MEASUREMENT OF FRACTURE SURFACES OF STEEL RODS

I. P. Onufrienok and M. I. Balabanova

The measurement of flat, ground surfaces presents no great difficulties, even if these surfaces are small. Their measurement can be carried out with a planimeter or by calculation after measuring the corresponding parameters. As for the measurement of uneven, rough, and, especially, small surfaces, their direct measurement presents enormous, and sometimes insurmountable, difficulties. At the same time, the true fracture surface of steel rods subjected to fracture testing is of great interest, since it is precisely this surface that should characterize the true strength of the steel. Therefore, in the autumn semester of the 1950–51 academic year, Associate Professor V. P. Shubin proposed a topic on measuring the fracture surface of a steel rod by means of some process occurring on the fracture surface. In particular, he proposed the use of the following reaction for this purpose:

\[ \mathrm{CuSO}_{4}+\mathrm{Fe}=\mathrm{FeSO}_{4}+\mathrm{Cu}. \]

We accepted this topic for execution within the student research circle, but the first failures in the experimental part compelled me, as the supervisor of this topic, not only to supervise the topic but also to take a major part in its execution. The work was completed in 1951.

Experimental Part

We had at our disposal four specimens of steel rods with various areas subject to measurement. It was decided to grind these areas and to measure the parameters accurately, using a microscope with micrometers for measurement, in order to calculate the areas. After measurement, the rod specimens were thoroughly washed with water, alcohol, ether, and again alcohol, and then dried at room temperature.

Next, the areas of the rods not subject to measurement were coated with black bakelite lacquer; for this purpose the lacquer was diluted with benzene to the consistency of liquid paint and, with great care, applied to the specimens with a brush. After two days of drying at room temperature, the specimens were ready for testing. The test was conducted as follows: into a chemical beaker of about 100 ml capacity, exactly 10 ml of a 0.05 N solution of \(\mathrm{CuSO}_{4}\cdot5\mathrm{H}_{2}\mathrm{O}\) was introduced with a pipette, and the suspended rod under test was immersed in it, where it was kept for exactly 20 minutes. The time was measured with a stopwatch. After 20 minutes had elapsed, the rod was removed, rinsed with water from a wash bottle into the beaker, and the remaining copper sulfate in the beaker was titrated with a 0.05 N solution of sodium thiosulfate. The consumption of the sodium thiosulfate solution for titrating the residual copper sul-

the consumption was read on the burette with an accuracy of up to 0.01 ml and was subtracted from the consumption of the same solution required for titrating 10 ml of a 0.05 N solution of copper sulfate. The difference obtained served as the criterion for the surface being tested, on which copper was deposited. The titration procedure was as follows: about 0.1 g of ammonium bifluoride, 1 drop of 2 N sulfuric acid solution, and about 1 g of potassium iodide were introduced into the beaker containing the remains of the copper sulfate; the solution with the precipitate that had formed was immediately titrated with a 0.05 N solution of sodium thiosulfate. Toward the end of the titration, when the iodine coloration had become much weaker, 1 ml of starch solution was added and the titration was continued until the blue coloration due to the iodine-starch disappeared. In order to obtain comparable results, the area of the reacting surface was referred to 1 ml of sodium thiosulfate deficit; in what follows this ratio is denoted by \(F'\). This method of preparing the specimens, testing them, and titrating was the same for all subsequent experiments, with the exception of the testing time and the method of depositing copper on the areas being tested, which consisted in the fact that the first two series of experiments were carried out in an electrolyte at rest, whereas the last two series of experiments were carried out with continuous stirring of the electrolyte.

The first series of experiments, the purpose of which was to determine \(F'\), is shown in Table 1.

Table 1

The results of the experiments given in Table 1 showed that under the given conditions one can, using this method, measure the area with an accuracy exceeding 1 sq. mm under the most favorable conditions; but if the deviations from the mean value of \(F'\) are taken into account, the accuracy of the measurement would be quite low. Furthermore, it was unclear whether the deviations from the mean value were accidental or whether they were regular. Therefore it was decided in the next series of experiments to test a larger number of areas, on the one hand, and to increase the reaction time to 30 minutes, on the other. The old areas were ground again; in addition, the opposite ends of the rods were also ground and yielded four new areas. The areas were again measured by means of a microscope with micrometers and prepared for the tests.

The results of the experiments of the 2nd series are summarized in Table 2.

The results of the experiments of the 2nd series turned out to be still more varied. At first glance it might have seemed that it was not worth pursuing this method further, since errors of up to 300% in the measurement of areas could occur; comparable results were obtained only for comparatively identical areas, and the worst thing was that the smaller the surface, the more copper was deposited on it. This last point was in direct contradiction to the fact that the reaction \(\mathrm{CuSO_4 + Fe = FeSO_4 + Cu}\) should be a direct function of the surface. Upon careful ana-

Table 2

In analyzing the results of the first two experiments, taking as a basis that the reaction

\[ \mathrm{CuSO_4 + Fe = FeSO_4 + Cu} \]

is a direct function of the surface of the iron, our further reasoning came down to the following.

1. If results are obtained that do not correspond to the reacting areas, this means that during the experiments these areas are not under identical conditions. Nonidentical conditions for the deposition of copper could have been created in the solution in the immediate vicinity of the reacting areas, since all other conditions were identical. Indeed, at one and the same diffusion rate, the concentration of copper cations changes less near a small area and, consequently, is equalized more rapidly than near a large area, where the solution is intensively depleted of copper cations. These nonidentical conditions can be eliminated by thorough and continuous stirring of the copper sulfate solution.

2. The amount of copper deposited in a quiescent copper sulfate solution, without stirring, is not in direct dependence on the time during which the specimen is in the solution; consequently, the residence time of the specimen in the solution can be shortened.

Therefore it was decided to conduct the next series of experiments with continuous stirring of the copper sulfate solution, in order to equalize the concentration of copper cations near the reacting areas, and to reduce the residence time of the specimen in the copper sulfate solution to 10 minutes. For the test, these same areas were again polished and prepared. The results of the third series of experiments are summarized in Table 3.

Table 3

The results of the experiments of the third series showed with sufficient clarity that the failures of the experiments of the first two series were indeed due to

absence of stirring of the copper sulfate solution. Further, although in the 3rd series of experiments the stirring cannot be considered uniform, since it was done manually, in such a way that the specimen was suspended and remained motionless in the solution, while the copper sulfate solution in the beaker was rotated by hand at a speed of 1–2 revolutions per second, nevertheless in this series of experiments there are still no such abrupt jumps in the results as in the preceding two series, and if there are deviations from the mean value, they are due only to nonuniform stirring. Moreover, despite the fact that the exposure time was reduced by a factor of 3, the rate of copper deposition increased by more than a factor of two. Thus, the results of this series of experiments showed that there is full possibility of proposing a new method for measuring the surface of steel rods with an accuracy of up to 0.25 sq. mm, if the consumption of sodium thiosulfate is recorded with an accuracy of up to 0.01 ml, under other favorable conditions. But before proposing working instructions for applying this method, it was necessary to carry out one more series of experiments on measuring the fracture surfaces of specimens that had undergone fracture testing, in order to take into account all the features that might be encountered in this case. Therefore we conducted a 4th series of experiments on measuring the fracture surfaces of specimens that had undergone fracture testing. The procedure for preparing these specimens was the same as for the preceding series, except that the fracture surface was not ground, but only carefully washed with water, alcohol, ether, again with alcohol, and dried at room temperature. The subsequent test was carried out in the same way as in the 3rd series of experiments. To calculate the fracture area we used the mean value \(F'\) from Table 3.

The results of the 4th series of experiments are given in Table 4.

Table 4

The first two experiments from Table 4 may be considered unsuccessful, since the copper was not deposited over the entire surface. This happened because, before immersion in the copper sulfate solution, not all air bubbles had been removed from the fracture surfaces; in subsequent experiments this was taken into account. The minimum fracture surface was not measured by us physically; however, judging from the approximate fracture area “by eye,” the fracture surface determined by us with the aid of the new method was in all cases much larger and in some cases was more than twice as large as the apparent fracture surface. Hence the conclusion suggests itself that, during fracture, in some cases the fracture surface develops greatly. The results of all the preceding experiments, as well as the work experience accumulated during the tests, enabled us to write working instructions for applying the new method of measuring fracture areas, which are given below.

Operating Instructions for Measuring Fracture Surfaces of Steel Rods

General Considerations

1. The new method for measuring fracture surfaces is based on the reaction of copper deposition from copper sulfate on an iron surface:

\[ \mathrm{CuSO_4} + \mathrm{Fe} = \mathrm{FeSO_4} + \mathrm{Cu}, \]

i.e., an oxidation–reduction reaction. The amount of copper deposited per unit time should be in direct dependence on the reacting surface of the iron, provided that there is only an insignificant change in the potential of copper deposition, which depends on the initial and final concentration of copper ions in the copper sulfate solution. The potential of copper deposition, according to Peters’ equation,

\[ E = E_0 + \frac{0.058}{n}\lg \frac{C_{\mathrm{oxid}}}{C_{\mathrm{red}}}, \]

depends on \(E_0\)—the normal potential—plus the logarithmic dependence on the concentration of the oxidized and reduced forms of copper. This latter circumstance imposes certain restrictions on the construction of a method for determining the fracture surface. On the one hand, the sensitivity of the method would be greater the more copper deposited from the copper sulfate solution; on the other hand, with strong depletion of the solution in copper ions, the deposition potential would change greatly, and the dependence between the surface of the reacting iron and the amount of deposited copper would cease to be close to linear. Therefore it is necessary to limit the sensitivity of the method, consuming only 30% of the copper ions taken for the experiment; moreover, if the measured area exceeds \(1\ \mathrm{sq.\ cm}\), then for the reaction it is necessary to take an additional \(10\ \mathrm{ml}\) of 0.05 N copper sulfate solution for each extra square centimeter, with a 10-minute test duration.

It would be more correct, in order to avoid fluctuations in the copper-deposition potential, to have the copper sulfate solution saturated, and to shorten the test time even further; but in that case determination of the deposited copper by the residue would be inaccurate, and determination of the directly deposited copper would be very difficult.

1. The surface of steel is not composed entirely of iron; this surface consists of iron, iron carbides, graphite, annealing carbon, and alloys of iron with alloying elements. Therefore, naturally, each grade of steel will react differently with copper sulfate, and for each grade of steel, with equal reacting areas, the deficit in the volume of sodium thiosulfate for titrating \(10\ \mathrm{ml}\) of 0.05 N copper sulfate solution will be different. Consequently, the operating method must provide for determining fracture surfaces in different grades of steel.

2. When a steel rod is fractured, two fracture surfaces are obtained, each belonging to its own end of the rod, and consequently it will be correct to regard the true fracture surface as the half-sum composed of both these surfaces; this must also be provided for in the measurement method.

Preparation of Specimens for Testing

Usually, for fracture testing, steel rods of either circular or square cross-section are prepared, with the intention of having a cross-sectional area of about \(1\ \mathrm{sq.\ cm}\); such specimens are about \(10\ \mathrm{cm}\) long. Let us agree

designate the individual sections (end faces) of these rods as shown in Fig. 1.

In preparing the rod specimen for measuring the fracture surfaces \(S_1\) and \(S_2\), it is necessary, carefully and without overheating, to grind the end face \(S'_0\) and measure its parameters with a microscope equipped with micrometers, in order to calculate the area \(S'_0\). Then both halves of the specimen are washed with distilled water, alcohol, and ether, and dried again at room temperature. Next, taking care not to touch the end faces with the fingers, a strong insulated copper wire is firmly attached to the middles of the specimen halves, with the calculation that the free end of the wire should be 10–15 cm long. The free end of the wire is subsequently used to hold the specimen during coating and for suspension.

Fig. 1

After this, the specimen is carefully painted with a brush with black Bakelite varnish diluted with benzene to the consistency of paint, leaving unpainted only the areas on which copper will subsequently be deposited, and the specimen is suspended for drying for two days (Fig. 2).

Testing of Specimens

The testing of specimens consists in depositing copper from a solution of copper sulfate onto the reacting areas of the steel rods and in determining, in the copper sulfate solutions, the residues of undeposited copper. For this purpose two chemical beakers are taken; into one of them exactly 10 ml of distilled water is poured with a pipette. This beaker is placed on a disk rotating at a speed of 2 revolutions per second, the beaker is centered, and the specimen is suspended, as shown in Fig. 3, with the intention that the specimen be immersed in the liquid to \(2/3\) of its depth and in such a way that the vertical axis of the specimen lies at \(1/3\) of the beaker radius from the axis of rotation (Fig. 3). When the specimen has been suspended as required, it is removed from the water, the beaker with water is taken away, and in its place another identical beaker is set, into which exactly 10 ml of a 0.05 N copper sulfate solution has been introduced with a pipette. The beaker with copper sulfate is centered. Next, the reacting area of the specimen wetted with water is examined and, if air bubbles or unwetted regions are noticeable, these bubbles are “knocked off” with a strong jet from a wash bottle and complete wetting of the area is achieved. After this, the specimen is lowered with the reacting area into the rotating beaker containing the measured copper sulfate solution, and the stopwatch is started simultaneously. Copper is allowed to deposit for exactly 10 minutes, after which the specimen is quickly lifted out of the liquid while simultaneously stopping the stopwatch, and the wetted end of the specimen is carefully rinsed from a wash bottle into the same beaker. After rinsing the reacting area, it is examined to see whether the copper has deposited uniformly; then the rod is suspended on another ring and the titration of the copper residue in the copper sulfate solution is begun.

Before titration, 0.1 g of ammonium bifluoride, 1 drop of 2N sulfuric acid, and about 1 g of potassium iodide are introduced into the beaker, and it is immediately titrated from a burette with a 0.05 N sodium thiosulfate solution.

Toward the end of the titration, when the yellow color from the liberated iodine has noticeably weakened, 1 ml of starch solution is added and titration is continued

Fig. 2

Fig. 3

Axis of rotation.

until the blue color of the iodine–starch disappears. The amount of sodium thiosulfate used for the titration is recorded, and the test results are then calculated. After titration the beaker is immediately rinsed with tap water so that the glass is not attacked by hydrofluoric acid.

Procedure for testing individual reacting areas and calculation of the results

First, the area \(S'_0\), or else \(S''_0\), is tested, i.e., areas with a previously measured surface area. Testing one of these areas, and in some cases both, is necessary in order to obtain \(F'\)—the area corresponding to 1 ml of sodium thiosulfate deficiency—by the formula:

\[ F'=\frac{S'_0}{a-b}, \tag{1} \]

where \(F'\) is the area, in sq. mm, corresponding to 1 ml of sodium thiosulfate deficiency,

\(S'_0\) is the area of the polished end surface in sq. mm,

\(a\) is the number of ml of 0.05 N sodium thiosulfate solution used to titrate 10 ml of 0.05 N copper sulfate solution,

$b$ — the number of ml of 0.05 N sodium thiosulfate solution used for titrating the copper residue after the test, in the copper sulfate solution.

Next, areas $S_1$ and $S_2$ are tested and their areas are calculated by the formula:

\[ S_1 = (a-b)F', \tag{2} \]

where $S_1$ is the fracture area in sq. mm,
$F'$ is taken from formula (1),
$a$ is, for the same solutions, the same as in formula (1),
$b$ is the number of ml of 0.05 N sodium thiosulfate solution used for titrating the copper residue after testing area $S_1$.

The true fracture area is calculated by the formula

\[ S=\frac{S_1+S_2}{2}, \tag{3} \]

where $S$ is the true fracture area in sq. mm of the tested specimen,
$S_1$ and $S_2$ are the fracture areas of the individual ends of the specimen in sq. mm.

Required equipment and reagents

(The quantity of reagents is given on the basis of 100 tests)