EFFECT OF THE HARDNESS OF HARDENED AND PRE-DEFORMED ShKh15 STEEL ON ITS PHYSICOMECHANICAL PROPERTIES AND MAIN PARAMETERS OF THE CUTTING PROCESS

G. L. KUFAREV, N. I. KHOVAKH

(Presented by the scientific seminar of the departments of mechanical-engineering technology, machine tools, and metal cutting)

A large number of works by Soviet and foreign researchers have been devoted to the influence of the physicomechanical characteristics of the material being machined on the chip-formation process and its constants. The desire of scientists to relate the characteristics of metals obtained in standard tests to the stresses and strains arising in the cutting process is quite natural, since in this case the need for a complex and laborious experiment is eliminated and it becomes possible, by calculation, to determine the cutting forces and to assign the most economical machining regime for the given material. Cutting forces are most often associated with the characteristics of strength, plasticity, and hardness of the metal. Of particular interest is the dependence of cutting forces on hardness, since determination of the latter does not require complex equipment or considerable time expenditure.

The aim of our investigations was to determine the influence of hardness on the chip-formation process in turning ShKh-15 steel. The workpieces studied had different hardness, obtained both by appropriate heat treatment and by preliminary deformation by axial compression.

The hardness of the hardened steel was as follows: \(HB = 250, 300, 350, 400, 500\ \text{kg/mm}^2\). The work-hardened blanks had hardness \(HB = 250, 270, 320\ \text{kg/mm}^2\); annealed blanks without preliminary work hardening had \(HB = 197\ \text{kg/mm}^2\).

In the first part of the work, the physicomechanical properties of the indicated steels were investigated. The investigations were carried out in tension and axial compression. Compression was performed in multiple stages with lubrication, which made it possible to obtain significant plastic deformations and eliminated the influence of friction on the end faces of the specimens [1]. Tensile tests of standard specimens of ShKh-15 steel hardened to different hardnesses made it possible for us to relate the hardness of the specimens to their strength and plasticity characteristics. The results of these tests are presented in Table 1.

As can be seen from Table 1, with increasing hardness the plasticity \((\delta\%; \Psi\%)\) decreases considerably more intensively than the yield strength \(\sigma_t\) and the ultimate strength \(\sigma_{\mathrm{pr}}\) increase. At a hardness of \(HV = 500\), the relative elongation and reduction of area are approximately 10 times smaller than in raw steel with hardness \(HV = 197\ \text{kg/mm}^2\), whereas the yield strength and ultimate strength have increased only threefold.

Table 1

The flow curves obtained in compression of raw, hardened, and pre-deformed steel are presented in Fig. 1. As follows from the flow curves for raw and hardened steel, with increasing strain intensity the stress intensity increases. In the region of small strains, the increase in stress intensity with increasing strain intensity proceeds the faster, the harder the tested specimens are. In the region of large strains, the dependences \((\sigma_i = f(e_i))\) have a rectilinear character with approximately the same angle of inclination for all specimens studied, regardless of their hardness. The higher the hardness, the higher the flow curves are located.

The flow curves for pre-compressed specimens in the region of large plastic strains likewise have a rectilinear character. However, unlike hardened steel, in this case the angle of inclination of the flow curves decreases with increasing hardness.

For a hardness of \(HB = 250\) kg/mm², the slope of the flow curves of hardened and deformed steel is approximately the same. When comparing the flow curves of hardened and pre-compressed specimens having \(HB > 250\) kg/mm², it is seen that strain hardening increases more slowly in the latter. Moreover, the lag in the increase of stress intensity with increasing strain intensity is the greater, the higher the hardness of the hardened and strain-hardened specimens being compared.

The compressed specimens were cut from blanks intended for cutting experiments, so that the secondary compression was carried out in the same

Fig. 1.

Vertical axis: \(\sigma_L,\ \mathrm{kg/mm^2}\)

Horizontal axis: \(e_i\)

Legend:

• ● \(H_B = 197\)
• △ \(H_B = 250\)
• ■ \(H_B = 300\)
• ▼ \(H_B = 350\)
• × \(H_B = 400\)
• ♦ \(H_B = 500\)

ShKh-15 after deformation [[unclear]]:

• △ \(H_B = 250\)
• □ \(H_B = 270\)
• \(\sigma H_B = 320\)

in the same direction as the preliminary deformation. Thus, simple stepwise compression takes place. This is confirmed by the fact that if the magnitude of the preliminary compression is added to the deformation obtained under repeated compression, the experimental points of the dependence \(\sigma_i = f(e_i)\) fall on the flow curve obtained in compression of raw ShKh15 steel. The exception is several points corresponding to specimens having a hardness of \(HB = 270\) and \(320\ \text{kg/mm}^2\) (marked in the figure by vertical strokes). The reason for the lower values of stress intensity for these points is the presence of curvilinear portions on the flow curves of preliminarily deformed steels with hardness \(HB = 270\) and \(320\ \text{kg/mm}^2\). The points marked by vertical strokes correspond to points lying on the curvilinear portions of the flow curves obtained without taking preliminary work hardening into account.

The experimentally obtained curvilinear portions of the dependence \(\sigma_i = f(e_i)\) for specimens having a sufficiently large preliminary deformation are, in our opinion, the result of recovery that has occurred.

The recovery process proceeds the more completely, the longer the recovery time and the greater the deformation [2]. In our case, compression tests were carried out 6 months after preliminary deformation. Such a long period, in our opinion, is quite sufficient for the noted softening, which is greater the higher the hardness of the specimens and, consequently, the greater the preliminary work hardening.

It should be noted that curvilinear portions on the flow curves during repeated compression of steels were obtained also in the experiments of A. M. Rozenberg and A. N. Eremin [3], as well as in work [4].

Measurement of hardness in the diametral section of compressed specimens made it possible to determine the relationship between hardness, stress, and deformation.

The dependence of the hardness of compressed specimens on stress is presented in Fig. 2. With scatter not exceeding the limits of experimental accuracy, in the region of large plastic deformations the relationship between hardness and stress is expressed by the equation

\[ \sigma_i = 0.37\,HV. \]

The deviation from this dependence is greater the smaller the compression deformation. If the points corresponding to the ratio of hardness and yield strength are not counted (marked in Fig. 2 by strokes), the error does not exceed 10%.

Upon a more detailed consideration of the described dependence separately for each material, taking into account also the relationship between hardness and the yield strength of the starting material, the following is found:

1. Each material has its own curve \(\sigma_i = f(HV)\).
2. The general dependence for all materials is close to an envelope.
3. The largest deviations from the general curve occur at small deformations.

An analogous dependence of the hardness of deformed specimens on stress intensity for various ferrous and nonferrous metals was obtained earlier by G. D. Del’ [5].

If the relationship between \(\sigma_i\) and \(HV\) in the region of large plastic deformations is satisfactorily expressed by a single-valued function irrespective of hardness, then the dependence of hardness and strain intensity for each material is expressed by its own curve over the entire range of deformations (Fig. 3). The higher the initial hardness, the greater the hardness of the specimens after compression.

Fig. 2

Fig. 3

The character and angle of inclination of the curves \(HV = f(e_i)\) for specimens having an initial hardness \(HV \geq 300\) are approximately the same. Steel hardened to a hardness \(HV = 250\) has a smoother curve, convex upward. The dependence \(HV = f(e_i)\) for specimens that did not undergo heat treatment is expressed by a general curve, which is quite natural, since in this case we have simple multistage compression.

The phenomenon of softening discussed above is found on the curve under consideration at the points marked by vertical strokes. As follows from the graphs, for specimens with hardness \(HV \geq 300\) a decrease in hardness is observed in specimens that received deformation within the range from \(e_i = 0.05\) to \(e_i = 0.1\).

Similar results were obtained in the experiments of P. Bridgman [1]. The results of our experiments coincided with those of P. Bridgman, despite the difference in method. We measured hardness not on the end face of a single specimen after each stage of compression, as P. Bridgman did, but in the diametral section of several specimens, each of which had been compressed to a different degree of deformation. P. Bridgman considers the indicated phenomenon possible as a result of the Bauschinger effect.

Our hardness measurements were carried out in a plane perpendicular to the end face of the specimen; therefore the compressive deformation from the penetration of the indenter is not superimposed on the preceding tensile deformation. This gives us grounds to state that P. Bridgman’s assumption concerning the causes of the decrease in hardness with increasing deformation is not confirmed by our experiments.

In the second part of the work, experiments were carried out on cutting hardened and pre-deformed steel. The experiments were performed in turning with cutters with mechanical clamping of a T15K6 hard-alloy insert. The grinding geometry was as follows: the rake angle was taken as \(\gamma = +10^\circ;\ 0^\circ;\ -10^\circ\); the remaining grinding angles were constant and equal to \(\varphi = 75^\circ\), \(\varphi_1 = 15^\circ\), \(\alpha = \alpha_1 = 10^\circ\), \(\lambda = 0^\circ\); the nose radius of the cutter was \(r = 0.3\) mm.

The cutting forces were measured with an elastic-electric dynamometer with inductive sensors [6]. As our experiments showed, the dependence of the cutting forces on speed, both for hardened steel and for ShKh-15 steel pre-compressed to different hardnesses, is expressed by the so-called typical curve characteristic of cutting ordinary annealed steel.

When turning pre-deformed steel at a constant cutting speed, all three components of the cutting force prove to be smaller than when machining non-work-hardened material (\(HB = 197\ \text{kg/mm}^2\)), and the greater the hardness of the pre-compressed material being machined, the smaller they are.

When machining hardened steel, the cutting forces do not depend on hardness and are approximately equal to the forces arising when turning steel \(HB = 197\ \text{kg/mm}^2\).

An exception is the cutting of steel hardened to a hardness \(HB = 250\text{–}300\ \text{kg/mm}^2\). In this case the cutting forces prove to be somewhat greater than when machining annealed steel and steels hardened to hardness \(HB = 300\text{–}500\ \text{kg/cm}^2\) [7].

Comparison of the components of the cutting force arising when machining ShKh-15 steel of the same hardness, obtained by heat treatment and by preliminary deformation, shows that the forces \(P_z\), \(P_x\), \(P_y\) are greater in the case of cutting hardened steels.

All the indicated dependences of the cutting forces on speed for hardened and pre-deformed ShKh-15 steel hold over a wide range of feeds \((S = 0.056—0.708\ \text{mm/rev})\) and for any of the tool rake-angle values adopted by us.

Figure 4 presents the dependence of the principal component of the force acting on the rake face of the cutter on the cutting speed for steel hardened and deformed to different hardnesses. (The cutting forces were resolved into forces acting on the rake and flank faces of the tool according to the method of Prof. A. M. Rozenberg [8]).

Fig. 4

As follows from the graph, all the regularities stated above, which relate to the cutting forces measured by the dynamometer, can be fully applied also to the vertical projection of the force acting on the rake face of the cutter. For the resultant horizontal projections of the forces acting on the rake face of the tools \((R_{2,3})\), this regularity is expressed indistinctly. In this case, at equal hardness of hardened and pre-compressed steel, the difference in forces proves to be insignificant or is entirely absent. Such leveling of the force \(R_{2,3}\) for hardened and deformed steel occurs because the forces on the flank face of the tool, which in turning hardened steel are higher than in machining work-hardened steel, exert a considerably greater influence on the horizontal projections of the cutting force than on the vertical projection. With increasing hardness, the forces on the flank face increase; moreover, their difference for hardened and pre-compressed steels is greater for the normal component than for the tangential one, and the greater, the higher the hardness of the material being machined.

If, in turning hardened steels, the cutting forces proved to be greater than in turning steels deformed to the same hardness, then one might have expected a similar relationship also for chip shrinkage. However, as our experiments showed (Fig. 5), the chip shrinkage $\xi$ in turning work-hardened steels proved to be higher than for hardened steels. Moreover, this difference is the greater, the lower the hardness of the steel.

Fig. 5

The reason for this apparent discrepancy, intensified still further by the fact that the coefficient of friction in turning deformed steels at the same shrinkage is higher than in turning hardened steels, was clarified by compression tests.

On the flow curves (Fig. 6), obtained in compression of work-hardened and hardened steel, points of the dependence $\sigma_i = f(e_i)$, calculated from cutting experiments, are plotted. The intensity of deformation in cutting was obtained by recalculating the relative shear $\varepsilon$, calculated from the equation

Fig. 6

from cutting experiments. The intensity of deformation in cutting was obtained by recalculating the relative shear $\varepsilon$, calculated according to the equation

\[ \varepsilon = \frac{\xi^2 - 2\xi \sin \gamma + 1}{\xi \cdot \cos \gamma}, \tag{1} \]

into the true shear \(g\) by the Nadai formula [9]

\[ g=\ln \left[1+\frac{\varepsilon}{2}\left(\varepsilon+\sqrt{4+\varepsilon^{2}}\right)\right], \tag{2} \]

and then into the strain intensity

\[ \zeta_i=\frac{g}{\sqrt{3}} . \tag{3} \]

As follows from Fig. 6, for hardened steels, at a smaller deformation, higher stresses occur, which, in our opinion, leads to an increase in the cutting forces for heat-treated steels in comparison with pre-deformed steels, despite the fact that, at a constant cutting speed, chip shrinkage is greater in the latter.

Brief conclusions

1. With an increase in the hardness of hardened steel, the ultimate strength and yield strength increase less intensively than the plasticity characteristics decrease.

2. In the range of large plastic deformations, the dependence \(\sigma_i=f(\varepsilon)\) is rectilinear in character. The higher the hardness, the higher the flow curves are located. The angle of inclination of the curves remains approximately constant for all heat-treated steels and decreases with increasing hardness of the pre-deformed steel.

3. The dependence of hardness on the stress intensity in the range of large plastic deformations can be expressed by the equation \(\sigma_i=0.37\,HV\) for all the steels investigated.

4. The dependence of hardness on the strain intensity is expressed by a common curve for all specimens that have not undergone heat treatment.

5. When turning hardened steel, the cutting forces measured by the dynamometer, and the vertical component of the force acting on the front face of the cutter (at \(V=\mathrm{const}\)), are greater than when cutting steel pre-compressed to the same hardness.

6. The resultant of the horizontal components of the forces acting on the front face of the tool is approximately the same in magnitude when turning hardened steel and steel pre-compressed to the same hardness.

7. Chip shrinkage at the same cutting speed proves to be greater when cutting work-hardened steel than hardened steel. This difference is the smaller, the greater the hardness of the steel.

8. The forces acting on the rear surfaces of the tool, at constant chip shrinkage, have higher values when turning hardened steel.

LITERATURE

1. P. Bridgman. Studies in Large Plastic Flow and Fracture. IL, Moscow, 1955.

2. A. M. Rozenberg, A. N. Eremin. The influence of deformation rate on stresses in the process of cutting a plastic metal. Izv. TPI, vol. 75, 1954.

3. Cutting of Metals and Tools, ed. A. M. Rozenberg. Mashinostroenie, Moscow, 1964.

4. Strength Reserves of Metallurgical and Machine-Building Equipment. Volgo-Vyatskii SNKh, 1965.

5. G. D. Del’. Investigation of plastic deformation by measuring hardness. Dissertation, Tomsk, 1965.

6. A. M. Rozenberg, N. I. Khovakh, V. I. Livshits. A lathe dynamometer for measuring forces up to 2 tons. Stanki i instrument, No. 9, 1964.

7. N. I. Khovakh. The influence of the hardness of ShKh-15 steel on the chip-formation process. Izv. TPI, vol. 147.

8. A. M. Rozenberg, A. N. Eremin. Elements of the Theory of the Metal-Cutting Process. Mashgiz, 1956.

9. A. Nadai. Plasticity and Fracture of Solids. IL, 1954.