TEMPERATURE–RATE DEFORMATION CONDITIONS DURING CUTTING

V. A. GOVORUKHIN, G. L. KUFAREV

(Presented by the scientific seminar of the Departments of Machine Tools and Metal Cutting and of Mechanical-Engineering Technology)

The process of chip formation during the cutting of ductile metals is a process of plastic deformation occurring in a space bounded by the lower and upper limits of the plastic-deformation zone, and over the time required for each particle of metal to pass through its path in the plastic-deformation zone. It is impossible to replace the plastic-deformation zone by a single shear plane, as is done by many researchers who give a theoretical solution to the cutting process. Such a replacement excludes from consideration the basic essence of the phenomenon—the deformation process—and makes it possible to analyze only the results of this process. Therefore it is natural that many features of the result of the deformation process during cutting remain unexplained.

Thus, the requirement for the further development of the theory of the cutting process leads to the need to evaluate and analyze the conditions under which the deformation process proceeds in the plastic zone; in addition to the mechanical scheme of deformation and the surrounding medium, these conditions include the rate and temperature of deformation [1].

The deformation rate in metal cutting was first determined experimentally in planing copper at microspeed [2], and later in works [3, 4] during planing at speeds up to 20 m/min. The method for calculating the deformation rate in the cutting zone is described in the cited works and provides for the obligatory use of the grid-line method or the method of applying marks parallel to the direction of cutter motion.

These studies showed that, during the motion of each elementary volume in the chip-formation zone, its deformation rate, equal to zero at the lower boundary, at first increases slowly and then very rapidly, reaching a maximum in the region of the conventional shear plane, after which it rapidly decreases to zero at the upper boundary of the plastic-deformation zone. In cutting [2] at a speed of 19 mm/min, the maximum value of the shear rate proved to be

\[ \gamma = 1.6\ \text{s}^{-1}, \]

which corresponds to a deformation-intensity rate

\[ \dot e_i = 0.925\ \text{s}^{-1}. \]

The maximum value of the deformation-intensity rate obtained in work [4] was

\[ \dot e_i = 1400\ \text{s}^{-1}. \]

Special apparatus and the use of the grid-line method in the investigation of the transverse turning process allowed the authors—

within the framework of this article, to conduct a study to determine the rate of strain intensity over a wide range of variation in the parameters of the cutting process. The cutting speed was varied from 5 to 250 m/min, the feed from 0.1 to 0.39 mm/rev, and the tool rake angle from \(+5^\circ\) to \(+22^\circ\). The studies were carried out in cutting brass L62 and steels ShKh15 and 2Kh13.

The rate of strain intensity was found by graphical integration of the curve of increase in the strain intensity of each elementary volume of the deformed zone with time. The strain intensity was calculated from the distortion of a dividing grid [5].

Fig. 1. Character of the change in strain rate along the path of motion of an elementary volume in individual layers of the cut metal (ShKh15, \(V=99\) m/min, \(S=0.31\) mm/rev, \(\gamma=15^\circ\), T5K10)

The results of these studies showed that the character of the curve of the change in strain rate along the path of motion of an elementary volume during cutting at high speeds remains the same as at low speeds (Fig. 1). The maximum value of the strain rate in the outer and middle layers of the chip (layers I–IX in Fig. 1) proves to be approximately constant. In the near-tool layers (layers X–XI in Fig. 1), the maximum value of the strain rate is 2–3 times greater than in the middle layers of the chip. This is explained by the somewhat shortened deformation path of the elementary volume in these layers and by the increased degree of its deformation as a result of secondary deformation.

In assessing the influence of cutting-process parameters on the strain rate, by strain rate we shall mean the average value of the maximum strain intensity rate only in the outer and middle layers of the chip.

Increasing the feed and the front rake angle of the cutter at a constant cutting speed leads to a decrease in the strain rate. It was found that an approximately fourfold increase in each of these parameters within the limits indicated above reduced the strain rate by almost a factor of two.

More substantial was the dependence of the strain rate on the cutting speed. As follows from the graph shown in Fig. 2, the strain rate increases somewhat faster than the cutting speed and, when cutting at high speeds, reaches the value \(\dot e_i = 1.9 \cdot 10^4\ \text{s}^{-1}\). The results shown in the graph also make it possible to conclude that the strain rate depends on the mechanical characteristics of the metal being machined. The stronger the material, the higher the strain rate when cutting at a constant cutting speed.

Fig. 2. Dependence of strain rate on cutting speed

The deformation temperature can be determined with sufficient reliability during cutting at microspeeds, when the deformation process may be considered isothermal. In this case the temperature in the deformation zone will be constant and equal to the temperature of the workpiece being machined. When working with cutting conditions that provide a contact temperature above \(600^\circ\text{C}\) (outside the built-up-edge formation region), the deformation process during cutting can, with a sufficient degree of accuracy, be considered adiabatic. Then the temperature at each point of the deformed volume can be calculated from the specific work of shape change:

\[ \Theta^\circ\text{C} = \frac{1000 \cdot a_V}{427 \cdot \rho \cdot c_p} + t_k^0, \]

where

\[ a_V \]

is the specific work of shape change, which can be calculated [6] by the formula:

\[ a_V = \frac{\sigma_i \cdot e_i}{k+1} \frac{\text{kg}\cdot\text{mm}}{\text{mm}^3}, \]

$\rho$ — density of the material being machined, in g/cm$^3$;

$c_\rho$ — average heat capacity of the material being machined, in $\dfrac{\text{cal}}{\text{g}\cdot{}^\circ\text{C}}$;

$t_k^0$ — temperature of the workpiece being machined and of the surrounding medium, in ${}^\circ$C.

The method of dividing grids, in combination with the method for determining stress intensity from hardness [7], makes it possible to determine the values $\sigma_i$ and $e_i$, and consequently also $d\nu$, at each point of the metal volume plastically deformed during cutting.

Fig. 3. Change in strain intensity $e_i$, rate of strain intensity $\dot e_i$, stress intensity $\sigma_i$, and temperature $\Theta^\circ$C along the path of motion of an elementary volume of metal in the chip-formation zone

Figure 3 presents a graph of the change in the principal process parameters characterizing the conditions under which deformation proceeds at each point of the path $l$ of an elementary volume located in the middle of the thickness of the layer being cut, as it passes through the zone of plastic deformation. Each of the characteristics shown in the graph—strain intensity $e_i$, rate of strain intensity $\dot e_i$, deformation temperature $\Theta^\circ$C, and stress intensity $\sigma_i$—was determined experimentally in a cutting test on steel ShKh15 under the cutting conditions indicated in Fig. 3.

Analysis of the graph (Fig. 3) makes it possible to draw the following conclusions, confirmed by data from analogous graphs obtained in processing cutting tests both for steel ShKh15 and for other metals when the cutting conditions were varied within the limits indicated above, for elementary volumes of metal located at different levels through the thickness of the removed layer.

1. At a cutting speed of 99 m/min, the path of an elementary volume of metal along which it undergoes the main deformation in the cutting zone is commensurate with the thickness of the layer being cut (at feed $S = 0.31$ mm/rev, the main deformation occurred along the path from $l = 0.15$ mm to $l = 0.45$ mm).

The same conclusion was obtained in analyzing experimental data on cutting brass L62 at a cutting speed of 250 m/min.

1. The deformation rate reaches its maximum value at the moment when the volume being deformed has not yet reached the conditional shear plane, whose position on the graph is characterized by point “K.”

2. Each point located within the plastically deformed zone is characterized by its own combination, inherent only to it, of deformation temperature and deformation rate. The temperature–rate conditions of deformation of each elementary volume change continuously as it moves through the plastic-deformation zone.

3. Since it is generally known [8, 9, 10] that an increase in the deformation rate at constant temperature leads to an increase in the resistance of the material to plastic deformation, while an increase in the test temperature at a constant deformation rate leads to a decrease in the material’s resistance to plastic deformation and to an increase in its plasticity, the constancy noted in item 3 of the temperature–rate deformation regime of each of the elementary volumes in the cutting zone must influence the relationship between both the current and final characteristics of deformation and stress \((\sigma_i — e_i)\).

A consequence of this is the conclusion that it is unjustified to extend to the cutting process the dependence \(\sigma_i — e_i\) obtained in static compression tests without taking into account the difference in the temperature–rate regimes of these processes being compared by a number of researchers [11, 12]. Calculations show that, when compressing specimens 15 mm high and 10 mm in diameter at a deformation rate of 6 mm/min, the average deformation rate proves to be \(\dot e_i = 0.008\ \text{s}^{-1}\), while the change in the temperature of the compressed specimen is not detected even by sufficiently sensitive instruments. Thus, both the temperature and the deformation rate in cutting at high speeds may differ from those in compression by ten orders of magnitude, which confirms the validity of the conclusion drawn.

REFERENCES

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4. V. A. Ostaf’ev, S. Kobayashi. Stress, deformation, and deformation rate in metal cutting. Express Information. Cutting Tools, No. 48, Moscow, 1967.

5. V. A. Govorukhin, G. L. Kufarev. Calculation of deformations in the cutting process. Proceedings of TPI, vol. 188, in press.

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1. I. Ya. Tarnovskii, A. A. Pozdeev et al. Mechanical Properties of Steel during Hot Pressure Working. Metallurgizdat, Moscow, 1960.

2. N. P. Ageev, S. I. Karatushin. Mechanical Testing of Metals at High Temperatures and Short-Time Loading. “Metallurgiya,” Moscow, 1968.

3. Yu. Ya. Voloshenko-Klimovitskii. Dynamic Yield Limit. “Nauka,” Moscow, 1965.

4. V. A. Krivoukhov, P. D. Bespakhotnyi. Study of deformation work in metal cutting. Izvestiya VUZov. Mashinostroenie, No. 1, Moscow, 1958.

5. V. V. Shpakovskii. Study of the deformation process in cutting difficult-to-machine materials. Author’s abstract of dissertation. MAI Printing House, Moscow, 1967.