Resistance of Gray Cast Iron under Plane Stress
Abstract Generated abstract
This paper reports an experimental study of the strength of gray cast iron under plane stress, focusing on its dependence on Brinell hardness and on the transition from uniaxial to biaxial compression. Solid round specimens were tested in torsion, and rectangular prisms of varying length to width ratios were compressed between parallel plates to produce different stress states, with empirical relations derived between hardness and ultimate strength. The results indicate that torsional strength and compressive breaking stress increase with hardness, while the coefficient in the compression relation depends on specimen proportions. The study concludes that gray cast iron strength is affected by the stress state, and that transition from linear compression to biaxial compression generally increases strength, although scatter and local defects become more significant in harder and longer specimens.
Full Text
Resistance of Gray Cast Iron under a Plane Stress State
L. M. Sedokov, B. L. Petri
(Presented by the scientific seminar of the Department of Strength of Materials)
The experimental relationship between hardness and strength of gray cast iron in tests for uniaxial tension and compression has been studied repeatedly [1, 2, 3]. However, there are few data on the resistance of gray cast iron under a complex stress state. Below are presented the results of an experimental study of the dependence of the strength of gray cast iron on hardness under a plane stress state.
The investigation was carried out in torsion of solid round specimens and in compression between parallel plates of rectangular prisms of various lengths. The specimens for testing were made from cast-iron plates \(400 \cdot 400 \cdot 400\) mm, which had first been planed to remove the chilled surface layer. Rectangular blanks were cut from them. From 4–5 measurements the average Brinell hardness was determined. Twenty-six torsion specimens 18 mm in diameter with a gauge length of 140 mm had hardness from 100 to 200 \(HB\). The ultimate strength in torsion is determined by the formula
\[ \tau_{\text{ult}} = \frac{M_{\text{ult}}}{W_p} = \frac{M_{\text{ult}}}{\dfrac{\pi d^3}{16}} \ \frac{\text{kg}}{\text{mm}^2}. \tag{1} \]
The fracture torque \(M_{\text{ult}}\) was recorded by the deflection of the pendulum of the testing machine and was checked by recording with an N-10 oscillograph, which received a signal from wire gauges glued to the shaft of the machine.
According to the results of the torsion tests, the relationship between the hardness and strength of gray cast iron can be approximated by the equation
\[ \tau_{\text{ult}} = 0.19\,HB - 6.6 \ \frac{\text{kg}}{\text{mm}^2}. \tag{2} \]
In transverse compression of prisms between parallel plates, as a result of contact friction a complex stress state arises. In compression of prisms with a large ratio of length to width, a plane stress state arises in the middle part. Therefore, by varying the ratio between the length and width of the prisms, it is possible to trace the change in the strength of gray cast iron in the transition from a linear stress state to a plane one.
All compression specimens had the same height, \(h = 15\) mm, measured in the direction of action of the force. The first series of experiments consisted in determining the dependence of the compressive strength of gray cast iron on its hardness when testing square prisms \(10 \cdot 10\) (93 specimens). In the subsequent series, specimens having dimensions \(10 \times 25\), \(10 \times 50\), \(10 \times 100\) mm were tested. In all, 183 specimens were tested. Compression was carried out on a 500-ton hydraulic press.
Although the test results gave a large scatter of values, arithmetic averaging made it possible to establish the following relation between the hardness and strength of cast-iron prisms:
\[ \sigma_{\text{pc}} = 0.59\,HB - c\ \frac{\text{kg}}{\text{mm}^{2}} \tag{3} \]
The coefficient \(c\) proved to be different, and its absolute value is the greater, the smaller the ratio of the specimen length to its width. For \(l : b = 1\), \(c = 20\); for \(l : b = 2.5\), \(c = 15\), and for \(l : b = 5\), \(c = 13\). Consequently, the breaking stress of prisms of one and the same hardness increases as the ratio \(l : b\) increases.
However, the specimens of the fourth series, having the greatest ratio \(l : b = 10\), gave a somewhat smaller value of the specific breaking force than the specimens of the third series, for which \(l : b = 5\).
The considerable scatter of the test results is explained by a characteristic feature of brittle materials—their poor resistance to local stresses arising in individual grains or groups of grains owing to the presence of nonmetallic inclusions and pores at the grain boundaries. In the case of brittle materials, local structural defects can sometimes be the cause of unforeseen fracture of a part.
As the present study has shown, for cast iron of lower hardness, possessing greater plasticity, the influence of local defects is insignificant; whereas for cast iron of higher hardness, having little plasticity, local defects substantially reduce the increase in strength.
This also explains a certain decrease in the specific breaking force in the last series of experiments, since the probability of local defects increases with increasing length. Here, too, a certain nonparallelism of the press plates may have had an effect.
The results obtained make it possible to conclude that the strength of gray cast iron depends on the type of stress state, and that the transition from linear compression to biaxial compression leads to an increase in the strength of gray cast iron over the entire investigated range of variation of its hardness.
LITERATURE
- Machine Building. Encyclopedic Reference Book, vol. 3, Moscow, GOSINTI, 1948.
- B. Fridman, Mechanical Properties of Metals, Oborongiz, 1952.
- S. D. Ponomarev, Strength Calculations in Machine Building, vol. 1, Mashgiz, 1956.