CIRP Annals - Manufacturing Technology 68 (2019) 41–44
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Controlling segmentation in cutting of metals Mojib Saei a, Anirudh Udupa a, Koushik Viswanathan b, Tatsuya Sugihara c, Rachid M’Saoubi (1)d,*, Srinivasan Chandrasekar a a
Center for Materials Processing and Tribology, Purdue University, West Lafayette, IN, USA Department of Mechanical Engineering, Indian Institute of Science, Bangalore, India Department of Mechanical Engineering, Osaka University, Osaka, Japan d R&D Material and Technology Development, Seco Tools AB, Fagersta, Sweden b c
A R T I C L E I N F O
Keywords: Machining Fracture analysis High-speed imaging
A B S T R A C T
We examine segmented chip formation and associated ﬂow dynamics in cutting of metals of low-tomoderate workability using high-speed imaging. Segmentation is initiated by a surface instability – formation of a ductile crack in a prow – on workpiece surface ahead of the tool, this crack then propagates towards the tool tip. Prow-crack initiation occurs at a critical strain~0.75 that is independent of material and deformation geometry. This ductile failure is analyzed in terms of local hydrostatic stress state and stress triaxiality. Material-agnostic methods to suppress and enhance segmentation using constrained cutting and a mechanochemical effect are demonstrated. © 2019 Published by Elsevier Ltd on behalf of CIRP.
1. Introduction Chip formation in ductile metals occurs by large strain deformation with effective strains of 1–10. When the deformation is uniform, and the geometry is 2-D (plane-strain), material ﬂow is well-described as arising by simple shear conﬁned to a narrow region – the shear plane/zone model . By analogy with ﬂuid ﬂow, this deformation can be termed as smooth laminar ﬂow. However, uniform deformation is by no means the norm in metals. Three distinct unsteady deformation modes, with different ﬂow features, are well-known to exist, the most prominent of these being segmented ﬂow [2–5] and shear-band ﬂow [6,7]. The former occurs with metals of low to moderate workability such as hard steels, and Mg and Zn; while the latter prevails in metals with low thermal conductivity/diffusivity, e.g., Ti and Ni. In both of these instances, the chip has a distinct serrated appearance but with key differences in the serration morphology. Furthermore, the underlying deformation mechanics is quite different, with ﬂow localization in shear banding occurring by intense adiabatic shear in thin zones (strains~10–25) [6– 8]; while with segmented ﬂow, periodic fracture in narrow regions restricts the deformation (strain~2) and the so-called saw-tooth chip results [2,3]. A third, less-studied unsteady mode – sinuous ﬂow – with folded chip morphology, is observed with highly strain-hardening metals . This mode too is distinguished by ﬂow localization but of lesser intensity than in shear banding. It is unclear as to whether the uniform deformation mode is preferable to one of the unsteady modes or vice versa; in fact, some examples presented in this study will attest to this statement. * Corresponding author. E-mail address: [email protected]
(R. M’Saoubi). https://doi.org/10.1016/j.cirp.2019.04.073 0007-8506/© 2019 Published by Elsevier Ltd on behalf of CIRP.
Regardless, it would be of value to be able to induce transitions between these ﬂow modes, i.e., effect ﬂow control, via suitable changes to the deformation geometry or process conditions, but without material modiﬁcations. An example of such ﬂow control was demonstrated with shear bands, by applying a constraint of sufﬁcient extent in the deformation zone [8,10] and converting the process into one of constrained cutting. This constrained cutting resulted in smooth laminar ﬂow, and a chip of uniform thickness and homogeneous microstructure with minimal ﬂow localization. This essentially geometric approach has been demonstrated in CPTi, Ti6Al4V and Inconel 718 at speeds of up to 3 m/s [8,10]. The constrained cutting method for suppressing intense ﬂow localization in shear bands emerged out of a direct observational study of the mechanics of band nucleation and propagation. A band was found to develop by formation of a weak interface in the chip (nucleation), followed by sliding of neighbouring material segments across this interface (propagation) . Nucleation started at the tool tip and spread almost “instantaneously” to the chip back-surface. Most of the localized band strain (> 90%) was, however, imposed in the band propagation phase; it was this phase that could be suppressed by the constraint application. Building on prior work [8–10], we explore, in this study, the mechanics of ﬂow/fracture in chip segmentation using the direct observational approach. Based on understanding of how segmentation nucleates and evolves, we propose material-agnostic methods for controlling segmentation. ‘Control’, here, is meant not only for suppression of segmentation but also as a means to induce it to occur in metals where segmented ﬂow would not be the norm. The observations also bring out some hitherto littleknown aspects of segmentation mechanics and suggest new routes for studying ductile failure in metals.
M. Saei et al. / CIRP Annals - Manufacturing Technology 68 (2019) 41–44
2. Experimental Plane-strain (2-D) cutting was carried out in linear (vc < 20 mm/s, HSS tool) and plunge rotary-machining (vc = 500–1000 mm/s, carbide tool) conﬁgurations, with tool rake angle (g ) of +15 to 70 [8,11]. The undeformed chip thickness h0 was set at 50– 300 mm. Plane-strain deformation was ensured in the linear set-up by clamping a glass block against the workpiece (WP) to prevent side ﬂow. The deformation zone was observed in situ through the glass block using a high-speed camera/optical microscope system (pco dimax, resolution~1.4 mm) at 200 frames/s. Images were analyzed by particle image velocimetry (PIV) to obtain velocity, strain ﬁelds and other ﬂow kinematics. In rotary plunge-turning, plane-strain was ensured by keeping the chip width > 30 h0. The WP materials, selected speciﬁcally to study segmentation, were CP-Zn (hcp, hardness = 37 HV), half-hard (H02) single-phase brass 260 (fcc, hardness = 105 HV), and annealed OFHC Cu (fcc, hardness = 68 HV). While the Zn and brass (H02) are alloys of low-to-moderate workability and prone to segmentation, the annealed Cu, with very high workability, does not typically segment in cutting, but deforms by sinuous-ﬂow  with large chip-strains (~8). It is used to show how segmentation can be induced even in a very ductile material. 3. Results and discussion The in situ observations have provided critical details about segmented ﬂow mechanics, essential for ﬂow control strategies. 3.1. Mechanics of segmentation 3.1.1. Segmentation is initiated from chip back-surface Fig. 1 shows selected frames from a high-speed image sequence of cutting of the Zn (g = -40 ), highlighting how a ﬂow instability triggers chip segmentation. A prow of material ﬁrst develops ahead of the tool, constituting the base of the chip (frame 1). This prow is inclined at angle u to the WP free surface (horizontal orange line). But the ﬂow is unsteady and the prow unstable, as seen in the sequence. This prow can be idealized as forming by shearing of surface elements, the shear occurring along planes inclined at 45 to the surface [11,12]. A crack then initiates on the prow surface (white arrow, frame 1), i.e., chip back-surface, and propagates some distance towards the tool tip (frames 1 to 4, interframe time = 0.125 s); this prow-crack formation triggers a ﬂow instability which is the nucleation phase of segmentation ﬂow. The (critical) prow angle u * when the crack forms is~40 (frame 1).
This segmented ﬂow with prow-crack propagation was observed for all g between 60 and 10 , with the crack tip extending increasingly closer to the tool tip as g was decreased. That is, the extent of segmentation was greater the more negative the g . In certain cases, the crack propagated all the way to the tool tip resulting in a discrete chip particle. At g = 70 , wedge-sliding replaced chip formation, while for g >0 the ﬂow was mostly laminar, with a continuous chip. Notably, even in some g >0 cases, there was prowcrack formation as in Fig. 1, but these cracks were arrested soon after initiation, resulting in small-scale waviness on chip back-surface. The average crack speed, as estimated from high-speed image sequences, was 0.9 mm/s, for g = 40 (frames 1–3 in Fig.1). This speed is notably close to the loading rate vc = 1 mm/s, analogous to shear-band ﬂow, wherein band propagation speed ~ vc . A similar evolution of segmented ﬂow has also been observed in cutting of H02 brass . These direct observations, together with other recent work , show conclusively that segmented (saw-tooth) chip formation is initiated by a ductile failure originating on the chip back- surface, thus conﬁrming earlier predictions and inferences [3,12,13]. 3.1.2. Segmentation occurs at a critical strain Prow formation may be idealized as occurring by shearing of surface elements along planes inclined at 45 to the WP surface . Based on this model, u provides a direct measure of the surface strain in the prow; the shear strain pis ﬃﬃﬃ just 2u (u in radians) pﬃﬃﬃ and the von Mises effective strain (e), 2u/ 3 (Hence, e = 2u*/ 3 is the strain at prow-crack initiation). That this is a good estimate of e was also established by comparison with direct strain measurements using PIV, both in prior work with brass , and again here with Zn. Hence, we use direct measurements of u* to estimate e at prow-crack initiation. Fig. 2 shows variation of prow-angle at crack initiation, u*, with g , for Zn and brass. Also plotted are e values. The singular feature of the plot is the relative constancy of u* (~37, dotted line) and, by extension, e (~0.75) for g between 60 and 10 (segmented-ﬂow). Furthermore, this u constancy is seen with both Zn and brass. Hence prowfailure is likely governed by a critical strain criterion, this critical strain value being independent of deformation geometry (g ). That segmentation occurs at constant strain in the cutting-deformation geometry is consistent with the simplest version of the CockroftLatham theory of ductile failure . Ongoing work is examining the dependence of this critical strain on material type.
Fig. 2. Variation of prow angle (u
Fig. 1. Segmentation and ﬂow dynamics in Zn cutting revealed by high-speed imaging. g = 40 , vc = 1 mm/s, h0 = 100 mm, inter-frame = 0.125 s.
To analyse crack propagation and ﬂow development, different points in the deformation/prow region were tracked using PIV. The motion of three points P1, P2 and P3 (frame 2) is used to describe the segmentation. P1, P2 are initially located very close to each other, and on either side of an incipient crack tip. Subsequent crack growth increases the separation between P1 and P2 (frames 2–4). In Fig. 1, the crack is arrested approximately half-way between the chip back-surface and tool tip (frame 4). At this point, the crack-tip driving force is reduced, a new prow and crack develop analogously, and the process repeats cyclically.
) at onset of cracking and prow strain (e) with g , in cutting of Zn and brass. vc = 1 mm/s. The dotted line is a least squares ﬁt of the segmentation data. For g = 70 , u was~10 and e~0.2 (Fig. 2), which is well below the critical (failure) e of 0.75; at this condition, only pure sliding occurred without any chip formation or prow-cracking. 3.1.3. Hydrostatic pressure and triaxiality condition at failure origin It is well known that ductile failure in metals is quite sensitive to the hydrostatic stress (p), with the strain at fracture increasing with increasing hydrostatic pressure, as established by the pioneering work of Bridgman and others [15,16]. Merchant and Shaw  were the ﬁrst to draw attention to the importance of p in metal cutting. Recent work on ductile failure  has suggested that the local stress triaxiality, as
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expressed by h = ratio of hydrostatic stress (p) to effective stress, has a major inﬂuence on failure strain, with ductile fracture predicted as being infeasible for h < 1/3. It is worth examining the prow failure in the framework of these theories. Consider 2-D plastic deformation of an element on the WP surface ahead of the tool to form a prow element. If the material is treated as a rigid, plastic solid with representative shear yield stress (k), then the principal stresses in the element are 2k, k and 0 (negative sign due to compressive stresses).pThis ﬃﬃﬃ stress state corresponds to an effective (von Mises) stress of 3 k, and p = k, pﬃﬃﬃ with h = 1/ 3 . Since h in the prow is independent of g , this explains the observed constancy of strain at prow failure. Interestingly, pﬃﬃﬃ in the present case, since failure occurs even with h (= 1/ 3) < 1/3, it is a counter-example to a popular ductile failure theory proposed by Wierzbicki . The observations suggest that segmented-chip formation could also provide a means for exploring ductile failure criteria for metals. 3.2. Controlling segmentation We now turn our attention to methods for suppressing segmentation as well as for enhancing it. 3.2.1. Segmentation can be suppressed by increasing hydrostatic pressure and reducing stress triaxiality Based on our observations that segmentation is initiated by a crack in the prow region, and in light of theories of ductile failure discussed above, it would appear that if prow crack nucleation were to be suppressed by decreasing p (i.e., increasing hydrostatic pressure and reducing h), then a smooth continuous chip should form by laminar ﬂow. In fact,pgiven that the effective stress in the deforming prow is ﬃﬃﬃ constant (= 3 k), the only means of varying h is via p. One way of increasing the hydrostatic pressure in the prow is by application of a local constraint, via a suitably placed die. This is analogous to the constraining die used to suppress shear banding . The use of constrained cutting to suppress segmentation and prow-cracking was studied both at low speeds, in linear cutting, and at higher speeds, using a rotary (radial) plunge-turning conﬁguration. A high-speed steel die (constraint), mounted across from the primary cutting tool, was pressed against the WP and chip backsurface as shown in Fig. 3. Fig. 3(a) shows the usual segmented chip formation that occurs in conventional (free) cutting of Zn at vc = 1 mm/s. The segmented chip is characterized by alternating regions of lower (1–2) and higher (3–4) strain. The dotted white line in the ﬁgure demarcates the WP surface and chip back-surface, and the segmentation morphology. Upon cutting with the constraint, the prow-crack and segmentation are completely suppressed (Fig. 3b). What results now is a chip of uniform thickness, with homogeneous laminar ﬂow (e ~2, Fig. 3b); this chip resembles a metal strip. The changeover from segmented chip to the smooth continuous chip in constrained cutting is quite striking. The strain ﬁeld also shows a thin deformed layer on the chip back-surface, akin to the secondary deformation zone at the tool-chip interface, indicating that the constraint does impose some frictional deformation.
Fig. 3. Suppressing segmentation by constrained cutting: strain ﬁelds in (a) conventional cutting, and (b) constrained cutting. The 2 streaklines in b) highlight laminar ﬂow. Zn, g = 10 , vc = 1 mm/s, h0 = 150 mm.
Constrained cutting was equally effective at suppressing segmentation in higher-speed cutting of Zn (vc = 0.5 to 1 m/s), as seen in Fig. 4. Figs. 4(a) and (b) show a continuous chip of uniform thickness, and relatively homogeneous microstructure, produced by con-
Fig. 4. Suppressing segmentation in turning by constrained cutting: (a) continuous smooth metal strip (chip) produced by constrained cutting, (b) through-thickness cross-section of strip showing homogeneous structure, and (c) chip cross-section from conventional cutting showing segmentation. Zn, g = 5 , vc = 500 mm/s. h0 = 250 mm.
strained cutting; this may be contrasted with the highly-segmented and irregular chip of Fig. 4(c), produced in conventional cutting. The back surface of the chip from the constrained cutting was quite smooth, with Ra~0.3 mm. There is no barrier to using constrained cutting at much higher speeds; in fact, it has been demonstrated to suppress shear banding in Ti and Ni alloys at up to 3 m/s [8,10]. While the forces applied by the constraint in the cutting system have not yet been characterized, it was clear that the exact location of the constraint needed to suppress segmentation was much less critical than with shear banding. In the latter case, the constraint had to be set based on the shear-band sliding distance in the band propagation phase. In the present instance, setting the constraint inward from the chip back-surface, by even a fraction of the segment amplitude was sufﬁcient to arrest the segmentation. The less severe constraint here can be explained by consideration of the hydrostatic stress state and stress triaxiality. Consider a plastically deforming element on the WP surface ahead of the tool, as before, but now located under the constraint. The stress state in the element is now (p0 + 2k), (p0 + k), and po, where po is the normal stress applied by the constraint; friction at constraint is neglected. pﬃﬃﬃ The effective stress in the element is again 3 k, unchanged from before. But the magnitude of the hydrostatic pressure in the element is (p0 + k) which is > k, the hydrostatic pressure in the same prow region of conventional cutting; pﬃﬃﬃ pﬃﬃﬃ and the stress triaxiality is h = (p0 + k)/ 3 k, which is < 1/ 3 (conventional cutting). A conservative assumption for the constraint stress is p0 = 2k (yield strength). Then the elemental hydrostatic pressure pﬃﬃﬃ = 3k, which is 3 times that in conventional cutting; and h = 3, which is < pﬃﬃﬃ 1= 3 of conventional cutting. Both factors inhibit ductile failure in the prow, suppressing segmentation. Furthermore, it is clear why even a constraint of moderate pressure (~2k) is effective in arresting segmentation. Measurement and simulation of constraint forces to be carried out soon should improve this analysis. Our analysis also explains another apparently paradoxical aspect of segmented chip formation. While a crack is initiated on the prowsurface at e~0.75, the bulk (interior) of the chip sustains strains as high as 2 - 3 (Figs. 3a and b) without cracking. This is likely due to a more compressive p prevailing in the chip interior, a consequence of greater constraint on the deformation, therein, from adjoining material. Suppression of segmentation can be beneﬁcial for multiple reasons. Segmented chip formation can cause force oscillations, with adverse consequences for process performance and product quality. By suppressing segmentation, it also becomes feasible to use (constrained) chip formation to produce sheet and strip in a single step by cutting-based deformation. This can be of value for producing strip/sheet products from specialty metals and metals of poor workability (e.g., Ti, Mg, Fe-Si electrical steels). 3.2.2. Enhancing segmentation using a chemical medium We now consider the possibility of inducing segmented-chip formation in metals of high workability that typically do not segment. Our observations show that segmentation propensity should be enhanced if the failure strain is reduced or prow-strain increased. The former can be inﬂuenced by loading (e.g., hydrostatic tension), material (e.g., reduced workability) or ambient conditions. There is no obvious route to creating hydrostatic tension in the prow. Thus one is led to attempt to promote segmentation by limiting the material’s (plastic) workability. This may be done, without altering the material state, by
M. Saei et al. / CIRP Annals - Manufacturing Technology 68 (2019) 41–44
application of chemical media to the WP surface. It is well-known that certain surface-active media can embrittle metals , one well-known example being that of Al by Ga. But this embrittlement route cannot be used with most machining processes because of its catastrophic nature. However, recent work [9,19] has shown that a benign, local form of “embrittlement” can be realized by application of common media (inks, adhesives) to the WP surface ahead of the tool. This application limits large-strain deformation (workability) of the metal by effecting a local ductile-to-brittle transition in the cutting zone – a mechanochemical effect. Fig. 5 shows the use of this mechanochemical route for effecting segmented chip formation even in a highly workable metal such as (soft) annealed Cu. In the experiment, one-half of the length of the Cu surface was coated with a common adhesive (Scotch Restickable Glue Stick) while the remaining length was left uncoated (bare). When cutting the bare surface, the chip formed by a highly unsteady mode of ﬂow – sinuous ﬂow – characterized by large-amplitude folding, extensive redundant deformation, and a very thick chip (16fold thickening, e~4–8), as highlighted by the streaklines and strain ﬁeld in Fig. 5(a). However, when cutting the glue-coated region, the chip is segmented and much thinner (Fig. 5b), with the forces also being much smaller (up to 80% reduction) than in the sinuous ﬂow case. Concurrently, the cut-surface quality, as characterized by roughness and defects (e.g., tears, pull-outs), was also much improved, by an order of magnitude compared to the sinuous-ﬂow cutting . The segmented-chip evolution exhibited all the key characteristics observed earlier – prow formation, incipient-fold transforming to prow-crack, and prow-crack propagation towards tool tip. Segmentation was initiated by fracture occurring in a prowfold. This mechanochemical effect, relatively material-agnostic, has been successful at effecting segmented-chip formation in highly workable metals like Al, Fe and Ni  – a consequence of reduction in failure strain in vicinity of notches (folds) in prow. The results attest also to potential beneﬁts of segmented-chip formation, viz. smaller forces and better surface quality.
Fig. 6. Force oscillations (or lack thereof) reﬂect 3-D chip morphology. Optical micrograph of chip back-surface showing a) straight segments in brass, h0 = 100 mm and (b) meandering segments in Zn, h0 = 250 mm; and (c) speciﬁc cutting forces for (a) and (b). g = 5 , vc = 500 mm/s.
on workpiece surface ahead of the tool, that then propagates towards the tool tip creating individual chip segments. Crack initiation appears to be governed by a critical strain criterion and is analysed in terms of local hydrostatic stress and stress triaxiality. Based on the observations, we formulate two methods to control the segmentation – constrained cutting, utilizing a die located across from the cutting tool, to suppress segmentation; and a mechanochemical effect via application of benign surface-active media to induce it, even in metals of highworkability. The use of segmentation for enhancing machining processes and analysing ductile failure is brieﬂy discussed. Acknowledgements Supported in part by NSF Grants CMMI 1562470 and DMR 1610094. References
Fig. 5. Inducing segmentation in ductile annealed Cu via chemical-medium (glue) application to WP surface. Flow attributes in chip depicted using strain ﬁelds and streaklines: a) without medium (sinuous ﬂow) and b) with medium (segmented ﬂow). g = 0 , vc = 2 mm/s. h0 = 50 mm.
3.2.3. Does segmentation always cause force oscillations? Contrary to what is often assumed – that segmentation causesforce oscillations – we observed that the oscillations are determined by the 3-D segmentation morphology. Figs. 6(a) and (b) show segment morphology across the chip (back-surface) width for conventional cutting of brass and Zn, respectively. The segments are seen to run straight across the width in brass while in Zn they meander. Both chips, however, showed similar saw-tooth morphology from the side. This difference in segmentation was reﬂected in the forces (Fig. 6c) – signiﬁcant oscillations at band frequency occurring with the straightsegment morphology (brass) and no discernible oscillation for the meandering-segment (Zn). We observed likewise in other systems also, including the mechanochemical segmentation case (Fig. 5b) wherein segmentation was of meandering type with no force oscillation. Similar morphology differences have also been observed with shear bands - CP-Ti (meandering) and Ti6Al4V (straight) . These differences appear to have a microstructural origin. 4. Conclusions An in situ study is made of segmentation and unsteady ﬂow dynamics in cutting of metals of low-to-moderate workability. Segmentation is triggered by a ductile crack (instability), nucleated
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