The New Plastic Flow Machining Process for Producing Thin Sheets

Université de Lorraine, CNRS, Arts et Métiers ParisTech, LEM3, F-57000 Metz, France Laboratory of Excellence on Design of Alloy Metals for Low-Mass Structures (DAMAS), Université de Lorraine, Metz, France Donetsk Institute for Physics and Engineering Named After O.O. Galkin, National Academy of Sciences of Ukraine, Kyiv, Ukraine Institute of Nanotechnology (INT), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany


Introduction
Severe plastic deformation (SPD) has been acclaimed as an effective technique for producing metals with superior properties which are unattainable by conventional thermomechanical processing. To date there have been a great number of SPD processes proposed, such as high pressure torsion (HPT) [1], equal channel angular pressing (ECAP) [2], accumulative roll bonding (ARB) [3], twist extrusion (TE) [4], repetitive corrugation and straightening (RCS) [5], to name a few. One of the most prominent benefits of SPD is its ability to transform an initial coarse-grained (CG) structure into an ultrafine-grained (UFG) structure at room temperature, which significantly increases the mechanical strength of the processed material via grain-boundary strengthening (also known as conventional Hall-Petch strengthening [6,7]). e main drawback of SPD is that the considerable increase of strength is inevitably accompanied by a significant loss of ductility which might limit the employment of this technique in industrial applications [8][9][10][11]. erefore, seeking a method imparting high strength while maintaining reasonable ductility is an enormous challenge in SPD research. A possible solution to this issue is to develop SPD methods which are able to produce metals with appropriate microstructures. A novel SPD process was recently proposed-called plastic flow machining (PFM)-which can produce gradient structures [12,13]. In PFM, a surface layer of a bulk workpiece is separated via a controllable lateral extrusion process to transform it into a fin or sheet with an ultrafine-grained and gradient structure, in a single deformation step, which is basically simple shear. PFM has a similar feature with another recently invented process, called large strain extrusion machining (LSEM) [14,15] in the sense that in LSEM continuous metal fins with UFG structure can also be produced by separating a surface layer from a bulk sample. e difference is that in LSEM a cutting tool is used together with a constraining channel, while in PFM, an extrusion process produces the fin. However, the microstructure produced by PFM is heterogeneous while it is mostly homogeneous in LSEM, and the hydrostatic pressure produced in the deformation zone in PFM is likely to be higher than that in LSEM. PFM also exhibits a common feature with nonequal channel angular pressing (NECAP) [16,17] in terms of the working principle. Indeed, lateral extrusion in PFM works in the same way as in NECAP. However, the main difference is that in PFM, only the surface layer of the sample is deformed while the whole bulk sample is deformed in NECAP. is allows PFM to reduce the load required for processing.
PFM was successfully applied on commercial pure Aluminum 1050 to fabricate fins with different thicknesses. e obtained fins, produced through the lateral extrusion process, exhibited gradients in terms of plastic strain, microstructure, and texture across their thickness. e mechanical properties and formability of those fins were found to be excellent. For example, a 0.65 mm thickness fin, produced by the one-step PFM operation, shows tensile strength equivalent to that obtained from four passes of incremental equal channel angular pressing (I-ECAP). e uniform elongation is also up to four times higher than that received after four I-ECAP passes [13]. e average Lankford value attained from the tensile tests at different directions of this fin is 0.92, which is much higher than that obtained from conventional rolling which ranges from 0.5 to 0.85 [13]. Owning to the ability to fabricate metallic sheets with superior mechanical properties and formability, PFM shows great potentials for industrial applications, and it is patented worldwide [12]. e aim of this paper is to give more information on this new process, especially concerning the role of the die geometry.

Experimental Procedures.
Commercial pure Al1050 samples were processed by PFM at room temperature. A description of the process was presented in a previous work [13] and schematically presented in Figure 1. Fins were produced with different thicknesses up to 1.5 mm, while keeping other geometrical parameters constant: the die angle α � 120 0 and the heights of the two die channels: H 0 � 20 mm and H 1 � 18 mm. A thickness ratio parameter was introduced for the fin, which is the ratio between the thickness of the fin and the thickness of the layer removed from the bulk: e effects of this parameter on the fin formation and its microstructure and mechanical properties were investigated. As the die was constantly the same with H 0 − H 1 � 2 mm, for the results presented in this work, t and h are simply related by t � h/2. e experiments were conducted applying a back pressure of 110 MPa and also without back pressure. e microstructures across the thickness of the fins were characterized by scanning electron microscopy (SEM) and electron back-scattering diffraction (EBSD) operated in a JEOL JSM-6500F field-emission gun-scanning electron microscope. Data acquisition and analyses were carried out by the Aztec HKL and the ATOM software [18], respectively. For the detection of grain boundaries, disorientation angles between neighboring pixels were required to be greater than 5°. In order to obtain and compare mechanical properties of the fins produced at different gap widths, tensile tests were performed at room temperature. e tensile direction was set parallel to the longitudinal direction of the fin, and the strain rate was 0.001 s −1 .

Simulation Procedures.
e commercial DEFORM-2D/3D V11.0 FE code was used for the FE simulations to obtain insight into the stress and strain distributions within the workpiece during the PFM process. All parts of deforming tools were defined as rigid bodies, whereas the workpiece was represented by 10000 tetragonal deformable elements. Adaptive meshing was used to accommodate large strains during the material flow within the lateral channel. e material behavior was taken isotropic using the von Mises model with the hardening law σ � 180ε 0.23 vM (MPa) (σ is the von Mises equivalent stress, and ε vM is von Mises strain). e parameters of the hardening law were obtained by approximating the stress-strain curve of Al1050 from [19]. Friction was modeled by the Siebel friction law τ � 0.2σ.

e Effect of Die Geometry and Back Pressure on the Formation of the Fin.
A special feature of PFM is that both forward and lateral extrusions occur concurrently during processing; see the illustration in Figure 1(b). e sample has a cross section of H 0 W which changes into H 1 W after processing, where W is the width of the workpiece. e outgoing fin has a cross section of hD. During the process, the incoming flow Q 0 is bifurcating into two flows: Q 1 and ese three flows are defined in terms of volumes moving across the cross sections per unit time: forward extrusion flow: lateral extrusion flow: where U 0 , U 1 , and U 2 are the respective material flow velocities. Now, we introduce a parameter x which is the lateral extrusion ratio defined by the fraction of the metal that flows into the lateral slit: Using Equations (2) and (4), we obtain 2 Advances in Materials Science and Engineering where U 2 and U 0 velocities can be expressed in terms of time T of the extrusion, the length of the n l, and the displacement of the sample L 0 in contact with the pressing punch: which leads to As can be seen from this expression, the parameter x is fully de ned by simple geometrical parameters that can be readily measured, just like the parameter t from Equation (1). e maximum possible value of x is 1; it happens when the back-pressure punch does not move: it is xed. is situation corresponds to the case of nonequal channel angular pressing (NECAP) which was examined analytically and experimentally in [16,17,20]. e lateral extrusion ratio (x) is plotted as a function of the n thickness ratio in Figure 2, from a number of experiments conducted with and without back pressure.
As can be seen, the lateral extrusion ratio increases with the gap-width size, and it is more prominent when processing with back pressure. erefore, in order to enhance the formation of the n and improve e ciency, PFM needs to be carried out with su ciently high n thickness ratio and with the assistance of a back pressure. When t was smaller than 0.35, the n was not produced in the absence of back pressure. With back pressure, this critical value was reduced to 0.2.
is means that at small-gap widths (h), the lateral extrusion stops at a certain point, and the forward extrusion is predominant during the process. High friction and the formation of a dead metal zone near the entrance of the lateral slit might be the causes that obstructed the lateral ow at narrow-gap widths of the side channel. With the rise of t, the process was improved. Bearing all the above in mind, when designing a PFM die, for a given n thickness, one should choose a reasonable value of t.

e E ect of Fin ickness Ratio on Strain and Microstructure in the Fin.
e microstructures of three ns corresponding to three-n thickness ratios, 0.325, 0.5, and 0.75, were characterized by EBSD measurements. e case of t 0.75 was selected to show the microstructure of the n, see Figure 3(b). Clearly, grain re nement with a microstructure gradient across the thickness can be seen.
A signi cant grain re nement and the strain gradient across the n thickness are documented in Figure 4. e initial grain size of about 100 µm was re ned to 3.81, 2.1, and 0.85 µm in the left edge area (LEA), middle area (MA), and right edge area (REA), respectively, of the n.
Regarding the strain gradient across the n thickness, the reason for this is that material points ow along di erent strain paths while moving from the bulk workpiece into the n. Each time the material point alters its ow direction, a shear strain is adding and accumulating. e diversity of  strain paths forms a complex strain eld in the deformation zone situated at the intersection of the forward and lateral channels. High friction at the interface between the right side of the n and the 120°inclined edge of the die (Figure 1(a)) also contributes to this strain gradient. e grain sizes corresponding to three di erent n thickness ratios can be evaluated using Figure 5. As can be seen, the grain size increased almost linearly across the n thickness, from the REA to the LEA in all three cases of the n thickness ratios. In addition, with the increase of t from 0.325 to 0.75, the average grain size in the REA did not change considerably, from 0.8 to 0.85 µm, respectively. At the same time, the average grain sizes in the MA and LEA were signi cantly increased, from 1.4 to 2.1 µm and from 1.9 to 3.81 µm, respectively. It is widely accepted in SPD research that the signi cant microstructure re nement under large plastic strain is associated with a continuous dynamic recrystallization phenomenon.
is process involves grain subdivision caused by the buildup of GNDs and new ne grain formation with high-angle grain boundaries (HAGBs) during large deformation at room temperature [21,22]. e smaller grain size change in the REA compared with that in the MA and LEA when t is varied implies that the strain imposed in the REA was less dependent on the geometry of the die. is is because the strain in the REA resulted not only from the abrupt change of material point trajectory (which depends on the die geometry) but also from the e ect of the high friction at the interface between the right side of the n and the die surface. An average gradient in grain size (g) can be de ned as the slope of the best-t line which represents the dependence of grain size on the distance ( Figure 5). is gradient was found to be the same 2.1 × 10 −3 for all t values from 0.0325 to 0.75.  this zone leads to the strain gradient of the produced fin, in which the strain values increase across the fin thickness from the left to the right. One can analyze this strain gradient by dividing the fin into three strain areas, namely, the left edge area (LEA), the middle area (MA), and the right edge area (REA). e greater deformation in the HSA can be attributed to high friction generated at the contact between the material and the inclined edge of the die, under high compression pressure.
e REAs in both cases t � 0.75 and 0.325 exhibit a similar range of von Mises strain values from 3 to 4. However, the LEAs show different features in the two cases. In the case t � 0.75 (Figure 6(a)), the REA displays lower von Mises strain values (from 1 to 1.5) than in the case t � 0.325 (about 1.5). is is consistent with the experimental results that the average grain size in the LEA decreased from 3.8 to 1.9 when t increased from 0.75 to 0.325, but that in the REA did not change considerably (from 0.85 to 0.8 µm). Figures 6(b) and 6(d) show the stress distribution for the two different t values. In both cases, high compressive stresses (with a maximum value of 400 MPa) are generated in the deformation zone due to a large hydraulic pressure which is enhanced by the applied back pressure.
erefore, microfractures such as microcracks and voids are suppressed in PFM, improving in this way the workability of the fin.

Mechanical Properties and the Effect of the Fin ickness
Ratio.
e tensile test results of the initial and PFMprocessed samples corresponding to different fin thickness ratios, ranging from 0.325 to 0.75, are presented in Figure 7(a). e geometry of tested samples is displayed in Figure 7(b) with h being the thickness of the sample. As can be seen, a significant increase in strength, about more than 2.5 times, was achieved in all produced fins. Good elongations-which were far higher than those in other SPD counterparts-were also attained. A comparison of ductility obtained at a similar strength range for Al1050 from several SPD processes is presented in Table 1. e data were collected from different studies. As can be seen, in a comparable range of UTS strength, PFM provides higher uniform and total elongations than other SPD processes. For example, compared with eight ECAP passes route Bc at room temperature (RT) followed by annealing at varying conditions, one PFM pass shows about twice higher uniform elongation and a 1.5 times higher total elongation. Another example is that when comparing with seven ARB passes at RT, one PFM pass presents about four to five times higher uniform elongation. is again highlights the novelty of PFM in terms of imparting high strength while maintaining reasonable ductility and sheds light on the benefit of the gradient microstructure in improving the strengthductility relation.
Regarding the impact of the fin thickness ratio on the mechanical properties, the strength decreased with the increase of t. A decrease from nearly 180 to 160 MPa in UTS took place when t varied from 0.325 to 0.75. e opposite trend was seen for the ductility: the uniform elongation increased from 6 to 8%, and the total elongation increased from 18 to 25%. ese results can be explained by correlating them with the effect of the fin thickness ratio on the strain and microstructure that are presented in the previous sections. e grain sizes in all areas, the LEA, MA, and REA, increased with the increase of t ( Figure 5). is means that the microstructure generally became coarser when t was increased, resulting in a decrease in strength and increase in ductility, as expected.
To this end, the mechanical properties of PFM-processed fins can be controlled by the fin thickness ratio. e target of obtaining high strength can be fulfilled by choosing a small t value. In this case, good ductility, higher than that in other SPD techniques (Table 1), can be reached.

Conclusions
(i) Lateral and forward extrusions occur simultaneously during the PFM process. e process should be conducted with a back pressure to improve its efficiency. In the condition of processing with a back pressure of 110 MPa, when t was smaller than 0.325, the fin was not formed because the lateral extrusion stopped at a certain point and the forward extrusion became predominant during the process. With the rise of t from 0.325 to 0.75, the lateral extrusion ratio increased, improving the formation efficiency of the fin. (ii) Ultrafine-grained microstructure and gradient microstructure were obtained after one-step PFM deformation. e average grain size varied from 0.8 to 3.81 µm across the fin thickness. When t was increased from 0.325 to 0.75, the degree of the gradient in the microstructure became more significant. is was in good agreement with the FEM simulation in which the strain gradient showed the same dependence on t. (iii) PFM exhibits superior strength-ductility balance with respect to other SPD counterparts.
A tensile strength of 160-175 MPa and total ductility of 18-25% were obtained for Al1050 samples after one-step deformation. An increase of t from 0.325 to 0.75 reduces the strength but improves the ductility of the produced fin. is can be attributed to the coarser microstructure obtained for larger t values.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding this publication. Advances in Materials Science and Engineering 7