On the Maximum Shear Stress During the Formation of Shear Chips
Abstract Generated abstract
This paper examines the stresses associated with shear-chip formation, focusing on crack initiation, crack propagation, and brittle fracture of a chip element during cutting. Experiments were performed in free cutting of LS59-1 brass at low speed, with synchronized force recording, cine filming, chip-root observation, and hardness measurements used to analyze the stress state near the shear plane. The study finds that tangential stresses in the sliding plane are relatively uniform before cracking, with an average value close to that calculated from dynamometer data, while crack formation reduces the effective load-bearing area and can raise stresses further. Using microhardness measured on the shear surface and a calibration curve, the maximum tangential stress at fracture is estimated at 38 to 41 kg/mm2.
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ON THE MAXIMUM TANGENTIAL STRESS DURING THE FORMATION OF SHEAR CHIPS
G. L. KUFAREV, M. G. GOLDSHMIDT
(Presented by the scientific seminar of the Department of Machine Tools and Metal Cutting)
In the study of the mechanics of shear-chip formation, an essential role is played by the analysis of the conditions that promote the formation of a crack, the mechanism of its propagation up to the moment of brittle fracture of the chip material, and the stresses acting at the moment of shearing of the element.
The investigation was carried out in free cutting of a specimen of brass LS59-1 at a speed \(V = 23\) mm/min, with feed \(a = 0.67\) mm, using a cutter with rake angle \(\gamma = +29^\circ\). The width of the specimen was \(b = 2.85\) mm. Cutting was performed by the transverse feed of the table of a 6N13P milling machine, on whose bed a dynamometer designed by VNII and a KS cine camera were mounted.
It is known [1] that, when cutting brass LS59-1, the tangential stresses in the shear plane do not depend on the cutting conditions, and the deformation over the entire cross section of the specimen may be taken as plane. These circumstances, which make it possible to analyze the cutting process at microspeeds and by means of cine filming of the side surface, predetermined the choice of experimental material.
Figure 1 shows the variation of the components of the cutting force during the formation of one chip element, and indicates the position after which a crack appears in the element. The latter follows from consideration of cine frames of the process, taken synchronously with the oscillograph recording of the components of the cutting force, and from the study of chip roots fixed at the stages of element formation. The crack that has appeared propagates for some time over 10–20% of the length of the shear plane, after which brittle fracture of the chip material occurs.
The formation of a crack promotes localization of deformation in a very narrow zone, so that, by measurement in the direction perpendicular to the principal cutting plane, it is difficult to obtain reliable information on the hardness reached by the material in the process of fracture. An idea of the maximum magnitude of work hardening can be obtained if the microhardness is determined directly on the shear surface of the element, in the direction perpendicular to this plane.
At the same time it should be noted that, after crack formation, the components of the cutting force remain for some time close to their maximum values; owing to the decrease in the area of action of the force, this should lead to a further increase in stresses.
The stressed state in the cutting zone was investigated by the method of hardness measurement [2] on the chip root (Fig. 2), fixed ...
at the moment preceding the formation of a crack. In this case, the calibration graph relating the hardness \(H\) to the intensity of the positive stresses \(\kappa\) was obtained by testing, under axial compression up to various degrees of deformation, 10 specimens made of the material under investigation.
Fig. 1
Fig. 2. Grid of slip lines in an element of a shear chip
material. Analysis of the stressed state showed that in the sliding plane of the element the distribution of normal stresses differs substantially
with a certain nonuniformity; the tangential stresses are distributed relatively uniformly, and the mean tangential stress is \(\tau_{\mathrm{avg}} = 26.7\ \mathrm{kg/mm^2}\), which differs by 3% from \(\tau\) calculated from the dynamometer data for the cutting force.
Assuming that separation of a chip element occurs along the envelope of the slip line [3] (and on the slip line the tangential stress is numerically equal to \(k\)), and having the value of the hardness measured directly on the shear surface, from the calibration curve \(k — H\) we find that the maximum tangential stress at the moment of fracture reaches the value
\[ \tau_{\max} = 38\text{–}41\ \mathrm{kg/mm^2}. \]
REFERENCES
- Metal Cutting and Tooling. Ed. by A. M. Rozenberg, Mashinostroenie, 1964.
- G. D. Del. Study of plastic deformation by hardness measurement, Izvestiya TPI, vol. 138, No. 1, 1965.
- S. A. Khristianovich. The plane problem of the mathematical theory of plasticity under external forces prescribed on a closed contour. Matematicheskii sbornik, new series, vol. I (43), issue 4, 1936.