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Orthogonal machining of single-crystal and coarse-grained aluminum
Journal of Manufacturing Processes 14 (2012) 126–134
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Technical paper
Orthogonal machining of single-crystal and coarse-grained aluminum Nithyanand Kota a , O. Burak Ozdoganlar a,b,∗ a b
Science Applications International Corporation, 2001 Jefferson Davis Highway, Arlington, VA 22202, USA Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
a r t i c l e
i n f o
Article history: Received 21 October 2011 Received in revised form 19 January 2012 Accepted 31 January 2012 Available online 4 April 2012 Keywords: Machining Micro-machining Single crystal Coarse grained polycrystals Microstructure Anisotropy Orthogonal cutting FIB-OIM Subsurface deformation
a b s t r a c t Orthogonal machining of single-crystal and coarse-grained (i.e., grain size considerably larger than the uncut chip thickness) materials has been a subject to many studies in the literature. The first part of this paper presents background on machining single-crystal materials, including experimental and modeling attempts. The second part briefly describes more recent modeling results from the authors, and presents new experimental results on planing and plunge-turning of single-crystal and coarse-grained aluminum using diamond tools. The experiments indicate that (1) cutting across grains of a coarse-grained aluminum workpiece produces distinctly varying forces and surface roughness from one grain to another, (2) plungeturning and planing of single crystal aluminum provide equivalent force data for large rake angles, (3) forces alter between two distinct levels while cutting single crystals with small rake angles, and (4) with small rake angles, subsurface damage on single-crystal aluminum is extensive, reaching depths comparable to the uncut chip thickness. © 2012 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers.
1. Introduction Machining of single-crystal and coarse-grained materials is of interest due to (a) the demand from various applications for singlecrystal parts due to their uniformity and reduced level of defects (e.g., turbine blades, precision mirrors), (b) the need for developing fundamental understanding of materials and material removal, since all crystalline materials are composed of grains and grain boundaries, which, to a large extent, dictate their mechanical properties. Recent interest in ultra-precision machining and micromachining also motivated single-crystal machining analysis, since those processes include chip-thicknesses commensurate with the grain size of many engineering materials, making crystallographic anisotropy critical in machining response. The first part of this paper provides extensive background on machining of single-crystal materials, including brief descriptions of authors’ work. In the second part, new experimental results on planing and plunge-turning of single-crystal and coarse-grained aluminum are presented. The experimental apparatuses used for planing and plunge-turning experiments are described in detail. Planing experiments are conducted on coarse-grained aluminum,
∗ Corresponding author at: Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA. E-mail address: [email protected] (O.B. Ozdoganlar).
and forces and surface roughness across the grains are analyzed. Next, plunge turning and planing of single-crystal aluminum are compared. Subsequently, the extent of subsurface damage during plunge turning of single-crystal aluminum is analyzed.
2. Background 2.1. Experimentation on machining of single-crystal and coarse-grained materials A number of experimental studies have confirmed that machining response including machining forces [1–12], chip lamellae [1,13–16], dynamic shear stress [2–6], and surface roughness [4,7,10] strongly depend on the crystallographic orientation in fcc metals. Some investigations also considered the effect of crystallographic anisotropy on the built-up edge (BUE) [13] and material side-flow [10]. Researchers have conducted both plunge-turning [3,4,12] and planing experiments [2,5–11,13–16] on single-crystal metals. Some of the experimentation was conducted inside a scanning electron microscope (SEM), allowing visual observation of chip formation [3,16]. Single-crystal fcc materials, mainly aluminum [1–4,8–11], and copper [3,5,6], have been tested in these studies. Table 1 tabulates the cutting conditions and materials considered in some of the works in the literature. Early studies on machining single crystals were aimed at observing the lamellae structure of the chips formed during machining.
1526-6125/$ – see front matter © 2012 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers. doi:10.1016/j.jmapro.2012.01.002
N. Kota, O.B. Ozdoganlar / Journal of Manufacturing Processes 14 (2012) 126–134 Table 1 Experimental studies on single-crystal machining from the literature, and associated machining parameters.
Clarebrough and Ogilivie [13] Black [14] Ramalingam and Hazra [2] Williams and Gane [6] Ueda and Iwata [16] Williams and Horne [5] Cohen [3] Sato et al. [8–10] Sato et al. [11] Moriwaki et al. [7] Yuan et al. [12] To et al. [4] Zhou and Ngoi [17] Lawson et al. (2007) [1]
Material
Rake angle
Feed (m)
Speed (mm/s)
Pb Cu, Al Al Cu ˇ-brass Cu Cu, Al Al Al Cu Cu, Al Al Al, Cu Al
60◦ – 40◦ 40◦ 0◦ , 20◦ 40◦ 50◦ –0◦ 35◦ 3◦ 0, 5◦ 0◦ 0◦ 0◦ 0◦
25 0.0025–2 127 1–100 0.1–200 100 114.3 100 0.5–3 0.01–3 1–10 1–10 5–10 5–20
– 1 0.27 0.1–1 0.0025 20 0.44 1.66 16.66 8833.33 0.16–0.83 0.16–0.83 1300 5–15
The first known study was published in 1950 by Clarebrough and Ogilivie [13], who microtomed large crystals of lead and observed a strong correlation between the crystallographic orientation and lamellae spacing. Subsequent studies of Black and von Turkovich shed light on various aspects of micro-scale chip formation in single-crystal cutting [14,15]. They performed a quantitative study of chip formation mechanisms in single-crystal copper and aluminum via an ultra-microtomy process. The lamellae thickness was seen to be affected by the crystallographic orientation and uncut chip thickness (below 2 m) [14]. Of all the machining responses, the variation of machining forces (and therefore the specific energies) while cutting singlecrystal materials at different orientations have been studied in greater detail by various researchers [1–3,5–12]. A majority of the researchers [1,5–11] used the planing configuration, in which the tool cuts along a particular crystal direction for a fixed length of the workpiece (see Fig. 1(a)). The planing data on aluminum consists primarily of cutting forces on (1 1 1) [6,10,11], (1 1 0) [6,10,11] and (0 0 1) [9,11] planes ([u v w] in Fig. 1(a)). Planing force data was also collected for cutting various directions about [0 0 1] [1] and [1 1 2] [10] zone axes on aluminum single crystals (i.e., the zone axis directions coincide with [a b c] in Fig. 1(a)). The planing forces on copper have been measured while cutting on (1 1 0) and (1 1 1) planes [6], and about [1 − 10] zone axis [5,7]. The results from the planing studies showed that the anisotropy of fcc crystals strongly affects the machining forces, inducing up to 312% variation in machining forces at different crystallographic orientations for a given zone axis [1]. The magnitude of variation in machining forces must be contrasted with results from nanoindentation, where the dependence of hardness on orientation is observed to be minimal [25]. For example, the observed variation in hardness in copper, between {1 1 0} and other surfaces was 6%. In addition to constant (stable) machining forces [1,2,6–8,11], monotonically-increasing [8], bi-stable [1,6] and periodicallyvarying [1,16] force signatures have been observed for different cutting parameters and crystallographic orientations during planing experiments. Abrupt, short-term reduction in forces was also observed in some studies [8]. While planing experiments provide detailed data in terms of cutting forces, only one crystal orientation can be machined at a time. As an alternative to the planing configuration, the plungeturning configuration shown in Fig. 1(b, c) has been used in [3,4,12]. This configuration provides near-continuous data for the entire range of cutting directions for a given zone axis. These turning experiments can be further divided into two types. Whereas Fig. 1(b) shows the case where the zone axis [a b c] serves as the axis of rotation, Fig. 1(c) has the cutting plane normal as the axis of
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(a)
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w
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h
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[hkl]
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SingleWorkpieCrystal ce Fig. 1. (a) Planing configuration, (b) plunge-turning configuration, and (c) in-plane machining.
rotation. Henceforth, the case shown in Fig. 1(c) will be referred to as in-plane machining for clarity. In the plunge turning experiments of Cohen [3], cutting forces were collected about the [0 0 1] zone axis ([a b c] in Fig. 1(b)) while cutting both aluminum and copper single-crystals. The force measurements from these experiments showed a repeatable four-fold symmetry expected from the crystallographic symmetry of [0 0 1] zone axis. While the [1 0 0] cutting direction produced the minimum force, the maximum force was consistently observed to occur at an offset of 15–20◦ from [1 1 0] cutting direction. The in-plane machining results [4,12] consist of machining force variation with cutting directions about (1 1 0) and (1 1 1) cutting plane normals. The experimental force variation with cutting directions on (1 1 0) plane were found to be larger than those on (1 1 1) cutting plane due to the increased crystallographic symmetry on (1 1 1) plane as compared to (1 1 0) plane. Apart from the machining forces, another important machining response is the roughness of the machined surface. Experimental
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studies have found a correlation between different crystallographic orientations and resulting surface roughness [4,7]. The roughness variation results showed expected crystallographic symmetries in the in-plane machining experiments on copper [4]. In a contrasting result, Moriwaki observed that for uncut chip thicknesses below 0.1 m when micromachining already-machined surfaces the surface roughness (and machining forces) was not affected by the crystallographic orientation [7]. This was explained by considering the significant sub-surface damage (dislocations) left from previous cutting passes. Despite the above described studies, the available data is scattered sparsely over the possible cutting conditions, posing a difficulty for validating the machining models or gaining a thorough understanding on the effects of crystallographic anisotropy during machining. While both planing and plunge-turning studies suggest a strong effect of crystallographic anisotropy on machining forces, the available data is insufficient to elaborate on the effects of rake angle, cutting velocity and uncut chip thickness while machining single crystal fcc metals. 2.2. Modeling attempts Although the relatively large body of experimental evidence suggests a strong dependence of machining response parameters on crystallographic orientation, relatively few attempts have been made to incorporate explicitly the effects of crystallographic anisotropy into machining models [9,18,19]. Modeling the effects of anisotropy requires incorporating the underlying physical phenomenon causing the anisotropy. The anisotropy observed in machining is the result of plastic deformation behavior of metallic crystals. Plastic deformation in crystals is due to the motion of crystal defects called dislocations on specific crystallographic planes along specific directions, i.e., a combination of slip direction on a slip plane is called a slip system. Face-centered cubic (fcc) metals have 12 such slip systems with slip directions belonging to 1 1 0 family, and slip plane normals belonging to {1 1 1} family. Furthermore, any arbitrary deformation can be achieved by activating 5 independent slip systems. The orientations of these planes and directions with respect to the cutting geometry (defined by cutting plane normal and cutting direction) determine the machining response. Additional complications in machining modeling arise from the lack of knowledge of the actual amount of deformation (often characterized by the shear angle). As a consequence, strategies for incorporating the effects of anisotropy must at first include the determination of shear angle. Researchers have considered a few different approaches for incorporating the anisotropy into machining models. An early work by Sato et al. [9] used the Schmid factor to obtain the active slip systems during machining. The amount of slip on each slip system was assumed to be proportional to the Schmid factor of that slip system. The value of shear angle was then calculated from the vector sum of slip directions on active slip systems. While the aforementioned approach provides some physical basis, the actual function of Schmid factor is only to predict one active slip system [20]. Hence, Schmid factor-based approaches are more relevant while discussing deformation caused solely by single slip, unlike deformations during machining. To obtain the shear deformation during machining-on any arbitrary orientationsrequires simultaneous activation of five or more independent slip systems. Recognizing this fact, later attempts by researchers incorporated Taylor-factor [20] based models, which are more relevant for multi-slip scenarios. Lee et al. [18] used a modified form of the Taylor factor, referred to as the effective Taylor factor, to predict the shear angle in singlecrystal cutting. For each crystallographic orientation, the Taylor factor was calculated for all possible shear angles. The effective
Taylor factor was then obtained by dividing the Taylor factor with cosine of two times the difference between the candidate shear angle and 45◦ . Essentially, the effective Taylor factor was used to incorporate the geometrical aspect of variation of strain with shear angle by penalizing those shear angle candidates away from the geometrically optimal 45◦ . This form of effective Taylor factor is only applicable for zero rake angle case, since 45◦ is not geometrically optimal for non-zero rake angles. While the goal was to choose the shear angle from the orientation that provided the minimum effective Taylor factor, this approach did not yield a unique solution in most cases. A texture softening factor was subsequently used to uniquely predict the shear angle as the angle that results in the minimum texture softening factor. This work was then extended to predict the variation in cutting forces with crystallographic orientation using Merchant’s model [19]. While the Taylor-factor based models significantly improve the prediction capability as compared to Schmid-factor based models, they do not incorporate the kinematic aspects (rake angle, strain variation with shear angle) and friction (on the rake face) while arriving at shear angle solutions. In determining the shear angles, all of the aforementioned models used only crystal plasticity models, while the mechanics of material removal was considered after the determination of shear angle. Therefore, the shear angles and shear forces were insensitive to the changes in friction on the rake face. 2.3. More recent modeling efforts To overcome the aforementioned shortcomings, Kota and Ozdoganlar [21] integrated Bishop and Hill’s crystal plasticity model within the framework of Merchant’s machining model to determine the shear angle and specific energies for fcc single-crystals. The plastic power required for shearing the material was calculated using Bishop and Hill’s plasticity theory, whereas Merchant’s machining force model was used to express the machining forces in terms of kinematics of cutting process. For a given crystallographic orientation (workpiece zone axis and cutting plane), the total power, including the shearing and rake-face friction power, was then minimized to determine the shear angle and specific energies. As expected, the forces (and specific energies) were found to vary in a periodic fashion, with a period corresponding to the crystallographic symmetry of the specific zone axis and cutting plane. Although the model in [21] successfully captured the amplitude of variation arising from the crystallographic anisotropy and the periodicity, there was a phase difference between the predicted and experimental force signatures in terms of crystallographic orientation. In other words, while the symmetry arising from the anisotropy was well-predicted, the location of the peak forces was not accurate (see Fig. 3; the model results are indicated as the “Simplified Model”). A simplification of the procedure by circumventing the minimization of total power and using Merchant’s shear angle also yielded similar results. Furthermore, although the model described above provided a scheme for combining the concepts of crystal plasticity and machining kinematics to arrive at machining forces and shear angles, the (potentially important) effects of lattice rotation and strain hardening during the calculation of plastic power were neglected. To make machining models of single crystals more accurate, lattice rotation and strain hardening effects must be taken into account. When metals are subjected to large deformations, such as those seen during machining, the material exhibits a hardening behavior due to increased dislocation density. As a result, the effective material properties become different than those of the undeformed material. In machining, this hardening occurs within the primary shear zone: as the material enters and progresses within the shear zone, the deformation imposed on the material induces the hardening.
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Fig. 3. Comparison of models and experiments. Fig. 2. Illustration of the lattice rotation; the final deformation is a result of slip on (a) only one system (along 1l ), and (b) two slip systems (simultaneously along 1l and 2l ), and a rotation. The same deformation is obtained with different lattice orientations.
Another important effect during large deformations arises due to kinematics of crystal plasticity determined by slip: The lattice rotates with respect to a fixed frame of reference during large deformations. As the material progressively deforms, lattice rotation causes the orientation of the crystal to change with respect to the cutting geometry (i.e., to a fixed reference frame). Fig. 2 illustrates lattice rotation and resulting change in the orientation for a simplified two dimensional crystal with two slip systems. The lattice frame is represented by 1l –2l and the fixed reference frame is represented by 1–2. For the two cases shown, the total deformations are identical (as observed from the initial and final shapes of the element). For the element shown in Fig. 2(a), the deformation is obtained by slip on a single active slip system along the 1l direction. For the element shown in Fig. 2(b), however, the two active slip systems operate simultaneously along the 1l and 2l directions. Note that a simple rotation is required in Fig. 2(b) to obtain the same orientation of the deformed element. Although the deformations are the same, the final crystal (lattice) orientations are different in Fig. 2(a) and (b). While the lattice did not rotate in Fig. 2(a), activated slip systems in Fig. 2(b) required the lattice to be rotated by an angle of ϕ to achieve the same deformation. There are two important consequences of lattice rotation and hardening for the calculation of shearing power. First, the determination of lattice rotation requires unique identification of the active slip systems (including the amount of slip on each active system). Such a unique identification of active slip systems is most easily obtained by using a rate-sensitive constitutive equation, in which the slip-rate on a slip system depends on the resolved shear stress on that slip system. Once the stress distribution within the material is determined, rate sensitive constitutive equations enable the identification of the active slip systems, and the amount of slip in each of those systems. Furthermore, since hardening is quantified by the amount of prior slip, using a hardening rule which relates material parameters to slip allows incorporating the hardening effect once the amount of slip is known. Second, the amount of work required to prescribe a fixed shear deformation depends on the lattice orientation prior to the deformation and the deformation history. Since the lattice orientation and deformation history (hardening) varies during large deformation, an incremental approach to the calculation of plastic work is required.
Following these strategies a new rate sensitive plasticity-based machining (RSPM) model was developed by Kota et al. to determine the specific energies (and thus forces) for orthogonal cutting of face centered cubic (fcc) single-crystals [22,23]. The RSPM model uses kinematics and geometry of orthogonal cutting for an ideally sharp cutting edge. The total power is expressed in terms of the plastic power, which is spent for shearing the material within a finite shear zone, and the friction power, which is spent for overcoming the friction at the rake face. In calculating the shearing power, rate-sensitive plastic behavior of fcc metals is considered, which facilitated including realistic effects such as lattice rotation and strain hardening in the model. Subsequently, the total power was minimized within the space of geometrically allowable shear angles to determine the shear angle solution, and associated cutting and thrust specific energies, as a function of cutting plane orientation, cutting direction (with respect to the crystal orientation), rake angle, and the coefficient of friction. Fig. 3 shows the comparison between the predicted specific energies from the simplified model [21], from the RSPM model [22,23], and experimental result [3] for plunge turning about [0 0 1] zone axis with a 40◦ rake angle tool. To apply the RSPM model, a calibration scheme to determine five parameters, including one rate-sensitivity exponent and four hardening-model parameters, was developed based on the Kriging approach. Incorporating more realistic physical phenomenon resulted in improved correlation between RSPM model and experimental results, as compared to those between the simplified model (without hardening and lattice rotation) and experiments. Specifically, the phase of the force data now matches that of the experimental data. Although the modeling efforts described show a progression in terms of including more physically realistic phenomenon, they still rely on many simplifying assumptions, including; (1) the deformation of the material within the shear zone is homogenous, and the shear zone is straight (a thin plane), (2) the formation of grain boundaries during large deformations is negligible, (3) the hardening behavior is isotropic (as opposed to latent hardening where individual slip systems harden at different rates), (4) energy spent for chip separation and new-surface generation is negligible, and (5) initial state of the material is free of stress and subsurface damage. Relaxing these assumptions would alter the predictive behavior of the model. For example, incorporating latent hardening would alter the slip kinematics by making it harder for slip to occur on nonactive systems. Such material behavior would increase the amount of work consumed on those cutting directions that require
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changes in active slip systems during the machining deformation; thus, latent hardening would amplify the effect of anisotropy. Unlike latent hardening, incorporating energy spent in new-surface generation can either increase or decrease the effect of anisotropy depending on the separation energy behavior with orientation. For example, constant separation energy would offset the power calculation by a positive value, thus reducing the effect of anisotropy. Future efforts will be aimed at incorporating the aforementioned effects to further enhance the models and their applicability to a wider range of conditions.
3. Current experimental efforts As mentioned above, there is strong need for experimental data on machining of single-crystal and coarse-grained materials covering a broad range of machining conditions. Although planing experiments allow easier setups and provide access to more detailed data and visual inspections, they can be applied to only one (cutting) crystal orientation at a time. Alternatively, plunge turning experiments allow capturing the variation in machining response over a range of orientations, and enable wider ranges of cutting speeds to be used. To address these complementary capabilities, a planing apparatus and a plunge-turning apparatus are constructed.
3.1. Planing apparatus A sliding microtome was modified to create an orthogonal planing set-up as shown in Fig. 4. The tool is connected to the vertical stage (see Fig. 4), the motion of which specifies the uncut chip thickness (feed). The workpiece is connected to the horizontal slide, which provides the cutting velocity. A low-compliance tool post is designed to ensure high loop stiffness, and thus, to avoid large variation of uncut chip thickness from the prescribed value. A set of preliminary tests was conducted to verify that the variation is indeed minimal [24]. Three orthogonal machining-force components are measured with a Kistler 9256C2 dynamometer connected between the tool and the vertical stage (see Fig. 4). To minimize the complexities arising from non-sharp tools, a custom made single crystal diamond tool is utilized for the experiments. The measured edge radius of the diamond tool was below 200 nm. The tool has an included angle of 60◦ , allowing the rake angle of the cutting to vary from 0 to 25◦ (with at least a clearance angle of 5◦ ) using various tool holders.
Fig. 4. Planing apparatus.
3.2. Plunge-turning apparatus Orthogonal plunge-turning experiments are performed on a precision turning apparatus assembled on a vibration isolation table. The setup consists of a precision spindle, a single-axis slide, a Kistler 9256C2 dynamometer, a single crystal diamond tool (same as the one described above), tool holders (to provide required rake angles) and a workpiece holder as shown in Fig. 5. The tool is connected to the slide, which provided the feed motion. A single-crystal aluminum workpiece used during plunge-turning experiments is given in Fig. 6. The workpiece is attached to the workpiece holder that is fixed on the spindle through a collet. The dynamometer was attached on the tool side to measure the forces during plunge turning. The choice of the components was made based on the stiffness, load capacity and accuracy. The set-up was designed to be of high rigidity to minimize experimental uncertainties. Since cutting forces are most strongly dependent on uncut chip thicknesses, the factors (and their values) affecting the uncertainty of uncut chip thickness are provided here for reference. These include the radial stiffness of the spindle, asynchronous component of the runout measured from the workpiece surface, alignment between slide motion axis and spindle rotation axis, and the accuracy of slide motion. The asynchronous component of the runout from the workpiece surface measured using a laser Doppler vibrometer was found
Fig. 5. Turning apparatus.
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Fig. 6. Single crystal workpiece.
to be less than 150 nm. The radial and axial stiffness of the spindle were 58 N/m and 56 N/m, respectively. To minimize experimental errors resulting from vibrations, the spindle was belt driven using a speed controlled vector drive motor. The motion axis of the slide was aligned perpendicular to the rotation axis of the spindle within a tolerance of 0.1◦ . The slide position was found to be within 1 m from the commanded position.
4. Results and discussion 4.1. Orthogonal machining of coarse-grained aluminum The planing apparatus described above is used to conduct a set of orthogonal machining experiments of coarse grained aluminum. The coarse grained aluminum samples were created by annealing pure aluminum (99.999% pure) at 400 ◦ C. Prior to machining, the workpiece is polished on its side, which revealed the grain boundaries. To confirm the location of grain boundaries, and determine the orientation of the grains, orientation image microscopy (OIM) is performed on the workpiece, both on the side plane and on the top (fresh) cutting surface. Cutting fluid was applied (using a brush) on the rake face prior to the experiments. Fig. 7 shows one of the workpieces, OIM image indicating crystallographic orientations, and sample machining forces obtained for an uncut chip thickness of 10 m (the width of the workpiece was 1.6 mm). Experiments were conducted at different cutting speeds (from 5 mm/s to 50 mm/s) and depths of cuts ranging from 10 m to 60 m. The rake angle during the experiments was kept at 0◦ . A similar force variation for grooving operation is provided in [26]. However, the grooving operation is not an orthogonal machining process due to the additional cutting action on the side edges of the tool. As seen in Figs. 7 and 8, the crystallographic anisotropy induced force variations up to 300% across different grains. Depending on the orientation of successive crystals, abrupt changes in machining forces were observed. On an average (across all grains) the machining forces at 50 mm/s were higher than those at 5 mm/s: For instance, the cutting specific energy was 22% higher for 50 mm/s. In addition, the uncut chip thickness was seen to have a significant effect on specific energies, i.e., the size effect was also observed. The cutting specific energies at 10 m were greater than those at 60 m by 21% (for a 50 mm/s cutting speed). Furthermore, an alternation phenomenon, where the forces varied significantly between two levels with consecutive cuts at certain orientations, was also observed. The average surface roughness Ra was seen to vary by as much as 687% across the grains. Moreover, this variation in the surface roughness was seen to be correlated to the variation in cutting forces, with higher forces resulting in poorer surface finish as shown in Fig. 8.
Fig. 7. Typical variation in forces during machining of coarse grained workpieces.
Fig. 8. Comparison between the variation in surface roughness and forces.
4.2. Comparison of plunge-turning and planing forces when machining single-crystal aluminum A set of experiments were performed on single-crystal aluminum with the aim of comparing plunge-turning and planing forces. Although for an isotropic material such comparison is not necessary, for an anisotropic material – before using turning
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Fig. 9. Cutting force variation about (a) [0 0 1] and (b) [1 1 1] zone axis.
experiments as a substitute for planing experiments – it is essential to show that varying orientation during turning does not affect the instantaneous force values at a given orientation. The workpieces were single crystal aluminum (99.999% pure) and were created by slicing from larger crystals using wire electrodischarge machining (WEDM). Both plunge turning and planing experiments for the study were performed using a 25◦ rake angle tool while cutting samples with [0 0 1] zone axis. In both setups, the cutting speed was maintained at 4 mm/s and the cutting depth was 20 m (the width of the workpiece was 1.7 mm). Cutting fluid was applied (using a brush) on the rake face prior to the experiments. It should be noted that no comparison between plunge-turning and planing of single crystals has been presented in literature. Additional plunge turning experiments about [1 1 1] zone axis were also performed for observing the effect of zone axis. To compare machining forces from planing and turning, 13 orientations were randomly chosen about the [0 0 1] zone axis for planing. To eliminate the effects of subsurface deformations, comparisons were made between planing data with and without clean-up cuts (5 cuts of 2 m deep each); the variations between those cases were found to be minimal. Fig. 9(a) shows the comparison between cutting forces from planing and plunge turning. In the case of [0 0 1] zone axis, the horizontal axis in Fig. 9(a) represents the orientation angle of the cutting plane normal measured from [0 1 0] direction. The plunge turning force presented in the figure is the mean of data collected over six revolutions, along with the standard deviations indicated. For planing, the experimental forces shown are the mean of four cutting passes. It is seen that the plunge turning and planing forces
match very well (except for one outlier). The force variations in plunge turning experiments showed the expected four-fold and six-fold symmetries for [0 0 1] and [1 1 1] zone axes respectively (see Fig. 9(a) and (b)). In the case of [1 1 1] zone axis, the horizontal axis in Fig. 9(b) represents the orientation angle of the cutting plane normal measured from [1 0 -1] direction. 4.3. Plunge-turning of single-crystal aluminum at zero rake angle To evaluate the force variations at a small (zero) rake angle, plunge turning experiments were conducted on single-crystal aluminum workpieces. Same cutting conditions as those above were used, except the workpiece zone axis of [1 0 1] was chosen. The cutting force results from the third study exhibited a large variation (the green lines indicating the standard deviation) in forces at certain orientations, as shown in Fig. 10(a). When observed closely by superimposing the machining results from consecutive cuts, it was seen that the forces were alternating between two distinct levels Fig. 10(b), resulting in large standard deviations. A possible cause for such behavior is the subsurface deformation left on the workpiece surface from the previous tool pass. To test this hypothesis, the subsurface deformation in the crystal was subsequently analyzed. 4.4. Analysis of subsurface damage To analyze the subsurface damage on single-crystal aluminum workpieces, we used a combined OIM and focused ion beam (FIB) equipment. The equipment includes two 180◦ apart stations for
Fig. 10. Cutting force variation about (a) [1 0 1] zone axis, and (b) alternation of force at orientation about [1 0 1] zone axis under planing.
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Fig. 11. Workpiece preparation in FIB for subsurface damage analysis.
performing the FIB milling to polish the material, and then to subsequently image the polished area using OIM. To prevent the rounding of edge during FIB milling, a platinum layer is deposited on the cut surface as shown in Fig. 11. The technique also allows observing the changes in orientation below the cut surface. The workpiece machined using zero degree rake angle is analyzed for subsurface damage. Fig. 12 shows the misorientation along the depth direction of the workpiece. The misorientation here refers to the change in angle between the lattice at a given position to the lattice in the bulk single crystal far away from the machined surface. Since the misorientation varies continuously, a pole figure map would depict the situation as a line on a stereographic projection and not as individual points, making it harder to reference with respect to the physical position. Hence, a plot of misorientation angle versus distance from machined surface is provided. The misorientation profile shows two slopes: although the smaller slope is hypothesized to be due to sample positioning accuracy, resulting in a small variation in the measured orientation over distance, the sudden change in this slope is, on the other hand, indicative of subsurface deformation. The depth at which this slope
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OIM OI M ma map p
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changes can be considered as the extent of subsurface deformation (in the case shown here, it is equal to approximately 20 m). Although based on the preliminary subsurface damage data presented (at only one position and orientation) it is hard to conclude whether the alternation of forces is due to sub-surface damage, the misorientation observed could be a potential cause. Considering that the uncut chip thickness was 20 m for the cut surface, a damage layer of 20 m implies the cutting orientation was different than the orientation expected from the macro geometry of the single crystal workpiece. As a result, the data for low rake angle machining of single crystals (including the ones in the literature [1,4,7,11,12,16]) may not be accurately correlated to the crystallographic orientations. 5. Summary In this paper a background of the available experimental and modeling results on the effect of anisotropy during machining was presented. The shortcomings of the available experiments and models were described and the current efforts at improving the understanding of the effects of anisotropy were explained. The experimental set-ups (planing and plunge-turning) for performing the current experiments were described along with the associated advantages of each set-up. Specific energy and surface roughness results from planing experiments on coarse grained aluminum crystals were seen to vary by 300% and 687%, respectively, with crystallographic anisotropy. Comparisons between planing and plunge-turning results on single crystal aluminum indicated that the machining forces obtained from the two configurations are similar. Additional turning experiments were performed on single crystal disks to observe the effect of anisotropy about [1 0 0], [1 1 1] and [1 1 0] zone axes. An alternation of force values with consecutive cuts was observed during plunge turning at 0◦ rake angle at certain orientations about [1 0 1] zone axis. To test the possibility of subsurface deformation being the cause for such alternations, measurements were made using OIM. It was observed that a significant lattice rotation due to deformations existed to a depth approximately equal to the cutting depth. Acknowledgements This work was supported by the National Science Foundation CAREER program under Award Number CMMI-0547534 (Ozdoganlar) and by MRSEC program of the National Science Foundation under award number DMR-0520425. The authors thank Professor Yoosuf N. Picard of Carnegie Mellon University for his assistance in performing FIB based OIM measurements.
Cut surface
Pt Coating Deformed zone
(b) Misorientation (deg.)
30
References 20
10
0
0
10
20
30
40
50
Distance (microns) Fig. 12. (a) Orientation map and (b) misorientation along the depth direction due to subsurface damage. The red arrow is shown to go from the bulk single crystal away from the machined surface to the machined surface in both figures. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
[1] Lawson BL, Kota N, Ozdoganlar OB. Effects of crystallographic anisotropy on orthogonal micromachining of single-crystal aluminum. Journal of Manufacturing Science and Engineering, Transactions of the ASME 2008;130(3):0311161–11. [2] Ramalingam S, Hazra J. Dynamic shear stress-analysis of single crystal machining studies. Transactions of the ASME, Journal of Engineering for Industry 1973;95B:939–44. [3] Cohen PH. The orthogonal in-situ machining of single and polycrystalline aluminum and copper. PhD thesis, Ohio State University; 1982. [4] To S, Lee WB, Chan CY. Ultraprecision diamond turning of aluminum single crystals. Journal of Materials Processing Technology 1997;63:157–62. [5] Williams J, Horne J. Crystallographic effects in metal cutting. Journal of Material Science 1982;17:2618–24. [6] Willams J, Gane N. Some observations on the flow stress of metals during metal cutting. Wear 1977;42:341–53. [7] Moriwaki T, Okuda K, Shen JG. Study on ultraprecision orthogonal microdiamond cutting of single-crystal copper. JSME International Journal, Series C: Dynamics, Control, Robotics, Design and Manufacturing 1993;36:400–6.
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[8] Sato M, Kato Y, Tsutiya K. Effects of crystal orientation on the flow mechanism in cutting aluminum single crystal. Transactions of the Japanese Institute of Metals 1979;20:414–22. [9] Sato M, Kato Y, Tsutiya K, Aoki S. Effects of crystal orientation on the cutting mechanism of aluminum single crystal. Bulletin of the JSME 1981;24:1864–70. [10] Sato M, Kato Y, Aoki S, Ikoma A. Effects of crystal orientation on the cutting mechanism of aluminum single crystal. Bulletin of the JSME 1983;26(215):890–6. [11] Sato M, Yamazaki T, Shimizu Y, Takabayashi T. A study on the microcutting of aluminum single crystals. Japanese Society of Mechanical Engineering International Journal 1991;34(4):540–5. [12] Yuan ZJ, Lee WB, Yao YX, Zhou M. Effect of crystallographic orientation on cutting forces and surface quality in diamond cutting of single crystal. CIRP Annals-Manufacturing Technology 1994;43(1):39–42. [13] Clarebrough LM, Ogilivie GJ. Microstructure by machining. In: Machining Theory and Practice. ASM; 1950. p. 110–21. [14] Black JT. Plastic deformation in ultramicrotomy of copper and aluminum. PhD thesis, University of Illinois; 1969. [15] von Turkovich B, Black JT. Micro-machining of copper and aluminum crystals. ASME Journal of Engineering for Industry 1970;92(Ser B):130–4. [16] Ueda K, Iwata K, Nakajama K. Chip formation mechanism in single crystal cutting ˇ-brass. CIRP Annals-Manufacturing Technology 1980;29(1):41–6. [17] Zhou M, Ngoi BKA. Effect of tool and workpiece anisotropy on microcutting processes. IMechE Journal of Engineering Manufacture 2001;215:13–9. [18] Lee WB, Zhou M. A theoretical analysis of the effect of crystallographic orientation on chip formation in micromachining. International Journal of Machine Tools and Manufacture 1993;33(3):439–47.
[19] Lee WB, Cheung CF, To S. A microplasticity analysis of micro-cutting force variation in ultra-precision diamond turning. Journal of Manufacturing Science and Engineering 2002;124:170–7. [20] Reid CN. Deformation geometry for material scientists. Pergamon Press; 1973. [21] Kota N, Ozdoganlar O. A model-based analysis of orthogonal cutting for singlecrystal fcc metals including crystallographic anisotropy. Machining Science and Technology 2010;14(1):102–27. [22] Kota N, Rollett AD, Ozdoganlar OB. A rate-sensitive plasticity-based force model for machining of face centered cubic single-crystals – Part 1. Model development. Journal of Manufacturing Science and Engineering, Transactions of the ASME 2011;133(3), 031017(8 pages). [23] Kota N, Rollett AD, Ozdoganlar OB. A rate-sensitive plasticity-based force model for machining of face centered cubic single-crystals – Part 2. Model calibration and validation. Journal of Manufacturing Science and Engineering, Transactions of the ASME 2011;133(3), 031018(9 pages). [24] Kota N, Ozdoganlar OB. Machining force and surface finish variation across grains during orthogonal micromachining of aluminum. In: Proceedings of 5th International Conference on Micro Manufacturing. 2010. p. 133–8. [25] Vlassak JJ, Nix WD. Measuring the elastic properties of anisotropic materials by means of indentation experiments. Journal of the Mechanics and Physics of Solids 1994;42:1223–44. [26] Ding X, Butler DL, Lim GC, Cheng CK, Shaw KC, Liu K, et al. Machining with micro-size single crystalline diamond tools fabricated by a focused ion beam. Journal of Micromechanics and Microengineering 2009;19:025005.
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Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Technical paper
Orthogonal machining of single-crystal and coarse-grained aluminum Nithyanand Kota a , O. Burak Ozdoganlar a,b,∗ a b
Science Applications International Corporation, 2001 Jefferson Davis Highway, Arlington, VA 22202, USA Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
a r t i c l e
i n f o
Article history: Received 21 October 2011 Received in revised form 19 January 2012 Accepted 31 January 2012 Available online 4 April 2012 Keywords: Machining Micro-machining Single crystal Coarse grained polycrystals Microstructure Anisotropy Orthogonal cutting FIB-OIM Subsurface deformation
a b s t r a c t Orthogonal machining of single-crystal and coarse-grained (i.e., grain size considerably larger than the uncut chip thickness) materials has been a subject to many studies in the literature. The first part of this paper presents background on machining single-crystal materials, including experimental and modeling attempts. The second part briefly describes more recent modeling results from the authors, and presents new experimental results on planing and plunge-turning of single-crystal and coarse-grained aluminum using diamond tools. The experiments indicate that (1) cutting across grains of a coarse-grained aluminum workpiece produces distinctly varying forces and surface roughness from one grain to another, (2) plungeturning and planing of single crystal aluminum provide equivalent force data for large rake angles, (3) forces alter between two distinct levels while cutting single crystals with small rake angles, and (4) with small rake angles, subsurface damage on single-crystal aluminum is extensive, reaching depths comparable to the uncut chip thickness. © 2012 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers.
1. Introduction Machining of single-crystal and coarse-grained materials is of interest due to (a) the demand from various applications for singlecrystal parts due to their uniformity and reduced level of defects (e.g., turbine blades, precision mirrors), (b) the need for developing fundamental understanding of materials and material removal, since all crystalline materials are composed of grains and grain boundaries, which, to a large extent, dictate their mechanical properties. Recent interest in ultra-precision machining and micromachining also motivated single-crystal machining analysis, since those processes include chip-thicknesses commensurate with the grain size of many engineering materials, making crystallographic anisotropy critical in machining response. The first part of this paper provides extensive background on machining of single-crystal materials, including brief descriptions of authors’ work. In the second part, new experimental results on planing and plunge-turning of single-crystal and coarse-grained aluminum are presented. The experimental apparatuses used for planing and plunge-turning experiments are described in detail. Planing experiments are conducted on coarse-grained aluminum,
∗ Corresponding author at: Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA. E-mail address: [email protected] (O.B. Ozdoganlar).
and forces and surface roughness across the grains are analyzed. Next, plunge turning and planing of single-crystal aluminum are compared. Subsequently, the extent of subsurface damage during plunge turning of single-crystal aluminum is analyzed.
2. Background 2.1. Experimentation on machining of single-crystal and coarse-grained materials A number of experimental studies have confirmed that machining response including machining forces [1–12], chip lamellae [1,13–16], dynamic shear stress [2–6], and surface roughness [4,7,10] strongly depend on the crystallographic orientation in fcc metals. Some investigations also considered the effect of crystallographic anisotropy on the built-up edge (BUE) [13] and material side-flow [10]. Researchers have conducted both plunge-turning [3,4,12] and planing experiments [2,5–11,13–16] on single-crystal metals. Some of the experimentation was conducted inside a scanning electron microscope (SEM), allowing visual observation of chip formation [3,16]. Single-crystal fcc materials, mainly aluminum [1–4,8–11], and copper [3,5,6], have been tested in these studies. Table 1 tabulates the cutting conditions and materials considered in some of the works in the literature. Early studies on machining single crystals were aimed at observing the lamellae structure of the chips formed during machining.
1526-6125/$ – see front matter © 2012 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers. doi:10.1016/j.jmapro.2012.01.002
N. Kota, O.B. Ozdoganlar / Journal of Manufacturing Processes 14 (2012) 126–134 Table 1 Experimental studies on single-crystal machining from the literature, and associated machining parameters.
Clarebrough and Ogilivie [13] Black [14] Ramalingam and Hazra [2] Williams and Gane [6] Ueda and Iwata [16] Williams and Horne [5] Cohen [3] Sato et al. [8–10] Sato et al. [11] Moriwaki et al. [7] Yuan et al. [12] To et al. [4] Zhou and Ngoi [17] Lawson et al. (2007) [1]
Material
Rake angle
Feed (m)
Speed (mm/s)
Pb Cu, Al Al Cu ˇ-brass Cu Cu, Al Al Al Cu Cu, Al Al Al, Cu Al
60◦ – 40◦ 40◦ 0◦ , 20◦ 40◦ 50◦ –0◦ 35◦ 3◦ 0, 5◦ 0◦ 0◦ 0◦ 0◦
25 0.0025–2 127 1–100 0.1–200 100 114.3 100 0.5–3 0.01–3 1–10 1–10 5–10 5–20
– 1 0.27 0.1–1 0.0025 20 0.44 1.66 16.66 8833.33 0.16–0.83 0.16–0.83 1300 5–15
The first known study was published in 1950 by Clarebrough and Ogilivie [13], who microtomed large crystals of lead and observed a strong correlation between the crystallographic orientation and lamellae spacing. Subsequent studies of Black and von Turkovich shed light on various aspects of micro-scale chip formation in single-crystal cutting [14,15]. They performed a quantitative study of chip formation mechanisms in single-crystal copper and aluminum via an ultra-microtomy process. The lamellae thickness was seen to be affected by the crystallographic orientation and uncut chip thickness (below 2 m) [14]. Of all the machining responses, the variation of machining forces (and therefore the specific energies) while cutting singlecrystal materials at different orientations have been studied in greater detail by various researchers [1–3,5–12]. A majority of the researchers [1,5–11] used the planing configuration, in which the tool cuts along a particular crystal direction for a fixed length of the workpiece (see Fig. 1(a)). The planing data on aluminum consists primarily of cutting forces on (1 1 1) [6,10,11], (1 1 0) [6,10,11] and (0 0 1) [9,11] planes ([u v w] in Fig. 1(a)). Planing force data was also collected for cutting various directions about [0 0 1] [1] and [1 1 2] [10] zone axes on aluminum single crystals (i.e., the zone axis directions coincide with [a b c] in Fig. 1(a)). The planing forces on copper have been measured while cutting on (1 1 0) and (1 1 1) planes [6], and about [1 − 10] zone axis [5,7]. The results from the planing studies showed that the anisotropy of fcc crystals strongly affects the machining forces, inducing up to 312% variation in machining forces at different crystallographic orientations for a given zone axis [1]. The magnitude of variation in machining forces must be contrasted with results from nanoindentation, where the dependence of hardness on orientation is observed to be minimal [25]. For example, the observed variation in hardness in copper, between {1 1 0} and other surfaces was 6%. In addition to constant (stable) machining forces [1,2,6–8,11], monotonically-increasing [8], bi-stable [1,6] and periodicallyvarying [1,16] force signatures have been observed for different cutting parameters and crystallographic orientations during planing experiments. Abrupt, short-term reduction in forces was also observed in some studies [8]. While planing experiments provide detailed data in terms of cutting forces, only one crystal orientation can be machined at a time. As an alternative to the planing configuration, the plungeturning configuration shown in Fig. 1(b, c) has been used in [3,4,12]. This configuration provides near-continuous data for the entire range of cutting directions for a given zone axis. These turning experiments can be further divided into two types. Whereas Fig. 1(b) shows the case where the zone axis [a b c] serves as the axis of rotation, Fig. 1(c) has the cutting plane normal as the axis of
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(a)
[uvw] α
Tool
[abc]
Vc
[hkl] V
h
Sing leWor Crysta kpie l ce
w
(b)
[uvw]
α
[hkl]
h
V
w
ω
[abc]
SingleWorkpieCrystal ce
(c) [abc] [uvw]
[hkl]
V [uvw]
ω
SingleWorkpieCrystal ce Fig. 1. (a) Planing configuration, (b) plunge-turning configuration, and (c) in-plane machining.
rotation. Henceforth, the case shown in Fig. 1(c) will be referred to as in-plane machining for clarity. In the plunge turning experiments of Cohen [3], cutting forces were collected about the [0 0 1] zone axis ([a b c] in Fig. 1(b)) while cutting both aluminum and copper single-crystals. The force measurements from these experiments showed a repeatable four-fold symmetry expected from the crystallographic symmetry of [0 0 1] zone axis. While the [1 0 0] cutting direction produced the minimum force, the maximum force was consistently observed to occur at an offset of 15–20◦ from [1 1 0] cutting direction. The in-plane machining results [4,12] consist of machining force variation with cutting directions about (1 1 0) and (1 1 1) cutting plane normals. The experimental force variation with cutting directions on (1 1 0) plane were found to be larger than those on (1 1 1) cutting plane due to the increased crystallographic symmetry on (1 1 1) plane as compared to (1 1 0) plane. Apart from the machining forces, another important machining response is the roughness of the machined surface. Experimental
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studies have found a correlation between different crystallographic orientations and resulting surface roughness [4,7]. The roughness variation results showed expected crystallographic symmetries in the in-plane machining experiments on copper [4]. In a contrasting result, Moriwaki observed that for uncut chip thicknesses below 0.1 m when micromachining already-machined surfaces the surface roughness (and machining forces) was not affected by the crystallographic orientation [7]. This was explained by considering the significant sub-surface damage (dislocations) left from previous cutting passes. Despite the above described studies, the available data is scattered sparsely over the possible cutting conditions, posing a difficulty for validating the machining models or gaining a thorough understanding on the effects of crystallographic anisotropy during machining. While both planing and plunge-turning studies suggest a strong effect of crystallographic anisotropy on machining forces, the available data is insufficient to elaborate on the effects of rake angle, cutting velocity and uncut chip thickness while machining single crystal fcc metals. 2.2. Modeling attempts Although the relatively large body of experimental evidence suggests a strong dependence of machining response parameters on crystallographic orientation, relatively few attempts have been made to incorporate explicitly the effects of crystallographic anisotropy into machining models [9,18,19]. Modeling the effects of anisotropy requires incorporating the underlying physical phenomenon causing the anisotropy. The anisotropy observed in machining is the result of plastic deformation behavior of metallic crystals. Plastic deformation in crystals is due to the motion of crystal defects called dislocations on specific crystallographic planes along specific directions, i.e., a combination of slip direction on a slip plane is called a slip system. Face-centered cubic (fcc) metals have 12 such slip systems with slip directions belonging to 1 1 0 family, and slip plane normals belonging to {1 1 1} family. Furthermore, any arbitrary deformation can be achieved by activating 5 independent slip systems. The orientations of these planes and directions with respect to the cutting geometry (defined by cutting plane normal and cutting direction) determine the machining response. Additional complications in machining modeling arise from the lack of knowledge of the actual amount of deformation (often characterized by the shear angle). As a consequence, strategies for incorporating the effects of anisotropy must at first include the determination of shear angle. Researchers have considered a few different approaches for incorporating the anisotropy into machining models. An early work by Sato et al. [9] used the Schmid factor to obtain the active slip systems during machining. The amount of slip on each slip system was assumed to be proportional to the Schmid factor of that slip system. The value of shear angle was then calculated from the vector sum of slip directions on active slip systems. While the aforementioned approach provides some physical basis, the actual function of Schmid factor is only to predict one active slip system [20]. Hence, Schmid factor-based approaches are more relevant while discussing deformation caused solely by single slip, unlike deformations during machining. To obtain the shear deformation during machining-on any arbitrary orientationsrequires simultaneous activation of five or more independent slip systems. Recognizing this fact, later attempts by researchers incorporated Taylor-factor [20] based models, which are more relevant for multi-slip scenarios. Lee et al. [18] used a modified form of the Taylor factor, referred to as the effective Taylor factor, to predict the shear angle in singlecrystal cutting. For each crystallographic orientation, the Taylor factor was calculated for all possible shear angles. The effective
Taylor factor was then obtained by dividing the Taylor factor with cosine of two times the difference between the candidate shear angle and 45◦ . Essentially, the effective Taylor factor was used to incorporate the geometrical aspect of variation of strain with shear angle by penalizing those shear angle candidates away from the geometrically optimal 45◦ . This form of effective Taylor factor is only applicable for zero rake angle case, since 45◦ is not geometrically optimal for non-zero rake angles. While the goal was to choose the shear angle from the orientation that provided the minimum effective Taylor factor, this approach did not yield a unique solution in most cases. A texture softening factor was subsequently used to uniquely predict the shear angle as the angle that results in the minimum texture softening factor. This work was then extended to predict the variation in cutting forces with crystallographic orientation using Merchant’s model [19]. While the Taylor-factor based models significantly improve the prediction capability as compared to Schmid-factor based models, they do not incorporate the kinematic aspects (rake angle, strain variation with shear angle) and friction (on the rake face) while arriving at shear angle solutions. In determining the shear angles, all of the aforementioned models used only crystal plasticity models, while the mechanics of material removal was considered after the determination of shear angle. Therefore, the shear angles and shear forces were insensitive to the changes in friction on the rake face. 2.3. More recent modeling efforts To overcome the aforementioned shortcomings, Kota and Ozdoganlar [21] integrated Bishop and Hill’s crystal plasticity model within the framework of Merchant’s machining model to determine the shear angle and specific energies for fcc single-crystals. The plastic power required for shearing the material was calculated using Bishop and Hill’s plasticity theory, whereas Merchant’s machining force model was used to express the machining forces in terms of kinematics of cutting process. For a given crystallographic orientation (workpiece zone axis and cutting plane), the total power, including the shearing and rake-face friction power, was then minimized to determine the shear angle and specific energies. As expected, the forces (and specific energies) were found to vary in a periodic fashion, with a period corresponding to the crystallographic symmetry of the specific zone axis and cutting plane. Although the model in [21] successfully captured the amplitude of variation arising from the crystallographic anisotropy and the periodicity, there was a phase difference between the predicted and experimental force signatures in terms of crystallographic orientation. In other words, while the symmetry arising from the anisotropy was well-predicted, the location of the peak forces was not accurate (see Fig. 3; the model results are indicated as the “Simplified Model”). A simplification of the procedure by circumventing the minimization of total power and using Merchant’s shear angle also yielded similar results. Furthermore, although the model described above provided a scheme for combining the concepts of crystal plasticity and machining kinematics to arrive at machining forces and shear angles, the (potentially important) effects of lattice rotation and strain hardening during the calculation of plastic power were neglected. To make machining models of single crystals more accurate, lattice rotation and strain hardening effects must be taken into account. When metals are subjected to large deformations, such as those seen during machining, the material exhibits a hardening behavior due to increased dislocation density. As a result, the effective material properties become different than those of the undeformed material. In machining, this hardening occurs within the primary shear zone: as the material enters and progresses within the shear zone, the deformation imposed on the material induces the hardening.
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Fig. 3. Comparison of models and experiments. Fig. 2. Illustration of the lattice rotation; the final deformation is a result of slip on (a) only one system (along 1l ), and (b) two slip systems (simultaneously along 1l and 2l ), and a rotation. The same deformation is obtained with different lattice orientations.
Another important effect during large deformations arises due to kinematics of crystal plasticity determined by slip: The lattice rotates with respect to a fixed frame of reference during large deformations. As the material progressively deforms, lattice rotation causes the orientation of the crystal to change with respect to the cutting geometry (i.e., to a fixed reference frame). Fig. 2 illustrates lattice rotation and resulting change in the orientation for a simplified two dimensional crystal with two slip systems. The lattice frame is represented by 1l –2l and the fixed reference frame is represented by 1–2. For the two cases shown, the total deformations are identical (as observed from the initial and final shapes of the element). For the element shown in Fig. 2(a), the deformation is obtained by slip on a single active slip system along the 1l direction. For the element shown in Fig. 2(b), however, the two active slip systems operate simultaneously along the 1l and 2l directions. Note that a simple rotation is required in Fig. 2(b) to obtain the same orientation of the deformed element. Although the deformations are the same, the final crystal (lattice) orientations are different in Fig. 2(a) and (b). While the lattice did not rotate in Fig. 2(a), activated slip systems in Fig. 2(b) required the lattice to be rotated by an angle of ϕ to achieve the same deformation. There are two important consequences of lattice rotation and hardening for the calculation of shearing power. First, the determination of lattice rotation requires unique identification of the active slip systems (including the amount of slip on each active system). Such a unique identification of active slip systems is most easily obtained by using a rate-sensitive constitutive equation, in which the slip-rate on a slip system depends on the resolved shear stress on that slip system. Once the stress distribution within the material is determined, rate sensitive constitutive equations enable the identification of the active slip systems, and the amount of slip in each of those systems. Furthermore, since hardening is quantified by the amount of prior slip, using a hardening rule which relates material parameters to slip allows incorporating the hardening effect once the amount of slip is known. Second, the amount of work required to prescribe a fixed shear deformation depends on the lattice orientation prior to the deformation and the deformation history. Since the lattice orientation and deformation history (hardening) varies during large deformation, an incremental approach to the calculation of plastic work is required.
Following these strategies a new rate sensitive plasticity-based machining (RSPM) model was developed by Kota et al. to determine the specific energies (and thus forces) for orthogonal cutting of face centered cubic (fcc) single-crystals [22,23]. The RSPM model uses kinematics and geometry of orthogonal cutting for an ideally sharp cutting edge. The total power is expressed in terms of the plastic power, which is spent for shearing the material within a finite shear zone, and the friction power, which is spent for overcoming the friction at the rake face. In calculating the shearing power, rate-sensitive plastic behavior of fcc metals is considered, which facilitated including realistic effects such as lattice rotation and strain hardening in the model. Subsequently, the total power was minimized within the space of geometrically allowable shear angles to determine the shear angle solution, and associated cutting and thrust specific energies, as a function of cutting plane orientation, cutting direction (with respect to the crystal orientation), rake angle, and the coefficient of friction. Fig. 3 shows the comparison between the predicted specific energies from the simplified model [21], from the RSPM model [22,23], and experimental result [3] for plunge turning about [0 0 1] zone axis with a 40◦ rake angle tool. To apply the RSPM model, a calibration scheme to determine five parameters, including one rate-sensitivity exponent and four hardening-model parameters, was developed based on the Kriging approach. Incorporating more realistic physical phenomenon resulted in improved correlation between RSPM model and experimental results, as compared to those between the simplified model (without hardening and lattice rotation) and experiments. Specifically, the phase of the force data now matches that of the experimental data. Although the modeling efforts described show a progression in terms of including more physically realistic phenomenon, they still rely on many simplifying assumptions, including; (1) the deformation of the material within the shear zone is homogenous, and the shear zone is straight (a thin plane), (2) the formation of grain boundaries during large deformations is negligible, (3) the hardening behavior is isotropic (as opposed to latent hardening where individual slip systems harden at different rates), (4) energy spent for chip separation and new-surface generation is negligible, and (5) initial state of the material is free of stress and subsurface damage. Relaxing these assumptions would alter the predictive behavior of the model. For example, incorporating latent hardening would alter the slip kinematics by making it harder for slip to occur on nonactive systems. Such material behavior would increase the amount of work consumed on those cutting directions that require
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changes in active slip systems during the machining deformation; thus, latent hardening would amplify the effect of anisotropy. Unlike latent hardening, incorporating energy spent in new-surface generation can either increase or decrease the effect of anisotropy depending on the separation energy behavior with orientation. For example, constant separation energy would offset the power calculation by a positive value, thus reducing the effect of anisotropy. Future efforts will be aimed at incorporating the aforementioned effects to further enhance the models and their applicability to a wider range of conditions.
3. Current experimental efforts As mentioned above, there is strong need for experimental data on machining of single-crystal and coarse-grained materials covering a broad range of machining conditions. Although planing experiments allow easier setups and provide access to more detailed data and visual inspections, they can be applied to only one (cutting) crystal orientation at a time. Alternatively, plunge turning experiments allow capturing the variation in machining response over a range of orientations, and enable wider ranges of cutting speeds to be used. To address these complementary capabilities, a planing apparatus and a plunge-turning apparatus are constructed.
3.1. Planing apparatus A sliding microtome was modified to create an orthogonal planing set-up as shown in Fig. 4. The tool is connected to the vertical stage (see Fig. 4), the motion of which specifies the uncut chip thickness (feed). The workpiece is connected to the horizontal slide, which provides the cutting velocity. A low-compliance tool post is designed to ensure high loop stiffness, and thus, to avoid large variation of uncut chip thickness from the prescribed value. A set of preliminary tests was conducted to verify that the variation is indeed minimal [24]. Three orthogonal machining-force components are measured with a Kistler 9256C2 dynamometer connected between the tool and the vertical stage (see Fig. 4). To minimize the complexities arising from non-sharp tools, a custom made single crystal diamond tool is utilized for the experiments. The measured edge radius of the diamond tool was below 200 nm. The tool has an included angle of 60◦ , allowing the rake angle of the cutting to vary from 0 to 25◦ (with at least a clearance angle of 5◦ ) using various tool holders.
Fig. 4. Planing apparatus.
3.2. Plunge-turning apparatus Orthogonal plunge-turning experiments are performed on a precision turning apparatus assembled on a vibration isolation table. The setup consists of a precision spindle, a single-axis slide, a Kistler 9256C2 dynamometer, a single crystal diamond tool (same as the one described above), tool holders (to provide required rake angles) and a workpiece holder as shown in Fig. 5. The tool is connected to the slide, which provided the feed motion. A single-crystal aluminum workpiece used during plunge-turning experiments is given in Fig. 6. The workpiece is attached to the workpiece holder that is fixed on the spindle through a collet. The dynamometer was attached on the tool side to measure the forces during plunge turning. The choice of the components was made based on the stiffness, load capacity and accuracy. The set-up was designed to be of high rigidity to minimize experimental uncertainties. Since cutting forces are most strongly dependent on uncut chip thicknesses, the factors (and their values) affecting the uncertainty of uncut chip thickness are provided here for reference. These include the radial stiffness of the spindle, asynchronous component of the runout measured from the workpiece surface, alignment between slide motion axis and spindle rotation axis, and the accuracy of slide motion. The asynchronous component of the runout from the workpiece surface measured using a laser Doppler vibrometer was found
Fig. 5. Turning apparatus.
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Fig. 6. Single crystal workpiece.
to be less than 150 nm. The radial and axial stiffness of the spindle were 58 N/m and 56 N/m, respectively. To minimize experimental errors resulting from vibrations, the spindle was belt driven using a speed controlled vector drive motor. The motion axis of the slide was aligned perpendicular to the rotation axis of the spindle within a tolerance of 0.1◦ . The slide position was found to be within 1 m from the commanded position.
4. Results and discussion 4.1. Orthogonal machining of coarse-grained aluminum The planing apparatus described above is used to conduct a set of orthogonal machining experiments of coarse grained aluminum. The coarse grained aluminum samples were created by annealing pure aluminum (99.999% pure) at 400 ◦ C. Prior to machining, the workpiece is polished on its side, which revealed the grain boundaries. To confirm the location of grain boundaries, and determine the orientation of the grains, orientation image microscopy (OIM) is performed on the workpiece, both on the side plane and on the top (fresh) cutting surface. Cutting fluid was applied (using a brush) on the rake face prior to the experiments. Fig. 7 shows one of the workpieces, OIM image indicating crystallographic orientations, and sample machining forces obtained for an uncut chip thickness of 10 m (the width of the workpiece was 1.6 mm). Experiments were conducted at different cutting speeds (from 5 mm/s to 50 mm/s) and depths of cuts ranging from 10 m to 60 m. The rake angle during the experiments was kept at 0◦ . A similar force variation for grooving operation is provided in [26]. However, the grooving operation is not an orthogonal machining process due to the additional cutting action on the side edges of the tool. As seen in Figs. 7 and 8, the crystallographic anisotropy induced force variations up to 300% across different grains. Depending on the orientation of successive crystals, abrupt changes in machining forces were observed. On an average (across all grains) the machining forces at 50 mm/s were higher than those at 5 mm/s: For instance, the cutting specific energy was 22% higher for 50 mm/s. In addition, the uncut chip thickness was seen to have a significant effect on specific energies, i.e., the size effect was also observed. The cutting specific energies at 10 m were greater than those at 60 m by 21% (for a 50 mm/s cutting speed). Furthermore, an alternation phenomenon, where the forces varied significantly between two levels with consecutive cuts at certain orientations, was also observed. The average surface roughness Ra was seen to vary by as much as 687% across the grains. Moreover, this variation in the surface roughness was seen to be correlated to the variation in cutting forces, with higher forces resulting in poorer surface finish as shown in Fig. 8.
Fig. 7. Typical variation in forces during machining of coarse grained workpieces.
Fig. 8. Comparison between the variation in surface roughness and forces.
4.2. Comparison of plunge-turning and planing forces when machining single-crystal aluminum A set of experiments were performed on single-crystal aluminum with the aim of comparing plunge-turning and planing forces. Although for an isotropic material such comparison is not necessary, for an anisotropic material – before using turning
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Fig. 9. Cutting force variation about (a) [0 0 1] and (b) [1 1 1] zone axis.
experiments as a substitute for planing experiments – it is essential to show that varying orientation during turning does not affect the instantaneous force values at a given orientation. The workpieces were single crystal aluminum (99.999% pure) and were created by slicing from larger crystals using wire electrodischarge machining (WEDM). Both plunge turning and planing experiments for the study were performed using a 25◦ rake angle tool while cutting samples with [0 0 1] zone axis. In both setups, the cutting speed was maintained at 4 mm/s and the cutting depth was 20 m (the width of the workpiece was 1.7 mm). Cutting fluid was applied (using a brush) on the rake face prior to the experiments. It should be noted that no comparison between plunge-turning and planing of single crystals has been presented in literature. Additional plunge turning experiments about [1 1 1] zone axis were also performed for observing the effect of zone axis. To compare machining forces from planing and turning, 13 orientations were randomly chosen about the [0 0 1] zone axis for planing. To eliminate the effects of subsurface deformations, comparisons were made between planing data with and without clean-up cuts (5 cuts of 2 m deep each); the variations between those cases were found to be minimal. Fig. 9(a) shows the comparison between cutting forces from planing and plunge turning. In the case of [0 0 1] zone axis, the horizontal axis in Fig. 9(a) represents the orientation angle of the cutting plane normal measured from [0 1 0] direction. The plunge turning force presented in the figure is the mean of data collected over six revolutions, along with the standard deviations indicated. For planing, the experimental forces shown are the mean of four cutting passes. It is seen that the plunge turning and planing forces
match very well (except for one outlier). The force variations in plunge turning experiments showed the expected four-fold and six-fold symmetries for [0 0 1] and [1 1 1] zone axes respectively (see Fig. 9(a) and (b)). In the case of [1 1 1] zone axis, the horizontal axis in Fig. 9(b) represents the orientation angle of the cutting plane normal measured from [1 0 -1] direction. 4.3. Plunge-turning of single-crystal aluminum at zero rake angle To evaluate the force variations at a small (zero) rake angle, plunge turning experiments were conducted on single-crystal aluminum workpieces. Same cutting conditions as those above were used, except the workpiece zone axis of [1 0 1] was chosen. The cutting force results from the third study exhibited a large variation (the green lines indicating the standard deviation) in forces at certain orientations, as shown in Fig. 10(a). When observed closely by superimposing the machining results from consecutive cuts, it was seen that the forces were alternating between two distinct levels Fig. 10(b), resulting in large standard deviations. A possible cause for such behavior is the subsurface deformation left on the workpiece surface from the previous tool pass. To test this hypothesis, the subsurface deformation in the crystal was subsequently analyzed. 4.4. Analysis of subsurface damage To analyze the subsurface damage on single-crystal aluminum workpieces, we used a combined OIM and focused ion beam (FIB) equipment. The equipment includes two 180◦ apart stations for
Fig. 10. Cutting force variation about (a) [1 0 1] zone axis, and (b) alternation of force at orientation about [1 0 1] zone axis under planing.
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Fig. 11. Workpiece preparation in FIB for subsurface damage analysis.
performing the FIB milling to polish the material, and then to subsequently image the polished area using OIM. To prevent the rounding of edge during FIB milling, a platinum layer is deposited on the cut surface as shown in Fig. 11. The technique also allows observing the changes in orientation below the cut surface. The workpiece machined using zero degree rake angle is analyzed for subsurface damage. Fig. 12 shows the misorientation along the depth direction of the workpiece. The misorientation here refers to the change in angle between the lattice at a given position to the lattice in the bulk single crystal far away from the machined surface. Since the misorientation varies continuously, a pole figure map would depict the situation as a line on a stereographic projection and not as individual points, making it harder to reference with respect to the physical position. Hence, a plot of misorientation angle versus distance from machined surface is provided. The misorientation profile shows two slopes: although the smaller slope is hypothesized to be due to sample positioning accuracy, resulting in a small variation in the measured orientation over distance, the sudden change in this slope is, on the other hand, indicative of subsurface deformation. The depth at which this slope
(a)
OIM OI M ma map p
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changes can be considered as the extent of subsurface deformation (in the case shown here, it is equal to approximately 20 m). Although based on the preliminary subsurface damage data presented (at only one position and orientation) it is hard to conclude whether the alternation of forces is due to sub-surface damage, the misorientation observed could be a potential cause. Considering that the uncut chip thickness was 20 m for the cut surface, a damage layer of 20 m implies the cutting orientation was different than the orientation expected from the macro geometry of the single crystal workpiece. As a result, the data for low rake angle machining of single crystals (including the ones in the literature [1,4,7,11,12,16]) may not be accurately correlated to the crystallographic orientations. 5. Summary In this paper a background of the available experimental and modeling results on the effect of anisotropy during machining was presented. The shortcomings of the available experiments and models were described and the current efforts at improving the understanding of the effects of anisotropy were explained. The experimental set-ups (planing and plunge-turning) for performing the current experiments were described along with the associated advantages of each set-up. Specific energy and surface roughness results from planing experiments on coarse grained aluminum crystals were seen to vary by 300% and 687%, respectively, with crystallographic anisotropy. Comparisons between planing and plunge-turning results on single crystal aluminum indicated that the machining forces obtained from the two configurations are similar. Additional turning experiments were performed on single crystal disks to observe the effect of anisotropy about [1 0 0], [1 1 1] and [1 1 0] zone axes. An alternation of force values with consecutive cuts was observed during plunge turning at 0◦ rake angle at certain orientations about [1 0 1] zone axis. To test the possibility of subsurface deformation being the cause for such alternations, measurements were made using OIM. It was observed that a significant lattice rotation due to deformations existed to a depth approximately equal to the cutting depth. Acknowledgements This work was supported by the National Science Foundation CAREER program under Award Number CMMI-0547534 (Ozdoganlar) and by MRSEC program of the National Science Foundation under award number DMR-0520425. The authors thank Professor Yoosuf N. Picard of Carnegie Mellon University for his assistance in performing FIB based OIM measurements.
Cut surface
Pt Coating Deformed zone
(b) Misorientation (deg.)
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Distance (microns) Fig. 12. (a) Orientation map and (b) misorientation along the depth direction due to subsurface damage. The red arrow is shown to go from the bulk single crystal away from the machined surface to the machined surface in both figures. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
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