Investigation of the Strength of Gray Cast Iron Under Radial Compression
Abstract Generated abstract
This paper examines radial compression as an indirect method for determining the tensile strength of gray cast iron, addressing the difficulty and scatter associated with direct tensile testing of brittle materials. Experiments on cast irons with Brinell hardness from 110 to 210 HB relate tensile strength, axial compressive strength, and the specific destructive force under radial compression to hardness, and assess the effects of specimen diameter, length, and deformation rate. The results indicate approximately linear hardness dependences, support use of an average coefficient of 0.85 to estimate tensile strength from radial compression load, and show that axial compressive strength is about 3.5 times the tensile strength for the materials studied. Specimen diameter had little effect, lengths with l/d at least 1.5 gave stable results, and deformation rates from 0.5 to 2 mm/sec had practically no influence.
Full Text
INVESTIGATION OF THE STRENGTH OF GRAY CAST IRON UNDER RADIAL COMPRESSION
Yu. S. Bogomolov, L. M. Sedokov
(Recommended for publication by the scientific seminar of the Department of Strength of Materials)
The tensile strength of a material is its most important mechanical characteristic. However, for brittle materials (cast iron, bronze, stone, concrete, some plastics, etc.), determining the tensile strength is difficult, which leads to substantial uncertainty in the results of tests.
Studies [1, 2, 3, 4, 5] indicate that, under radial compression of a cylindrical specimen of a brittle material, the tensile strength can be determined by the formula
\[ \sigma_{\mathrm{t}} = A \frac{P}{dl}. \tag{1} \]
Here \(P\) (kgf) is the maximum force during the test,
\(d\) and \(l\) (mm) are the diameter and length of the specimen,
\(A\) is a dimensionless coefficient.
Let us introduce the concept of the specific destructive force under radial compression \(\sigma_{dl}\), as the ratio of the maximum force during the test to the area of the diametral section,
\[ \sigma_{dl} = \frac{P}{dl}. \tag{2} \]
Obviously, the dimensionless coefficient \(A\) is the ratio of the tensile strength to the specific destructive force under radial compression,
\[ A = \frac{\sigma_{\mathrm{t}}}{\sigma_{dl}}. \tag{3} \]
The methods of the theory of elasticity make it possible to determine the magnitude of the tensile stresses on areas coinciding with the plane of action of the force during radial compression of a disk, according to the formula [6]
\[ \sigma_x = \frac{2}{\pi} \cdot \frac{P}{dl} = \mathrm{const}. \]
If the validity of Hooke’s law under radial compression of a specimen is extended to brittle materials up to failure, then the value of the dimensionless coefficient \(A\) should be taken equal to \(\frac{2}{\pi} \simeq 0.64\).
In real materials, however brittle they may be, some plastic deformation will always precede fracture. Therefore the coefficient \(A\) for real materials is greater than 0.64.
To determine the actual value of this coefficient for gray cast iron, as the most widespread brittle material in machine building, the present work was carried out. The dependence of the dimensionless coefficient \(A\) on the hardness of gray cast iron in the range from \(110HB\) to \(210HB\) was investigated, as was the influence of test conditions on the experimental results.
Special gray-cast-iron castings measuring \(400 \times 100 \times 30\) mm, after removal of the surface layers to a depth of not less than 5 mm, were cut into bars \(400 \times 25 \times 20\) mm. Along the length of these bars the hardness was carefully measured on a Brinell press with a 10 mm ball. Bars of constant hardness (independent of the absolute value of the hardness) were selected for preparing specimens.
In this way tensile specimens of diameter 8 mm and with a working section of 70 mm were prepared, as well as specimens for axial and radial compression, of diameter 12 mm and length 24 mm, of various hardnesses.
Figures 1 and 2 show graphs representing the dependences of the tensile strength, axial compression strength, and specific destructive force under radial compression on the hardness of the cast iron. The obtained
Fig. 1. Dependence of the rupture strength \(\sigma_{pch}\) and of the specific destructive force under radial compression on the \(HB\) hardness of gray cast iron.
results give a linear relation between the indicated quantities in the form of equations of straight lines that do not pass through the origin:
\[ \sigma_{pch} = 0.15\,HB - 6.4, \]
\[ \sigma_{pch}^{\mathrm{comp}} = 0.56\,HB - 29, \tag{4} \]
\[ \sigma_{dl} = 0.15\,HB - 4.2. \]
The scatter of the experimental points from the straight lines expressed by equations (4) lies within \(\pm 11\%\) for tension and axial compression and is about \(\pm 8\%\) under radial compression.
Eliminating the hardness value \(H_B\) from equations (6), one can relate the tensile strength, the axial compressive strength, and the specific destructive force under radial compression by the following ratios.
Table
Relationship between the tensile and compressive strengths and the specific destructive force under radial compression
| Tensile strength, \(\sigma_{\text{t}}\) | Strength under axial compression, \(\sigma_{\text{c}}^{\text{ax}}\) | Specific destructive force under radial compression, \(\sigma_{dl}\) | |
|---|---|---|---|
| \(\sigma_{\text{t}}=\dfrac{4P}{\pi d^2}\) | \(3.8\sigma_{\text{t}}-4.6\) | \(1.02\sigma_{\text{t}}+2.3\) | |
| \(\sigma_{\text{c}}^{\text{ax}}=\dfrac{4P}{\pi d^2}\) | \(0.26\sigma_{\text{c}}^{\text{ax}}+1.2\) | — | \(0.27\sigma_{\text{c}}^{\text{ax}}+0.36\) |
| \(\sigma_{dl}=\dfrac{P}{dl}\) | \(0.98\dfrac{P}{dl}-2.26\) | \(3.73\dfrac{P}{dl}-1.33\) | — |
Fig. 2. Dependence of the compressive strength \(\sigma_{\text{c}}^{\text{ax}}\) on the hardness \(H_B\) of gray cast iron.
As is seen from Fig. 1, the plots of the dependence of the tensile strength and of the specific destructive force under radial compression on the hardness \(H_B\) are parallel straight lines, since the tangents of the angles of inclination of these straight lines are equal to 0.15. The character of these lines indicates an analogy between the fracture process under axial tension and under radial compression. In the investigated hardness range of gray cast irons, the dimensionless coefficient \(A\) changes somewhat, increasing with increasing hardness. However, this change is small.
On average, the value of the coefficient \(A\) for the cast irons studied may be taken as equal to 0.85. In this case, the change in the value of the dimensionless...
the dimensional coefficient \(A\) will be \(\pm 6\%\). Consequently, formula (1) for the cast irons investigated may be written as follows:
\[ \sigma_{\mathrm{pc}} = 0.85\,\frac{P}{dl}. \tag{5} \]
The dependence between the compressive strength limit and the Brinell hardness is shown in Fig. 2. In this case a straight line was also obtained, but with a larger angle of inclination, whose tangent is 0.56. The specific breaking load under radial compression can be related to the strength under axial compression through the coefficient \(B\).
\[ \sigma_{\mathrm{pc}}^{\mathrm{comp}} = B\,\frac{P}{dl}. \tag{6} \]
The value of the coefficient \(B\) does not remain constant. As the hardness of gray cast iron increases, the value of the coefficient \(B\) also increases. On average, the value of this coefficient is 3.0 for the hardness range investigated. The deviation is \(\pm 8\%\), which will likewise fall within the scatter of the experimental results. Thus, for the cast irons investigated, formula (6) may be written as follows:
\[ \sigma_{\mathrm{pc}}^{\mathrm{comp}} = \frac{3P}{dl}. \tag{7} \]
Consequently, it may be considered established that the strength under axial compression of gray cast iron of the investigated hardness is 3.5 times higher than its direct tensile strength.
In the course of the study, the influence of specimen dimensions on the results of mechanical tests of cast iron under radial compression was examined. For this purpose, two series of experiments were carried out.
The first series was performed on specimens of constant length, equal to \(20\) mm, and of a range of diameter values from \(10\) to \(80\) mm. Figure 3 shows the dependence of the specific breaking force under radial compression on the specimen diameter for three hardness values, \(HB\): 155, 170, and 190 units. The experimental points are plotted as the mean values of tests on \(5\)–\(10\) specimens. When the diameter is changed by a factor of 8, i.e. when the ratio of the diameter
Fig. 3. Influence of specimen diameter on the magnitude of the specific breaking force under radial compression.
as the ratio of the specimen diameter to its length varied from 0.5 to 4, a tendency was observed for the specific breaking force under radial compression to decrease as the diameter of the specimens increased. However, this change is small and amounts to about 5%. Thus, within the investigated range of values of \(d/l\), the specific breaking force under radial compression may be regarded as practically independent of changes in the specimen diameter.
In the second series the specimen diameter remained constant, equal to 12 mm, while the length was varied tenfold: from 4 to 40 mm. Figure 4 gives the dependence of the specific breaking force under radial compression on the specimen length for three hardness values of gray cast iron: 135, 160, 190 HB.
Experimental points in this figure represent mean values from 5–10 tests. The results of processing the tests show that, for a ratio \(l/d \geqslant 1.5\), the change in the specific breaking force under radial compression may be considered insignificant and lying within the scatter of the experimental results. A decrease in specimen length, when \(l/d < 1.5\), causes an increase in the specific breaking force, especially noticeable for gray cast iron with hardness 160–190 HB. Thus, specimens 6 mm long, in comparison with specimens 20 mm long, give a value of the specific breaking load greater by approximately 20%.
Fig. 4. Influence of specimen length on the value of the specific breaking force under radial compression.
The influence of the deformation rate, equal to the speed of displacement of the crosshead (or platen) of the machine within the range from 0.5 to 2 mm/sec, has practically no effect on the performance of radial-compression tests of cylindrical specimens made of gray cast iron.
LITERATURE
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