INVESTIGATION OF THE EFFECT OF NOTCHES ON THE MECHANICAL FRACTURE CHARACTERISTICS OF GRAY CAST IRON UNDER STATIC COMPRESSION

L. M. SEDOKOV, V. I. MAKSAK

(Presented by the scientific seminar of the Department of Strength of Materials)

Most machine parts have abrupt changes in cross section. These changes are commonly called notches. The influence exerted by notches on the strength and deformation of structures is extremely great. A notch causes nonuniformity of the stressed state of elementary volumes of materials at different points of the loaded body.

A theoretical calculation of the stressed and deformed state in the plastic region for many loading cases and notch shapes has not yet been developed. The effect of notches under axial tension, bending, and torsion has been studied experimentally. The effect of notches under axial compression has been studied very little.

Knowledge of the mechanical characteristics of the fracture process of brittle materials—of which gray cast iron is a typical representative—obtained under static compression of specimens with notches, will help refine calculations for the strength and stiffness of machine parts operating in compression.

To obtain the actual characteristics of resistance to compression of specimens made of brittle materials with notches, it is necessary to record the force and deformation during the fracture process of these specimens. Therefore, in order to study the influence of notches on the strength of brittle materials under compression, low-inertia apparatus must be used. For this purpose, the force-measuring device of a 100-ton Olsen-type machine was re-equipped.

The elastic deformation of four load columns arising during the loading process is detected by wire resistance gauges glued along the axis of all the columns. For temperature compensation, exactly the same gauges were glued perpendicular to the axis of the columns.

To eliminate the influence of eccentric application of the load, the gauges glued to columns located diagonally were connected into one arm of the bridge. Figure 1 shows the assembly diagram of the force-measuring device. \(P_1, P_2, P_3, P_4\) are the working gauges; \(K_1, K_2, K_3, K_4\) are the compensating gauges. \(A\) and \(B\) are the input of the system, \(C\) and \(D\) are the output of the system. The instrument for measuring deformations also

is based on the use of wire sensors and consists of a flexible cantilever beam on which sensors are glued, capable of registering large deformations in the elastic range. This instrument was made in the laboratory of the Tomsk Polytechnic Institute.

Fig. 1. Electrical wiring diagram of the force-measuring device.

The electrical signals coming from these instruments were fed to a TU amplifier and then, with the aid of an MPO-2 oscillograph, were recorded on film.

Before each series of experiments, the position of the oscillograph trace was recorded for a number of loads fixed in the usual way, which served as the calibration curve. The same was done for the measurement of deformation. Then 5–6 specimens were fractured with recording on film, and this calibration was repeated again.

To investigate the effect of notches on the mechanical characteristics of brittle materials under compression, three series of experiments were carried out on round cylindrical specimens with the ratio \(h/d = 2\). This ratio between the height of the specimen and its diameter was chosen in order to eliminate as much as possible the influence of friction at the specimen ends on the test results [1]. Figure 2 gives the dimensions and shape of the specimens for all three series of experiments. The specimens were turned from cast-iron rods. The criterion of material homogeneity was hardness, which varied within the range \(HB = 180\text{–}200\).

In the first series of experiments, the mechanical characteristics of specimens with one groove located at mid-height were investigated. The depth of the groove was varied from 1 to 3 mm in increments of 0.5 mm (Fig. 2a).

Taking into account a certain inhomogeneity of the specimen material, each experiment was repeated 7–8 times.

As a result of this series of tests, a relationship was established between the true and nominal values of the ultimate strength and the depth of the groove, between the deformation corresponding to the moment of fracture, and the depth of the groove.

Fig. 2. Standard dimensions of specimens.

The results of this series of tests are presented in Fig. 3. The nominal ultimate strength was calculated as the ratio of the breaking load to the cross section of the unnotched part of the specimen:

\[ \sigma_{\mathrm{pch}}^{u}=\frac{P_{\max}}{\dfrac{\pi\cdot 2.5^{2}}{4}}. \]

Fig. 3. Effect of groove depth on the nominal ultimate strength (a) and the true ultimate strength (b):
\(\circ\)—specimens with one groove; \(\times\)—specimens with two grooves.

The true ultimate strength was determined as the ratio of the breaking load to the actual cross-sectional area of the specimen (without taking into account the change in the cross section of the specimen as a result of its deformation and the complex stress state that arises at the notch root):

\[ \sigma_{\mathrm{pch}}^{i}=\frac{P_{\max}}{\dfrac{\pi(2.5-2t)^2}{4}}. \]

With an increase in groove depth, the nominal ultimate strength decreases, while the true ultimate strength increases. In comparison—

Compared with the smooth specimen, the true ultimate strength of a specimen with a groove depth of 3 mm increases by approximately 30% (Fig. 3b). The relative deformation decreases as the groove depth increases. For the same specimens, the relative deformation decreases by approximately 40% (Fig. 4).

Fig. 4. Effect of groove depth on the relative deformation of the specimen: ○ — specimens with one groove; × — specimens with two grooves.

In the second series of experiments, the effect of two grooves, located at a distance from one another equal to the diameter of the specimen (Fig. 2b), on the mechanical characteristics was investigated while varying the depth of these grooves. Taking into account that the shear displacements during fracture occur at an angle of approximately 45°, it could be assumed that the presence of two grooves at a distance equal to the diameter of the specimen would promote fracture, and that the true ultimate strength would be lower than in specimens with one groove.

Fig. 5. Effect of groove width on the true ultimate strength (a) and relative deformation (b).

The results of this series of experiments are presented in Fig. 3. As the groove depth increases, the conditional and true ultimate strengths and the relative deformation change practically in the same way as in specimens with one groove, and have the same magnitude.

In the third series of experiments, the effect of the groove width, at a constant depth equal to 2 mm (Fig. 2c), on the value of the strength limit was investigated. The groove width was varied from 2 mm to 25 mm. The results of this series are presented in Fig. 5. As the groove width is increased, the true strength limit decreases and approaches the strength limit of the smooth specimen. With increasing groove width, the relative deformation also increases and approaches the deformation value of the smooth specimen.

Conclusions

1. The presence of notches substantially changes the mechanical fracture characteristics of specimens made of gray cast iron. The true strength limit of a specimen with groove depth \(t = 3\) mm is higher than the strength limit of a smooth specimen by 30%, while the decrease in the relative shortening of the specimen at the moment of fracture amounted to 40%. Consequently, one cannot agree with Ya. B. Fridman [2] that sensitivity to a notch under compression does not change substantially.

2. In strength calculations, especially for the limit state, it is necessary to take into account the influence of notches on the static strength of gray cast iron.

In the presence of sharp notches, the actual margin of strength will be somewhat higher than that calculated from the usual strength characteristics of cast iron.

1. Under static loading of gray-cast-iron machine parts having sharp notches, some increase in the load is possible, especially if it acts for a short time.

2. Gray-cast-iron parts with sharp notches will resist impact loads significantly worse than parts without notches, since the presence of notches produces a decrease in the relative deformation corresponding to the strength limit.

3. The presence of more or less wide grooves does not cause a substantial change in the mechanical characteristics of gray cast iron under static compression.

4. Further investigations are needed of the effect of notches on the mechanical characteristics of brittle materials. It is also necessary to develop a method for assessing the sensitivity of brittle materials to compression resistance.

Literature

1. L. M. Sedokov. Investigation of the plasticity and strength of gray cast iron. Izv. vuzov. Fizika, No. 5, 1959.

2. Ya. B. Fridman. Mechanical Properties of Metals. Oborongiz, 1952.