Microstructure and Microhardness in the Cutting Zone during Machining with a Chamfered Tool

M. F. Poletika

(Presented by Prof. Dr. of Technical Sciences A. M. Rozenberg)

General Remarks

Investigations carried out earlier in the cutting laboratory of TPI \[1, 2, 3\] made it possible to clarify a whole series of features inherent in the cutting process with a chamfered tool. It was established that on a chamfered tool there is always a built-up edge, which retains its stability both at very low cutting speeds, measured in millimeters per minute, and at speeds on the order of 300–400 m/min, that is, under such conditions in which a built-up edge does not remain on an ordinary tool. The geometric parameters of the built-up edge on a chamfered tool depend on the cutting conditions and, in turn, determine the chip shrinkage, and through it also affect the cutting force. The mean front angle of the built-up edge, which determines the direction of chip flow in the main cutting plane, may vary most noticeably. This angle, which we shall hereafter call the chip-flow angle \((\gamma_0)\), depends on the ratio between the cut thickness and the width of the tool chamfer \((a/f)\), increasing as this ratio grows. The cutting speed has a less significant influence on the chip-flow angle; as it increases, the angle \(\gamma_0\) decreases.

Observations of the process of built-up-edge formation, as well as measurement of the chip-flow angle in the investigations indicated, were carried out by studying the side surface of the machined workpiece and the chip during cutting through a microscope with low magnification. The chief advantage of such a method is the possibility of continuous observation of the cutting zone over an arbitrarily long interval of time. During cutting, the built-up edge continuously changes its configuration, which leads to fluctuations in the magnitude of the chip-flow angle, especially noticeable at low cutting speeds. The chosen method was good precisely because it made it possible to find, with considerable reliability, the mean value of the chip-flow angle for a given regime, that is, the value that determines the average chip shrinkage and cutting force.

For a detailed study of the configuration of the built-up edge and its structure, the method mentioned is insufficient, since:

1) the instability of the built-up edge prevents the details of its structure from being recorded by visual observation during cutting, and
2) the shape of the cross section of the built-up edge may be nonuniform in sections located differently along the length of the tool cutting edge.

Consequently, a more detailed study of the built-up edge requires the use of other methods. The metallographic method, consisting in the instantaneous cessation of

of the cutting process at the required moment, after which the chip root is cut out, a microsection is prepared, and it is then subjected to study.

Below are presented the methodology and results of an investigation of the geometry of the build-up on a chamfered tool using a metallographic method.

Research Methodology

For instantaneous termination of the cutting process, a special knock-off device of impact action, of the “falling tool” type, was made; its diagram is shown in Fig. 1.

In tool holder 1 of the lathe, bracket 3 is installed. In it, on rolling bearings, the tail of holder 2 is fastened; in the cavity of this holder cutter 4 is secured by means of bolts 5. Bar 7 is rigidly screwed to the holder; it bears against latch 8, clamped by screws 9 in bracket 6. The latter is also fastened in tool holder 1.

Fig. 1

Knocking off the cutter at the required moment is carried out by a hammer blow on the upper plane of bar 7, which leads to shearing of latch 8 and rotation of holder 2 about axis I—I. The necessary contact of the supporting plane of bar 7 with the upper plane of the latch is ensured by shifting brackets 3 and 6 in height by means of shims. Bending of holder 2 in the horizontal plane under the action of the axial force $P_x$ is prevented by means of rod 10, the position of which is adjusted before each experiment by screw 11.

The cutter is set in height by means of shims.

If necessary, a spring operating in compression may be placed between bracket 6 and holder 2. However, experiments showed that even without the spring the device described ensures that undamaged chip roots are obtained up to speeds of 170–190 m/min.

The experiments were carried out on steel 4 ($H_B = 126$) and steel 30 ($H_B = 146$–150). To facilitate cutting out the chip roots, the specimens consisted of rings mounted on a mandrel of ordinary design. All specimens were annealed beforehand.

Both high-speed-steel (steel R9) and carbide-tipped (alloy T15K6) cutters were used, with rake angles from 30 to 60° and chamfers of various widths (0.3–0.6 mm). The cutting-edge angle in plan was varied from 45 to 90°. The clearance angle $\alpha = 8^\circ$ and the auxiliary cutting-edge angle in plan $\varphi_1 = 10^\circ$ were kept unchanged.

In each experiment, after instantaneous interruption of cutting, the chip root was cut out; its side surface was subjected to grinding, polishing, and etching, and was then visually examined and photographed with an MIM-6 metallographic microscope. In a number of experiments, repeated regrinding of the chip roots was performed in order to obtain photographs of the built-up edge in various sections along the length of the cutting edge.

In addition, in each experiment the chip-flow angle $\eta_0$, the longitudinal shrinkage $\zeta$, and the chip widening $\zeta_{\mathrm{v}}$ were measured, and the transverse shrinkage $\zeta_a$ was calculated.

Microstructure in the Cutting Zone

At very low cutting speeds, observation through a microscope of the side surface of the cutting zone makes it possible to examine in considerable detail the details of the process of built-up-edge formation. In order to compare the picture observed in this way with a photomicrograph of the structure in the cutting zone, the first experiments were carried out at a cutting speed of 0.01 m/min (tool rake angle $\gamma = 60^\circ$; chamfer width $f = 0.6$ mm; depth of cut $a = 1.0$ mm). The corresponding photomicrographs are shown in Figs. 2 and 3, where the same microsection is shown at different magnifications.

Considering Figs. 2 and 3, one can see that the built-up edge is quite clearly separated from the chip and from the cut surface. The contours of the blunt apex of the built-up edge are less pronounced. This is quite understandable, since between the material of the chip and the built-up edge, as well as between the material lying below the cut surface and the built-up edge, there is continuous relative motion. The blunt apex of the built-up edge acts on the material lying ahead as a punch; the deformation propagates forward gradually, and we observe there predominantly plastic flow. It is important to note that the chip being formed does not touch the rake face of the tool, which is protected by the edge of the built-up edge protruding beyond the chamfer.

Judging by the texture, the degree of deformation of the metal in the built-up edge is high and in any case much higher than in the chip. In this case the longitudinal chip shrinkage is $\zeta = 1.35$, the widening is $\zeta_{\mathrm{v}} = 1.08$, and the transverse shrinkage is $\zeta_a = 1.25$. The high degree of deformation in the built-up edge indicates that, despite the absence of rupture along most of the boundary of the built-up edge, the latter moves together with the tool, being its continuation.

The built-up edge periodically increases owing to the propagation of deformation into the depth of the work material (below the cut surface). However, such an increase of the built-up edge leads to a disturbance of dynamic equilibrium; rupture occurs, as a result of which the deformed volume that had previously been the body of the built-up edge remains in the surface layer under the tool, forming a characteristic serration. One such serration is visible in Fig. 2.

The built-up edge does not have a sharp apex. In front it is bounded by a surface of comparatively small curvature. And, despite this, the chip shrinkage proves to be much smaller than on a tool without a chamfer with a rake angle of \(30^\circ\), where the shrinkage is \(\zeta = 1.9 \div 2.1\) at medium cutting speeds, while at a speed of \(0.01\ \text{m/min}\) the degree of deformation is so high that an elemental chip is formed. Undoubtedly, the reason for this apparent contradiction lies in the distinctive shape of the built-up edge, which is not prescribed in advance,

Fig. 2

but is formed naturally in the course of cutting. In this connection one must acknowledge the aptness of the analogy between the process of cutting with a chamfered tool and the process of splitting, drawn by M. I. Klushin [4].

Observation of the side surface of the cutting zone showed that, despite the high stability of the built-up edge on a chamfered tool, its shape nevertheless changes somewhat during cutting; it does not remain constant, and the chip-flow angle oscillates about a certain mean value. To check how substantially the outlines of the built-up edge change in this case, we obtained several chip roots under the same cutting conditions: tool rake angle \(\gamma = 56^\circ\); chamfer width \(f = 0.3\ \text{mm}\); depth of cut \(a = 0.239\ \text{mm}\); cutting speed \(v = 40\ \text{m/min}\); mean value of the chip-flow angle \(\gamma_a = 43.5^\circ\); mean shrinkage values: longitudinal \(\zeta = 1.54\), spreading \(\zeta_{\mathrm{в}} = 1.07\), transverse \(\zeta_a = 1.44\).

The study of these polished sections showed that the general configuration of the built-up edge is approximately the same for all the chip roots obtained, while the front angles of the built-up edges are different. For illustration, in Figs. 4 and 5 we present photographs of two polished sections on which the common features are clearly visible: the built-up edge occupies the entire plane of the chamfer and, with its front part, protrudes below the cutting edge of the tool; the chip flows off without touching the rake face of the tool. However, the front angles and the radii of rounding of the apex of the built-up edges

Fig. 3

Fig. 4

Fig. 5

are not the same. This once again proves the unsuitability of the metallographic method of studying the built-up edge for determining the average value of the chip-flow angle.

The polished sections shown in Figs. 4 and 5 were made in sections close to the side surface of the workpiece and the chip (no more than 0.5 mm from the side surface, with a width of cut of 2.6–2.7 mm). It was important to determine whether the shape of the built-up edge is retained in deeper layers. For this purpose the specimens were reground many times, which made it possible to obtain a whole series of sections of the built-up edge by planes parallel to the main cutting edge. It turned out that the contours of the transverse section do not undergo substantial changes along the entire length of the cutting edge. This is illustrated by Fig. 6, which shows a polished section of the same specimen as in Fig. 4, in a section located 1.4 mm from the side surface (Fig. 6). With a width of cut of 2.65 mm, this approximately corresponds to the middle section.

Fig. 6

In the next series of experiments we changed the rake angle of the tool. Previously it had been selected so as to ensure free chip flow \((\gamma_0 < \gamma)\), that is, conditions under which the chip does not touch the rake face of the tool but contacts only the edge of intersection of the chamfer plane and the rake face (in the photographs presented, this edge is protected by the built-up edge). We now sharpened the tool with a rake angle of \(30^\circ\). As experiments performed earlier [2] showed, at such an angle free chip flow is ensured only in the case of a small ratio \(a/f\) of the thickness of cut to the width of the chamfer; at a large value of the ratio \(a/f\), the chip touches the rake face of the tool, and the base of the built-up edge also spreads onto the rake face. The results of these experiments, carried out on steel 4, are presented in Figs. 7, 8, 9 and in Table 1.

Examining Figs. 7–9, it is not difficult to notice that at a rake angle of \(30^\circ\) the contours of the built-up edge are outlined more sharply, and the radius of curvature of its tip is smaller than at \(\gamma = 60^\circ\). This is undoubtedly due to a more

Fig. 7

Fig. 8

a high degree of deformation (the shrinkage here is greater). It is characteristic that the built-up edge is most distinctly delineated at the maximum shrinkage and the smallest chip-flow angle (Fig. 7). With an increase in the chip-flow angle, the contours of the built-up edge become less sharp.

Fig. 9

Table 1

If, with free chip flow, the shape of the transverse section of the built-up edge is unchanged along its entire length (along the cutting edge), then at a lead angle of $30^\circ$ this is no longer observed. Figures 10, 11, and 12 show three different sections of the built-up edge at a ratio $a/f = 0{,}65$: the first at a distance of 0,4 mm, the second at a distance of 1,7 mm, and the third at a distance of 2,9 mm from the lateral surface of the chip (cut width—3,3 mm). It is easy to see that the height of the built-up edge is different in the different sections.

In addition, in the middle section the built-up edge extends over a considerable portion of the rake face, covering it with a distinctive “tongue.”

Observing the side surface of the built-up edge during cutting, we noticed that the inner part of the built-up edge, adjacent to the chamfer plane, is the most stable and breaks away very rarely. The “outer” part of the built-up edge,

Fig. 10

together with the “tongue,” on the contrary, breaks away and is built up again very often and with regular periodicity. As a result, the contact surface of the chip proves to be covered with such “tongues,” located at approximately equal distances from one another.

Finally, in Figs. 13 and 14 the structure of the built-up edge is recorded for high-speed cutting of steel 30 with a carbide tool having a chamfer.

The first microphotograph was obtained under the following conditions: \(v = 145\ \text{m/min};\ \gamma = 40^\circ;\ f = 0.36\ \text{mm};\ a = 0.361\ \text{mm};\ b = 1.95\ \text{mm};\ \gamma_d = 27^\circ;\ \zeta = 1.67;\ \zeta_v = 1.15;\ \zeta_a = 1.45.\) The polished section was polished together with a piece of the tool, which broke off when the holder was tipped back. Fig. 14 was obtained under the following conditions: \(v = 180\ \text{m/min};\ \gamma = 40^\circ;\ f = 0.44\ \text{mm};\ a = 0.43\ \text{mm};\ b = 2.44\ \text{mm};\ \gamma_d = 26^\circ;\ \zeta = 1.55;\ \zeta_v = 1.14;\ \zeta_a = 1.36.\) In both cases, by selecting the rake angle of the tool, free chip flow was ensured \((\gamma_\delta < \gamma)\).

It is not difficult to see that the structure of the built-up edge is expressed quite clearly on both polished sections. This is convincing proof of the existence of a built-up edge on a chamfered tool at such high speeds, when it is absent on an ordinary tool.

Fig. 11

Fig. 12

Fig. 13

Fig. 14

Microhardness in the Cutting Zone

It was of considerable interest to measure the hardness of the chip and of the built-up edge when cutting with a chamfered tool. Until now such measurements have been made only for an ordinary tool without a chamfer [5, 6, 7].

To determine the hardness in various regions of the cutting zone we used the instrument of M. M. Khrushchev and E. S. Berkovich (PMT-3), which provides the smallest indentation sizes after pressing in the indenter. Studying the distribution of hardness by this method presents known difficulties because of the considerable scatter of hardness values at neighboring points, which is inevitable with the nonuniform structure of the material being machined. The hardness of the structural constituents of the low-carbon steel with which we worked is: ferrite—$H_B = 50 \div 115$, pearlite $H_B = 150 \div 250$ [8]. This means that, with an indentation diameter comparable with the grain size, even in the initial (undeformed) structure we may obtain hardness fluctuations in the range $50 \div 250$, i.e., by a factor of five. Similar hardness fluctuations will also be observed in deformed structures. Indeed, if we look at the results of microhardness measurements in the cutting zone carried out by a number of investigators [5, 6, 7], we immediately find a scatter of hardness values which, naturally, complicates the study of the overall pattern of hardness distribution.

In order to limit this scatter somewhat and make it possible to average hardness values over various areas, we carried out tests with the greatest load permitted by the instrument (200 g), arranging the indentations on a coordinate grid with the smallest recommended spacing between them [9]. An exception was made only for the built-up-edge zone and the layers close to the surfaces of the chip and the workpiece, where the small sizes of the indentations (increased hardness) made it possible to place them closer to one another than in the other areas, while the curvilinear contours of the bounding surfaces required a departure from the coordinate grid.

For measuring hardness we first selected a microsection whose microstructure is shown in Fig. 7 (material being machined—steel 4, cutting speed $v = 40$ m/min, ratio $a/f = 0.295$). The measurement results are presented in Fig. 15.

Although the indentations were obtained with the greatest load, the scatter of hardness values proved to be rather significant. In order that this should not prevent the identification of typical zones with different hardness, the entire hardness interval was divided into groups, with the circles of each group shaded in a definite tone. In this way the diagram shown in Fig. 16 was obtained. In this diagram the following are clearly visible:

1) a zone of undeformed metal with the initial hardness (hardness predominantly within the range $101 \div 130$, with isolated harder inclusions);

2) a zone of preliminary deformation with an average thickness of about $0.36$ mm, or $3a$, where $a$ is the chip thickness (the hardness in the deeper layers is predominantly within the range $131 \div 160$, with isolated inclusions of lower hardness; in the surface layers—$H_p = 161 \div 200$);

3) a deformed zone in the chip (hardness mainly within the range $241 \div 280$, but with a considerable number of harder inclusions);

4) a built-up-edge zone with very high hardness (predominantly within the range $321 \div 370$, and at some points up to 430).

Figures 17 and 18 show the results of hardness measurements on a microsection taken from tests with a high cutting speed on grade steel 30 ($v = 180$ m/min, Fig. 14). Here the same zones can be distinguished:

1) a zone of initial hardness (predominantly $H_p = 130 \div 165$, with occasional harder inclusions);

Fig. 15.

Visible annotations in the figure: \(\delta = 30^\circ\); \(0.1\ \text{mm}\); \(D = 2/10\); \(1/10\).

2) the zone of preliminary deformation (the hardness continuously decreases with increasing depth from a hardness of \(H_{\text{p}} = 236 \div 275\) to the initial value);

3) the deformed zone in the chip (predominantly \(H_{\text{p}} = 236 \div 275\), but there are inclusions with hardness above 300);

4) the built-up-edge zone with high hardness (up to 440).

Fig. 16

In addition, an increased hardness in the contact layer of the chip was clearly revealed here. In the preceding case we were unable to detect this because of the small thickness of the contact layer.

Figs. 19 and 20 interpret the results of measuring the hardness of a polished section obtained at a cutting speed of \(0.01\ \text{m/min}\) with a large ratio of chip thickness to chamfer width \((a/f = 1.73;\ \gamma = 60^\circ;\ \gamma_d = 57^\circ;\ \zeta = 1.42;\ \zeta_{\text{в}} = 1.06;\ \zeta_a = 1.34)\).

The corresponding experiments were carried out while planing the specimen on a milling machine, and before removal of the chip the upper surface of the specimen was cleaned with emery paper in order to eliminate the work-hardened layer from the preceding pass. Therefore, here we do not see a strengthened zone in the surface layers ahead of the cutter. The region of preliminary deformation is small in volume, which is explained by the slight degree of deformation in the chip (small shrinkage, large shear angle). On the other hand, the hardness of the cut surface and of the contact layer of the chip is high owing to the presence of burrs. The latter, as we have already indicated, are formed as a result of the periodic propagation of the deformed zone of the built-up edge inward ahead of the cutter (burrs on the cut surface) and the tearing away of particles of the built-up edge by the flowing chip (burrs on the chip). Naturally, the hardness of these burrs is comparable with the hardness of the built-up edge.

Fig. 17

Visible labels in the figure:

• $\delta = 40^\circ$
• $\gamma = 0.4$
• $a = 0.50$
• $t = 0.44$
• $0.8$
• $0.07$

In the process of cutting without a chamfer, under conditions where there is no built-up edge, the shear angle in the chip, as is known, is determined from the relation:

\[ \tg \beta = \frac{\cos \gamma}{\zeta_a - \sin \gamma}, \tag{1} \]

where \(\beta\) is the shear angle, \(\gamma\) is the rake angle of the cutter, and \(\zeta_a\) is the transverse shrinkage of the chip. In cutting with a built-up edge, when the rake surface becomes curvilinear and the actual rake angle is larger than the cutter’s sharpening angle, the above formula can no longer be used. Still less can it be applied to the case of cutting with a chamfered tool, when a built-up edge is present at all cutting speeds.

Fig. 18

Earlier [2], we put forward the assumption that, when a chamfered cutter is used, deformation in the chip is determined by the mean value of the rake angle \(\gamma_0\), and, consequently, for calculating the shear angle one may use expression (1), replacing \(\gamma\) in it by \(\gamma_0\):

\[ \tg \beta = \frac{\cos \gamma_0}{\zeta_a - \sin \gamma_0}. \tag{2} \]

In order to verify the correctness of this assumption, we performed, in Figs. 16, 18, and 20, geometrical constructions in accordance with formula (2), showing the direction of the shear plane. As is not difficult to see, despite the fact that the shape of the built-up edge differs sharply from a triangle, in all three cases the traces of the shear planes that we constructed coincide extremely closely with the lines delimiting the zone of preliminary deformation and the zone of the chip with increased hardness.

Fig. 19.

For an overall assessment of the hardness distribution, the average microhardness in each zone was calculated. The results of these calculations are given in Table 2, while Table 3 gives the percentage ratio between the hardnesses in the various zones. These tables also give the values of chip shrinkage and relative shear \((\varepsilon)\). The latter was calculated by the well-known formula:

\[ \varepsilon = \operatorname{ctg}\beta + \operatorname{tg}(\beta - \gamma), \]

in which, instead of the rake angle \(\gamma\), the value of the chip-flow angle \(\gamma_c\) was substituted.

In the figure legend:
\(H_\mu < 80\ \mathrm{kg/mm^2}\); \(H_\mu = 80\text{–}120\); \(H_\mu = 121\text{–}150\); \(H_\mu = 151\text{–}200\); \(H_\mu = 201\) and higher.

Fig. 20

Table 2

Table 3

The boundaries of the zone of preliminary deformation, within which the hardness was averaged, are shown in Figs. 16, 18, and 20 by a dotted line. In this connection it must be taken into account that in the first and second cases the cutting process is continuous (machining on a lathe), and consequently the outer surface to the right of the cutter was obtained during the preceding revolution of the workpiece, i.e., under the same conditions as the cut surface to the left of the cutter. Here the hardness was averaged within the entire zone bounded by the dotted line. For Fig. 16, in addition, the hardness in the surface layer ahead of the cutter was also calculated for a thickness equal to the depth of cut, since it is precisely from this layer that the material for chip formation is drawn. In the third case the chip was removed from an unwork-hardened surface; therefore here only the region ahead of the cutter is assigned to the zone of preliminary deformation.

Analysis of Tables 1 and 3 shows that in all three experiments, corresponding to such different cutting conditions, the hardness increases continuously in the successive transition from the undeformed zone to the zone of preliminary deformation and then to the chip and to the built-up edge. The hardness of the built-up edge is 2–3 times higher than the initial hardness and approximately 30% higher than the hardness of the chip. This means that, on a chamfered cutter, the built-up edge, by virtue of its hardness, can quite well play the role of a cutting element supplementing the cutter, although the character of plastic flow in the deforming material ahead of the built-up edge is undoubtedly different here than when cutting with an ordinary cutter. It is especially characteristic that the hardness of the built-up edge at a high cutting speed, where one might have expected softening of the built-up edge as a result of the high temperature, proves to be greater than at a speed of 0.01 m/min (a difference in speed by a factor of 18,000). This once again indicates the absence of fundamental differences between the nature of the built-up edge in the one and the other cases.

Another circumstance also attracts attention. It is natural to expect that the hardness in the deformed zone should be the greater, the higher the degree of deformation. This is indeed what follows from Table 3; moreover, it turns out that the relative increase in hardness in the transition from the undeformed zone to the preliminarily deformed zone (for the second experiment, Fig. 16, at a thickness \(a = 0.121\) mm), and from the latter to the chip and to the built-up edge, is determined not by the shrinkage of the chip, but by the magnitude of the relative shear. For example, in the second and third experiments the shrinkages are identical, whereas the relative shears and hardness differ substantially. Consequently,

and in the process of cutting with a chamfered tool, the degree of deformation is determined not by shrinkage, but by the relative shear. For an ordinary cutter this was shown earlier by A. M. Rozenberg and A. N. Eremin [10].

Summarizing the results of the present investigation, we arrive at the following conclusions.

1. The structure of the built-up edge on a chamfered cutter is fundamentally the same at all cutting speeds.

2. Under conditions of free chip flow, when the chip does not touch the rake face of the cutter ($\gamma_0 < \gamma$), the contours of the cross section of the built-up edge remain unchanged along its entire length.

3. With non-free chip flow ($\gamma_0 > \gamma$), the shape of the built-up edge is not the same in different sections.

4. Regardless of the cutting speed, the hardness of the built-up edge on a chamfered cutter is approximately 30% higher than the hardness of the chip.

5. The relative increase in hardness in the deformed zones (the zone of preliminary deformation, the chip, the built-up edge) is the greater, the greater the degree of deformation in the chip, expressed through the relative shear.

REFERENCES

1. Eremin A. N.—The Physical Nature of Phenomena in Steel Cutting. Mashgiz, 1951.

2. Poletika M. F.—Investigation of the Cutting Process with a Tool Having a Double Rake Face. Abstract of dissertation. Tomsk, 1951.

3. Rozenberg A. M. and Poletika M. F.—Features of the Cutting Process with a Chamfered Tool in High-Speed Turning. Proceedings of the Tomsk Polytechnic Institute, Vol. 75, 1954.

4. Klushin M. I.—Metal Cutting. Mashgiz, 1953.

5. Dyachenko P. E.—Investigation of the Dependence of Surface Microgeometry on the Conditions of Mechanical Machining. Publishing House of the Academy of Sciences of the USSR, 1949.

6. Isaev A. I.—The Process of Formation of the Surface Layer in the Machining of Metals by Cutting. Mashgiz, 1950.

7. Zorev N. N.—Investigation of Elements of the Mechanics of the Cutting Process. Mashgiz, 1952.

8. Mechanical Engineer’s Handbook. Vol. II, Mashgiz, 1952.

9. Khrushchev M. M. and Berkovich S. S.—PMT-2 and PMT-3 Instruments for Microhardness Testing. Publishing House of the Academy of Sciences of the USSR, 1950.

10. Rozenberg A. M. and Eremin A. N.—Plastic Deformation of the Chip in Metal Cutting. Proceedings of the Tomsk Polytechnic Institute, Vol. 75, 1954.