12, Part 2, page 392.)
Within the elastic limit, the elongation would vary inversely as the first power of the section modulus and within ranges of height of drop usual for the first blow, would be expected to follow about the same law. The writer is not aware, however, that it has been determined from experimental data, how closely this law is followed.
The deflection of the rail on the first blow (which is a measure of the stiffness) decreases as the carbon increases and likewise the elongation of the fibers in tension decreases with increase of carbon. The quantitative effect of carbon on the elongation on the first blow of the drop was worked out for 80 lb. A.R.A. type A rails and the results of the research were presented in a diagram in Report 40 on the “Influence of Carbon on the Properties of Rails.” (See Proceedings American Railway Engineering Association for 1915, Vol. 16, p. 165.) Taking the curves of elongation on the first blow for head tension and base tension as a basis of calculation, it figures out that each.01 per cent. change in carbon causes a change of approximately one per cent. in the elongation on the first blow, when the elongation with carbon at .70 per cent. is taken as a basis of comparison.
If the elongation at .70 per cent. carbon is taken at 100, and the carbon is expressed in .01 per cent., then the elongation varies inversely as the carbon plus 30. This is to say, the elongation varies inversely as the per cent. of carbon plus .30.
From the above considerations a formula may be constructed for calculating the elongation on the first blow for different conditions of rail section, height of drop and carbon content. The following symbols may be used.
E= elongation in per cent in the maximum inch on the first
blow. Supports 3 ft. apart.
X (C+.30) The value of K must, of course, be determined from the results of elongation 'measurements and through the kindness of the Illinois Steel Company, elongation figures obtained at Gary in the course of inspection work, were used for the purpose. A variety of rail sections were represented and the results from about twenty heats for each section were used. Three tests had been made of each heat and the average longation of the three maximum inches were used as the elongation of that heat on the first blow. For each section, the section modulus and height of drop remained the same, but there were variations of carbon and elongation on the first blow. K was solved for each heat and then the arithmetical average for each section determined, separate averages being determined for the head tension and base tension tests. The results of the determinations of K are given in Table 1, which are figured from the Gary inspection work, except those for the 80 lb. A.R.A. type A rail, which were taken from Report 40 mentioned above. Of course for precise work, the elongation measurements should be much more refined than is the practice in inspection work, but these figures will answer as a first approximation
Taking K as 4.8 the formula then becomes
4.8 h E=
X(C+.30) It is usual in specifications to require a minimum elongation of six per cent and the heights of drop which would be required to just give this amount of elongation in the maximum inch on the first blow, as calculated by the formula, are shown in the Table 2 for the RE, the ARA and the ASCE sections.
TABLE 2-HEIGHTS OF DROP FOR Six PER CENT. ELONGATION
These heights have been figured for the average specified carbon and it will be interesting in this connection to consider the quantative influence of variations in the amount of carbon on the height of drop required to produce six per cent. elongation. It figures out for the 100 lb. rails that to reduce the carbon to the lower limit of the specifications would reduce the height of drop about 1/2 ft. and to increase the carbon to the upper limit would raise the height of drop about 1/2 ft. to produce the same elongation. In other words there is a range of about 3 ft. in the heights required to produce six per cent. elongation, between the lowest and highest carbons specified.
Rail specifications usually fix the height of drop to be used in testing rails and the normal elongations of the maximum inch produced by the first blow from the heights specified in the 1920 AREA specifications are shown in Table 3 for RE, ARA and ASCE sections. It will be noted that for the purpose intended, the height is adjusted about right for the 90 lb. rails, but is high for the lighter weight rails and low for the heavier rails.
Finally it may be remarked that the primary quality determined by the drop test is the longitudinal ductility of the part in tension and when the height of drop is used as the measure of ductility it should be adjusted for each section as well as weight of rail, and perhaps also for the carbon content of the steel in the rail being tested.
BIBLIOGRAPHY AND DISCUSSION OF INTERIOR FISSURES
By M. H. WICKHORST
A bibliography of the subject of interior fissures in rails was prepared covering the literature of the years 1911 to 1915 inclusive and was contained in Report 52 on the subject of "Internal Fissures in Rails." (See Proceedings American Railway Engineering Association, Vol. 17, 1916, pages 587-590.) The discussion on fissures has been revised and the bibliography has been extended five years, to include the year 1920.
Types of Interior Fissures Interior fissures may be divided into three types as follows: (1) Simple transverse fissure. (2) Simple horizontal fissure. (3) Compound fissure. An illustration of the simple transverse fissure is given in Fig. 1.
This type of failure first came prominently to public attention in J. E. Howard's report on the Manchester wreck on the Lehigh Valley Railroad, that occurred August 25, 1911. The transverse fissure is an oval spot in the interior of the head varying in size from 14 inch or less in diameter to almost the full section of the head. A characteristic and constant feature of this type of fissure is the “nucleus," a granular or crystalline spot surrounded by the smooth or polished part of the fissure. The nucleus is ordinarily about 14 inch in diameter but may be smaller or much larger. The surrounding smooth part has been found in all sizes from nothing to almost the full size of the head. Our present information indicates that the nucleus is a shrinkage check in the interior of the head, which acts as a center of growth, from which the fissure develops under repeated "alternations of stress” or the "wave action" under moving trains.