DIVIDING GRIDS FOR THE EXPERIMENTAL STUDY OF LARGE PLASTIC DEFORMATIONS

G. L. KUFAREV, M. G. GOLDSHMIDT, V. A. GOVORUKHIN

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

The study of the deformed state by the method of dividing grids makes it possible to obtain the most complete information about the process. At present, methods are widely known for applying dividing grids for the study of comparatively small deformations [1]. The use of dividing grids for studying large plastic deformations, especially those occurring in small volumes (for example, the study of the cutting process), is associated with a number of difficulties caused by the insufficient development of methods for applying the dividing grids required for these conditions. This article sets forth the results of work carried out in the metal-cutting laboratory on improving methods for applying grids to a specimen for the study of the cutting process.

The specific conditions of metal deformation in the chip-formation zone impose serious requirements on dividing grids: a relatively small base, strength, contrast, and, in the case of studying the cutting process at high speeds, heat resistance.

The dimensions of the grid base, which largely determine the technology by which it is obtained, are limited by the requirement of uniformity of deformation within a single cell, since otherwise the grid elements—circles and squares—after deformation take the form, respectively, of irregular ellipses and quadrilaterals with curvilinear sides, figures from which determination of the deformation does not appear possible. Because achieving ideal uniformity of deformation in an elementary volume is practically impossible, in order to reduce the error in calculations associated with this (all calculation formulas are obtained under the assumption of uniformity of deformation within a single cell), one should strive in every way to reduce the grid base.

On the other hand, reduction of the grid base is limited by the following. First, all real metals are anisotropic to a certain degree, and the degree of anisotropy depends (up to a certain limit) on the volume under consideration: the larger the dimensions of the plastic region considered, the more justified it is to regard the deformed material as isotropic. The crystalline structure of a metal, as experiments have shown, manifests itself even in such homogeneous metals as copper already at side dimensions of the elementary-

of the cell on the order of 0.03 mm. Secondly, at large degrees of deformation the surface of the body polished before deformation becomes rough. This phenomenon also occurs when the surface of interest is placed inside a built-up specimen. The height of the irregularities proves to be so considerable that it is extremely difficult to record marks smaller than 0.03–0.05 mm.

When choosing the grid base, it is also necessary to take into account the dimensions of the plastic region, which, for a given cutting speed and rake angle of the tool, depend mainly on the thickness of the layer being cut. If the chip thickness is varied within the range 0.3–1 mm, then in order to obtain reliable results it is necessary to use a grid with a base on the order of 0.05–0.1 mm. The specimens for the study were assembled from two plates, and the applied dividing grid was placed in the midsection. Analysis of the distortions of the grid was carried out by studying chip roots, which were fixed with the aid of special devices, or, when cutting at microspeed, by stopping the machine table.

The material for investigation should, as far as possible, have a fine-grained structure. Good results were obtained when using the dividing-grid method with a base of 0.05 mm to study the cutting process of steel ShKh15, steel 15 (rolled), and 2Kh13. The use of grids with such a base for work on steel 40 and steel Kh17N13M2T proved practically impossible. This is well explained by the character and size of the grains in the structure of the indicated materials. Photographs of the microstructures of these materials in Fig. 1, a, b, c, d, taken at a magnification of 500 times, on which cells of a dividing grid with a base of 0.05 mm are drawn at the same magnification, make it possible to predict in advance that the deformation within a cell may be taken as homogeneous for the fine-grained steels ShKh15 and steel 15, and will be knowingly nonuniform when steels 40 and Kh17N13M2T are deformed. Thus, microstructural analysis must be an obligatory condition when choosing a material for the study of large deformations by means of the dividing-grid method.

The type of dividing grid largely predetermines the method and technology of producing it. For studying the cutting process in planing, either grids made from a system of circles or grids with square cells are used [2, 3, 4]. From the standpoint of the laboriousness of their subsequent processing (measurement) and the accuracy of the deformation calculation, they are practically equivalent. However, the technology for producing a square grid is simpler, and therefore it should be preferred when working at microspeeds.

It is most expedient to carry out a study of the cutting process in turning by means of a dividing grid whose cells are formed by superimposing on an Archimedean spiral with a pitch of 0.05 mm a system of radial rays, the central angle between which is equal to 5′ [5].

The methods for applying dividing grids are determined to a considerable extent by the research problem. Thus, for studying the process of chip formation in planing, it is possible to use any of the five methods of applying grids analyzed below; in turning, only the scratching method can be used, and practically only in the case when, with the aid of appropriate devices, it is possible to fix the chip root in a preselected region of the specimen.

One of the simplest methods may be considered the production of grids by pressing a conical indenter into the surface of the specimen, for example—

Fig. 1. Microstructure of materials, ×500: a) ShKh15, b) steel 15, c) 2Kh13, d) Kh17N13M2T

for example, a corundum needle [2]. Such a grid is applied on an instrument for measuring microhardness; in this case the needle is selected so that the impressions on the specimen surface have the form of circles. Both the grid pitch and the diameter of the impressions can be made practically as small as desired (Fig. 2, a). The disadvantages of the indentation method include its laboriousness, the need to select a material with a homogeneous structure (so that the impressions are uniform), and also possible errors associated with disruption of continuity and with changes, as a result of indentation, in the physicomechanical properties in the impression zone.

Applying grids by the photochemical method with subsequent etching, i.e., according to the technology for producing typographic screened plates, makes it possible to avoid the above-mentioned shortcomings of the indenter-indentation method. Here it is possible either to use plates manufactured in typographic ...

Fig. 2. Distortion of dividing grids on the roots of chips fixed during cutting:
a) M1 copper ($\gamma = 27^\circ$, $a = 2 \text{ mm}$, $V = 23.5 \text{ mm/min}$); grid base $0.02 \text{ mm}$, circle diameter $0.01 \text{ mm}$;
b) steel 15 ($\gamma = 30^\circ$, $a = 1.5 \text{ mm}$, $V = 1 \text{ m/min}$); grid base $1 \text{ mm}$;
c) steel 20Kh ($\gamma = 30^\circ$, $a = 0.55 \text{ mm}$, $V = 57 \text{ m/min}$; grid base $0.3 \text{ mm}$, circle diameter $0.2 \text{ mm}$);
d) steel; pitch of the Archimedean spiral $0.05 \text{ mm}$, central angle between radial rays $5^\circ$.

photography of the cliché, or by applying the grid by the cliché method to materials previously coated, by galvanic means, with a thin (5–15 microns) layer of zinc [3]. The second technique should be considered more universal and more correct: in this case the etched points have a depth equal to the thickness of the galvanic coating, i.e., they constitute a system of “flat circles.” Such a grid is obtained with very good contrast and is convenient for analysis and photography (Fig. 2, б).

The method of depositing grids in vacuum is attractive above all because it makes it possible to obtain a contrasting grid whose color differs from that of the specimen material and which is therefore readily visible under those conditions in which a relief grid (for example, a scratched one) may be obscured by surface microroughnesses.

The grids were deposited on an installation analogous to that described in [6]. A metal grid with a pitch of 0.15 mm was used as the mask. Before deposition and during it, the specimen was heated to a temperature of 300°, which, owing to better adhesion, ensured greater grid strength. Deposition was carried out for 10 minutes at a vacuum of \(10^{-5}\)–\(10^{-6}\) mm Hg. The thickness of the deposited grid proved to be approximately 1 micron.

Under cutting-process conditions, the strength of grids obtained by depositing aluminum on copper and brass, copper on brass, and steel 20Kh was tested. The best was a copper grid deposited on a steel specimen. A photograph of the chip root with such a grid is presented in Fig. 2, в.

Depending on the grid-mask used, the deposition method can produce various grids, including a system of circles. In this case, however, difficulties arise in obtaining masks with sufficiently small (0.05–0.1 mm) openings. The issues of adhesion of the deposited material to the specimen material also require further development. Nevertheless, the experiments performed showed that dividing grids obtained by vacuum deposition can be successfully used in the study of large plastic deformations.

As the investigations showed, quite satisfactory grids can be obtained by galvanic means. The principle of applying the grids is analogous to vacuum deposition: a thin layer of metal is applied by electroplating to a specimen with a grid-mask. By selecting the color of the coating appropriately, it is possible to obtain sufficiently contrasting grids. The principal shortcoming of this method may be considered the difficulty of obtaining the necessary masks, since the contrast of the grid lines depends on the tightness with which the mask adheres to the specimen.

Scratched grids (Fig. 2, г) were obtained with the aid of a simple attachment on a toolmaker’s microscope—when applying grids for investigating deformations in planing—or by applying an Archimedean spiral with a pitch of 0.05 mm on a lathe, and radial rays on a toolmaker’s microscope—when obtaining specimens for turning.

As the cutting tool, knives of high-speed steel or hard alloy may be used. The best results are obtained with the use of a diamond. The investigations showed that the tool must have an included angle of no more than 30° and the smallest possible radius at the tip.

Preliminary galvanic coating (most often copper plating was used in the investigations) of the specimen surface significantly increases the contrast of the grids.

Grids applied by this method made it possible to study the deformed state during cutting of various metals (L62 brass, 2Kh13 steel) at speeds from 23 mm/min to 250 m/min and with changes in the rake angle within the range from \(+45^\circ\) to \(+5^\circ\). The degree of deformation in these experiments reached \(e_i = 1.5 \div 2\).

REFERENCES

1. Ya. B. Fridman, T. K. Zilova, N. I. Demina. Study of Plastic Deformation and Fracture by the Method of Rolled Grids. Oborongiz, Moscow, 1962.

2. A. M. Rozenberg, G. L. Kufarev. Determination of the degree of plastic deformation in cutting. Vestnik mashinostroeniya, No. 6, Moscow, 1958.

3. G. D. Del, M. G. Goldshmidt. Study of plastic deformation on models made from typographic screened clichés. Zavodskaya laboratoriya, No. 4, Moscow, 1966.

4. V. A. Krivoukhov, P. D. Bespakhotnyi. Investigation of the deformation work in metal cutting. Izvestiya vuzov. Mashinostroenie, No. 1, Publishing House of the Bauman Moscow Higher Technical School, 1958.

5. G. L. Kufarev, V. A. Govorukhin. Investigation of the deformed state of the chip-formation zone at high cutting speeds. Izvestiya vuzov. Mashinostroenie, No. 1, Publishing House of the Bauman Moscow Higher Technical School, 1969.

6. L. M. Rybakova. A new method for applying dividing grids to specimens. Zavodskaya laboratoriya, No. 11, Moscow, 1958.