Keywords

1 Introduction

Manufacturing industries have recently started focusing on developing advanced micro-fabrication facilities in order to meet the rising demand for miniaturization and the fast-growing use of custom micro-products that are fabricated from ultra-thin sheets (foils). Scaling down conventional forming techniques for real-world applications is challenging due to the difficulty of reducing the size of the machinery and supporting equipment [1]. The major challenges/issues that have been encountered (understanding the micro-deformation behavior [size-effect], material characterization, product handling, forming limit qualification, process modeling, interfacial considerations, etc.) are the critical elements that determine the industrial acceptability of this process [2, 3]. Forming foils into complex 3D geometries requires great precision to serve high-end applications, like in micro-electronics, avionics, and the biomedical and defense industries [4]. Incremental sheet forming (ISF) technology was first patented in 1967 by Leszak [5]. In 1978, Mason [6] started a small-batch production of metallic components by forming metal sheets. Jeswiet et al. [7] proposed a detailed analysis of the fundamental aspects of the incremental forming process. The process mechanics of the ISF process were nicely defined by Jackson and Allwood [8] and Duflou et al. [9]. Singh and Agrawal [10, 11] studied the combination of structure thinning and ISF to generate complex shapes of thin monolithic structures. Nirala and Agrawal [12] developed a fractal geometry-based toolpath to produce incremental deformations in sheets to achieve the better uniformity of the thickness distribution in ISF.

Micro-incremental sheet forming (µISF) is a new die-less method for the production of miniature parts in which a forming tool navigates through the surface of a foil to deform it to a complex 3D part. Saotome and Okamoto [13] first implemented the µISF experiment to fabricate miniature components from thin Al foils. Obikawa et al. [14] developed a micro-milling machine to produce a collection of tiny dots and pyramids on thin sheets. Bansal et al. [15] produced geometrical profiles of different shapes using µISF for studying the formability of foils with different working parameters. Beltran et al. [16] also executed micro-forming tests on SS304 foils for different geometrical shapes. Later, Song et al. [17] carried out a numerical and experimental investigation to understand the micro-scale deformation mechanism of the µISF process.

In this paper, an attempt has been made to study the formability of SS316L foils at different forming angles (α) for developing conically shaped geometries. Within the selected range of α, the critical values of the wall angle and sheet thickness are calculated at the locations of fractures.

2 Work Methodology

2.1 Material and Experimental Details

A series of experiments were performed on a rectangular 30 × 25 mm SS316L foil with a thickness of 100 µm in order to validate the repeatability of the µISF process. A forming tool (Tungsten Carbide) using a hemispherical end with a radius of 500 µm was developed in-house using the µ-turning method. Reverse-µEDM is also an established technique for electrode dressing [18], which was studied by Pal et al. [19] for the production of a precise µISF tool. A micro-forming fixture was designed and fabricated to avoid any unwanted distortion of a workpiece at the primary stage of the process. The experiments were performed on a numerically controlled hybrid-µEDM machine (Mikrotools Pte Ltd., DT-110i) following a spiral incremental toolpath that was developed in GUI in MATLAB® R2021a (as shown in Fig. 1a, b). Initially, three different forming angles (α) of 45°, 60°, and 75° were chosen to measure the formability of SS foils at a step depth (∆z) of 30 μm. The tool was given a clockwise rotation of 500 rpm and a feed rate of 20 mm/min. Furthermore, critical wall angle (αcr) of failure was calculated by considering a higher wall angle range (from 70° to 74°). To investigate the effect of ∆z on the failure depth of the component, forming tests were conducted at three different levels of ∆z (10, 20, and 30 μm) for the 75° wall angle. Based on the obtained results, finite element analysis (FEA) was carried out on ABAQUS® to validate this with the experimental outcome.

Fig. 1
figure 1

a Incremental spiral toolpath for conically shaped geometry; b experimental set-up for µISF

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2.2 Numerical Simulation

A 3D elastic–plastic isotropic hardening model based on the von Mises yielding criterion was used for the FEA of the µISF process using ABAQUS®/Explicit. The thickness of the foil (100 μm) was comparatively smaller than the workpiece dimensions and the tool-head radius (500 μm). The tool was considered to be an analytic rigid body, and the SS316L foil was taken to be deformable. For the meshing part, S4R shell elements with a size of 0.4 × 0.4 mm with five integration points along the thickness direction were used with reduced integration. The simulated kinematics of these shell elements provided high accuracy and a low CPU computational run time of 31–32 h. for the current study. The CPU was configured with a clock speed of 2.00 GHz and 128 GB of RAM. The mechanical properties of the material were calculated through uniaxial tensile test (Fig. 2a) and are tabulated in Table 1. The master–slave contact algorithm was used for the tool/foil surface interactions, with a friction coefficient (µ) of 0.34 [20]. Ductile damage fracture criteria based on the void growth model (VGM) were used for predicting the failure during the µISF of the SS316L. This model calculates the onset of the failure of the material based on the growth, nucleation, and coalescence of the voids during the deformation stage. Through this model, the initial fracture of the material is predicted if the damage accumulates up to a certain value. During the plastic deformation, material fragmentation occurs; this results in the growth of voids and nucleation, which cause fractures in the material due to the different plastic strains. The FE model assumes that the material is isotropic and homogenous. The damage initiation and evolution can be introduced through the approach of strain energy, stress triaxiality, fracture strains, etc. in the numerical simulation. Here, the model assumes that the equivalent plastic strain Ɛpl (1) at which the failure of the material occurs is the function of stress triaxiality ƞ (2) and the equivalent plastic strain rate (έpl) [21]. The stress triaxiality value that was incorporated in the simulation was calculated from the initial simulation runs. For the ductile materials, the damage-initiation criteria work when Situation (3) achieves a satisfactory response in which Ɛf is the equivalent plastic strain of the fracture and WD represents the damage-initiation variable. WD ≥ 0 is taken for each increment during the finite element analysis.

(1)
$$\eta \, = \,{\text{Hydrostatic}}\,{\text{stress}}\,\left( p \right)/{\text{von}}\,{\text{Mises}}\,{\text{stress}}\,\left( q \right)$$
(2)
(3)
Fig. 2
figure 2

a Engineering stress–strain curves in rolling direction (RD) and transverse direction (TD) for SS316L; b FEA result of deformed conical geometry

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Table 1 Properties of SS316L foil used in numerical simulation
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For calculating the value of the step time and step distance of the tool movement in the x, y, and z coordinates (toolpath amplitude), Eqs. (4) and (5) were used. The FEA of the deformed conical geometry is shown in Fig. 2b.

$${\text{Step}}\,{\text{distance}}\,\left( d \right)\, = \,\left[ {\left( {x_{2} {-}x_{1} } \right)^{2} \, + \,\left( {y_{2} {-}y_{1} } \right)^{2} \, + \,\left( {z_{2} {-}z_{1} } \right)^{2} } \right]^{1/2}$$
(4)
$${\text{Step}}\,{\text{time}}\,\left( t \right)\, = \,{\text{Step}}\,{\text{distance}}\,\left( d \right)/{\text{Tool}}\,{\text{velocity}}\,\left( v \right)$$
(5)

3 Results and Discussion

3.1 Formability Assessment of Formed Micro-components

To study the formability of the micro-components, the µISF experiment was initially carried out at three different forming angles (α) (45°, 60°, and 75°) at a constant step depth of 30 µm. The wall angle in µISF is a major parameter in determining the formability of the sheet metal [7]. The opening diameter of the conical geometry was taken as 10 mm. From the experimental results, it could be observed that the part that was formed with angles α of 45° and 60° achieved the target average depths of 4.8 and 8.32 mm, respectively, without any fractures. However, early failure of the part could be observed with an angle of 75° at an average depth of 1.74 mm (Fig. 3a). The higher wall angle resulted in high stress at the tool-foil interface due to the smaller contact area at the higher wall angles. This led to the excessive thinning of the sheet as per the law of sines [7], which resulted in the premature failure of the micro-part. Furthermore, three different values of ∆z were considered for investigating the effect of changing the step depth (∆z) on the forming limit of the part. The results revealed that a higher ∆z assisted in increasing the formability of the component. The forming height increased from 1.32 to 1.74 mm with the increase in ∆z. The FEA results also showed reasonable agreement with the experimental results as per the formability that was achieved in both cases. The µISF results of the experimental and simulation are shown in Table 2. Figure 3b, c display the simulation outcome of the cross-sectional profile and thickness distribution, respectively, for 75°. In comparison with the 10 and 20 µm levels of ∆z, the greatest forming depth (1.92 mm) and lowest foil thickness reduction at the fracture point (84.2 µm) could be observed with the 30 µm step depth. For the 10 µm step depth, the fracture thickness of the foil was close to 83.1 µm (max. thinning) at the lower forming depth of 1.67 mm.

Fig. 3
figure 3

a Formed components at wall angles of 72° and 75°; FEA results: b cross-sectional profile at different step depths for 75°; c sheet thickness variation with forming depth until fracture; d cross-sectional thickness distribution at constant step depth (30 µm)

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Table 2 Experimental and simulation results of µISF process
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3.2 Determination of Critical Wall Angle (αcr) and Critical Foil Thickness (tcr)

The results demonstrated that, at higher wall angles, the fracture of a component is more likely to occur; therefore, the value of α was varied from 70° to 74° in order to determine the critical wall angle (αcr) and critical foil thickness (tcr) at the location of the fracture. The experimental and FEA results are shown in Table 2. At an angle of 70°, no failure of the component was initially observed at a forming depth of 8.32 mm.

A similar trend in the formability was witnessed when α was increased to 71° and 72°. However, at an angle of 73°, a sudden failure in the formed geometry could be observed. With an increase in the wall angle from 73° to 75°, a reduction in the forming depth could be observed in both the experimental and simulation results. Therefore, the formability was limited to an αcr of 72º; beyond this angle, the failure of the component took place. The thickness distribution graph in Fig. 3d shows the fracture location where the maximum thinning of the foil was observed. For wall angles of 73º, 74º, and 75º, the thicknesses of the sheets at the times of fractures could be observed as 84.75, 84.62, and 84.2 µm, respectively. Therefore, for designing the μISF process for SS316L foil, it can be concluded that when the foil thickness is reduced below the 85 µm limit (tcr), the failure of the component takes place.

4 Conclusions

This paper presents a new approach for developing miniature-sized products that are made from ultra-thin SS316L foils. µISF experiments were carried out at three different forming angles at a constant step depth. The fracturing of the component could be observed in the high wall angle (α = 75°) as compared to the other two angles. A higher step depth (∆z = 30 µm) helped to increase the formability of the formed geometry. A similar trend could be observed in both the FEA and experimental results. A critical wall angle (αcr) of 72° and critical foil thickness (tcr) of 85 µm could be observed at the location of the fracture. Further work in the direction of the FE validation of sheet thickness distribution, stress variation, etc. with the experimental results will be focused on a detailed study of the process.