On Static and Dynamic Fracture of Materials
Abstract Generated abstract
This paper examines how static and impact loading affect material fracture in relation to the performance of hand-held pneumatic hammers. Using tensile diagrams for St. 3 low-carbon steel obtained under static testing and drop-weight impact loading, the authors compare total specific work of deformation and find that the dynamic value is about 1.52 times the static value. The study also reports how deformation work for a KE-16 pneumatic hammer varies with air pressure and pressing force, and proposes physical modeling in polarized light using transparent materials, with celluloid representing plastic metals and polystyrene representing brittle materials.
Full Text
ON STATIC AND DYNAMIC FRACTURE OF MATERIALS
V. F. Gorbunov, A. I. Pashnin
(Presented by the scientific seminar of the Department of Mining Machines, Mine Transport, and Mining Mechanics)
At the present time, hand-held pneumatic hammers are finding ever wider application in industry in the mechanization of many operations: the breaking off of gates, the removal of burrs, the cutting out of cavities, etc. In investigating ways of increasing the productivity of chipping-and-riveting pneumatic hammers, knowledge of the physico-mechanical properties of the materials being processed is of great importance, as is the influence of the energy and frequency of blows on the rate of deformation of the material.
The insufficient study of this question is connected with the absence of data on the dynamic fracture of metals, since the determination of their strength properties—the proportional limit, yield point, and ultimate strength—is carried out under static tension (compression). The tensile (compressive) load increases gradually, without jolts or blows. The results of measurements are presented in the form of a tensile diagram, which in most cases is plotted automatically by testing machines. The tensile diagram makes it possible to establish yet another mechanical characteristic, which can characterize the resistance of a material to impact fracture. This resistance proves to be the greater, the greater the work that must be expended in order to fracture the specimen under static conditions. Therefore, as a characteristic of a material’s ability to resist the action of impact loads, one may take the magnitude of the work expended on stretching the specimen. It is easy to show that this work, on a definite scale, is expressed by the area of the tensile diagram. The quantity characterizing the material, and not the specimen, is equal to the ratio of the work of deformation to the volume of the specimen and is called the total specific work of deformation.
A tensile diagram analogous to that obtained in carrying out static fracture of a specimen can be obtained under rapid (impact) application of forces.
In conducting dynamic tests, impact installations with free fall of the striker are most often used. In this case, taking into account the small resistance due to friction, the energy of each blow can be determined as
\[ A = m \cdot g \cdot h,\ \text{kgm}, \]
where \(m\) is the mass of the striker, \(\text{kg}\cdot\text{sec}^2/\text{cm}\);
\(g\) is the acceleration of gravity, \(9.8\ \text{m}/\text{sec}^2\);
\(h\) is the height of fall of the striker, \(\text{m}\).
It was noted [2] that, under rapid (impact) application of tensile forces, the stresses increase approximately twofold in comparison with static tension; consequently, the specific works of deformation should also differ. For the study, standard specimens of low-carbon steel St. 3 of circular cross section, 12 mm in diameter and with a working length of 120 mm, were taken. The static tensile diagram was obtained on a CDM testing machine (Leipzig, GDR), and the dynamic one on a drop-weight installation manufactured at the Department of Mining Machines of TPI. The diagrams are given in Fig. 1.
Fig. 1. Tensile diagrams. a) under static tension: 1 — polystyrene, 2 — celluloid; b) tensile diagrams of St. 3 steel: 3 — under static tension, 4 — under impact tension.
As a result of planimetering the diagrams, the specific work of deformation under static tension was determined as
\[ a=\frac{S \cdot m_p \cdot m_t}{V}, \]
where \(S\) is the area of the tensile diagram;
\(m_p\) is the force scale;
\(V\) is the volume of the specimen; \(m_t\) is the deformation scale.
According to the measurement data, the specific work of deformation is, under static tension,
\[ 39\ \frac{\text{kgf}\cdot\text{cm}}{\text{cm}^3}, \]
and under dynamic tension,
\[ 59\ \frac{\text{kgf}\cdot\text{cm}}{\text{cm}^3}. \]
Thus, the specific work under dynamic (impact) tension is approximately 1.5 times greater than under static tension. Studies [2] show that, in impact tensile testing, the specific work of deformation of steel is 20–60% higher than under static—
...because of the increase in stresses under impact. Similar results are obtained for most other metals as well. The increase in dynamic stresses and in the specific work of plastic deformation depends on the strain rate, as is evident from Fig. 2.
The rate and work of deformation in the cutting and riveting of metals are determined to a large extent by the internal processes in the pneumatic hammer and by its energy parameters. As the investigations carried out have shown, the work expended on deformation of the material for the KE-16 hammer increases with an increase in the air pressure in the network at constant pressing force and decreases with an increase in the pressing force at constant air pressure in the network (Fig. 3).
Studying the influence of these parameters on the work and rate of deformation directly or by modeling on electronic models is difficult, since the nonlinear character of impact and the nonconstancy of the coefficients of the equations make it hard to find a realizable electronic analogue. The simplest method for studying the influence of the energy and frequency of the impacts of a pneumatic hammer on the strain rate of the material is the method of physical modeling on optically transparent materials.
Fig. 2. Dependence of the specific work of deformation on the rate of load application.
1 — low-carbon steel, \(C = 0.09\%\); 2 — carbon steel, \(C = 0.15\%\); 3 — carbon steel, \(C = 0.5\%\); 4 — duralumin D16; 5 — copper; 6 — zinc.
Fig. 3. Influence of the test conditions of a pneumatic hammer on the work of deformation. 1 — dependence of the work of deformation on the pressing force at an air pressure in the network of 5 atm; 2 — dependence of the work of deformation on the air pressure in the network, at a pressing force of 25 kg.
As a model of brittle materials one may take polystyrene, whose tensile diagram ...
whose tensile diagram is shown in Fig. 1, a. Polystyrene, like brittle materials, has a small relative deformation and an almost complete absence of a yield plateau. As a model for plastic metals, the most suitable material is celluloid, whose tensile diagram is shown in Fig. 1, a. Celluloid has a clearly pronounced yield plateau and large relative deformations.
Conclusions
- In this work, additional data have been obtained on the dynamic (impact) and static tension of St. 3 steel. These two tests were compared in terms of the total specific work of deformation.
For St. 3 steel it was obtained that
\[ \frac{Q_{\mathrm{dyn}}}{Q_{\mathrm{st}}}=1.52. \]
- For the KE-16 pneumatic hammer, dependences of the work of deformation on the air pressure in the line and on the pressing force have been obtained. It is proposed to solve this problem by the method of physical modeling on optically transparent models in polarized light. Celluloid and polystyrene are proposed as models of plastic and brittle materials, and their static tensile diagrams are given.
References
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B. A. Avdeev. Technique for Determining the Mechanical Properties of Materials, Novosibirsk, 1965.
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Encyclopedic Handbook of Mechanical Engineering, vol. 3, Mashinostroenie, 1962.
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L. I. Baron, G. M. Veselov, Yu. G. Konyashin. Experimental Studies of the Processes of Fracture of Rocks by Impact. Akademizdat, 1962.