Adiabatic Shearing in Metal Machining

Synonyms

See Definition: Extended Definition

Definition

Adiabatic shearing in metal machining is plastic straining to form a chip so quickly that the heat generated has no time to flow away. If the heating causes the metal to soften (overcoming the strain hardening), further straining may concentrate in the soft part so that it becomes even hotter and softer. Shearing becomes localized in a narrow band of increasingly hot metal.

Extended Definition

Strain softening, shear localization, and shear banding are all associated with adiabatic shearing, but they are not synonyms as they can also occur, for other reasons, in isothermal conditions.

Shear localization or banding due to thermal softening does not require truly adiabatic (i.e., no heat flow) conditions. All that is required is a condition in which enough heating occurs. The term catastrophic thermal shear covers this. It focuses more on the observed behavior, less so on its cause. Catastrophic thermal shear leads to chips with a segmented or serrated or sawtooth form when viewed from a direction normal to the cutting tool’s cutting edge (see Application for examples). It is theory and applications of shear localization, leading to segmented, serrated, or sawtooth chip formation, that is the subject of this entry.

Theory and Application

The kinematic and geometrical conditions of serrated chip formation are more complex than those of deformation in simple shear, torsion, compression, and punching tests that are commonly used to study adiabatic shearing fundamentals. Figure 1 shows a cycle of flow during serrated chip formation from (a) localized shear in a shear band to (b) mixed localized flow and upsetting (upsetting is needed to accommodate the displacement of the cutting edge into the work material as the shear band moves up the rake face), to (c) homogeneous flow as the shear band moves out of the chip formation region (the shear band is deformation rather than load driven), and to (d) localized flow again (h is the uncut chip thickness, v_c the cutting speed).

Adiabatic Shearing in Metal Machining, Fig. 1

Numerical simulation of serrated chip formation at relative displacement intervals (a–d) of the work toward the tool of 0.5 h, from the author’s work. The particular strain-rate values are associated with h = 0.1 mm and v_c = 50 m/min

The role of theory is to determine the conditions of h, v_c, tool geometry (rake angle), and work material thermo-physical-mechanical properties that give rise to serrated rather than continuous or other classifications of chips and, in the conditions of serrated chip formation, to predict such measurable features of the serration as the maximum and minimum chip thickness h₁ and h₂, the angle θ at which the saw teeth are inclined to the back face of the chip, the teeth face separation L, and the shear-band width δ. If such quantities are predicted, then the cycles of temperature and stress in the tool will also be known.

Critical Conditions for Shear Localization

Strain softening is necessary for shear localization to occur but is not always due to adiabatic shear. Figure 2a, b show example dependencies of shear stress τ on shear strain γ from simple shear tests. The data are from tests on a free-machining mild steel but are intended to be considered qualitatively. In both figures, strain hardening at low strains gives way to strain softening at higher strains.

Adiabatic Shearing in Metal Machining, Fig. 2

The influences of (a) imposed pressure and (b) heating on a metal’s stress versus strain behavior (example of a low carbon re-sulphurized steel)

In Fig. 2a, from data in Shaw (2004), the test conditions are at room temperature and low strain rate. Conditions are isothermal, and strain softening is due to the nucleation and growth of voids. The different curves result from applying compressive pressure p to the shear plane. The larger the ratio p/k, where k is the peak shear flow stress from the test, the larger is the strain γ at which dτ/dγ = 0.

Figure 2b considers the effect of heating on the stress–strain curve. The curve marked “isothermal” is that for p/k = 0.6 from Fig. 2a. That marked “adiabatic” is obtained from the isothermal curve assuming all of the plastic work is converted to heat and that the shear flow stress reduces with temperature rise at the rate of 30 MPa per 100 °C (a reasonable value). The two curves marked “intermediate” suppose one third and two thirds of the heat to be conducted away. In these cases, softening is the result of heating. The strain at which dτ/dγ = 0 increases from the adiabatic to the isothermal condition.

As has already been written, the conditions of serrated chip formation are more complicated than those of simple shear. Even continuous chip formation (Fig. 3a) is more complicated than simple shear. In the primary shear zone of a continuous chip, strain increases along a streamline, for example, from A to B, so strain softening is most likely at the exit boundary. Along the exit boundary, both temperature and pressure vary. Small amounts of softening can be supported, without a change from continuous to banded flow, by hydrostatic pressure variations in the flow field. If shear localization does develop, it will occur during the buildup to continuous chip formation, not after the steady state has been established. Nonetheless, the conditions in which a continuous chip flow gives way to shear localization can be qualitatively considered in terms of the material behavior shown in Fig. 2 (assuming localization to set in when dτ/dγ ≈ 0) and the flow field of continuous chip formation.

Adiabatic Shearing in Metal Machining, Fig. 3

(a) Continuous chip formation; (b) shear strain dependencies on thermal number, thick lines for the initiation of shear localization due to void nucleation and thermal softening, and thin lines A to C for different circumstances of continuous chip formation considered in main text

Theories of heating in metal cutting show that conditions in the primary shear zone of a continuous chip change from isothermal to adiabatic as the thermal number hv_ctanφ/a increases through the range ≈1–100 where φ is the shear plane angle and a is the thermal diffusivity (the ratio of thermal conductivity to heat capacity) of the machined material. In Fig. 3b, the critical strains from Fig. 2 at which dτ/dγ = 0 are plotted against the thermal number. Although the strain axis could have been labeled from 0 to 10, from the data in Fig. 2, numbers have been omitted because it is intended that the figure’s use be qualitatively generalized beyond its particular example. At low values of the thermal number (isothermal conditions), critical strains are due to void nucleation and growth. As the number increases through the range ≈10–100, thermal softening becomes the critical factor. Critical strains for void nucleation vary with pressure (Fig. 2a), but only one level is shown in Fig. 3b.

Figure 3b also includes, as the dashed lines, the variation with thermal number of a range of possible variations of shear strains associated with continuous chip formation. For case A, these strains are greater than the critical strains for shear localization at all values of the thermal number. With increasing magnitude of the product hv_c, a transition will occur from serrated or sawtooth chip formation resulting from instability due to void formation to such chips caused by thermal instability. In case B, a change from continuous to serrated chip formation will occur as the thermal softening boundary is crossed. In case C, serrated chip formation will not occur at any value of hv_c.

Observed dependencies of the critical hv_c combinations for the onset of adiabatic shear banding on the material being machined and the tool geometry may be considered in terms of Fig. 3b. Observed transitions to localized shear and serrated chip formation with increasing h and v_c are only likely to be due to increasingly adiabatic conditions if hv_ctanφ/a is in the range ≈10–100. Certainly any transition at hv_ctanφ/a <1 or >100 is unlikely to be the result of adiabatic shear. Heat treatments that increase machined material hardness and reduce strain hardening, or prior working that also reduces strain hardening, will reduce the process strain at which thermal softening occurs and will reduce the critical values of h and v_c for serrated chip formation. Reducing the tool rake angle will increase the strain level of continuous chip formation and thus will also reduce the critical values of h and v_c at which serrated chips occur.

Developing a quantitative theory of the conditions for shear localization is the subject of ongoing numerical (finite element-based) research. Key earlier papers are (Recht 1964) in which the instability criterion dτ/dγ = 0 was first applied, (Semiatin and Rao 1983) in which it was argued that dτ/dγ needed to be substantially negative and (Hou and Komanduri 1997) in which the complexities of temperature distributions in shear localized chips were examined in more detail than in previous work. Adiabatic shearing has been the subject of a number of general reviews, for example, Walley (2007), and books, for example, Bai and Dodd (1992). These mention but do not have a main focus on machining. Walley (2007) mentions nine earlier reviews.

Development of Shear Localization

Once shear localization is initiated, flow of heat from the shear band is predominantly normal to its surface. From the theory of heat diffusion and given that a shear band is active (Fig. 1) for a time ≈(h/v_c), the minimum width over which conditions may be considered adiabatic ≈(a[h/v_c])^0.5 This is expected to be the minimum width δ of an adiabatic shear band, or (δ/h)_min ≈(a/[hv_c])^0.5. For typical machining conditions, δ_min is of the order of 10 μm. Experiments generally do show δ to be of this order and reducing with reducing h/v_c but not always to the power of 0.5.

Furthermore, δ depends on material properties in addition to a. δ may not achieve its minimum value. The thinning of a shear band is driven by the slope of the strain-softening curve. This varies widely between metals. Microstructural transformations, for example, dynamic recrystallization and phase changes (e.g., ferrite to austenite transformations in steels or α to β transformations in Ti alloys), greatly affect softening behavior and are observed in the shear bands of serrated chips at high cutting speeds. A metal’s softening response as well as its thermal diffusivity determines its shear-band thickness.

How the homogeneous deformation (Fig. 1c) develops between shear bands, in response to the stresses acting on it from the just formed shear band and from the tool, determines segmentation shape – such dimensions as h₁, h₂, L, and θ. Softening in the shear band thus influences segmentation shape as well as shear-band thickness.

Quantitative modeling and simulation of all these matters is the subject of ongoing research and cannot be sensibly reviewed in a short entry such as this.

Applications

Table 1 lists, for a range of metals of interest to machining and from published literature, experimentally observed minimum values of the product of h and v_c for serrated chip formation due to adiabatic shear localization. They are to be regarded only as indicative as in fact they depend on rake angle, a factor not considered in collecting material for the table and on material heat treatment, sometimes not recorded in the literature. Furthermore, transitions from one chip form to another are not sharp.

Adiabatic Shearing in Metal Machining, Table 1 Minimum values of hv_c for serrated chip formation by adiabatic shearing

Although the minimum values of hv_c range from <100 to >1,000 mm²/s, when divided by thermal diffusivity a, a narrower range of 20–100 is obtained. Considering that typical values of continuous chip shear plane angle are 20–40°, hv_ctanφ/a values are in the range expected from Fig. 3b.

In practice, the ranges in Table 1 are so broad that machinists or other interested people with a particular need to know the transition to adiabatic shearing for a particular work material heat treatment and tool geometry would be well advised to carry out their own experiments, for example, varying cutting speed over their range of interest at a fixed uncut chip thickness. However, some guidelines can be given in terms of Fig. 3b’s three cases A to C.

α and α-β titanium alloys almost always follow case A behavior although a small number of exceptions (case B behavior) may be found. Figure 4 shows a change from irregularly (void nucleated) to regularly (adiabatic sheared) serrated chips for a Ti-6Al-4V alloy as hv_c increases.

Adiabatic Shearing in Metal Machining, Fig. 4

Chip forms for a Ti-6Al-4V alloy, tool rake angle −6°, and scale bars 100 mm (From original work of J. Barry, see Acknowledgments)

By contrast, nickel-base superalloys and ferrous alloys almost always show case B behavior (with zero or negative rake tools, behavior can change to type C with increasingly positive rake angle). Figure 5 shows changing chip form from continuous to serrated with increasing speed for an Inconel 718 alloy, while Fig. 6 shows forms obtained for an AISI 1045 steel quenched and tempered to HRC50. In Fig. 5, the shear bands show deformed microstructure up to the highest speed, but in Fig. 6, a transformed shear band is seen at v_c = 240 m/min.

Adiabatic Shearing in Metal Machining, Fig. 5

Chip forms for Inconel 718, tool rake angle −6°, and h = 0.07 mm (From original work of E. Uhlmann and R. Zettier, see Acknowledgments)

Adiabatic Shearing in Metal Machining, Fig. 6

Chip forms for AISI 1045 steel, HRC50, tool rake angle −10°, and h = 0.15 mm (From original work of C.Z. Duan and L.C. Zhang, see Acknowledgments)

Finally, aluminum alloys show highly variable responses. Behavior of a single composition can vary from case A to case C dependent on heat treatment. Figure 7 shows overaged and underaged AA7075 chips. The overaged chip is continuous even though hv_ctanφ/a >100 (type C). The underaged chip is serrated. It maintains this to the lowest cutting speeds (type A).

Adiabatic Shearing in Metal Machining, Fig. 7

Chip forms for AA7075 v_c = 7,000 m/min and tool rake angle 0°: (a) overaged, h = 0.14 mm and (b) underaged, h = 0.07 mm (From original work of C. Mueller, see Acknowledgments)

More examples can be found in two textbooks, Shaw (2004), which takes the view that fracture (void nucleation) is more important than adiabatic shear for the initiation of serrated chip formation, and Trent and Wright (2000), which considers secondary shear (stick–slip motion between the chip and tool) as additionally influencing behavior, and one research monograph (Tönshoff and Hollmann 2005).

Cross-References

Chip-forms, Chip Breakability and Chip Control

Cutting of Inconel and Nickel Base Materials

Cutting Temperature

Cutting, Fundamentals

Hard Material Cutting

High Speed Cutting