SPIF process of axisymmetric parts made of AA1060-H14 aluminum alloy tested on 2 axis-NC lathe machine

This paper deals with an experimental and numerical study focused on the SPIF process of a dome part manufactured by means of a 2-axis NC lathe machine. The main objective is to enhance the understanding of a set of parameters in connection with ISF operations applied to this type of machine unusually used in incremental forming processes, despite the high degree of development of NC lathe machines. Nowadays 4 and 5 axis lathe centers are widely used in industrial applications. This makes NC lathe machines useful in SPIF process especially in the case of axisymmetric parts. The present results, covering thinning, appearance of cracks, surface quality and FLD diagram; prove the efficiency of NC turning machines to perform SPIF application of parts commonly manufactured by a 3-axis NC milling machine.


Introduction
During the Incremental sheet forming process, the sheet metal is shaped by the action of a rigid tool following a programmed trajectory similar to the desired part geometry [1,2]. An NC program implemented in a numerically controlled machine generates this tool path. Based on plastic deformation, ISF is a slow process compared to deep drawing or stamping processes, in fact, it is dedicated for rapid prototyping of small batches of complex parts with high precision [3]. Time cycles are quite important (several minutes) during this process, which leads in simulations to a high computational time. Which conducts the majority of researchers to study two classic specimens having even a conical or pyramidal final shape. Indeed, these two usual parts allow the study of several process parameters like forming efforts, springback phenomenon, dimensional accuracy , thinning, formability limits, damage mechanisms, etc. [4][5][6][7] which are the main problems investigated in sheet metal forming processes [8] . Rimašauskas et al. [9] proved the efficiency of SPIF process in rapid production of molds used to manufacture composite structure. In fact, SPIF technology lessen the manufacturing time and cost in comparison with conventional technics used to manufacture these molds. Experimental investigations carried out in incremental forming fields are in the majority of cases performed by means of SPIF process applied to NC machine tools [10]. 3-axis NC milling machines are the most commonly used in incremental forming. In fact, these machines are very available, easy to use with the same NC program and the same CAM method used in NC milling process. A multitude of Computer Aided Manufacturing (CAM) software such as CATIA, MasterCam, CamWorks etc., which contain database rich in digital emulators, are compatible with a multitude of NC machines in terms of tools and trajectories. Moreover, the 3-axis NC milling machines have shown a high rigidity that convinces their use in incremental forming. However, other machines have been used; several research groups chose the industrial robotic arm as an alternative [11][12]. However, the major disadvantage is the less precision of the tool position; especially under high loads condition that limit robot arm capabilities in ISF operations. Belchior et al. [13] and I. 2 Paniti [14] used a serial industrial robot in order to evaluate its ability to manufacture by incremental forming thin sheet metal. Authors demonstrate that this process reduces process forces, improves the dimensional accuracy and increases the formability of materials. The robotic machines are less rigid in view of their open kinetic chain; which increase the difficulty in the toolpath programming. This difficulty makes the application of robotic arms in ISF process more expensive compared to a conventional numerical controlled milling machine. Besides the NC milling machines, tests were carried out on machines specialized for the incremental manufacturing. Several researchers tested new designs of incremental forming setups [15][16][17]. Authors designed special ISF machines having the 3axis configuration like the AMINO machine used in [18]. The use of this type of 3-axis ISF machines in industrial applications remains few and very specific, but it is interesting as alternative to study.
From experimental investigations, it was revealed that SPIF process achieves higher forming limits than conventional stamping process [19]. Malhotra et al. [20] stated that excessive thinning happens on parts having severely sloped regions. Moreover, Jackson and Allwood [21] conducted a similar conclusion. In addition, the authors showed that steep walled parts, with complex final shape, have a big difficulty to be manufactured without failure using the SPIF process. However, the proper allocation of materials during forming is a key factor that makes difficulties to get uniform thickness distribution, in order to avoid the occurrence of fractures. Damage phenomenon in SPIF process is promoted by the increase of material wall angle and the decrease of the tool radius for parts [22]. Multi-step strategy has been proposed as an alternative solution to solve all these limitations during SPIF process. Duflou et al. [23] proposed multi-step tool paths that made possible the manufacture of parts with vertical walls. Liu et al. [24] revealed that a combination of increasing diameter and wall angle in steps is the most effective strategy. Indeed, they showed that this strategic combination is the optimal way to achieve the forming target. Moreover, Multi-stage incremental forming is compared to the single stage forming process in terms of forming forces, using numerical and experimental investigations [25]. Authors proved that multi-stage procedure reduces resulting forces during ISF operations.
It can be denoted from the previous state of the art, that 3-axis NC milling machines are widely applied in ISF field contrariwise to other types of NC machines. Considering the evolution of NC lathe machines and the availability of turning centers with four and five axes, they can be well considered to be applied in SPIF operation of revolution parts. The main objective of this paper is to verify the viability of a 2-axis NC lathe machine in incremental forming process, applied for axisymmetric parts made of AA1050-H14 aluminum alloy. The first section summarizes the main constitutive equations used in the elasto-plastic model with quadratic yield criteria of Hill'48 and isotropic hardening. The second section contains the results of the material characterization tests of the sheet metal used in this work. The experimental procedure, used to practice SPIF operations on NC lathe machine, is described in the third section. The obtained results will be discussed in the fourth section, which deploys the covering thinning, appearance of cracks, surface quality and FLD diagram.

Elasto-plastic constitutive equations
In the material mechanical behavior, the hypoelastic stress-strain relation is assumed to be written as The stress-strain tensor of Hook. 3 For isotropic elasticity, the tensor D is given by: 2 12 In addition, the following hypothesis of decomposition of the strain rate is given e p =+ ε ε ε (2.3)  We consider here the Hill'48 quadratic yield function given with isotropic hardening, as follow: The initial yield stress  : The isotropic hardening P : The fourth order tensor that define the Hill`48 criterion.
The Hill`48 yield function includes the classical J2 plasticity yield condition. So in 3D modeling the considered yield criterion is obtained by taking: The anisotropic coefficients F, G, H, N, M and L are obtained by tensile tests performed on specimens cut in several orientations.
In isotropic elastic material, P and D can be calculated as given Considering the associated plasticity, the flow rule can be written as  represents the plastic multiplier. In Eq. (2.4),  is given by In the end, the loading/unloading conditions, formulated in standard Kuhn-Tucker form, are formulated as:

Integration algorithm
The flow rule is integrated over a step of time using the implicit Euler method, at the aim to obtain the plastic strain 1 p n+ ε , which lead to 11 This provides a nonlinear scalar equation that can be solved with Newton's method. Here we need the derivative of the yield function if the Newton's iteration is used to solve the yield equation. At the k iteration, this is given by The simple local iteration procedure is needed to solve the Eq. (2.15), the integration algorithm is recapitalized in Table 1.

Experimental procedure and tensile test results
The mechanical properties of AA1050-H14 aluminum alloy used in our SPIF tests are obtained from uniaxial tensile tests performed on samples, which have been cut in 0 ,15 ,30 , 45 ,60 ,75 ,90 from the rolling direction RD (Figure 1.a). The dimensions of the normalized specimen were depicted in Figure 1.b. The thickness of the as-received sheet was 0.6mm .
(a) (b) Fig 1. (a) Specimen orientation to Rolling Direction (RD), (b) Specimen shape for uniaxial tensile test 6 During the tensile test, two extensometers are used to measure simultaneously true strains xx  and yy  , as schematically illustrated in Figure 2. The material flow behavior was characterized on the base of the true stress-strain curves plotted during the tensile test for the seven orientations ( Figure 2). It can be obviously observed through these curves that texture and anisotropy are present in the flow behavior with respect to the sheet orientations.

Lankford coefficients
The anisotropy coefficients are usually computed based on Lankford coefficients ( r  ) determined from the ratio of width through thickness plastic strain. The expressions used to calculate these coefficients are well detailed in the work of Shunying et al [27]. Using the strain measures from two extensometers, the Lankford coefficients were determined by line slope expressing the evolution of

Application to Hill 48 anisotropic function
In this section, the proposed associated model is derived for the specific case of Hill 48 quadratic function. In the case of plane stresses, Hill 48 anisotropic plasticity criteria can be formulated, for a tensile test, as a function of the applied stress   , which depends on the anisotropy directions. Two illustrative aspects are examined to calculate the values of the four Hill's anisotropic parameters [27] Hill_R: The parameters of anisotropy are calculated using the experimental Lankford coefficients r  Hill_S: The parameters of anisotropy are calculated using the experimental stress ratios s  The Lankford coefficients listed in table 2 are used to determine the anisotropy coefficients of Hill'48 ( , , , , , Table 3 as below.  The comparison between the measured and predicted values of yield stresses and r-ratios are given in Figure 4.b and 4.c. It should be emphasized that, according to these figures, the two different identification methods Hill_R and Hill_S for Hill 48 model cause different predictions of the material behavior. The calibrations, based on yield stresses, give a good description of the yield stress anisotropy. However, poor description of the anisotropy in the Lankford coefficients. In addition, the calibration, based on r-ratios, gives a good description of the anisotropy in the Lankford coefficients but it is poor for the yield stress anisotropy.

Identification of the hardening law
The isotropic hardening that estimates the size of the yield surface is suited to characterize the material behavior for the large deformation encountered during SPIF process. The isotropic hardening law is usually described by an exponential law function as given in the following equation. In which, y  is the initial yield stress, Q and β are material constants. 8 Figure 5 describes the evolution of the isotropic hardening law from experimental data obtained along the rolling direction0 o . The hardening parameters are deployed in Table 4.

Overview of experimental
The experimental procedure, used to investigate ISF operations, can be explained in Figure 6.

Experimental Set-up
Experiments were carried out using a 2-axis Realmeca T2-numerical control lathe type with a Num1060-numerical calculator type. A hemispherical punch having a diameter of 10mm made of C45 steel is used as forming tool. SPIF tests performed on circular blanks of 150mm of diameter. The material selected for this study was AA1050-H14 aluminum alloy sheet. The thickness of the asreceived sheet was 0.6mm . The conventional tensile tests used to characterize this material are given 9 in the previous section. The deformed specimens took in the shape of dome as shown in Figure 7.a. Besides, the tool feeding rate was set to be 0.05 / mm rev , and the low spindle speed was kept at 75rpm . In addition, a lubricant was sprayed on the blank before forming to avoid excessive friction at the interface between tool and sheet. Before SPIF operation, and in order to measure the major and minor strains for plotting the forming limit diagram "FLD", the initial blank surfaces were marked by circles-grid, as depicted in Figure 7.b. The experimental set-up of SPIF tests applied to a 2-axis turning machine is shown in Figure 8, which presents the necessary elements for a successful SPIF test of the axisymmetric parts.

Tool Path
The generation of the tool path has a direct impact on the thickness variation, the formability, the surface finish, the processing time, and the dimensional accuracy. In order to improve the final product quality, two methods were used to manufacture these shapes of the dome: the first is to produce the dome in a single pass, which corresponds to the conventional SPIF-T operation as shown in Figure 9.b. The second method consists in manufacturing the dome with double-pass SPIF-T operation. Hence, a truncated cone with a depth of 40mm obtained in the first pass and the other pass corresponding of manufacturing the final shape as illustrated in Figure 9.a.
The tool path used during these two methods is automatically generated by the numerical calculator of the machine, through the manual programming of a paraxial roughing cycle used to dress an internal shape in turning (case of conventional SPIF-T) or a series of paraxial roughing cycles (case of double-pass SPIF-T). A penetration increment of 0.1 mm is used during these cycles.

Efficiency of double-pass strategy
Results carried out from experimental tests show the efficiency of SPIF-T operation with recovery pass (double pass) to manufacture parts having a hemispherical final shape.
It should be emphasized that according to the literature, domes always present a problem of cracks, which occur during the incremental operation. As shown in Figure 10, the cracks happened at the beginning of the forming process at a depth of 15 mm. Figure 10.b shows that this straight circumferential crack has a propagation path similar to that occurring in deep drawing operations. This type of crack propagation is triggered by a stretching mechanism due to circumferential stress. Moreover, as shown in Figure 10.a, SPIF-T operation was successful without visually detecting defects when we use the double-pass procedure.  Figure 10.c, for the two incremental forming procedures reveals an improvement of the strain values when the double-pass strategy is used. The preferential zone of the highest strain values, as marked in this figure, is located in the most vertical wall of this dome. However, material belonging to the first fillet of the dome, as well as its bottom has the lowest strain values. In addition, the strain values were significantly decreased due to the rapid appearance of cracks when conventional SPIF-T is used.
In order to evaluate thinning along the rolling direction X and along the dome depth, the workpiece has been cut into two halves to facilitate thickness measurement using a micrometer. Figure 11.a shows the thinning evolution along the rolling direction of the blank sheet for the two cases of forming strategies. It can be denoted that the use of an intermediate pass during the SPIF-T of the dome part greatly reduces the material thinning and improves its distribution, which has increased 11 the formability by avoiding cracks. Contrariwise to the dome part made by means of a single pass, a high-thinning value located in a small zone is encountered.
The evolution of the thickness with the dome depth is illustrated in Figure 11.b. The cracking depth represents the position that has undergone the highest thinning values. In the case of conventional SPIF-T, the cracks appeared at a depth of 15 mm. This crack depth was increased in SPIF-T using a recovery pass. The highest value of thinning during the double-pass operation is located in a zone between a depth of 30 and 40 mm, which confirms the high strain value at the most vertical wall indicated in the FLD diagram studied previously in Figure 10.c.

Choice of the intermediate pass
In spite of the efficiency of SPIF-T using an intermediate pass to manufacture parts having zones with vertical walls, it has been found that this intermediate pass should be well chosen. In fact, the width ( pv l ) of the area containing a vertical wall has to be minimized before the final pass giving the dome shape. Figure 13 shows an unsuccessful part despite the use of an intermediate pass. The problem in this case can be explained by the fact that the truncated cone manufactured during the intermediate pass has a low cone wall angle. This leaves a relatively high material width of the zone with vertical wall, which causes the appearance of cracks. Although the appearance of cracks is delayed and the crack appearance depth has increased as shown in Figure 13.b, Compared to the result of conventional strategy using a single pass. And even compared to the strategy using an intermediate pass creating a truncated cone with a lower cone wall angle as seen in Figure 13

Effect of the penetration increment
The choice of the penetration increment is important for a good working process to improve the final product quality. Figure 14.a shows a part manufactured by a double pass SPIF-T using a penetration increment of 0.2 mm higher than the value used previously. It can be obviously observed a low surface quality for this part depicted by the presence of wrinkles.
From the previous observations, we can confirm practically the efficiency of SPIF using a multipass strategy, applied to NC lathe machine, to avoid the appearance of cracks. Essentially, if the intermediate form is used, this reduces considerably the width of the remaining area before the final shape of the most vertical wall zone. The problem of tool path marks (wrinkles) remains impelled by the amplification of the penetration increment value. The advantage of using NC lathe machines (compared to milling machines) is that a finishing pass can be added to eliminate these marks when a high penetration increment is used during the first pass. This is not possible with NC milling machine without the use of more than 3-axis. Figures 14.b and 14.c show the effect of the finishing pass added to the initial roughing pass to improve the quality of the part presented in Figure 13. In addition, a polishing effect was observed on the inner surface of the manufactured part as illustrated in figure  14.c which is caused by the grinding phenomenon. On a NC milling machine, the execution of such finishing pass in a relatively short production time requires the use of the 4-axis mode allowing the rotation of workpieces about the Z-axis (tool axis).

Numerical results
A 3-D finite element code ABAQUS/Explicit was adopted to conduct the simulation of ISF process of the dome studied in the previous section. The blank, die and forming tool are modeled with shell elements (the die and tool are considered as rigid bodies). Fine mesh (S3R shell elements) is used in the center of the blank sheet. A five integration points are defined in thickness direction. The friction coefficient is equal to 0.1 to consider a lubricated contact [22]. An elastoplastic constitutive model with quadratic yield criteria of Hill'48 and isotropic hardening behavior has been adopted during ISF operation. To be close to reality, we adopted in this simulation the same machine conditions as the tool trajectory and the penetration value. The finite element model is shown in Figure 15. The distribution of the Von Mises stress concentrated on the contact zone is as shown in Figure  16.a. According to this figure, the major Von Mises stress is located in the center of the dome. Distribution of major strain, shown in figure 16.b, is in concordance with the experimental FLD diagram illustrated in Figure 10.c. The preferential zone of the highest strain values is located at the Appearance of wrinkles 14 most vertical wall of the dome. Contrariwise, to material belonging to the first fillet of the dome as well as its center have the lowest strain values. Figures 17 and 18 highlight a comparison between numerical and experimental results in terms of thinning evolution in the rolling direction and the strain state within the FLD diagram. According to these figures, it can be noticed that the numerical results are in concordance with the experimental results unless a small difference is observed at the level of thinning. This difference can be firstly explained by the existence of measurement errors using the micrometer to measure the thickness of the deformed part. Secondly, the material behavior model integrating just the isotropic hardening underestimates the prediction of thickness evolution, which is proved in the work done by Jackson and Allwood [21]. From there, the integration of kinematic hardening and material damage parameters improve this prediction.

Conclusion
In the incremental forming field, NC milling machines are the most used instead of NC lathe machines, despite NC lathes are useful for axisymmetric parts and this can lead to a reduced cost and better results. The present paper presented a numerical and experimental study focused on SPIF process of a dome part manufactured by the use of a 2-axis NC lathe machine. Results covering thinning, appearance of cracks, surface quality and FLD diagram proved the efficiency of NC lathe machines in SPIF application of parts usually manufactured by a 3-axis NC milling machines. Compared to a milling machine NC lathes have the advantage that a contouring pass can be added to finish the part. Which improve the final shape accuracy and the surface quality especially when a high penetration value is used during the first pass. This contouring operation is very easy and rapid using just a 2-axis configuration if the part is in rotation around the tool axis. Which is equivalent to the use of a fourth axis in milling machines. In the case of axisymmetric parts manufactured by means of SPIF process, NC lathes can be a good choice to replace milling machines, especially when the cost of using this type of NC machine is reduced compared to the use of NC milling machines or machining center. It is possible even to manufacture axisymmetric parts containing different stamping on their peripheral surfaces, by means of NC turning machines having more than 2 axes like turning centers. For example, where milling and turning operation can be combined to manufacture more complex parts.

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