Metallurgical and Materials Transactions A

, Volume 39, Issue 11, pp 2645–2655 | Cite as

Analysis of Severe Plastic Deformation by Large Strain Extrusion Machining

  • M. Sevier
  • H.T.Y. Yang
  • W. Moscoso
  • S. Chandrasekar
Article

Abstract

Large strain extrusion machining (LSEM), a constrained chip formation process, is examined as a method of severe plastic deformation (SPD) at small deformation rates for production of ultra-fine-grained (UFG) materials. A finite element procedure is developed for prediction of deformation field parameters such as effective strain, strain rate, and their variation across the thickness of the chip for various cutting (extrusion) ratios. The cutting force (extrusion pressure) and hydrostatic pressures within the deformation zone are also analyzed. A consideration of the deformation occurring in chip formation suggests bounds on the extrusion ratios that can be realized. Implications of the results for production of bulk chip samples of controlled geometry and with an UFG microstructure are discussed.

1 Introduction

Severe plastic deformation (SPD) has emerged as a promising route for effecting microstructure refinement and producing nanostructured and ultra-fine-grained (UFG) materials with enhanced mechanical properties.[1] Typical methods of SPD include equal channel angular pressing (ECAP),[2] high pressure torsion,[3] and, more recently, chip formation by machining.[4,5] The SPD is usually carried out at small deformation rates to minimize temperature rise and resultant coarsening (annealing) of the microstructure during the deformation.[6] The ECAP involves multiple passes of deformation to impose large plastic strains, while machining is effective at imposing moderate to large strains in the chip in a single pass of deformation. The reason for the latter lies in the fact that chip formation is unconstrained. This enables a greater level of strain to be imposed in the chip than in conventional SPD methods. Furthermore, the strain rate can be varied over a wide range in machining by varying the machining speed. However, this very lack of constraint in chip formation also makes it difficult to control the shape and dimensions of the resulting fine-grained material.

To overcome the lack of geometric control in chip formation, a constrained machining process, large strain extrusion machining (LSEM), has recently been demonstrated for producing bulk nanostructured materials.[7] The LSEM combines microstructure refinement via SPD by machining, with simultaneous shape and dimensional control of extrusion in a single step deformation process, as illustrated in Figure 1. By carrying out the SPD at small deformation rates, thereby minimizing temperature influences,[6] LSEM has been used to produce bulk UFG chips in various cross-sectional geometries including plates, bars, rods, and foils.[7] Because LSEM involves constrained chip formation, the mechanics of machining is converted into a problem of constrained plastic flow akin to deformation processing (e.g. extrusion, rolling, or drawing) where the exit geometry of the material is predefined.
Fig. 1

Schematic of the LSEM process in plane strain

The basic framework for extrusion machining is illustrated in Figure 1, where a sharp tool removes a preset depth of material (undeformed chip thickness), to, from the workpiece in the form of a chip with predetermined thickness, tc. An appropriately shaped constraining tool (or edge) is placed such that it controls the thickness of the chip at the point of its formation. This tool also lays flat against the incoming undeformed workpiece material, thereby preventing unwanted buildup of material ahead of the chip formation zone (primary deformation zone). The extended parallel faces of the cutting and constraining tools also allow for chip formation with negligible curvature of the chip.

In practice, extrusion machining may be realized in a number of kinematic configurations. For example, a specially designed tool that combines the cutting and constraining functions described previously can be moved radially into a disk-shaped workpiece (disk radius r ≫ to) that is rotated on a lathe spindle at a constant peripheral speed, Vo.[7] The undeformed material is continuously fed into the machining zone by advancing the tool radially into the workpiece at a constant rate of feed, to, per revolution. The result is a smooth chip of predetermined thickness, tc, extruding through the tool at a velocity, Vc = Vo(to/tc), under plane strain conditions. In this configuration, material production is essentially continuous with layers being “peeled” away from the disk. Another adaptation is through implementation of the LSEM on a press (or compression test machine), where the material is pushed past a well-reinforced tool in a linear machining configuration analogous to that shown in Figure 1. This configuration is particularly useful in instances where high extrusion pressures are needed, as in the production of samples with large cross-sectional areas.

De Chiffre[8] originally proposed the idea of extrusion machining for the purpose of producing soft metal strips (chips) using geometrically controlled chip formation at high machining speeds (large deformation rates). While use of high-machining speeds enables a high production rate of the strip, the associated heating results in an annealed (soft) microstructure in the strip. De Chiffre’s configuration closely resembles that of Figure 1, except that the constraining tool is slanted away from the back edge of the chip (essentially a point constraint) so as to ensure minimal rubbing with the chip. For a range of constraining tool positions relative to the undeformed chip thickness, that is, values of the ratio tc/to, De Chiffre proposed a simple upper bound model for estimating the strain in the chip assuming sticking friction between the chip and tool over the length of contact along the tool rake face. Assuming deformation to be confined to a shear plane, this upper bound solution for effective strain[7] may be expressed as
$$ \varepsilon _{{\text{eff}}} = \frac{\gamma } {{\sqrt 3 }} = \frac{1} {{\sqrt 3 }}\left( {\frac{\lambda } {{\cos \alpha }} + \frac{1} {{\lambda \cos \alpha }} - 2\tan \alpha } \right) $$
(1)
where α is the tool rake angle, and λ is the cutting (extrusion) ratio defined as tc/to (Figure 1). This equation is identical to the equation for strain in conventional machining if the thickness of the chip after its formation (deformed chip thickness) is fixed a priori at a value equal to tc. This equation is of fundamental interest as the imposed strain is one of the main determinants of microstructure and mechanical properties of the chip. Another parameter of significant importance is the cutting (extrusion) pressure, the pressure (pc) imposed by the tool in the direction of the cutting velocity Vo in Figure 1. For this, the upper bound model[8] yields
$$ \frac{{p_c }} {k} = \frac{\lambda } {{\cos \alpha }} + \frac{2} {{\lambda \cos \alpha }} - 3\tan \alpha $$
(2)
where k is the shear yield strength of the material. It is important to note that the lack of a constraining tool face adjacent to the chip in De Chiffre’s model results in a reduced chip-tool contact area, making Eq. [2] more of a guideline for the upper bound on cutting pressure than a true upper bound for the many extrusion machining configurations typically implemented in practice.

The present study describes a finite element model to analyze the effect of the main LSEM parameters, viz. the cutting ratio λ and tool-chip friction, on the deformation, chip strain, strain rate, cutting pressure, and hydrostatic stress. The SPD at only small-deformation rates (low machining speeds) is considered so as to ensure minimal temperature increases in the chip.[6] This is because the objective is to analyze deformation conditions that will enable an UFG microstructure to be realized in the chip. Consequently, thermal effects associated with deformation and friction are neglected in the model. Chip strain and cutting pressure are calculated for various deformation conditions to evaluate LSEM as a method of SPD. The calculated strain and pressure values are compared with those derived from an upper bound analysis to assess the model developed. Implications for LSEM as a method of SPD and for large-scale manufacture of bulk UFG materials are discussed.

2 Finite element model

2.1 Models for Chip Formation

The model proposed here is based upon prior well-established finite element simulations of two-dimensional machining procedures.[9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24] In conventional machining, the extreme plastic deformation will distort a finite element mesh such that instability will occur after incipient cutting.[9] One of the early approaches to overcome this has been to use incremental advances of the tool on a predefined, steady-state chip geometry.[10] Strenkowski and Carroll introduced the idea of nodes separating along a predefined “parting line.”[11] As the tool advances, these nodes would “unhook” according to some type of limiting criteria (e.g., critical strain, specified distance from the tool tip, etc.).[11, 12, 13, 14, 15, 16] Noting that this approach assumes tensile rupture near the tool tip instead of plastic shear, as observed experimentally,[17,18] models have since moved away from the use of a rupture process to realize chip formation. For this purpose, Carroll and Strenkowski employed an Eulerian reference frame wherein the mesh is held constant for viscoplastic material to flow through the given control volume.[19] More recent analyses have found considerable success using a standard Lagrangian formulation combined with periodic remeshing to prevent mesh instability.[20, 21, 22] Other models have incorporated a type of arbitrary Lagrangian Eulerian (ALE) formulation for this purpose. This technique automatically resituates nodes based either on constraints from material motion (Lagrangian), spatial location (Eulerian), or an arbitrary constraint defined by the user, greatly reducing the computational time necessary for the simulations.[23,24] Keynote articles produced by the CIRP working group “Modeling of Machining Operations” contain a good summary of the current development of finite element techniques for machining processes.[25,26]

2.2 Model for LSEM

The simulation of LSEM holds the advantage of the chip shape being geometrically constrained, thereby obviating issues associated with unconstrained chip formation in conventional machining. With this in consideration, a two-dimensional plane strain finite element model has been created, which employs Eulerian boundaries at the left and right edges and at the top edge of a predefined chip (Figures 2(a) and (b)). The advantage of this model lies in the arrangement of elements: smaller more densely packed elements are defined within the chip, deformation zone, and machined surface, while larger elements may constitute the remainder of the workpiece. It should be noted that although boundaries used to describe regions through which material flows through are described as “Eulerian,” the solution method for the model is an ALE formulation.[27] This means that unlike a genuine Eulerian increment primarily used in computational fluid dynamics problems, where the mesh remains constant as fluid moves through it, the nodes and elements in this model follow the movement of the underlying material. Periodically, in the primarily Lagrangian simulation presented here, a “remesh” increment occurs where nodes are relocated to improve the aspect ratio of distorted elements, thereby maintaining the integrity of the mesh throughout the course of the simulation. It is during these remesh increments that nodes prescribed as part of the Eulerian boundary are moved back to their original locations as defined by the adaptive mesh constraints. At the “inlet” Eulerian boundary (left side of workpiece, Figure 2(a)), new material is gained and the properties of the given material are defined as those of the “old” material immediately adjacent to it. The non-Eulerian boundaries are not spatially constrained so that the ensuing deformation may take its natural shape. The “outlet” boundaries are only constraints applied in the direction parallel to the flow of the material. Therefore, if the width of material varies at either the top of the chip or the right side of the workpiece (Figure 2), then the width of that boundary will reflect that adjustment.
Fig. 2

Finite element model for LSEM

The aforementioned Eulerian model has been found to be particularly useful when the value of the cutting ratio λ (=tc/to) is small (≤2). As λ increases, it has been found that the predefined chip geometry becomes detrimental to the simulation as the chip’s outer edge becomes separated from the constraining tool. For larger values of λ, it has been found effective to let the chip material naturally “grow” in the space between the cutting and constraining tools by replacing the assumed chip geometry with a level plane. Throughout the simulation, this boundary will grow as material accumulates into a chip (Figures 2(c) and (d)). This method has been shown to produce nearly identical results as the model employing an Eulerian boundary at the chip surface (Figures 2(a) and (b)) for λ = 1.5 and 1.75.

ABAQUS\Explicit is employed for computation in this nonlinear simulation. By using an explicit integration rule and diagonal “lumped” element mass matrices,[28,29] ABAQUS\Explicit is much better equipped to handle large displacement analyses than a conventional force/displacement matrix solver. The model is comprised of isoparametric, plane strain quadrilateral elements with four nodes and eight degrees of freedom (Figure 2).[30,31] Reduced integration with hourglass control is used for computing the elemental stiffness matrix.[32] This avoids the problem of “volumetric locking,” where spurious pressure stresses can cause the element to behave orders of magnitude too stiffly. In addition, the relative simplicity of this element sacrifices negligible accuracy for the sake of economical computation run time. For SPD at small deformation rates such as in low-speed machining, the temperature rise is small;[6] hence, thermal effects are not included in the element selection in the present study. Proceeding further in the direction of expeditious processing, the material density of the smaller elements is artificially increased to expand the stable time increment.[29,31] Because material inertia is not a significant factor in this low-speed analysis, moderate “mass scaling” does not appear to affect the results in any detectable manner, but significantly reduces processing time.

A similar modeling approach was used by Sevier et al.[33] to examine SPD in conventional plane-strain machining, wherein there is no constraint on the chip formation. Strain and strain rate fields in the machining deformation zone were measured at high resolution for a range of tool rake angles, from positive to negative.[33,34] The results of the finite element analysis from the prior work, which is similar to that implemented for the LSEM in Figure 2(d) here, showed reasonable agreement with the measurements in all cases. This detailed validation of the analysis by comparison with experimental results[33] provides sufficient confidence for applying it to study the LSEM.

3 Results and discussion

3.1 Input Parameters

A cutting tool with rake angle 0 deg is assumed to remove a surface layer, 250 μm in thickness, to, from the workpiece at a cutting speed, Vo, of 10 mm/s (Figure 2(a)). In order to compare perfectly-plastic vs strain-hardening plastic behavior, two model workpiece material systems are selected: lead (perfectly-plastic) and oxygen-free high conductivity (OFHC) copper. The properties for lead are as follows: density of 11 g/cm3, Young’s modulus of 13 GPa, and yield stress of 10 MPa that is constant for any value of plastic strain (perfectly-plastic). The copper workpiece is assumed to have the following properties: density of 8.94 g/cm3, Young’s modulus of 115 GPa, and Poisson’s ratio of 0.308. The stress-strain curve for copper is derived from indentation hardness measurements on machined chips created with different levels of plastic strain. The stress-strain curve is created by linear interpolation between tabulated flow stresses of 320, 488, and 518 MPa at effective plastic strains of 0, 1.27, and 2.48, respectively. The cutting and constraining tools are assumed to be rigid and much harder than the workpiece material, with no permissible rotation or displacement. The tool cutting edge is assumed to have a sufficiently small radius (≤1/10 depth of cut, to) so as to model machining with sharp tools. For simulations where λ is small (<2), this corresponds to an edge radius of 15 μm, while for larger values of λ, the edge is assumed to have a radius of 25 μm. In the simulation, the value of λ is varied from 0.25 to 7.4 corresponding to deformed chip thickness values between 62.5 μm and 1.85 mm, with a special focus on values of λ < 2.

Two interfacial friction conditions are modeled for the tool-chip contact along the rake face: Coulomb friction with μ = 0.3; and rough contact, sticking friction with \( \tau _{{{\text{interface}}}} {\text{ = }}k{\text{ = }}{\sigma _{y} }/{{\sqrt{\text{3}} }} \). These two conditions are representative of interface extremes, the former resembling a lubricated condition and the latter being more typical of deformation processing and machining processes. The interface between the constraining tool and workpiece is taken as frictionless, a condition suggested by experimental observations.[7]

3.2 Strain Distribution

One major advantage of finite element analysis is its ability to describe the distribution of field variables throughout the body under investigation. In Figure 3, this capability is used to display the variation of strain through the chip and workpiece in LSEM. Two prominent regions of deformation may be observed in Figure 3. The primary region of deformation, marked AB in Figure 3(a), is a narrow zone where most of the strain associated with chip formation is imposed. A secondary region of deformation, marked BC in Figure 3(a), extends some small distance into the chip along the chip-tool interface. This is the secondary shear zone usually observed in machining and is a consequence of the additional deformation arising from friction at the tool-chip interface.
Fig. 3

Effective strain contours for LSEM. Lead, to = 250 μm

Strain distributions in the chip are given in Figure 4 for lead and copper at λ = 1.5 and μ = 0.3. It can be seen from this figure that the strain distribution is essentially independent of the work material, as may be expected for a constrained deformation process. The secondary shear zone adjoining the chip-tool interface, wherein the strain is relatively high but varying, is seen to extend into about one-third of the chip thickness from the interface with the cutting tool at E. The strain is essentially constant elsewhere throughout the remainder of the chip. These gradients in strain arising from the secondary shear could potentially be identified using micro- or nanoindentation. It should be noted that although the sticking friction interaction causes significantly higher strains near the tool-chip interface and the cutting tool (Figure 3), the secondary region of shear still remains within the first 1/3 of the chip thickness similar to results in Figures 3 and 4 for μ = 0.3.
Fig. 4

Distribution of strain through the thickness of the chip. λ = 1.5, μ = 0.3, and to = 250 μm. The term E is located on the tool rake face

Figure 5 shows the variation of chip strain with λ, taking the strain estimated in the middle of the chip thickness as being representative of the chip as a whole. These strains are found to be very close to that predicted by the upper bound model,[8] diverging only slightly as λ becomes large. The minimum value for the chip strain (ε ∼ 1.05) is seen to occur at λ ∼ 1, with a nearly linear increase in strain with increasing λ up to the unconstrained chip formation case. For λ < 1, the strain increases rapidly with decreasing λ, this increase being particularly pronounced for λ < 0.25. The chip strain is primarily controlled by λ and, as in ECAP, is independent of the material properties and friction conditions at the chip-tool interface.
Fig. 5

Variation of effective strain in the chip with λ. to = 250 μm

The realization of very high strains at small values of λ is particularly interesting for effecting high levels of microstructure refinement in the chip. Figure 6 illustrates effective strain contours in the extrusion machining of lead for λ = 0.25 and 0.5. As λ becomes small, the secondary shear at the tool-chip interface arising from friction becomes much more pronounced. Furthermore, the edge of the chip near the constraining tool experiences secondary shear in these cases. Under these conditions, the strain values in the chip are much higher than at larger λ, suggesting possibilities for higher levels of microstructure refinement. Furthermore, at small λ, the strain values are quite high underneath the cutting tool and into the machined surface of the workpiece, indicating that this condition could be exploited to produce UFG microstructures in the machined subsurface. This holds the potential for further refinement of the chip microstructure by removing this strained surface in a subsequent pass of the LSEM tool.
Fig. 6

Effective strain contours for lead at λ < 1. μ = 0.3, and to = 250 μm

3.3 Strain Rate

Figure 7 shows the variation of effective strain rate with λ, this strain rate being that prevailing in the middle of the primary deformation zone. The strain rate values are in the range of 30 to 150 per second, which compare favorably with strain rate values measured in machining for this cutting speed.[34] Also, the strain rates are similar for different materials and friction conditions. Indeed, when investigating the primary deformation region as a whole for a given λ and rake angle, α, the strain rate distribution is similar for each material and friction interaction studied (Figure 8). The strain rate increases approximately linearly with increasing cutting speed and may be easily controlled by varying Vo. These results highlight the potential of using LSEM as a method of SPD.
Fig. 7

Variation of effective strain rate with λ. to = 250 μm

Fig. 8

Strain rate distribution in the primary deformation zone. μ = 0.3, and to = 250 μm

3.4 Incipient Stage of Chip Formation

One concern for LSEM, and for that matter in machining or ECAP in general, is the level and extent of deformation in the incipient stages of chip formation. This pertains to the deformation that is imposed in the initial portion of the chip as it is formed. It has been observed in experiments that in this incipient stage, microstructure refinement is not fully realized and a region of relatively undeformed material with large-sized grains prevails at the leading edge of the chip. This region does not exhibit the enhanced mechanical properties of the bulk of the chip. Figure 9 shows strain contours in the chip in the incipient stages of its formation; the strain is seen to be nonuniform over a distance of length, ls, extending from the leading edge of the chip. Also, ls is seen to increase with increasing λ, as shown in Figure 10. These observations are consistent with experimental observations pertaining to microstructure refinement in the early stages of chip formation and in the incipient stages of ECAP. It is easy to see that the deformation field in ECAP is very similar to that in chip formation.[35,36] Figure 9 also shows another region extending a distance lt from the leading edge of the chip, wherein the chip thickness has not developed to its full extent and reached the constraining tool. For cutting under sticking friction conditions, lt is essentially the same or greater than ls. However, for the lower friction condition (μ = 0.3), simulations show that lt is often less than ls. These results provide some guidelines as to the length of chip material that would have to be discarded prior to use in applications where uniform mechanical properties would be a requirement.
Fig. 9

Strain contours in the incipient stage of chip formation showing the length, ls, from the leading edge of the chip at which the chip strain becomes uniform, and the length, lt, at which the chip is fully developed with its thickness extending up to the constraining edge. λ = 1.5, and to = 250 μm

Fig. 10

Dependence of ls on λ. Copper, to = 250 μm

3.5 Limits on λ : Conventional Machining and Extrusion

An upper limit for λ is observed in the simulation, which corresponds to the onset of conventional machining. This upper limit occurs when the deformation of the chip is not sufficiently large for its back surface to reach the constraining tool. In the finite element simulation, this result occurs for λ = 2.5 in extrusion machining of lead with μ = 0.3. However, for machining lead with the sticking friction condition, this limit was found to lie beyond λ = 7.4. In the machining of copper, both friction conditions gave a limit beyond λ = 7.4. At small values of λ, especially λ ≤ 0.75, the primary deformation region was observed to extend well underneath the machined surface, and the velocity of chip flow became close to zero with the “chip” resembling a zone of dead metal. The material flow in and around the cutting edge, for this case, resembles extrusion with the tool edge serving as one face of an “extrusion die.” Extrusion machining may be said to have ceased to occur at this stage. This transition from extrusion machining to extrusion by reduction represents a lower limit for λ in LSEM.

3.6 Cutting and Hydrostatic Pressures

Figure 11 shows the relationship between the nondimensional cutting pressure, pc/k, and λ, where pc is the cutting (or extrusion) force divided by the undeformed chip cross-sectional area. The results from the finite element model follow a similar trend as the upper bound given in Eq. [2]. However, at first sight, it may seem unsatisfactory that the pressures calculated using the finite element analysis are greater than those predicted by the upper bound. This is, however, due to the fact that the upper bound model[8] uses a reduced channel length (in fact, a zero length) for the constraining tool, as noted earlier. By only having a constraining “point,” the chip is free to curve once it deforms through the opening. This gives limited contact between the chip and the cutting tool in the upper bound model, and therefore smaller values for the pressure compared with those obtained with the finite element model.
Fig. 11

Variation of the nondimensional cutting pressure (pc/k) with λ

The minimum value for the cutting pressure, pc/k, from the finite element simulation is found to occur at λ ∼ 1.414 in Figure 11, as predicted by the upper bound model. Beyond this point, the cutting pressure increases nearly linearly with λ. However, the cutting pressure increases nearly exponentially as λ moves from this minimum toward zero (Figure 11), similar to the variation of strain at small values of λ observed in Figure 5. In contrast to the strain results, there is a dependence of the cutting pressure on friction and material properties. The cutting pressure for the strain hardening copper is much greater that that for the perfectly-plastic lead (Figure 11). In addition, the increased friction adds more resistance in the extrusion machining of copper, but is barely noticeable for lead. This effect is likely due to the excessive strain increasing the flow stress of copper while having a negligible effect in the lead. In Figure 11(b), a significant rise in cutting pressure may be observed for λ < 1.5. One possible reason for this somewhat unexpected increase is that the chip strain in these situations is smaller, with more of the material deformation occurring underneath the cutting tool. This likely marks the onset of a transition from LSEM to an extrusion type process.

The high cutting pressures observed at small λ coincide with large hydrostatic pressures distributed nearly uniformly throughout the primary deformation zone (Figure 12), these stresses being larger near the surfaces of the cutting and constraining tools. As λ increases, the hydrostatic stresses become less uniformly distributed with the largest values occurring near the constraining tool edge. In Figure 12(d) for λ = 3.0, this effect is especially apparent with hydrostatic stresses being close to zero near the cutting tool edge and increasing approximately linearly through the primary deformation zone toward the edge of the constraining tool. Figure 13 shows the variation of the nondimensional hydrostatic pressure (ph/k) as measured in the center of the deformation zone. It is seen that the hydrostatic pressure follows a type of exponential decay as λ increases for each case considered. The value of ph/k decreases sharply from an initially high value at small λ, subsequently leveling off to a near constant value at large λ. The significance of enhanced friction and strain hardening are also readily seen in Figure 13, each effecting larger hydrostatic stresses for a given λ. These results suggest that hydrostatic stresses within the deformation zone may be a reasonable indicator for the lower limit of λ realizable in LSEM, with large stress values coinciding with the flow of workpiece material underneath the cutting tool instead of through the channel between the cutting and constraining tools. This limit is important in practical application of LSEM for creating thin foils with highly refined microstructures.
Fig. 12

Hydrostatic pressure (MPa) in the primary deformation zone. Copper, μ = 0.3, and to = 250 μm

Fig. 13

Variation of nondimensional hydrostatic pressure with λ. to = 250 μm

4 Concluding remarks

Large strain extrusion machining at small deformation rates is an attractive alternative to conventional machining for production of UFG materials due to the enhanced controllability of chip geometry and strain. As a result, plates, foils, and bars of predefined geometry and strain may be effectively produced. The addition of a constraining tool offers exciting possibilities for geometry and strain control, while imposing only minor new restrictions due to additional frictional forces. The finite element simulation has provided good estimates of deformation field parameters such as strain, strain rate, and deformation zone characteristics, and limits on the extrusion ratios that can be effectively realized. These results may be used as guidelines for optimization of an LSEM process.

An analysis of the variation of deformation parameters with the extrusion ratio, λ, has provided important insights. It has been determined that the strain produced in the chip, for a given rake angle, is entirely controlled by the extrusion (cutting) ratio, λ. Furthermore, the strain is seen to be uniformly distributed through the chip thickness with a thin primary deformation zone allowing for the application of high strain rates. As λ becomes small (<1.414), a significant rise in extrusion pressure is observed. This increase eventually results in inhibition of chip formation at λ values well below one, a consequence of a transition in the deformation from one concentrated in the chip to extension of the deformation well underneath the workpiece surface. Thus, the process at small values of λ is more akin to conventional extrusion than machining. This sets a lower limit to the extrusion ratios that can be realized. This “lower limit” for λ is concomitant with large values for the hydrostatic pressure within the deformation zone. The results also show that at small values of λ, the deformation conditions are favorable for imposing large strains on the machined surface, suggesting exciting possibilities for engineering surfaces with UFG microstructures and enhanced wear resistance.

More case-specific simulations will be of great value in tightly defining process capabilities for producing bar, rod, foil, and plate of desired size, shape, and microstructure. These will be undertaken in ensuing work.

Notes

Acknowledgments

We acknowledge NASA GSRP fellowship NND04CR12H and NSF Grant Nos. CMS-0200509 and CMMI-0626047 for support of this work.

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Copyright information

© The Minerals, Metals & Materials Society and ASM International 2008

Authors and Affiliations

  • M. Sevier
    • 1
    • 2
  • H.T.Y. Yang
    • 1
  • W. Moscoso
    • 3
  • S. Chandrasekar
    • 3
  1. 1.Department of Mechanical EngineeringUniversity of CaliforniaSanta BarbaraUSA
  2. 2.ATA Engineering, Inc.HerndonUSA
  3. 3.Center for Materials Processing and Tribology, School of Industrial EngineeringPurdue UniversityWest LafayetteUSA

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