Abstract
Micro-incremental sheet forming (µISF) has advantages over existing micro-forming processes (due to its die-less nature of material deformation) and vast applications in sophisticated industries. In µISF, a flexible ultra-thin sheet (foil) is plastically deformed into a complex 3D geometrical shaped component. It is precisely governed by the user-defined toolpath of the forming tool on the surface of the foil. This study investigated the deformation behavior of 100-μm-thick SS316L foils; the foils were deformed into small conical shapes with a tool-tip with a radius of 500 μm. The µISF process set-up consisted of a rigid fixture to avoid any unwanted distortions during the forming. To test the formability of the foils at different working parameters, experimental and numerical examinations were conducted by varying the wall angle (α = 45°, 60°, 75°) of the forming with three different step depths (∆z = 10, 20, and 30 μm). A finite element analysis of the process was carried out using ABAQUS® software; the results revealed that the forming angle in µISF had a direct relationship with the formability of the material. Higher values of the step depth assisted in increasing the formability of the SS316L foils. To examine the critical wall angle (αcr) and critical foil thickness (tcr) at the fracture location, a higher range of α (70°–74°) was selected in order to establish a correlation with the depth of the forming.
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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.
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.
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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.
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.
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.
References
Geiger M, Kleiner M, Eckstein R, Tiesler N, Engel U (2001) Microforming. CIRP Ann Manuf Technol 50:445–462. https://doi.org/10.1016/S0007-8506(07)62991-6
Qin Y (2006) Micro-forming and miniature manufacturing systems—development needs and perspectives. J Mater Process Technol 177:8–18. https://doi.org/10.1016/j.jmatprotec.2006.03.212
Messner A, Engel U, Kals R, Vollertsen F (1994) Size effect in the FE-simulation of micro-forming processes. J Mater Process Tech 45:371–376. https://doi.org/10.1016/0924-0136(94)90368-9
Pradeep Raja C, Ramesh T (2021) Influence of size effects and its key issues during microforming and its associated processes—a review. Eng Sci Technol Int J 24:556–570. https://doi.org/10.1016/j.jestch.2020.08.007
Leszak E (196) Apparatus and process for incremental dieless forming. United States Patent Office, pp 1964–1966
Mason B (1978) Sheet metal forming for small batches. B.Sc thesis, University of Nottingham
Jeswiet J, Micari F, Hirt G, Bramley A, Duflou J, Allwood J (2005) Asymmetric single point incremental forming of sheet metal. CIRP Ann Manuf Technol 54:88–114. https://doi.org/10.1016/s0007-8506(07)60021-3
Jackson K, Allwood J (2009) The mechanics of incremental sheet forming. J Mater Process Technol 9:1158–1174. https://doi.org/10.1016/j.jmatprotec.2008.03.025
Duflou JR, Habraken AM, Cao J, Malhotra R, Bambach M, Adams D et al (2018) Single point incremental forming: state-of-the-art and prospects. Int J Mater Form 11:743–773. https://doi.org/10.1007/s12289-017-1387-y
Singh A, Agrawal A (2016) Investigations on structural thinning and compensation stratagem in deformation machining stretching mode. Manuf Lett 9:1–6. https://doi.org/10.1016/j.mfglet.2016.06.001
Singh A, Agrawal A (2017) Experimental and numerical investigations on structural thinning, thinning evolution and compensation stratagem in deformation machining stretching mode. J Manuf Process 26:216–225. https://doi.org/10.1016/j.jmapro.2017.02.013
Nirala HK, Agrawal A (2018) Fractal geometry rooted incremental toolpath for incremental sheet forming. J Manuf Sci Eng 140:1–9. https://doi.org/10.1115/1.4037237
Saotome Y, Okamoto T (2001) An in-situ incremental microforming system for three-dimensional shell structures of foil materials. J Mater Process Technol 113:636–640. https://doi.org/10.1016/S0924-0136(01)00651-3
Obikawa T, Satou S, Hakutani T (2009) Dieless incremental micro-forming of miniature shell objects of aluminum foils. Int J Mach Tools Manuf 49:906–915. https://doi.org/10.1016/j.ijmachtools.2009.07.001
Bansal A, Jiang B, Ni J (2019) Die-less fabrication of miniaturized parts through single point incremental micro-forming. J Manuf Process 43:20–25. https://doi.org/10.1016/j.jmapro.2019.03.046
Beltran M, Malhotra R, Nelson AJ, Bhattacharya A, Reddy NV, Cao J (2013) Experimental study of failure modes and scaling effects in micro-incremental forming. J Micro Nano-Manuf 1:1–15. https://doi.org/10.1115/1.4025098
Song X, Zhang J, Zhai W, Taureza M, Castagne S, Danno A (2018) Numerical and experimental investigation on the deformation mechanism of micro single point incremental forming process. J Manuf Process 36:248–254. https://doi.org/10.1016/j.jmapro.2018.10.035
Nirala CK, Saha P (2016) Evaluation of μEDM-drilling and μEDM-dressing performances based on online monitoring of discharge gap conditions. Int J Adv Manuf Technol 85:1995–2012. https://doi.org/10.1007/s00170-015-7934-0
Pal M, Kishore H, Agrawal A, Nirala CK (2022) Fabrication of precise hemispherical end tool for micro incremental sheet forming using reverse-µEDM. Procedia CIRP 107:1600–1605. https://doi.org/10.1016/j.procir.2022.06.001
Sridhar R, Shanmugasundaram D, Rajenthirakumar D (2023) Investigation on single-point incremental forming process of SS316 sheets at elevated temperatures. Lecture notes in mechanical engineering. Pp 85–96. https://doi.org/10.1007/978-981-19-3866-5_8
Dassault Simulia ABAQUS/CAE (2018) ABAQUS analysis user manual, version 6.8. 2022 damage initiation for ductile metals, p 2080
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Pal, M., Pandya, V., Nirala, C.K., Agrawal, A. (2024). Determining Critical Wall Angle in Micro-incremental Sheet Forming of SS316L Foils for Formability Assessment. In: Kusiak, J., Rauch, Ł., Regulski, K. (eds) Numerical Methods in Industrial Forming Processes. NUMIFORM 2023. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-58006-2_21
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